U.S. patent number RE38,229 [Application Number 09/918,420] was granted by the patent office on 2003-08-19 for method and apparatus for seismic signal processing and exploration.
This patent grant is currently assigned to Core Laboratories Global N.V.. Invention is credited to Michael S. Bahorich, Steven L. Farmer, R. Lynn Kirlin, Kurt J. Marfurt.
United States Patent |
RE38,229 |
Marfurt , et al. |
August 19, 2003 |
Method and apparatus for seismic signal processing and
exploration
Abstract
A method, a map and an article of manufacture for the
exploration of hydrocarbons. In one embodiment of the invention,
the method comprises the steps of: accessing 3D seismic data;
dividing the data into an array of relatively small
three-dimensional cells; determining in each cell the
semblance/similarity, the dip and dip azimuth of the seismic traces
contained therein; and displaying dip, dip azimuth and the
semblance/similarity of each cell in the form a two-dimensional
map. In one embodiment, semblance/similarity is a function of time,
the number of seismic traces within the cell, and the apparent dip
and apparent dip azimuth of the traces within the cell; the
semblance/similarity of a cell is determined by making a plurality
of measurements of the semblance/similarity of the traces within
the cell and selecting the largest of the measurements. In
addition, the apparent dip and apparent dip azimuth, corresponding
to the largest measurement of semblance/similarity in the cell, are
deemed to be estimates of the true dip and true dip azimuth of the
traces therein. A color map, characterized by hue, saturation and
lightness, is used to depict semblance/similarity, true dip azimuth
and true dip of each cell; true dip azimuth is mapped onto the hue
scale, true dip is mapped onto the saturation scale, and the
largest measurement of semblance/similarity is mapped onto the
lightness scale of the color map.
Inventors: |
Marfurt; Kurt J. (Houston,
TX), Kirlin; R. Lynn (Surrey, CA), Farmer; Steven
L. (Tulsa, OK), Bahorich; Michael S. (Houston, TX) |
Assignee: |
Core Laboratories Global N.V.
(AN)
|
Family
ID: |
27738958 |
Appl.
No.: |
09/918,420 |
Filed: |
July 27, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
|
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353934 |
Dec 12, 1994 |
5563949 |
|
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Reissue of: |
707674 |
Sep 13, 1996 |
05930730 |
Jul 27, 1999 |
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Current U.S.
Class: |
702/16 |
Current CPC
Class: |
G01V
1/288 (20130101); G01V 1/301 (20130101); G01V
2210/65 (20130101) |
Current International
Class: |
G01V
1/30 (20060101); G01V 1/28 (20060101); G06F
019/00 (); G01V 001/28 () |
Field of
Search: |
;702/10,13,16
;367/42,47,9,29,68,72 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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0181216 |
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Jul 1985 |
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EP |
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2066467 |
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Jul 1981 |
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GB |
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2 132 350 |
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Jul 1984 |
|
GB |
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0172065 |
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Aug 1963 |
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SU |
|
Other References
Houston, L. M. and Potter, J. R., 1993, Multiple suppression using
a local coherence filter, 63rd Ann. Internat. Mtg: Soc. of Expl.
Geophys., 1090-1094. .
Darche, G., 1992, Seismic blind zone detection by image pr, 54th
Mtg Eur Assoc Expl Geophys., p22-23. .
Alam, A., Matsumoto, S., Hurst, C. and Caragounis, P., 1995,
Qualitative porosity prediction from seismic attributes: 65th
Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, ,
95, 313-315. .
Bahorich, M. and van Bemmel, P., 1994, Stratigraphic interpretation
of seismic data on the workstation, 64th Ann. Internat. Mtg: Soc.
of Expl. Geophys., 481-484. .
Bahorich, M. S. and Farmer, S. L., 1995, 3-D seismic discontinuity
for faults and stratigraphic features: The coherence cube: 65th
Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, ,
95, 93-96. .
Bahorich, M. S., Lopez, J., Haskell, N. L., Nissen, S. E. and
Poole, A., 1995, Stratigraphic and structural interpretation with
3-D coherence: 65th Annual Internat. Mtg., Soc. Expl. Geophys.,
Expanded Abstracts, , 95, 97-100. .
Barnes, A. E., 1991, Instantaneous frequency and amplitutde at the
envelope peak of a constant-phase wavelet (short note): Geophysics,
Soc. of Expl. Geophys., 56, 1058-1060. .
Barnes, A. E., 1994, Theory of two-dimensional complex seismic
trace analysis: 64th Annual Internat. Mtg., Soc. Expl. Geophys.,
Expanded Abstracts, , 94, 1580-1583. .
Barnes, A. E., 1996, Theory of 2-D complex seismic trace analysis:
Geophysics, Soc. of Expl. Geophys., 61, 264-272. .
Bodine, J.H., 1984, Waveform analysis with seismic attributes:
Presented at the 54th Annual International Meeting of the S.E.G. in
Atlanta, Georgia. .
Douze, E. J. and Laster, S. J., 1979, Statistic of semblance (short
note): Geophysics, Soc. of Expl. Geophys., 44, 1999-2003. .
Haskell, N. L., Nissen, S. E., Lopez, J. A. Bahorich, M. S., 1995,
3-D seismic coherency and the imaging of sedimentological features:
65th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded
Abstracts, , 95, 1532-1534. .
Heggland, R., 1995, Detection of ancient morphology and potential
hydrocarbon traps using 3-D seismic data and attribute analysis:
65th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded
Abstracts, , 95, 316-318. .
Johnston, D. H., 1993, Seismic attribute calibration using neural
networks: 63rd Annual Internat. Mtg., Soc. Expl. Geophys., Expanded
Abstracts, , 93, 250-253. .
Kemp, L. F., Threet, J. R. and Veezhinathan, J., 1992, A neural net
branch and bound seismic horizon tracker: 62nd Annual Internat.
Mtg., Soc. Expl. Geophys., Expanded Abstracts, , 92, 10-13. .
Kirlin, R. L., 1992, The relationship between semblance and
eigenstructure velocity estimators: Geophysics, Soc. of Expl.
Geophys., 57, 1027-1033. .
Lefeuvre, F. and Chanet, A., 1993, Reservoir characterization: A
seismic attributes approach: 63rd Annual Internat. Mtg., Soc. Expl.
Geophys., Expanded Abstracts, , 93, 289-293. .
Lefeuvre, F., 1994, Fracture related anisotropy detection and
analysis: and if the P-waves were enough?: 64th Annual Internat.
Mtg., Soc. Expl. Geophys., Expanded Abstracts, , 94, 942-945. .
Lefeuvre, F. E., Wrolstad, K. H., Zou, K. S., Smith, L. J., Maret,
J-P. and Nyein, U. K., 1995, Sand-shale ratio and sandy reservoir
properties estimation from seismic attributes: An integrated study:
65th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded
Abstracts, , 95, 108-110. .
Leslie, R. B., 1994, Digital image processing of 3-D seismic
attributes benefits exploration and production interpreters: 64th
Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, ,
94, 813. .
Lewis, C., 1995, Seismic attributes for reservoir monitoring: A
feasibility study using forward modeling: 65th Annual Internat.
Mtg., Soc. Expl. Geophys., Expanded Abstracts, 95, 309-312. .
Marfurt, K. J., Scheet, R. M., Sharp, J. A., Cain, G. J. and
Harper, M. G., 1995, Suppression of the acquisition footprint for
seismic sequence attribute mapping: 65th Annual Internat. Mtg.,
Soc. Expl. Geophys., Expanded Abstracts, , 95, 949-952. .
Nelson, H. R. Jr., Mastoris, S. and Huxohl, C., 1991, Visualization
of map and seismic attributes: 53rd Mtg. Eur. Assoc. Expl Geophys.,
Abstracts, , 91, 86-87. .
Nissen, S. E., Haskell, N. L., Lopez, J. A., Donlon, T. J. and
Bahorich, M. S., 1995, 3-D seismic coherency techniques applied to
the identification and delineation of slump features: 65th Annual
Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts., 95,
1535-1536. .
Ortmann, K. A. and Wood, L. J., 1995, Successful application of 3-D
seismic coherency models to predict stratigraphy, offshore eastern
Trinidad: 65th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded
Abstracts, , 95, 101-103. .
Possato, S., Saito, M., Curtis, M. P. and Martinez, R. D., 1983,
Interpretation of three-dimensional seismic attributes contributes
to stratigraphic analysis of Pampo oil field: 53rd Annual Internat.
Mtg., Soc. Expl. Geophys., Expanded Abstracts, , 83, Session:S16.2.
.
Robertson, J.D., and Fisher, D.A., 1988, Complex seismic trace
Attributes: The Leading Edge, 7, No. 6, 22-26. .
Robertson, J.D., and Nogami, H.H., 1984, Complex seismic trace
analysis of thin beds: Geophysics, 49, 344-352. .
Ronen, S., Hattori, M., Hoskins, J. C. and Schultz, P., 1993,
Seismic guided estimation of reservoir properties, 63rd Ann.
Internat. Mtg: Soc. of Expl. Geophys., 281-284. .
Sibille, G., Keskes, N., Fontaine, L. and Lequeux, J. L., 1984,
Enhancement of the perception of seismic facies and sequences by
image analysis techniques, 54th Ann. Internat. Mtg: Soc. of Expl.
Geophys., Session:S7.2. .
Sonneland, L., Barkved, O., Olsen, M. and Snyder, G., 1989,
Application of seismic wave-field attributes in reservoir
characterization: 59th Annual Internat. Mtg., Soc. Expl. Geophys.,
Expanded Abstracts, , 89, 813. .
Sonneland, L., Barkved, O. and Hagenes, O., 1990, Construction of
reservoir maps from seismic classifier maps: 60th Annual Intenat.
Mtg., Soc. Expl. Geophys., Expanded Abstracts, , 90, 241-244. .
Taner, M. T., Matsuoka, T., Baysal, E., Lu, L. and Yilmaz, O.,
1992, Imaging with refractive seismic waves, 62nd Ann. Internat.
Mtg: Soc. of Expl. Geophys., 1132-1135. .
Versteeg, R., Geoltrain, S. and Ehinger, A., 1991, Use of migration
coherency panels for velocity model determination, 61st Ann.
Internat. Mtg: Soc. of Expl. Geophys., 1255-1258. .
Versteeg, R., Ehinger, A. and Geoltrain, S., 1991, Sensitivity of
migration coherency panels to the velocity model, 61st Ann.
Internat. Mtg: Soc. of Expl. Geophys., 1251-1254. .
From: Reflection Seismology: A Tool for Energy Resource
Exploration, 2nd Edition, 1981, Kenneth H. Waters. pp. 260, 284,
285 and 196. .
From: Encyclopedic Dictionary of Exploration Geophysics by Sheriff,
p. 35 (clutter to comb), no date. Supplemented by Encyclopedic
Dictionary of Exploration Geophysics by Sheriff, 3rd Edition, 1991
pp. 42 and 264 (see coherence and semblance). .
From: An Introduction to Probability Theory and Its Applications by
W. Feller, p. 236, 1968. .
"On the history and culture of geophysics, and science in general"
by Christopher L. Liner, University of Tulsa, The Leading Edge, 16,
No. 06, 939-940. Jun. 1997. .
Keskes, N., Zaccagnino, P., Rether, D. and Mermey, P., 1983,
Automatic extraction of 3-D seismic horizons, 53rd Ann. Internat.
Mtg: Soc. of Expl. Geophys., Session:S21.1, p. 557-559. .
Keskes, N., Boulanouar, A., Lechevalier, Y. and Zaccagnino, P.,
1982, Image analysis techniques for seismic data, 52nd Ann.
Internat. Mtg: Soc. of Expl. Geophys., Session:S16.7, p. 221-222.
.
Stark, T. J., 1996, "Surface Slice Generation and Interpretation--A
Review"; The Leading Edge, 15, 818-819. .
Neff, D. B., 1990, "Incremental Pay Thickness Modeling of
Hydrocarbon Reservoirs"; Geophysics, 55, 556-566. .
Neff, D. B., 1990, "Estimated Pay Mapping Using Three-Dimensional
Seismic Data and Incremental Pay Thickness Modeling"; 55, 567-575.
.
Mondt, J. C., 1990, The use of dip and azimuth horizon attributes
in 3-D seismic interpretation: SPE 20943, 71-77. .
Cohen, 1993, "Instantaneous Anything," IEEE Int. Conf. Acoust.
Speech Signal Processing, 4, p. 105-109. .
"Estimation of Three Dimensional Dip and Curvature from Reflection
Seismic Data", By Christopher J. Finn, Master's Thesis, University
of Texas at Austin, May 1986. .
Bahorich, Michael S., Amoco Production Research and Bridges, S.
Rutt, Advance Geophysical Case Histories 1: Seismic
Stratigraphy/Seismic Sequence Attribute Map (SSAM) CH1.1, Oct. 26,
1992; SEG New Orleans The Society of Exploration Geophysicists
Sixty-Second Annual International Meeting & Exposition, Oct.
25-29, 1992. .
Yanovskiy, A.K., and Bogolyubskiy A.D., "Sposob avtomaticheskoy
approksimatsii vertikal'nogo godografa, osnovannyy na
posledova-Tel'nom vydelenii plastov" in Prikladnaya geofizika, No.
82, 1976; pp. 95-100. (Translation from Russian). .
Bahorich, Mike and Farmer, Steve; 3-D seismic discontinuity for
faults and stratigraphic features: The Coherence Cube, The Leading
Edge, The Society of Exploration Geophysicists ISN 1070-485X Oct.
1995, p. 1053-1058. .
Neidell, N.S. and Taner, M. Turhan; "Semblance and Other Coherency
Measures for Multichannel Data", Geophysics, vol. 36, No. 3 (Jun.
1971), p. 482-497, 6 FIGS. .
Vossler, donald A., Landmark Graphics Corp., Automatic Whole
Section Selsmic Reflection Mapping: The Society of Exploration
Geophysicists Sixty-Second Annual International Meeting &
Exposition, 1988. .
Vossler, Donald A., Landmark Graphics Corp., Automatic Declination
of Lateral Facies Changes in Clatic Environments; SEG Dallas The
Society of Exploration Geophysicists Fifty-Ninth Annual
International Meeting & Exposition, Oct. 29-Nov. 2, 1989. .
Taner, M.T., Koehler, F. and Sheriff, R.E., Complex Seismic Trace
Analysis,Geophysics, vol. 44, No. 6 (Jun. 1979), p. 1041-1063, 16
FIGS, 1 table. .
"The Seismic Sequence Attribute Map (SSAM)" by Mr Bahorich,
Extended Abstracts of Papers, European Association of Exploration
Geophysicists, 56th Meeting and Technical Exhibition, Jun. 6-10,
1994, Abstract. .
"Image Processing as a Tool for Interpreting 3D and 2D Seismic
Data", by Messrs Keskes and Camy-Peyret Supplement to Nature vol.
350, pp. 6-7; Apr. 18, 1991. .
"Image Analysis Techniques for the Purpose of Structural
Interpretation of 3D and 2D Seismic Data", by Keskes and
Camy-Peyret; Mem. Soc. Geol. France 1992 Ser. No. 161 P133-140.
.
"Dip and Azimuth Displays for 3D Seismic Interpretation" by RM
Dalley et al, First Break vol. 7, No. 3, Mar. 1989. .
"Attribute extraction: An Important Application in any Detailed 3-D
Interpretation Study", by EJH Rijks & ICEM Sauffred,
Geophysics: The Leading Edge of Exploration, Sep. 1991. .
"Image Processing of Interpreted 3D Seismic Data to Enhance Subtle
Structural Features/Lineations" by LA Tilbury and D. Bush,
Exploration Geophysics (1991) pp. 22, 391-396. .
"The Binary Consistancy Checking Scheme and Its Applications to
Seismic Horizon Detection" by Cheng and Lu, IEEE Transactions on
Pattern Analysis and Machine Intelligence vol. 11, No. 4, Apr.
1989. .
"Poststack Estimation of Three-Dimensional Cross-line Statics" by
Messrs Schultz and Lau, Geophysics, vol. 49, No. 3, Mar. 1984 pp.
227-236. .
"Signal Coherence Measure in Seismic Data Processing" by Boiardi
and Cardamone, Technical program and abstracts of papers--European
Association of Exploration Geophysicists; vol. 51, p. 76. .
"The Signal Coherence as a Versatile Diagnostic Tool to Improve
Seismic Data Processing Effectiveness" by Boiardi and Cardamone,
Technical program and abstracts of papers--European Association of
Exploration Geophysicists; vol. 53, p. 12-13, 1984. .
"Seismic Attributes Revisited" by M. T. Taner et al. Expanded
Abstracts with Author's Biographies, Society of Exploration
Geophysicists International Exposition and Sixty-Fourth Annual
Meeting, Oct. 23-28, 1994. .
"Automatic Whole Section Seismic Reflection Mapping" by D.A.
Vossler, Expanded Abstracts, Society of Exploration Geophysicists
Fifty-Eight Annual International Meeting & Exposition, Oct.
30-Nov. 3, 1988, p. 689-691. .
"Interpretive nomenclature--a plea for conformity" (Round Table
Reply) by A. R. Brown, The Leading Edge, vol./ISS 9 Oct. 10, 1990,
p. 47. .
"Seismic Character Mapping Using Multivariate Statistical Pattern
Integration" by Partyka, Prasad and Bahorich, Extended Abstracts of
Papers, European Association of Exploration Geophysicists,
Fifty-Fifth Meeting and Technical Exhibition, Jun. 7-11, 1993.
.
"New Spatial Visualizatin Techniques in Tectonic and Stratigraphic
Interpretation Optimize Reservoir Delineation of th Roar Field,
Danish North Sea", Abatzis Geological Survey of Denmark and J. D.
Kerr, p. 81. .
"Sismage: The Techniques of Image Analysis at the Service of the
Structural Interpretation of Seismic Data", Naamen Keskes and
Jacqueline Camy-Peyret, Soc. Nat. Aquitaine, 1991, pp. 271-278.
.
Applied Geophysics by R. E. Sheriff et al. (Cambridge University
Press), p. 393, p. 395, (date unavailable). .
"Image-Processing display techniques applied to seismic
instantaneous attributes over the Gorgan gas field", R. Burnett
Oliveros and Barbara J. Radovich, Society of Exploration
Geophysicists International Exposition and Sixty-Seventh Annual
Meeting, pp. 2064-2067, no date. .
"The Coherence Cube", Mike Bahorich and Steve Farmer, The Leading
Edge, Oct. 1995, pp. 1053-1059. .
"Reflection Seismic: A Tool For Energy Resource Exploration",
Kenneth Waters and John Wiley, 1981, pp. 259-263. .
"Automatic Delineation of Lateral Facies Changes in Clasic
Environments" by Donald Vossler, Extended Abstracts of Papers,
European Association of Exploration Geophysicists, 59th Meeting and
Technical Exhibition, Oct. 29-Nov. 2, 1989, p 803-804. .
The Coefficient of Coherence: Its Estimation and Use in Geophysical
Data Processing, By M.R. Foster and N.J. Guinzy, Geophysics, vol.
33, No. 4, Aug. 1967, pp. 602-616. .
"Semblance and Other Coherency Measures for Multichannel Data", by
N. S. Neidell and M. Turhan Taner, Geophysics, vol. 36, No. 3, Jun.
1972, pp. 482-497. .
"Seismic Sequence Attribute Map (SSAM)", by Michael Bahorich and S.
Rutt Bridges, Technical Program Expanded Abstracts with Authors
Biographies, The Society of Exploration Geophysicists, Sixty-Six
Annual International Meetin and Exposition, Oct. 25-29, 1992, pp.
1-3. .
"Time-Slice Versus Statistical Slice (stat-slice: A Comparison of
their Use for 3-D Seismic Interpretation", by John D. Kerr and Gary
L. Jones, Technical Program Expanded Abstracts with Authors
Biographies, The Society of Exploration Geophysicists, Sixty-Fifth
Annual International Meetin and Exposition, Oct. 8-13,1995, pp.
319-321..
|
Primary Examiner: McElheny, Jr.; Donald E.
Attorney, Agent or Firm: Madan,Mossman & Sriram P.C.
Parent Case Text
CROSS-REFERENCE
This patent application is a continuation in part of a provisional
patent application filed Oct. 6, 1995, and having a Ser. No.
60/005,032 and a U.S. patent application to Bahorich and Farmer,
having a Ser. No. 08/353,934 and a filing date of Dec. 12, 1994,
now U.S. Pat. No. 5,563,949.
Claims
We claim:
1. A method for the exploration of hydrocarbons, comprising the
steps of: (a) obtaining a representation of a set of seismic traces
distributed over a pre-determined three-dimensional volume of the
earth, said volume of the earth having subterranean features
characterized by dip and dip azimuth that are defined relative to a
pre-defined dip azimuth measurement axis; (b) dividing said
three-dimensional volume into at least one horizontal time layer,
and dividing said time layer into a plurality of three-dimensional
analysis cells, wherein each analysis cell has two pre-determined,
mutually perpendicular lateral dimensions and has portions of at
least five laterally separated seismic traces located therein; (c)
calculating, within each of said analysis cells, a plurality of
measures of the semblance of said traces located therein, wherein
each measure of semblance is at least a function of time, the
number of seismic traces within said analysis cell, and the
apparent dip and apparent dip azimuth of said traces within said
analysis cell; (d) identifying, within each analysis cell, the
largest of said calculated measures of semblance and defining the
corresponding apparent dip and apparent dip azimuth to be an
estimate of the true dip and an estimate of the true dip azimuth of
the seismic traces within said analysis cell; and (e) forming, from
all of said analysis cells, a seismic attribute display from said
largest calculated measures of semblance and said corresponding
estimates of the true dip and the true dip azimuth of the seismic
traces within said time layer.
2. The method of claim 1, where step (e) is performed by forming a
color map that is characterized by hue, saturation and lightness,
wherein one of said estimates of true dip azimuth, said estimates
of true dip, and said largest calculated measures of semblance is
mapped onto one of a lightness scale, hue scale, and a saturation
scale; wherein another of said estimates of true dip azimuth, said
estimates of true dip, and said largest calculated measures of
semblance is mapped onto another of said lightness scale, said hue
scale, and said saturation scale; and wherein the remaining one of
said estimates of true dip azimuth, said estimates of true dip, and
said largest calculated measures of semblance is mapped onto the
remaining one of said lightness scale, said hue scale, and said
saturation scale.
3. The method of claim 2, where step (e) is performed by mapping
said estimates of true dip azimuth onto said hue scale.
4. The method of claim 2, where step (e) is performed by mapping
said estimates of true dip onto said saturation scale.
5. The method of claim 2, where step (e) is performed by mapping
said largest calculated measures of semblance onto a lightness
scale.
6. The method of claim 1, where in performing step (c) each measure
of semblance is at least a function of the energy of said traces;
and wherein said energy of said traces is a function of time, the
number of seismic traces within said analysis cell, and the
apparent dip and apparent dip azimuth of said traces within said
analysis cell.
7. The method of claim 6, wherein each measure of semblance is at
least a function of ##EQU10##
and ##EQU11##
where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances measured
from the center of the analysis cell, where p and q are the
apparent dips in the x and y directions respectively, and where
u.sub.f (t, p,q,.Iadd.x.sub.j.Iaddend.
[x],.Iadd.y.sub.j.Iaddend.[y]) is a seismic trace within the
analysis cell; and wherein the true dip d and dip azimuth .phi. are
related to p and q by p=d sin .phi. [p] and q=d cos .phi..
8. The method of claim 7, wherein each measure of semblance is a
function of: ##EQU12##
9. The method of claim 7, wherein each measure of semblance for
each dip, dip azimuth, and analysis point are smoothed by
performing a running window time integration over the partial sums
from -K to +K: ##EQU13## where K is the half width of the time
window in samples.
10. The method of claim 1, wherein said traces within said analysis
cells are characterized by a maximum dip and a maximum temporal
frequency component; and wherein step (c) includes the steps of:
obtaining an estimate of the maximum true dip and the maximum
temporal frequency component of said traces in said analysis cell;
using said maximum true dip, said maximum temporal frequency and
said pre-determined lateral dimensions of said analysis cell to
calculate apparent dip increments in two generally perpendicular
directions relative to said dip azimuth measurement axis.
11. The method of claim 1, where in performing step (c) said
measure is at least a function of: ##EQU14## where J is the number
of traces in said analysis cell, where u.sub.j (.tau.,p,q) is a
representation of the seismic trace in said analysis cell, where
.rho. is the time, p is the apparent dip in the x direction, and q
is the apparent dip in the y direction; wherein p and q are
measured in ms/m and the x and y directions are mutually
perpendicular.
12. The method of claim 11, where in performing step (c) said
measure is also a function of ##EQU15##
13. The method of claim 12, where in performing step (c) said
measure is a function of: ##EQU16##
14. A method of locating subterranean features, faults, and
contours, comprising the steps of: (a) accessing 3D seismic data
covering a pre-determined volume of the earth; (b) dividing said
volume into an array of relatively small three-dimensional cells
wherein each of said cells is characterized by at least five
laterally separated and generally vertical seismic traces located
therein; (c) determining in each of said cells the
semblance/similarity of said traces relative to two pre-determined
directions; and (d) recording said semblance/similarity of said
cells in a form for display as a two-dimensional map of
subterranean features.
15. The method of claim 14, where in performing step (c) said
pre-determined directions are mutually perpendicular; and said
semblance/similarity of said traces within each cell is a function
of at least time, the number of seismic traces within said analysis
cell, and the apparent dip and apparent dip azimuth of said traces
within said analysis cell.
16. The method of claim 15, where said semblance/similarity of said
traces within each cell is determined by computing a plurality of
measurements of the semblance/similarity of said traces within each
cell and selecting the largest of said measurements of said
semblance/similarity of each cell; and wherein step (c) further
includes the step of defining the apparent dip and apparent dip
azimuth corresponding to said largest of said measurements to be an
estimate of the true dip and an estimate of the true dip azimuth of
the seismic traces within said analysis cell.
17. The method of claim 16, wherein each of said plurality of
measurements of said semblance/similarity of at least a function of
the energy of said traces; and wherein said energy of said traces
is a function of time, the number of seismic traces within said
analysis cell, and the apparent dip and apparent dip azimuth of
said traces within said analysis cell.
18. The method of claim 16, wherein said map is a color map that is
characterized by hue, saturation and lightness; wherein one of said
estimates of true dip azimuth, said estimates of true dip, and said
largest calculated measures of semblance is mapped onto one of a
lightness scale, hue scale, and a saturation scale; wherein another
of said estimates of true dip azimuth, said estimates of true dip,
and said largest calculated measures of semblance is mapped onto
another of said lightness scale, said hue scale, and said
saturation scale; and wherein the remaining one of said estimates
of true dip azimuth, said estimates of true dip, and said largest
calculated measures of semblance is mapped onto the remaining one
of said lightness scale, said hue scale, and said saturation
scale.
19. The method of claim 18, wherein step (d) comprises the steps
of: mapping said estimates of true dip azimuth onto said hue scale,
mapping said estimates of true dip onto said saturation scale, and
mapping said largest calculated measures of semblance onto a
lightness scale.
20. In seismic exploration wherein 3D seismic data comprising
reflected seismic energy is recorded as a function of time and
wherein a computer is used that is programmed to process such
seismic traces and to produce an image therefrom that is
representative of subterranean features, an article of manufacture
comprising: a medium that is readable by a computer and that
carries instructions for said computer to perform a process
comprising the steps of: (a) accessing 3D seismic data over a
predetermined volume of the earth, said data comprising seismic
traces that are characterized by time, position and amplitude; and
(b) ascertaining the similarity of nearby regions of said 3D
seismic data of said volume by: (1) dividing at least a portion of
said data into an array of relatively small, adjacent,
three-dimensional analysis cells, wherein each of said analysis
cells contains portions of at least five seismic traces; and (2)
computing a seismic attribute for each cell that is a function of
the largest of a plurality of measurements of semblance and the
corresponding apparent dip and the corresponding apparent dip
azimuth.
21. The article of manufacture of claim 20, wherein said medium
carries instructions for the computer to perform step (2) by making
measurements of semblance that are a function of: ##EQU17## where x
and y are distances measured from the center of the analysis cell
along mutually perpendicular x and y axes, where J traces is the
number of seismic traces, where U.sub.j (.pi.,p,q) represents a
seismic trace, where .pi. is the time, p is the apparent dip in the
x direction, and q is the apparent dip in the y direction; and
wherein p and q are measured in ms/meter.
22. The article of manufacture of claim 21, wherein said medium
carries instructions for the computer to perform step (2) by making
measurements of the semblance that are also a function of:
##EQU18##
23. The article of manufacture of claim 21, wherein said medium
carries instructions for said computer to perform step (1) by
forming analysis cells having an elliptical cross-section.
24. The article of manufacture of claim 23, wherein said
predetermined volume is characterized by a fracture having an
ascertainable direction; and wherein said medium carries
instructions for said computer to form analysis cells that are
generally elliptical in shape and that have major axes aligned in
the direction of said fracture.
25. In seismic exploration wherein reflected seismic energy is
recorded as a function of time to produce a series of seismic
traces, a method comprising the steps of: (a) accessing a data set
of seismic traces distributed over a three-dimensional volume of
the earth, said volume of the earth having subterranean features
characterized by dip and dip azimuth; (b) calculating a plurality
of measures of the semblance of said traces within a relatively
small three dimensional analysis cell that is located within said
volume and at one part of a predetermined time layer, wherein each
measure of semblance is at least a function of time, the number of
seismic traces within said analysis cell, and the apparent dip and
apparent dip azimuth of said traces within said analysis cell; (c)
computing a seismic attribute for said analysis cell that is at
least a function of the largest of said plurality of calculated
measures of semblance and the corresponding apparent dip and the
corresponding apparent dip azimuth, wherein said corresponding
apparent dip and said corresponding apparent dip azimuth are
defined to be estimates of the true dip and an estimate of the true
dip azimuth of the seismic traces within said analysis cell; (d)
repeating steps (b) and (c) along other parts of said time layer;
and (e) forming a map of said seismic attributes over said time
layer.
26. The method of claim 25, wherein step (a) comprises the steps
of: (1) accessing 3D seismic data over a predetermined volume of
the earth, said 3D seismic data comprising at least eleven seismic
traces that are characterized by time, position and amplitude; and
(2) dividing a portion of said volume into at least one time layer
comprising an array of relatively small, three-dimensional cubes
that contain at least five seismic traces; and wherein said cubes
are used as the cells to perform step (b).
27. The method of claim 26, where in performing step (b) each
measure of semblance is a function of: ##EQU19## where each
analysis cell contains portions of at least J seismic traces, where
J is at least 5, where x and y are distances measured from the
center of the analysis cell along mutually perpendicular x and y
axes, where p and q are the apparent dips in the x and y
directions, where u.sub.j (t,p,q,x,y) represents a seismic trace
within said analysis cell, and where the true dip d and dip azimuth
.phi. are related to p and q by p=d sin (.phi.) and q=d cos
(.phi.).
28. The method of claim 27, wherein each measure of semblance for
each dip, dip azimuth, and analysis point are smoothed by forming a
running window time integration over partial sums of a time window
within said horizontal time layer.
29. A method of seismic exploration, comprising the steps of: (a)
reading a 3D seismic data set comprising seismic signal traces that
are distributed over a volume of the earth; (b) selecting at least
one horizon slice from said volume and forming therein cells that
are arranged into laterally extending rows and columns, each of
said cells having at least five seismic traces extending generally
therethrough; (c) computing for each of said cells; (1) a plurality
of semblance measurements of said traces, wherein each measurement
is at least a function of time, the number of seismic traces within
said analysis cell, and the apparent dip and apparent dip azimuth
of said traces; (2) the largest of said plurality of measurements
of semblance; and (3) an estimate of the true dip and an estimate
of the true dip azimuth of the seismic traces within said analysis
cell from the apparent dip and apparent dip azimuth corresponding
to said largest measurement of semblance; and (d) displaying, over
said at least one horizon slice, of representations of said largest
measurements of semblance and said estimated true dips and said
estimated true dip azimuths of each of said cells.
30. The method of claim 29, wherein step (b) is performed by
selecting a horizon slice that is characterized by a common time;
and wherein step (d) is performed by displaying across said time
slice representations of said largest measurements of semblance and
said estimated true dips and said estimated true dip azimuths of
said cells.
31. The method of claim 29, wherein step (d) is performed by
forming a color map that is characterized by hue, saturation and
lightness, wherein for each of said cells: one of said estimates of
true dip azimuth, said estimates of true dip, and said largest
calculated measurements of semblance is mapped onto one of a
lightness scale, hue scale, and a saturation scale; wherein another
of said estimates of true dip azimuth, said estimates of true dip,
and said largest calculated measurements of semblance is mapped
onto another of said lightness scale, said hue scale, and said
saturation scale; and wherein the remaining one of said estimates
of true dip azimuth, said estimates of true dip, and said largest
calculated measurements of semblance is mapped onto the remaining
one of said lightness scale, said hue scale, and said saturation
scale.
32. In the exploration for gas and oil wherein over a volume of the
earth seismic traces are recorded, a method comprising the steps
of: (a) grouping at least parts of at least five relatively close
seismic traces into a plurality of relatively small
three-dimensional analysis cells; (b) performing in each of said
cells a plurality of measurements of the semblance of said parts of
said traces as a function of at least time, the number traces
therein, the apparent dip of said traces, and the apparent dip
azimuth; (c) identifying in each of said cells the largest of said
plurality of measurements of semblance, the corresponding apparent
dip, and the corresponding dip azimuth; and (d) converting said
largest measurements of semblance, said corresponding dip and said
corresponding dip azimuth of said cells into color attributes of
hue, saturation and lightness, wherein for each cell: one of said
dip azimuth, said dip, and said largest measurements of semblance
is mapped onto one of a lightness scale, hue scale, and a
saturation scale; another of said dip azimuth, said dip, and said
largest measurements of semblance is mapped onto another of said
lightness scale, said hue scale, and said saturation scale; and the
remaining one of said dip azimuth, said dip, and said largest
measurements of semblance is mapped on the remaining one of said
lightness scale, said hue scale, and said saturation scale.
33. A device adapted for use by a workstation wherein 3D seismic
data is read into memory and processed into a color display of
subterranean features, comprising: computer readable means carrying
instructions for a process comprising the steps of: (1) digitally
locating said 3D seismic data in an array of relatively small
three-dimensional cells, wherein each of said cells contains
representations of a part of at least five seismic traces; (2)
calculating for each of said cells an estimate of the semblance,
and estimate of the true dip, and an estimate of the true dip
azimuth of said parts; and (3) converting said estimates of
semblance, said estimates of true dip, and said estimates of true
dip azimuth into an array of digital values corresponding to the
color attributes of hue, saturation, and lightness.
34. The device of claim 33, wherein one of said estimates of true
dip azimuth, said estimates of true dip, and said estimates of
semblance is mapped onto one of a lightness scale, a hue scale, and
a saturation scale for each of said cells; wherein another of said
estimates of true dip azimuth, said estimates of true dip, and said
estimates of semblance is mapped onto another of said lightness
scale, said hue scale, and said saturation scale for each of said
cells; and wherein the remaining one of said estimates of true dip
azimuth, said estimates of true dip, and said estimates of
semblance is mapped onto the remaining one of said lightness scale,
said hue scale, and said saturation scale for each of said
cells.
35. The device of claim 33, wherein said computer readable means
carries instructions to perform step (2) by: (i) calculating a
plurality of semblance measurements relative to at least two
directions, and selecting the largest of said measurements; (ii)
selecting the apparent dip corresponding to said largest
measurement of semblance from step (i); and (iii) selecting the
apparent dip azimuth corresponding to said largest measurement of
semblance from step (i).
36. The device of claim 33, wherein said computer-readable means is
selected from the group consisting of a magnetic tape, a magnetic
disk, an optical disk and a CD-ROM.
37. A method of prospecting for hydrocarbon deposits, comprising
the steps of: (a) obtaining a color seismic attribute display of 3D
seismic data for a predetermined three-dimensional volume of the
earth, said display being generated by using data obtained by a
computer and at least one program for said computer that instructs
said computer to perform the following steps: (1) convert said
volume into an array of relatively small three-dimensional cells,
wherein each of said cells has a portion of at least five seismic
traces located therein; (2) make plurality of semblance
measurements within each of said cells, wherein each measurement is
at least a function of time, the number of seismic traces within
said cell, the apparent dip of said traces and apparent dip azimuth
of said traces; (3) select the largest of said plurality of
measurements of semblance in each cell; (4) use as an estimate of
the true dip and an estimate of the true dip azimuth in each cell
the apparent dip and apparent dip azimuth that correspond to said
largest measurement of semblance in said cell; (5) map said
estimates of true dip azimuth onto a hue scale; (6) map said
estimates of true dip onto a saturation scale; and (7) map said
largest calculated measures of semblance onto a lightness scale;
and (b) using said color display to identify subsurface structural
and sedimentological features commonly associated with the
entrapment and storage of hydrocarbons.
38. The method of claim 37, further including the step of using
said map to identify drilling hazards.
39. The method of claim 38, further including the step of drilling
at a location identified in step (b).
40. The method of claim 37, wherein step (a)(2) comprises the step
of computing: ##EQU20## where each cell is characterized by two
perpendicular dimensions, where x and y are distances measured from
the center of the cell along mutually perpendicular x and y axes,
where J is the number of seismic traces, where U.sub.j (.tau.,p,q)
represents a seismic trace, where .tau. is the time, p is the
apparent dip in the x direction, and where q is the apparent dip in
the y direction.
41. The method of claim 40, wherein step (a)(2) comprises the step
of computing: ##EQU21##
42. In a computer workstation wherein 3-D seismic data obtained
over a predetermined three-dimensional volume of the earth is read
into memory, wherein a computer divides such volume into an array
of three-dimensional analysis cells, wherein each cell has at least
a portion of five laterally separated seismic traces located
therein, and wherein the computer is used to transform such data
into a display of seismic attributes, the computer CHARACTERIZED BY
performing a process comprising the steps of: (1) calculating in
each of the cells a semblance value for said seismic traces,
wherein said semblance value is at least a function of time, the
number of seismic traces within said cell, the apparent dip of said
traces, and the apparent dip azimuth of said traces; and (2)
displaying said semblance value of each cell that lies between two
planes within the 3-D volume to identify subsurface features
commonly associated with the entrapment and storage of
hydrocarbons.
43. The computer workstation of claim 42, wherein the computer
performs step (1) by: making a plurality of semblance measurements
within each of said cells; and selecting the largest of said
plurality of measurements as said semblance value of said cell.
44. The computer workstation of claim 43, wherein after performing
step (1) the computer performs the step of: using the apparent dip
and the apparent dip azimuth that correspond to said largest
measurement of semblance in said cell as an estimate of true dip
and as an estimate of true dip azimuth of said cell.
45. The computer workstation of claim 44, wherein the display of
step (2) is characterized by color components of hue, saturation
and lightness; and wherein step (2) comprises the steps of mapping
said estimate of true dip azimuth for each cell onto a hue scale;
mapping said estimate of true dip for each dell onto a saturation
scale; and mapping said largest calculated measures of semblance
onto a lightness scale..Iadd.
46. The method of claim 14 wherein said semblance/similarity is at
least a function of time, amplitude and the number of traces within
said cells..Iaddend..Iadd.
47. The method of claim 14 wherein said semblance/similarity is
determined for data samples of a constant time
value..Iaddend..Iadd.
48. The method of claim 14 wherein said semblance/similarity is at
least a function of:.Iaddend. ##EQU22##
and ##EQU23##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
49. The method of claim 48 wherein said semblance/similarity is a
function of:.Iaddend. ##EQU24## .Iadd.
50. The method of claim 49 wherein said semblance/similarity is an
arithmetic inverse of a function of:.Iaddend. ##EQU25## .Iadd.
51. The method of claim 48 wherein said semblance/similarity is
determined by performing a running window time integration over the
partial sums from -K to +K:.Iaddend. ##EQU26##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
52. The method of claim 14 wherein said semblance/similarity is at
least a function of:.Iaddend. ##EQU27##
.Iadd.and.Iaddend. ##EQU28##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, where p and q are apparent dips in the x and y
directions, respectively, and where u.sub.f (t,p,q,x.sub.j,y.sub.j)
is a portion of a seismic trace with said cell..Iaddend..Iadd.
53. The method of claim 52 wherein said semblance/similarity is a
function of:.Iaddend.
##EQU29## .Iadd.
54. The method of claim 52 wherein said semblance/similarity is an
arithmetic inverse function of:.Iaddend. ##EQU30## .Iadd.
55. The method of claim 52 wherein said semblance/similarity is
determined by performing a running window time integration over
partial sums from -K to +K:.Iaddend. ##EQU31##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
56. The method of claim 52 wherein p=0 and q=0..Iaddend..Iadd.
57. The method of claim 14 wherein step (d) includes recording said
semblance/similarity in a form for display mapped to at least one
of: (i) a lightness scale (ii) a hue scale, and, (iii) a saturation
scale..Iaddend..Iadd.
58. In seismic exploration wherein 3D seismic data from geologic
formations of the earth are recorded as a function of time and
wherein a computer is used that is programmed to process such 3D
seismic data so that an image may be produced therefrom that is
representative of subterranean features, an article of manufacture
comprising: a medium that is readable by a computer and that
carries instructions for said computer to perform a process
comprising: (a) accessing 3D seismic data over a predetermined
volume of geologic formations the earth, said 3D seismic data
comprising seismic traces that are characterized by time, position
and amplitude; and (b) ascertaining a seismic attribute of said 3D
seismic data by: (1) dividing at least a portion of said 3D seismic
data into a plurality of relatively small three-dimensional
analysis cells, wherein each of said analysis cells contain
portions of at least five seismic traces; and (2) computing a
seismic attribute that is a function of semblance for each analysis
cell..Iaddend..Iadd.
59. The article of manufacture of claim 58 wherein said semblance
is at least a function of:.Iaddend. ##EQU32##
.Iadd.and.Iaddend. ##EQU33##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
60. The article of manufacture of claim 59 wherein said semblance
is a function of:.Iaddend. ##EQU34## .Iadd.
61. The article of manufacture of claim 59 wherein said semblance
is an arithmetic inverse of a function of:.Iaddend. ##EQU35##
.Iadd.
62. The article of manufacture of claim 59 wherein said semblance
is determined by performing a running window time integration over
the partial sums from -K to +K:.Iaddend. ##EQU36##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
63. The article of manufacture of claim 58 wherein the process
performed by the computer further comprises displaying said seismic
attribute in a form that is at least one of (i) a planar display,
(ii) a cross-sectional display, (iii) a 2D display and, (iv) a 3D
display..Iaddend..Iadd.
64. The article of manufacture of claim 58 wherein the computed
seismic attribute is a number that is at least 0 and at most
1..Iaddend..Iadd.
65. The article of manufacture of claim 58 wherein the process
further comprises displaying the computed seismic attributes in a
visual format to display the subterranean
features..Iaddend..Iadd.
66. The article of manufacture of claim 65 wherein the visual
format to display the subterranean features is at least one of (i)
a cube of discontinuity values, (ii) a cube of dissimilarity
values, (iii) a cube of semblance values, (iv) a cube of the
inverse of semblance values, and (v) a cube of coherence values.
.Iaddend..Iadd.
67. In seismic exploration wherein 3D seismic data from geologic
formations of the earth are recorded as a function of time and
wherein a computer is used that is programmed to process such 3D
seismic data so that an image may be produced therefrom that is
representative of subterranean features, an article of manufacture
comprising: a medium that is readable by a computer and that
carries instructions for said computer to perform a process
comprising: (a) accessing 3D seismic data over a predetermined
volume of geologic formations of the earth, said 3D seismic data
comprising seismic traces that are characterized by time, position
and amplitude; and (b) dividing at least a portion of said data
into a plurality of relatively small, three-dimensional analysis
cells, wherein each of said three-dimensional analysis cells
contains portions of at least five seismic traces; and (c)
computing a seismic attribute for each cell that is a function
of.Iaddend. ##EQU37##
.Iadd.and.Iaddend. ##EQU38##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
68. The article of manufacture of claim 67 wherein said seismic
attribute is a function of:.Iaddend. ##EQU39## .Iadd.
69. The article of manufacture of claim 67 wherein said seismic
attribute is an arithmetic inverse of a function of:.Iaddend.
##EQU40## .Iadd.
70. The article of manufacture of claim 67 wherein said seismic
attribute is determined by performing a running window time
integration over the partial sums from -K to +K:.Iaddend.
##EQU41##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
71. The article of manufacture of claim 67 wherein the process
performed by the computer further comprises displaying said seismic
attribute in a form that is at least one of (i) a planar display,
(ii) a cross-sectional display, (iii) a 2D display and, (iv) a 3D
display..Iaddend..Iadd.
72. The article of manufacture of claim 67 wherein the computed
seismic attribute is a number that is at least 0 and at most
1..Iaddend..Iadd.
73. The article of manufacture of claim 67 wherein the process
further comprises displaying the computed seismic attributes in a
visual format to display the subterranean
features..Iaddend..Iadd.
74. A method for locating geologic features of an earth volume, the
method comprising: (a) accessing 3D seismic data over a
predetermined volume of the earth, said data comprising seismic
traces that are characterized by time, position and amplitude; (b)
dividing at least a portion of said 3D ismic data into a plurality
of relatively small, three-dimensional analysis cells, wherein each
of said analysis cells contains portions of at least five seismic
traces; and (c) computing a seismic attribute for each cell that is
a function of.Iaddend. ##EQU42##
.Iadd.and.Iaddend. ##EQU43##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
75. The method of claim 74 wherein said seismic attribute is a
function of:.Iaddend. ##EQU44## .Iadd.
76. The method of claim 74 wherein said seismic attribute is an
arithmetic inverse of a function of:.Iaddend. ##EQU45## .Iadd.
77. The method of claim 74 wherein said seismic attribute is
determined by performing a running window time integration over the
partial sums from -K to +K:.Iaddend.
##EQU46##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
78. The method of claim 74 further comprising displaying said
seismic attribute in a form that is at least one of (i) a planar
display, (ii) a cross-sectional display, (iii) a 2D display, and
(iv) a 3D display..Iaddend..Iadd.
79. The method of claim 74 wherein the computed seismic attribute
is a number that is at least 0 and at most 1..Iaddend..Iadd.
80. The method of claim 74 further comprising displaying the
computed seismic attributes in a visual format to display the
subterranean features. .Iaddend..Iadd.
81. A method of locating subterranean features, the method
comprising: (a) accessing 3D seismic data covering a pre-determined
volume of the earth; (b) dividing said volume into an array of
relatively small three- dimensional cells wherein each of said
cells is characterized by at least five laterally separated and
generally vertical seismic traces located therein; (c) determining
in each of said cells a semblance/similarity of said traces; and
(d) recording said semblance/similarity of said cells..Iaddend.
.Iadd.
82. The method of claim 81 wherein said semblance/similarity is at
least a function of:.Iaddend. ##EQU47##
.Iadd.and.Iaddend. ##EQU48##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
83. The method of claim 82 wherein said semblance/similarity is a
function of:.Iaddend. ##EQU49## .Iadd.
84. The method of claim 82 wherein said semblance/similarity is an
arithmetic inverse of a function of:.Iaddend. ##EQU50## .Iadd.
85. The method of claim 82 wherein said semblance/similarity is
determined by performing a running window time integration over the
partial sums from -K to +K:.Iaddend. ##EQU51##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
86. The method of claim 81 further comprising displaying said
semblance/similarity in a form that is at least one of (i) a planar
display, (ii) a cross-sectional display, (iii) a 2D display, and
(iv) a 3D display..Iaddend..Iadd.
87. The method of claim 81 wherein the semblance/similarity of said
traces is a number that is at least 0 and at most
1..Iaddend..Iadd.
88. The method of claim 81 further comprising displaying the
semblance/similarity in a visual format to display the subterranean
features..Iaddend..Iadd.
89. A method of locating geologic formations, the method
comprising: (a) accessing 3D seismic data covering a pre-
determined volume of the earth; (b) dividing said volume into an
array of relatively small three-dimensional cells wherein each of
said cells is characterized by at lest five laterally separated and
generally vertical seismic traces located therein; (c) determining
in each of said cells an inverse of a semblance/similarity of said
traces relative to two pre-determined directions; and (d) recording
said inverse of said semblance/similarity of said
cells..Iaddend..Iadd.
90. The method of claim 89 wherein the inverse of said
semblance/similarity is an additive inverse..Iaddend..Iadd.
91. A method of generating a discontinuity cube for displaying
subterranean geologic features of a volume of earth formation, the
method comprising: (a) accessing 3D seismic data covering a
pre-determined volume of the earth; (b) dividing said volume into
an array of relatively small three-dimensional cells wherein each
of said cells is characterized by at least five laterally separated
and generally vertical seismic traces located therein; (c)
assigning a signal discontinuity value to each said cell; and (d)
assigning a unique color to each said signal discontinuity value in
said cells..Iaddend..Iadd.
92. The method of claim 91 wherein the signal discontinuity value
is at least a function of.Iaddend. ##EQU52##
.Iadd.and.Iaddend. ##EQU53##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
93. The method of claim 92 wherein said signal discontinuity value
is a function of: ##EQU54##
.Iaddend..Iadd.
94. The method of claim 92 wherein said signal discontinuity value
is an arithmetic inverse of a function of:.Iaddend. ##EQU55##
.Iadd.
95. The method of claim 92 wherein said signal discontinuity value
is determined by performing a running window time integration over
the partial sums from -K to +K:.Iaddend. ##EQU56##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
96. The method of claim 91 further comprising displaying said
signal discontinuity value in a form that is at least one of (i) a
planar display, (ii) a cross-sectional display, (iii) a 2D display,
and (iv) a 3D display..Iaddend..Iadd.
97. The method of claim 91 wherein the signal discontinuity value
of said cells is a number that is at least 0 and at most
1..Iaddend..Iadd.
98. The method of claim 91 further comprising displaying the signal
discontinuity value in a visual format to display the subterranean
features..Iaddend..Iadd.
99. A method of generating a cube for displaying geologic features,
faults and contours of a cubic volume of an earth formation wherein
3D seismic data samples covering said cubic volume of the earth
formation are accessed, said cubic volume of the earth formation
divided into an array of relatively small 3D cells containing at
least a portion of the 3D seismic data samples, the cube
representing said cubic volume of said earth formation enclosing a
plurality of the 3D seismic data samples, the method comprising:
(a) assigning a semblance value to each seismic data sample in said
cube; and (b) assigning a unique color to each semblance value in
said cube..Iaddend..Iadd.
100. The method of claim 99 wherein the semblance value is at least
a function of .Iaddend. ##EQU57##
.Iadd.and .Iaddend. ##EQU58##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.f(t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
101. A method of generating a cube for displaying a set of geologic
features, faults and contours of a cubic volume on an earth
formation wherein a plurality of 3D seismic data samples covering
said cubic volume of the earth formation is accessed, said cubic
volume of the earth formation divided into an array of relatively
small 3D cells, said cube representing said cubic volume of said
earth formation enclosing at least a portion of said plurality of
3D seismic data samples, the method comprising: (a) assigning an
inverse of semblance value to each seismic data sample in said
cube; and (b) assigning a unique color to each said inverse of
semblance value in said cube..Iaddend..Iadd.
102. The method of claim 101 wherein the inverse of semblance value
is at least a function of .Iaddend. ##EQU59##
.Iadd.and.Iaddend. ##EQU60##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
103. The method of claim 101 wherein said inverse of semblance
value is an additive inverse..Iaddend..Iadd.
104. A method of generating a cube for displaying a set of geologic
features, faults and contours of a cubic volume of an earth
formation wherein 3D seismic data samples covering said cubic
volume of the earth formation are accessed, said cubic volume of
the earth formation divided into an array of relatively small 3D
cells containing at least a portion of the 3D seismic data samples,
said cube representing said cubic volume of said earth formation
enclosing at least a portion of a plurality of the 3D seismic data
samples, the method comprising the steps of: (a) mapping a
semblance value to each seismic data sample in said cube; and (b)
mapping a unique color to each semblance value in said
cube..Iaddend..Iadd.
105. The method of claim 104 wherein the semblance value is at
least a function of.Iaddend. ##EQU61##
.Iadd.and.Iaddend. ##EQU62##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.f (t,x,.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
106. A method of generating a cube for displaying geologic
features, faults and contours of a volume of an earth formation
wherein a plurality of seismic data samples covering the volume of
the earth formation is accessed, said volume of the earth formation
divided into an array of relatively small three-dimensional cells,
said cells characterized by at least five laterally separated and
generally vertical seismic traces located therein, the method
comprising: (a) assigning a signal discontinuity value to each
seismic data sample in said cube; and (b) assigning a unique color
to each said signal discontinuity value in said
cube..Iaddend..Iadd.
107. The method of claim 106 wherein the signal discontinuity value
is at least a function of.Iaddend. ##EQU63##
.Iadd.and.Iaddend. ##EQU64##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
eismic traces, where x and y are distances from the center of the
cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
108. A method to generate a coherence cube for locating
subterranean features, faults, and contours, the method comprising:
(a) accessing 3D seismic data covering a pre-determined volume of
the earth; (b) dividing said volume into an array of relatively
small three-dimensional cells wherein each of said cells is
characterized by at least five laterally separated and generally
vertical seismic traces located therein; (c) determining in each of
said cells the ratio of incoherent energy and coherent energy of
said traces relative to two pre-determined directions; and (d)
recording said ratio of incoherent energy and coherent energy of
said cells in a form for display as a map of subterranean
features..Iaddend..Iadd.
109. A method of locating subterranean features, faults, and
contours, the method comprising: (a) accessing 3D seismic data
covering a pre-determined volume of the earth; (b) dividing said
volume into an array of relatively small three-dimensional cells
wherein each of said cells is characterized by at least five
laterally separated and generally vertical seismic traces located
therein; (c) determining in each of said cells the
discontinuity/dissimilarity of said traces relative to two
pre-determined directions; and (d) recording said
discontinuity/dissimilarity of said cells in a form for display as
a map of subterranean features..Iaddend..Iadd.
110. The method of claim 109 wherein the
discontinuity/dissimilarity is at least a function of.Iaddend.
##EQU65##
.Iadd.and.Iaddend. ##EQU66##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.f (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
111. A device adapted for use by a workstation wherein 3D seismic
data is read into memory and processed into a color display of
subterranean features, the device including computer readable means
carrying instructions for a process comprising: (a) digitally
locating said 3D seismic data in an array of relatively small
three-dimensional cells, wherein each of said cells contains
representations of a part of at least five seismic traces; (b)
calculating for each of said cells an estimate of the semblance;
and (c) converting said estimate of semblance into an array of
digital values corresponding to color
attributes..Iaddend..Iadd.
112. The device of claim 111, wherein said computer-readable means
is selected from the group consisting of a magnetic tape, a
magnetic disk, an optical disk and a CD-ROM..Iaddend..Iadd.
113. The device of claim 111 further comprising means for
displaying the computed estimates of semblance in a visual format
of subterranean features..Iaddend..Iadd.
114. In a computer workstation wherein 3D seismic data obtained
over a predetermined three-dimensional volume of the earth is read
into memory, wherein a computer divides such volume into an array
of three-dimensional analysis cells, wherein each cell has at least
a portion of five laterally separated seismic traces located
therein, and wherein the computer is used to transform such data
into a display of seismic attributes, the computer CHARACTERIZED BY
performing a process comprising: (a) calculating in each of the
cells a semblance value for said seismic traces, wherein said
semblance value is at least a function of amplitude, time, and the
number of seismic traces within said cell; and (b) displaying said
semblance value of each cell within the 3D volume to identify
subsurface features commonly associated with the entrapment and
storage of hydrocarbons..Iaddend..Iadd.
115. The computer workstation of claim 114, wherein the display of
step (b) is characterized by color components of at least one of
hue, saturation and lightness, and wherein step (b) comprises
mapping said semblance for each cell onto one of (i) a hue scale,
(ii) a saturation scale, and (iii) a lightness
scale..Iaddend..Iadd.
116. A method of seismic exploration for locating geologic
formations, faults, contours and unconformities, the method
comprising: (a) reading a 3D seismic data set comprising seismic
signal traces that are distributed over a volume of the earth; (b)
selecting at least one time slice from said volume and forming
therein cells that are arranged into laterally extending rows and
columns, each of said cells having at least five seismic traces
therein; (c) computing for each of said cells a plurality of
semblance measurements of said traces, wherein each measurement is
at least a function of amplitude, time, and the number of seismic
traces within said cell; and (d) recording in a form for display,
over said at least one time slice, measurements of
semblance..Iaddend..Iadd.
117. A method of seismic exploration for locating geologic
formations, faults, contours and unconformities, the method
comprising: (a) reading a 3D seismic data set comprising seismic
signal traces that are distributed over a volume of the earth; (b)
selecting at least one time slice from said volume and forming
therein cells that are arranged into laterally extending rows and
columns, each of said cells having at least five seismic traces
therein; (c) computing for each of said cells at least one seismic
attribute wherein said at least one seismic attribute is at least a
function of:.Iaddend. ##EQU67##
.Iadd.and.Iaddend. ##EQU68##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell and where u.sub.f (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell; and (d) recording in a form for
display, over said at least one time slice, said at least one
seismic attribute..Iaddend..Iadd.
118. The method of claim 14 wherein said semblance/similarity is at
least a function of:.Iaddend. ##EQU69##
.Iadd.and.Iaddend. ##EQU70##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
119. The method of claim 118 wherein said semblance/similarity is a
function of:.Iaddend. ##EQU71## .Iadd.
120. The method of claim 119 wherein said semblance/similarity is
an arithmetic inverse of a function of:.Iaddend. ##EQU72##
.Iadd.
121. The method of claim 118 wherein said semblance/similarity is
determined by performing a running window time integration over the
partial sums from -K to +K:.Iaddend. ##EQU73##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
122. The method of claim 14 wherein said semblance/similarity is at
least a function of:.Iaddend. ##EQU74##
.Iadd.and.Iaddend. ##EQU75##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, where p and q are apparent dips in the x and y
directions, respectively, and where u.sub.j (t,p,q,x.sub.j,y.sub.j)
is a portion of a seismic trace within said
cell..Iaddend..Iadd.
123. The method of claim 122 wherein said semblance/similarity is a
function of: .Iaddend. ##EQU76## .Iadd.
124. The method of claim 122 wherein said semblance/similarity is
an arithmetic inverse of a function of:.Iaddend. ##EQU77##
.Iadd.
125. The method of claim 122 wherein said semblance/similarity is
determined by performing a running window time integration over the
partial sums from -K to +K:.Iaddend. ##EQU78##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
126. The method of claim 122 wherein p=0 and
q=0..Iaddend..Iadd.
127. The article of manufacture of claim 58 wherein said semblance
is at least a function of:.Iaddend. ##EQU79##
.Iadd.and.Iaddend. ##EQU80##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
128. The article of manufacture of claim 127 wherein said semblance
is a function of:.Iaddend. ##EQU81## .Iadd.
129. The article of manufacture of claim 127 wherein said semblance
is an arithmetic inverse of a function of:.Iaddend. ##EQU82##
.Iadd.
130. The article of manufacture of claim 127 wherein said semblance
is determined by performing a running window time integration over
the partial sums from -K to +K:.Iaddend. ##EQU83##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
131. In seismic exploration wherein 3D seismic data from geologic
formations of the earth are recorded as a function of time and
wherein a computer is used that is programmed to process such 3D
seismic data so that an image may be produced therefrom that is
representative of subterranean features, an article of manufacture
comprising: a medium that is readable by a computer and that
carries instructions for said computer to perform a process
comprising: (a) accessing 3D seismic data over a predetermined
volume of geologic formations of the earth, said 3D seismic data
comprising seismic traces that are characterized by time, position
and amplitude; (b) dividing at least a portion of said data into a
plurality of relatively small, three-dimensional analysis cells,
wherein each of said three-dimensional analysis cells contains
portions of at least five seismic traces; and (c) computing a
seismic attribute for each cell that is a function of.Iaddend.
##EQU84##
.Iadd.and.Iaddend. ##EQU85##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
132. The article of manufacture of claim 131 wherein said seismic
attribute is a function of:.Iaddend. ##EQU86## .Iadd.
133. The article of manufacture of claim 131 wherein said seismic
attribute is an arithmetic inverse of a function of:.Iaddend.
##EQU87## .Iadd.
134. The article of manufacture of claim 131 wherein said seismic
attribute is determined by performing a running window time
integration over the partial sums from -K to +K:.Iaddend.
##EQU88##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
135. The article of manufacture of claim 131 wherein the process
performed by the computer further comprises displaying said seismic
attribute in a form that is at least one of (i) a planar display,
(ii) a cross-sectional display, (iii) a 2D display and, (iv) a 3D
display..Iaddend..Iadd.
136. The article of manufacture of claim 131 wherein the computed
seismic attribute is a number that is at least 0 and at most
1..Iaddend..Iadd.
137. The article of manufacture of claim 131 wherein the process
further comprises displaying the computed seismic attributes in a
visual format to display the subterranean
features..Iaddend..Iadd.
138. A method for locating geologic features of an earth volume,
the method comprising: (a) accessing 3D seismic data over a
predetermined volume of the earth, said data comprising seismic
traces; (b) dividing at least a portion of said 3D seismic data
into a plurality of relatively small, three-dimensional analysis
cells, wherein each of said analysis cells contains portions of at
least five seismic traces relative to two directions; and (c)
computing a seismic attribute for each cell that is a function
of.Iaddend. ##EQU89##
.Iadd.and.Iaddend. ##EQU90##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
139. The method of claim 138 wherein said seismic attribute is a
function of:.Iaddend. ##EQU91## .Iadd.
140. The method of claim 138 wherein said seismic attribute is an
arithmetic inverse of a function of:.Iaddend. ##EQU92## .Iadd.
141. The method of claim 138 wherein said seismic attribute is
determined by performing a running window time integration over the
partial sums from -K to +K:.Iaddend. ##EQU93##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
142. The method of claim 138 further comprising displaying said
seismic attribute in a form that is at least one of (i) in planar
display, (ii) a cross-sectional display, (iii) a 2D display, and
(iv) a 3D display..Iaddend..Iadd.
143. The method of claim 138 wherein the computed seismic attribute
is a number that is at least 0 and at most 1..Iaddend..Iadd.
144. The method of claim 138 further comprising displaying the
computed seismic attributes in a visual format to display the
subterranean features..Iaddend..Iadd.
145. The method of claim 81 wherein said semblance/similarity is at
least a function of:.Iaddend. ##EQU94##
.Iadd.and.Iaddend. ##EQU95##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
146. The method of claim 145 wherein said semblance/similarity is a
function of:.Iaddend. ##EQU96## .Iadd.
147. The method of claim 145 wherein said semblance/similarity is
an arithmetic inverse of a function of:.Iaddend. ##EQU97##
.Iadd.
148. The method of claim 145 wherein said semblance/similarity is
determined by performing a running window time integration over the
partial sums from -K to +K:.Iaddend. ##EQU98##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
149. The method of claim 91 wherein the signal discontinuity value
is at least a function of.Iaddend. ##EQU99##
.Iadd.and.Iaddend. ##EQU100##
.Iadd.where each analysis cell contains portions of at least J
(J.gtoreq.5) seismic traces, where x and y are distances from the
center of the cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a
portion of a seismic trace within said cell..Iaddend..Iadd.
150. The method of claim 149 wherein said signal discontinuity
value is a function of:.Iaddend. ##EQU101## .Iadd.
151. The method of claim 149 wherein said signal discontinuity
value is an arithmetic inverse of a function of:.Iaddend.
##EQU102## .Iadd.
152. The method of claim 149 wherein said signal discontinuity
value is determined by performing a running window time integration
over the partial sums from -K to +K:.Iaddend. ##EQU103##
.Iadd.where K is the half width of the time window in
samples..Iaddend..Iadd.
153. The method of claim 99 wherein the semblance value is at least
a function of.Iaddend. ##EQU104##
.Iadd.and.Iaddend. ##EQU105##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
154. The method of claim 101 wherein the inverse of semblance value
is at least a function of.Iaddend. ##EQU106##
.Iadd.and.Iaddend. ##EQU107##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
155. The method of claim 104 wherein the semblance value is at
least a function of.Iaddend. ##EQU108##
.Iadd.and.Iaddend. ##EQU109##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
156. The method of claim 106 wherein the semblance value is at
least a function of.Iaddend. ##EQU110##
.Iadd.and.Iaddend. ##EQU111##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
157. The method of claim 109 wherein the
discontinuity/dissimilarity is at least a function of.Iaddend.
##EQU112##
.Iadd.and.Iaddend. ##EQU113##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell..Iaddend..Iadd.
158. A method of seismic exploration for locating geologic
formations, faults, contours and unconformities, the method
comprising: (a) reading a 3D seismic data set comprising seismic
signal traces that are distributed over a volume of the earth; (b)
selecting at least one time slice from said volume and forming
therein cells that are arranged into laterally extending rows and
columns, each of said cells having at least five seismic traces
therein; (c) computing for each of said cells at least one seismic
attribute wherein said at least one seismic attribute is at least a
function of:.Iaddend. ##EQU114##
.Iadd.and.Iaddend. ##EQU115##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
seismic traces, where x and y are distances from the center of the
cell, and where u.sub.j (t,x.sub.j,y.sub.j) is a portion of a
seismic trace within said cell; and (d) recording in a form for
display, over said at least one time slice, said at least one
seismic attribute..Iaddend..Iadd.
159. The method of claim 74 further comprising storing said seismic
attributes for each cell as a data set..Iaddend..Iadd.
160. The method of claim 81 further comprising storing said
semblance/similarity of said cells as a data
cube..Iaddend..Iadd.
161. The method of claim 89 further comprising storing said inverse
of said semblance/similarity of said cells as a data
cube..Iaddend..Iadd.
162. The method of claim 138 further comprising storing said
seismic attributes for each cell as a data cube..Iaddend..Iadd.
163. A method of generating a data cube for displaying geologic
features, faults and contours of a cubic volume of an earth
formation wherein 3D seismic data samples covering said volume of
the earth formation are accessed, said volume of the earth
formation divided into an array of relatively small 3D cells
containing at least a portion of the 3D seismic data samples
relative to two spatial directions, the cube of
semblance/similarity values representing said volume of said earth
formation enclosing a plurality of the 3D seismic data samples, the
cube of semblance/similarity values formed by: (a) forming an
analytic trace from each seismic trace; and (b) assigning a
semblance/similarity value to each analytic trace data sample in
said cube..Iaddend..Iadd.
164. The method of claim 163 wherein said analytic trace, v.sub.j
(t), is a function of u.sub.j (t) +iu.sub.j.sup.H
(t)..Iaddend..Iadd.
165. A method for creating an analytic coherence cube of
semblance/similarity values, the method comprising: (a) accessing
3D seismic data covering a pre-determined volume of the earth; (b)
forming an analytic trace from each seismic trace; (c) dividing
said volume into an array of relatively small three-dimensional
cells wherein each of said cells is characterized by at least five
laterally separated and generally vertical analytic traces located
therein; (d) determining in each of said cells the
semblance/similarity of said analytic traces relative to two
pre-determined directions; and (e) recording an analytic coherence
cube from said semblance/similarity of said
cells..Iaddend..Iadd.
166. The method of claim 165 wherein said analytic traces, v.sub.j
(t,x.sub.j,y.sub.j), are a function of u.sub.j (t,x.sub.j,y.sub.j)
+iu.sub.j.sup.H (t,x.sub.j,y.sub.j)..Iaddend..Iadd.
167. The method of claim 165 wherein each semblance/similarity
value is at least a function of.Iaddend. ##EQU116##
.Iadd.and.Iaddend. ##EQU117##
.Iadd.where each cell contains portions of at least J (J.gtoreq.5)
analytic traces, where x and y are distances from the center of the
cell, and where v.sub.j (t,x.sub.j,y.sub.j) is a portion of an
analytic trace within said cell..Iaddend..Iadd.
168. The method of claim 167 wherein said semblance/similarity is a
function of:.Iaddend. ##EQU118## .Iadd.
169. The method of claim 165, wherein said pre-determined
directions are mutually perpendicular, and said
semblance/similarity of said analytic traces within each cell is a
function of at least time and the number of analytic traces within
said analysis cell..Iaddend..Iadd.
170. The method of claim 165 wherein said semblance/similarity is
at least a function of the energy of said analytic traces; and
wherein said energy of said analytic traces is a function of time,
and the number of said analytic traces within said
cell..Iaddend..Iadd.
171. The method of claim 165 wherein said semblance/similarity is
at least a function of the apparent dip and apparent dip azimuth of
said analytic traces within said analysis cell..Iaddend..Iadd.
172. The method of claim 165, wherein said semblance/similarity of
said cells are characterized by hue, saturation and lightness;
wherein one of said estimates of true dip azimuth, said estimates
of true dip, and said largest calculated measures of semblance is
mapped onto one of a lightness scale, hue scale, and a saturation
scale; wherein another of said estimates of true dip azimuth, said
estimates of true dip, and said largest calculated measures of
semblance is mapped onto another of said lightness scale, said hue
scale, and said saturation scale; and wherein the remaining one of
said estimates of true dip azimuth, said estimates of true dip, and
said largest calculated measures of semblance is mapped onto the
remaining one of said lightness scale, said hue scale, and said
saturation scale..Iaddend..Iadd.
173. The method claim 172, wherein said estimates of true dip
azimuth are mapped onto said hue scale, said estimates of true dip
are mapped onto said saturation scale, and said largest calculated
measures of semblance are mapped onto a lightness
scale..Iaddend..Iadd.
174. A method for locating geologic features of an earth volume,
the method comprising: (a) accessing 3D seismic data over a
predetermined volume of the earth, said data comprising seismic
traces that are characterized by time, position and amplitude
values; (b) dividing at least a portion of said 3D seismic data
into a plurality of relatively small, three-dimensional analysis
cells, wherein each of said analysis cells contains portions of at
least five seismic traces relative to two directions; (c) computing
a seismic attribute for each cell that is a function of i) the
square of the sum of the seismic trace amplitude values for the at
least five traces, and ii) the sum of the squares of said seismic
trace amplitude values for the at least five traces; and (d)
recording said seismic attribute..Iaddend..Iadd.
175. A method of locating subterranean features, faults, and
contours, comprising the steps of: (a) accessing 3D seismic data
covering a pre-determined volume of the earth; (b) dividing said
volume into an array of relatively small three-dimensional cells
wherein each of said cells is characterized by at least five
laterally separated and generally vertical seismic traces located
therein; (c) determining in each of said cells a
semblance/similarity of said traces relative to two pre-determined
directions; and (d) recording said semblance/similarity of said
cells..Iaddend.
Description
TECHNICAL FIELD
This invention relates to the general subject of seismic
exploration and, in particular, to methods and devices for
identifying structural and stratigraphic features in three
dimensions.
BACKGROUND OF THE INVENTION
In seismic exploration, seismic data is acquired along lines (see
lines 10 and 11 of FIG. 1) that consist of geophone arrays onshore
or hydrophone streamer traverses offshore. Geophones and
hydrophones act as sensors to receive energy that is transmitted
into the ground and reflected back to the surface from subsurface
rock interfaces. Energy is often provided onshore by Vibroseis.RTM.
vehicles which transmit pulses by shaking the ground at
pre-determined intervals and frequencies on the surface. Offshore,
airgun sources are usually often used. Subtle changes in the energy
returned to surface often reflect variations in the stratigraphic,
structural and fluid contents of the reservoirs.
In performing three-dimensional (3D) seismic exploration, the
principle is similar; however, lines and arrays are more closely
spaced to provide more detailed subsurface coverage. With this high
density coverage, extremely large volumes of digital data need to
be recorded, stored and processed before final interpretation can
be made. Processing requires extensive computer resources and
complex software to enhance the signal received from the subsurface
and to mute accompanying noise which masks the signal.
After the data is processed, geophysical personnel assemble and
interpret the 3D seismic information in the form of a 3D data cube
(See FIG. 2) which effectively represents a display of subsurface
features. Using this data cube, information can be displayed in
various forms. Horizontal time slice maps can be made at selected
depths (See FIG. 3). Using a computer workstation, an interpreter
can also slice through the field to investigate reservoir issues at
different seismic horizons. Vertical slices or cross-sections can
also be made in any direction using seismic or well data. Seismic
picks of reflectors can be contoured, thereby generating a time
horizon map. Time horizon maps can be converted to depth to provide
a true scale structural interpretation at a specific level.
Seismic data has been traditionally acquired and processed for the
purpose of imaging seismic reflections for structural and
stratigraphic interpretation. However, changes in stratigraphy are
often difficult to detect on traditional seismic displays due to
the limited amount of information that stratigraphic features
present in a cross-section view. While working with both time
slices and cross-sections provides an opportunity to see a much
larger portion of faults, it is difficult to identify fault
surfaces within a 3D volume where no fault reflections have been
recorded.
Coherence is one measure of seismic trace similarity or
dissimilarity. The more two seismic traces increase in coherence,
the more they are alike. Assigning a coherence measure on a scale
from zero to one, "0" indicates the greatest lack of similarity,
while a value of "1" indicates total or complete similarity (i.e.,
two identical, perhaps time-shifted, traces). Coherence for more
than two traces may be defined in a similar way.
One method for computing coherence was disclosed in U.S. Pat. No.
5,563,949 to Bahorich and Farmer (assigned to Amoco Corporation)
having a Ser. No. 353,934 and a filing date of Dec. 12, 1994.
Unlike the shaded relief methods that allow 3D visualization of
faults, channels, slumps, and other sedimentary features from
picked horizons, the coherency process devised by Bahorich and
Farmer operates on the seismic data itself. When there is a
sufficient change in acoustic impedance, the 3D seismic coherency
cube developed by Bahorich and Farmer can be extremely effective in
delineating seismic faults. It is also quite effective in
highlighting subtle changes in stratigraphy (e.g., 3D images of
meandering distributary channels, point bars, canyons, slumps and
tidal drainage patterns).
Although the process invented by Bahorich and Farmer has been very
successful, it has some limitations. An inherent assumption of the
Bahorich invention is the assumption of zero mean seismic signals.
This is approximately true when the correlation window exceeds the
length of a seismic wavelet. For seismic data containing a 10 Hz
component of energy, this requires a rather long 100 ms window
which can mix stratigraphy associated with both deeper and
shallower time horizons. Shortening the window (e.g., to 32 ms
results in higher vertical resolution, but often at the expense of
increased artifacts due to the seismic wavelet. Unfortunately, a
more rigorous, non-zero mean running window cross correlation
process is an order of magnitude more computationally expensive.
Moreover, if seismic data is contaminated by coherent noise,
estimates of apparent dip using only two traces will be relatively
noisy.
Thus, there is a need for methods and apparatus that would overcome
the shortcomings of the prior art. In particular, improved
resolution and computational speed are desirable. In addition, it
would be highly desirable to improve estimates of dip in the
presence of coherent noise.
SUMMARY OF THE INVENTION
In accordance with the present invention, a method and an article
of manufacture is disclosed for locating subterranean features,
faults, and contours. In one embodiment of the invention, the
method comprises the steps of: accessing 3D seismic data covering a
pre-determined volume of the earth; dividing the volume into an
array of relatively small three-dimensional cells, wherein each of
said cells is characterized by at least five laterally separated
and generally vertical seismic traces located therein; determining
in each cell the semblance/similarity of the traces relative to two
predetermined directions; and displaying the semblance/similarity
of each cell in the form a two-dimensional map. In one embodiment,
semblance/similarity is a function of time, the number of seismic
traces within the cell, and the apparent dip and apparent dip
azimuth of the traces within the cell; the semblance/similarity of
a cell is determined by making a plurality of measurements of the
semblance/similarity of the traces within the cell and selecting
the largest of the measurements. In addition, the apparent dip and
apparent dip azimuth, corresponding to the largest measurement of
semblance/similarity in the cell, are deemed to be estimates of the
true dip and true dip azimuth of the traces therein. Finally, a
color map, characterized by hue, saturation and lightness, is used
to depict semblance/similarity, true dip azimuth and true dip of
each cell; in particular, true dip azimuth is mapped onto the hue
scale, true dip is mapped onto the saturation scale, and the
largest measurement of semblance/similarity is mapped onto the
lightness scale of the color map.
In another embodiment of the invention, an article of manufacture
is disclosed that comprises a medium that is readable by a computer
and that carries instructions for the computer to perform a seismic
exploration process. In one embodiment, the computer accesses 3D
seismic data covering a pre-determined volume of the earth and the
medium instructs the computer to: divide the volume into an array
of relatively small three-dimensional cells, wherein each cell is
characterized by at least five laterally separated and generally
vertical seismic traces located therein; determine in each cell the
semblance/similarity of the traces relative to two pre-determined
directions; and store the semblance/similarity of each cell for
display in the form a two-dimensional map. In one embodiment, the
instructions on the medium define semblance/similarity as a
function of time, the number of seismic traces within the cell, and
the apparent dip and apparent dip azimuth of the traces within the
cell; the semblance/similarity of a cell is determined by making a
plurality of measurements of the semblance/similarity of the traces
within the cell and by selecting the largest of the measurements.
In addition, the apparent dip and apparent dip azimuth,
corresponding to the largest measurement of semblance/similarity in
the cell, are deemed to be estimates of the true dip and true dip
azimuth of the traces therein. The computer comprises means for
producing a color display that is characterized by hue, saturation
and lightness; and the medium has instructions to map true dip
azimuth onto a hue scale, true dip onto a saturation scale, and the
largest measurement of semblance/similarity onto a lightness
scale.
The process of the invention is particularly well suited for
interpreting fault planes within a 3D seismic volume and for
detecting subtle stratigraphic features in 3D. This is because
seismic traces cut by a fault line generally have a different
seismic character than traces on either side of the fault.
Measuring multi-channel coherence or trace similarity along a time
slice reveals lineaments of low coherence along these fault lines.
Such measures can reveal critical subsurface details that are not
readily apparent on traditional seismic sections. Also by
calculating trace similarity along a series of time slices, these
fault lineaments identify fault planes or surfaces.
The process of the invention presents a multitrace semblance method
that is generally more robust in noisy environments than a three
trace cross correlation method for estimating seismic coherency. In
addition, the semblance process presented in this patent
application provides: higher vertical resolution for good quality
data than that of a three trace cross correlation measurement of
seismic coherency; the ability to map the 3D solid angle
(dip/azimuth) of coherent events; the ability to generalize the
concept of complex "trace" attributes to one of complex "reflector"
attributes; and by combining these enhanced complex trace
attributes with coherency and solid angle, the basis of
quantitative 3D seismic stratigraphy data attributes that are
amenable to geostatistical analysis methods.
Moreover, seismic coherency versus dip maps of picked horizons
allow analysis of: the structural and stratigraphic framework
before detailed picking starts; structural and stratigraphic
features of the entire data volume, including zones that are
shallower, deeper, and adjacent to the primary zone of interest;
subtle features that are not respresentable by picks on peaks and
troughs; and features internal to the top and bottom of formation
or sequence boundary picks.
Coupled with coherency, data cubes of the solid angle dip of
coherent seismic reflection events allow one to quickly see
structural as well as stratigraphic relationships (such as onlap
and offlap) between the seismic data and interpreted sequence
boundaries.
Numerous other advantages and features of the present invention
will become readily apparent from the following detailed
description of the invention, the embodiments described therein,
from the claims, and from the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
.Iadd.The patent or application file contains at least one drawing
executed in color. Copies of this patent or patent application
publication with color drawings (s) will be provided by the Office
upon request and payment of the necessary fee..Iaddend.
FIG. 1 is a schematic diagram showing an arrangement of geophones
to obtain 3D seismic data from the earth's subsurface for
processing in accordance with the present invention;
FIG. 2 is a pictorial representation of the information obtained
from the data acquired using the arrangement of FIG. 1;
FIG. 3 is a pictorial representation of a horizontal time slice
(t=1200 ms) of 3D seismic data processed in accordance with the
prior art;
FIGS. 4A through 4H illustrate various analysis windows
(computational stars) that may be used in running window analysis
of seismic coherence, dip and dip azimuth;
FIG. 5 is a pictorial representation of the process of the
invention using an elliptical window centered about an analysis
point;
FIGS. 6A and 6B are examples of a rectangular dip/azimuth
tessellation useful when analyzing a survey having strikes and dips
parallel to the acquisition axes, and when illuminating faults
cutting perpendicular to a dominant reflector strike and dip
(p.sub.O, q.sub.O);
FIGS. 7A through 7C are pictorial representations of three
tesselations of solid angle dip/azimuth space;
FIGS. 8A through 8D depict the mapping of 3D seismic attributes
(.phi.,c,d) to 3D color space (H,L,S);
FIG. 9 shows four surfaces through the color hemisphere of FIG. 8A
for four values of coherence;
FIGS. 10A through 10C depict ordinary vertical slices of the
seismic data of FIG. 3;
FIGS. 11A through 11C depict the seismic attributes, dip, dip
azimuth and coherency obtained by applying the process of the
invention, to data corresponding to that of FIGS. 10A through
10C;
FIGS. 12A and 12B are time slices (t=1200 ms and t=1600 ms) through
the dip azimuth cube giving rise to FIGS. 11A and 11B;
FIGS. 13A and 13B are gray scale displays of coherency;
FIGS. 14A through 14C depict coherency slices corresponding to the
data of FIGS. 10A through 10C;
FIGS. 15A and 15B depict the results of applying a semblance
algorithm and applying dip/azimuth algorithm in accordance with the
present invention; and
FIGS. 16A and 16B are schematic diagrams depicting the processing
flow of the steps performed in one embodiment of the invention.
DETAILED DESCRIPTION
While this invention is susceptible of embodiment in many different
forms, there is shown in the drawings, and will herein be described
in detail, specific embodiments of the invention. It should be
understood, however, that the present disclosure is to be
considered an exemplification of the principles of the invention
and is not intended to limit the invention to any specific
embodiment or algorithm described herein.
Before describing the invention in detail, an overview will be
given so that the detailed description, which follows, may be
better understood. One embodiment of the process of the invention
is illustrated in FIG. 16A. Briefly, the method comprises the steps
of: accessing 3D seismic data 10 covering a pre-determined volume
of the earth; dividing 12 the volume into an array of relatively
small three-dimensional cells, wherein each of said cells is
characterized by at least five laterally separated and generally
vertical seismic traces located therein; determining 14 in each
cell the semblance/similarity of the traces relative to two
pre-determined directions; selecting 16 the largest of the
measurements; and displaying 24 the semblance/similarity of each
cell in the form a two-dimensional map. The semblance/similarity
measurements may be recorded 18 for future use, or sent 20 to an
interactive workstation for further analysis; or printed or
displayed as a color map 22, characterized by hue, saturation and
lightness, may be used to depict semblance/similarity, true dip
azimuth and true dip of each cell.
The first step of the process (See FIG. 16A) is to obtain a set of
seismic data in the form of seismic signal traces distributed over
a three dimensional volume of the earth. Methods by which such data
is obtained and reduced to digital form for processing as 3D
seismic data are known to those skilled in the art.
The Semblance Process
The next step is to generate a "coherence cube." This is done by
applying a multi-trace semblance algorithm to the 3D seismic data.
This algorithm may take many forms. Whatever its form, its function
is to compare the similarity of nearby regions of seismic data
within the 3D seismic volume. This value (or attribute) serves as a
rather robust estimate of signal discontinuity within geologic
formations, as well as signal discontinuities across faults and
erosional unconformities.
We define an analysis grid (or computational star) to be either an
elliptical or rectangular pattern of "J" traces centered about a
given output trace (See FIGS. 4A through 4H).
In the drawings "X" denotes the center of the analysis window while
"O" denotes additional traces used in the semblance calculation.
Minimum size circular and rectangular windows used to analyze data
with equal trace spacings (.DELTA.x=.DELTA.y) are shown in FIGS. 4A
and 4D. Minimum circular and rectangular windows used to analyze
data with trace spacing in the cross-line/strike (y) direction
twice that in the in-line/dip (x) direction (.DELTA.y=2.DELTA.x)
are shown in FIGS. 4B and 4E. Such nonequal spacings are commonly
used to exploit the slower change of geology in the strike
direction. Larger analysis windows used for greater resolution of
reflector dip and azimuth, or to increase signal to noise ratio in
poor data areas, are shown in FIGS. 4C and 4F.
Elliptical and rectangular analysis windows centered about an
analysis point defined by a major axis, a minor axis, and the
azimuth of major axis are shown in FIGS. 4G and 4H. The acquisition
(x,y) axes are rotated by .phi..sub.O degrees from the North-East
(x', y') axes. Such assymmetric windows are useful in fracture
detection.
If we center the (x, y) axis about the center of an analysis window
containing J seismic traces, u.sub.j (t, x.sub.j, y.sub.y), we
define the semblance .sigma.(.tau.,p,q) to be: ##EQU1##
where the triple (.tau.,p,q) defines a local planar event at time
.tau., and p and q are the apparent dips in the x and y directions
measured in ms/m. Since, p=d sin .phi. and q=d cos .phi., where d
is the true dip and .phi. is the dip azimuth, it follows that:
Those skilled in the art will recognize that, in the denominator of
equation (1), J serves as a normalization factor. The numerator
represents the average energy and the summation term in the
denominator represents the total energy of the traces. In effect,
equation (1) is representative of a ratio of coherent and
incoherent energy.
The objective is to perform a simultaneous 2D search (See FIG. 5)
over apparent dips (p,q) in the in-line and cross-line directions.
However, the semblance estimate given by equation (1) will be
unstable for small but coherent values of seismic events, such as
might occur if we were to sum along the zero crossings of a plane
coherent wavelet. To avoid this, we estimate the coherence c
(.tau.,p,q) at time .tau. and apparent dips (p,q) to be the average
semblance over a time window (or vertical analysis window of height
2 w ms of half length K=w(.DELTA.t samples): ##EQU2##
In general, we do not know but wish to estimate that value of (p,q)
associated with the local dip and azimuth of a hypothetical 3D
reflection event.
In one embodiment of the process of the invention, we estimate
(p,q) through a brute force search over all possible apparent dips
(See FIGS. 6A and 6B). We assume that the interpreter is able to
estimate the maximum true dip, d.sub.max (measured in ms/m) from
conventional seismic displays of the data (e.g., vertical data
slices), thereby limiting the dips to be:
If x.sub.max and y.sub.max are the half width and half length of a
rectangular analysis window, and if f.sub.max is the highest
temporal frequency component contained in the seismic data, then
the Nyquist criterion of sampling the data at two points per period
restricts the apparent dip increments, .DELTA.p to .DELTA.q,
to:
It should be noted that the Nyquist criterion is valid for linear
operations on the seismic data; and that equation (2) is nonlinear.
In practice, we have found it necessary to limit .DELTA.p and
.DELTA.q to half that required by the Nyquist sampling criterion to
obtain an accurate semblance for a coherent dipping event.
Thus, our search for an estimate of the apparent dip (p, q) of a
seismic reflector is reduced to the calculation of semblance
c(p.sub.l, q.sub.m) over n.sub.p * n.sub.q discrete apparent dip
pairs (p.sub.l, q.sub.m) where:
The apparent dip pair (p.sub.l, q.sub.m) is deemed to be an
estimate of the reflector apparent dips when:
for all -n.sub.p <1.ltoreq.+n.sub.p,
-n.sub.1.ltoreq.m.ltoreq.+n.sub.1.
The estimated apparent dips (p, q) are related to the estimated
true dip d and dip azimuth .phi. by the simple geometric
relationships: ##EQU3##
where d is measured in ms/m and the angle .phi. is measured
clockwise from the positive x' (or North) axis. A simple coordinate
rotation by angle .phi..sub.O is necessary when the in-line
acquisition direction x is not aligned with the N-S (x') axis (See
FIG. 4G).
Solid Angle Discretization and Display
Optimal angular discretization is important for two reasons:
minimization of computational cost, and limitation on the number of
colors that can be displayed using commercial interpretation
workstation software (e.g., currently 64 with Landmark's
"Seisworks" and 32 with Geoquest's "IESX" systems).
FIG. 7A shows the discretization of apparent dip using equal
increments .DELTA.p and .DELTA.q in a rectangular grid of 69
angles. FIG. 7B shows the discretization using equal increments
.DELTA.d and .DELTA..phi. in a radial grid of 97 angles. Clearly,
we do not wish to sample the dip d=0 ms/m for ten different
azimuths. The "Chinese Checker" tessellation of FIG. 7C more
closely represents an equal and therefore more economic sampling of
the (d, .phi.) surface with a minimum number of points (i.e., 61
angles). Each tesselation of FIGS. 7A and 7C represents an
approximately equal patch of solid angle .DELTA..OMEGA.. For the
angular discretization shown in FIG. 7C and for a circular analysis
radius, a, the incremental dip .DELTA.d is chosen to be:
##EQU4##
Display
While it is possible to independently map semblance, dip, and
azimuth, it is clear that the latter two attributes are coupled to
each other. Furthermore, the confidence we have in these estimates
is proportional to the coherency/semblance. Others (See U.S. Pat.
No. 4,970,699 to Bucher et al. and assigned to Amoco Corporation.
"Method for Color Mapping Geophysical Data") have shown that the
color HLS (hue, lightness, saturation) model can be quite effective
in displaying multicomponent seismic attributes (Also see Foley, J.
D. and Van Dam, A., 1891, Fundamentals of Interactive Graphics,
Addison-Wesley, Reading, Mass.).
Refering to FIGS. 8A through 8D, in this scheme, we directly map
azimuth, .phi., onto the hue axis H:
where both H (commonly known as the "color wheel") and .phi. vary
between -180 and +180 degrees (See FIG. 8B). Blue corresponds to
North, salmon to East, yellow to South, and forest green to West
azimuth. Azimuths corresponding to zero dip are arbitrarily
assigned a value of 0 degrees (North) and are thus plotted as
blue.
Next, we map (See FIG. 8C) average semblance/coherence c, onto the
lightness axis L:
where
.alpha. is a scale constant less than 100, since changes in hue and
saturation near L=0 (black) and L=100 (white) are difficult to
distinguish. White, or L=100, corresponds to high semblance or c=1,
while black, or L=100, corresponds to low semblance, c=0.
Intermediate semblances correspond to intermediate shades of gray,
(such as silver, gray and charcoal gray). Lightness (sometimes
referred to as "brightness") expresses the amount of illumination.
It represents a gray scale ranging from black to white.
Finally, we map dip d onto the saturation axis S:
The saturation (S=0) and hue chosen are arbitrary; we could just as
easily have displayed this attribute for a value of (H=0, S=100)
giving us semblance displayed as white, pastel blue, pure blue,
midnight blue and black. Saturation expresses the lack of dilution
of a color by white light. A fully saturated color has no white
added; adding white "washes out" the color without changing its
hue. (See FIG. 8D).
FIG. 9 illustrates four constant surfaces through the 3D (H,L,S)
color hemisphere of (.phi.c, d) shown in FIG. 8A, corresponding to
c=100, c=0.75, c=0.50 and c=0.00.
Appendix 1 describes the color scheme in greater detail. Some
advantages of the HLS color model are: azimuth is cyclic and maps
neatly to the cyclic color wheel (hue); the azimuths corresponding
to d=0 are meaningless; all azimuths converge smoothly to gray for
shallow dips; and lower confidence in estimating dip and azimuth in
zones of weak, low semblance (such as across faults) is indicated
by darker colors.
Implementation of Mathematical Process
Landmark and GeoQuest interpretive workstations (See FIG. 16B), for
example, can be used to view and interpret faults and stratigraphic
features by loading the processed data as a seismic volume.
Visualization software (e.g., Landmark's SeisCube software) may be
employed to rapidly slice through the seismic volume to aid in
understanding complex fault relationships.
Computer Program
A FORTRAN 77 program was written to perform the calculations and
provide the information for the displays previously described.
Additional details are given in Appendix 2. Each trace U.sub.MN is
accessed by its in-line and cross-line indices, M and N. The user
specifies a rectangular or an elliptical spatial analysis window or
cell about each point/trace in the input data set (See FIG. 4G).
The major and minor axis of this analysis window, a and b are given
by a=aplength and b=apwidth. The orientation or azimuth of the
major axis .phi..sub.a is given by .phi..sub.a =apazim. A
rectangular analysis window (FIG. 4H) is indicated by specifying -R
on the command line. The 2J indices relative to the center of this
analysis window (and corresponding to the traces that fall within
this window) are tabulated as a simple list, with m(j) and n(j)
indicating the trace index (relative to the analysis trace
U.sub.MN) in the x and y directions, respectively. The program
performs a simultaneous 2D search over apparent dips (p,q) in the
in-line and cross-line directions, where (p.sup.2 +q.sup.2).sup.1/2
<+smax. The increments dp and dq are chosen such that the data
are sampled at four points per period<1/(fref) at the edge of
the analysis window. For interpretation, it may be convenient to
express each apparent dip pair (p,q) in spherical coordinates as a
true (time or depth) dip d and dip azimuth .phi..
The data in the analysis window are interpolated to the fractional
time, .tau.-px-qy, for each trial dip and azimuth (See FIG. 5), in
essence, "flattening" of data. The semblance for this trial dip at
the analysis point is defined to be the semblance of these
flattened traces in the analysis window.
For time domain data, we flatten the jth trace about the analysis
point (M,N) by:
where x and y are distances measured from the center of the
analysis window. This may be expressed
where .DELTA.x and .DELTA.y are the in-line and cross-line trace
spacings.
For depth domain data we flatten the jth trace using:
The semblance is ;then calculated for all subsequent dips and
azimuths using: ##EQU5##
As in velocity analysis, the semblance for each dip, azimuth and
analysis point are smoothed by forming a running window time
integration over the partial sums from -K to +K where
K=apheight/dt. We therefore define the coherence, c(.tau.,p,q) to
be: ##EQU6##
That dip and azimuth pair .OMEGA.=(d, .phi.) which has the maximum
(running window integrated) coherency c is taken to be an estimate
of the coherency, c, dip and azimuth (d, .phi.) for the analysis
point.
EXAMPLES
FIGS. 11A through 11C are displays of the 3D seismic attributes
(.phi., c, d) corresponding to FIGS. 10A through 10C using the
semblance based coherency algorithm expressed by equation (6), and
the color display technique depicted in FIGS. 8 and 9. The input
data were temporarily sampled at 4 ms, have an in-line trace
spacing of .DELTA.x=12.5 m, and have a cross-line trace spacing of
.DELTA.y=25 m, with the in-line acquisition oriented along a N-S
axis. For FIGS. 11A through 11C, a circular analysis window or cell
of a=b=60 m was used (See FIG. 4A), so as to include a total of 11
traces in the calculation. The maximum search dip (See FIG. 7C) was
d.sub.max =0.25 ms/m, giving rise to 61 search angles. The temporal
integration time used was w=16 ms, or K=4, thereby averaging the
semblance calculation over 9 samples.
In FIGS. 10A and 10B lines AA' and BB' were chosen as S to N and W
to E vertical slices through the center of a salt dome. Line CC" is
an offset S to N line and illustrates the appearance of radial
faults on a vertical slice. In FIGS. 11A through 11C, the interior
of the salt dome is represented by dark colors, corresponding to an
area of generally low coherency. Low areas of coherency correspond
to the radial faults seen on line CC". Coherent, flat dips are
represented as light gray and dominate the section away from the
salt dome, in particular line CC". The blue color on the north side
of the salt dome (seen on N-S line AA') corresponds to sediments
dipping steeply (D=D.sub.max) to the North. These dips become
progressively shallower away from the salt dome, and are thus
displayed first as blue (saturation, S=100.0), cadet blue (S=0.75)
and steel blue (S=0.50), before they flatten and are displayed as
gray (S=0.0). The yellow color on the south side of the salt dome
(seen on line AA') corresponds to sediments dipping steeply to the
South. The salmon color on the East flank of the salt dome (shown
on the E-W line BB') corresponds to sediments dipping steeply to
the East. These dips also become progressively shallow away from
the salt dome, and are displayed first as salmon (S=100.00),
through sienna (S=50.0), and finally to gray, corresponding to flat
dip. Finally, the forest green color on the West flank of the salt
dome (shown on line AA') corresponds to sediments dipping steeply
to the West. These dips also flatten away from the salt dome and
are displayed using the colors shown on the West part of the legend
shown in FIG. 9. N-S line CC' is not aligned radially with the salt
dome. Thus, out-of-the-plane rotation of different fault blocks are
depicted, with the green block corresponding to dips to the SW and
the cyan block with dips to the NW.
Since these 3D attributes were calculated for every point on the
input seismic volume, they can be displayed as horizontal attribute
time slices (See FIGS. 12A and 12B); these correspond to a time
slice of the unprocessed seismic data. The interior of the salt
dome, as well as the radial faults are displayed as dark colors,
corresponding to incoherent zones of the data. Because of the
nearly radial symmetry of the salt diapir at t=1,200 ms (See FIG.
12A), the dipping sediments that flank the diapir also radiate
outward in an azimuthally simple fashion such that their azimuths
correspond quite closely to the color legend on the left side of
FIG. 9. This pattern is somewhat less symmetric at t=1,600 ms (See
FIG. 12B), where there are shallower dips to the South than to the
North. In addition, internal blocks of coherent data can be seen
within the salt dome.
The color legend displayed in FIG. 9 allows for only four "buckets"
of coherency. In order to examine the coherency in greater detail,
it can be plotted as a single attribute. This is shown in FIGS. 13A
and 13B where all 184 colors are applied to the simple gray scale
shown of FIG. 8C. In this display, maximum coherency (c=1.0) is
rendered as white; minimum coherency (c=0.0) is rendered as black.
While the interior of the salt diapir is shown as a highly
incoherent zone, this display better shows subtle details in the
radial faults patterns. In particular, faults emanating from the
salt dome are shown, with some bifurcating as we move away. In
addition to more continuous binning of the coherency attribute,
part of this difference in perception is due to the fact that the
human retina sees colors and black and white using different (cone
vs. rod) receptors. There is also a physiological difference in the
ability to differentiate between greens and blues between male and
female populations. For this reason, male interpreters often prefer
the simple single attribute coherency display shown in FIGS. 13A,
13B and FIG. 15A over the multiattribute (.phi.,c,d) display shown
in FIGS. 11A through 12B and FIG. 15B. In actuality, these displays
are quite complimentary: the 3D component display being useful in
recognizing the appearance of conflicting dips azimuths between
adjacent rotated fault blocks; and the single component display
being used to enhance the edge, or incoherent fault discontinuity,
separating them.
Process Considerations
Careful study of FIGS. 13A and 13B reveals a ring-like pattern of
incoherent energy circumscribing the salt dome. To investigate the
cause of these artifacts, vertical slices were taken through the
single component coherency cube corresponding to the seismic data
in FIGS. 10A through 10C. This is shown in FIGS. 14A through 14C.
The interior of the salt dome is clearly incoherent. An incoherent
submarine canyon feature (described by Nissen et al., "3D Seismic
Coherency Techniques Applied to the Identification and Delineation
of Slump Features", 1995 SEG Expanded Abstracts, pages 1532-1534)
is shown to the north of the salt dome. If the seismic data shown
in FIGS. 10A through 10C were overlayed on the coherency section
shown in FIGS. 14A through 14C, one would see a close
correspondence between areas of low coherency of FIGS. 14A through
14C with zero crossings of the seismic reflection events in FIGS.
10A through 10C. This is easily understood if it is assumed that
there is a fixed, but incoherent, level of seismic noise throughout
the data. For analysis points where the apparent dips are aligned
with the peaks or troughs of strong amplitude seismic reflectors
(such that the estimate of signal energy is high with respect to
the incoherent noise), one can expect the signal-to-noise ratio to
be high, giving rise to an estimate of high coherency. However, if,
our analysis point is such that there are apparent dips aligned
with the zero crossings of these same seismic reflectors, such that
the signal is low with respect to our incoherent noise, one can
expect the signal-to-noise ratio to be low, giving rise to a low
estimate of coherency.
We have found three methods for increasing the signal-to-noise
ratio: the first more appropriate for structural analysis; the
second more appropriate for stratigraphic analysis, and the third
appropriate for both.
For the case of steeply dipping (less than 45 degrees from the
vertical) faults, the signal-to-noise ratio can be increased by
simply increasing the size of our vertical analysis window w given
in equation (2). Two effects will be observed. First, the
structural leakage corresponding to the zero crossing points of the
reflectors diminishes as vertical integration window size
increases. Second, since few of the faults are truly vertical, the
lateral resolution of the faults appears to decrease as the
vertical window size increases. An analysis window of w=16 ms
(which would encompass a full cycle of the peak 30 Hz energy in the
data) appears to be in good compromise.
The second method (equally appropriate for stratigraphic and
structural analysis) of increasing the signal-to-noise ratio, is to
extract coherency along an interpreted stratigraphic horizon. If
this stratigraphic horizon is associated with an extremum of the
seismic data, such as a peak or trough, those data having only a
relatively high signal-to-noise ratio are selectively displayed.
Clearly, extracting coherency data corresponding to a zero crossing
would greatly exacerbate the coherency display. A more economic
version of this approach is to first flatten the data along the
horizon of interest and then calculate the seismic attributes only
along the picked horizon. This approach is somewhat more sensitive
to busts in automatic (and human!) pickers, since cycle skip
glitches in the picking are somewhat random and therefore will
almost always appear as incoherent.
Shallow features (e.g., shallow channels; shallow tidal channel
features corresponding to reworked deltaic sands; and small en
echelon faulting) do not exist for any distance above or below an
interpreted stratigraphic horizon; therefore, the inclusion of any
data from above or below the horizon in which they are located adds
uncorrelated amplitude variations, thereby making these
discontinuities look more coherent, and hence washed out. If the
time samples above or below the interpreted horizon contain
independent, perhaps strong amplitude discontinuities, these
discontinuities will bleed into the analysis for large windows,
giving a stratigraphic horizon containing features mixed from
stratigraphic different horizons generated at different geologic
times.
The third method is a generalization of the original collection of
seismic traces u.sub.j to that of an analytic trace v.sub.j defined
as:
where u.sub.j.sup.H (t) is the quadrature, or Hilbert transform of
u.sub.j (t), and i denotes -1. The calculation of
.sigma.(.tau.,p,q) and c(.tau.,p,q) is entirely analogous to
equations (1) and (2), where we note that the definition of
v.sub.j.sup.2 is given by
The third method avoids numerical instabilities in the semblance
estimate of equation (1) at the "zero-crossings" of an otherwise
strong reflector.
The Effect of the Horizontal Analysis Window
By examining equation (2), it is clear that the computational cost
of analysis increases linearly with the number of traces included
in the analysis. However, by comparing a semblance based 11-trace
coherency time slice with those of a 3-trace cross correlation
coherency time slice, (where each has an identical vertical
analysis window of w=32 ms) one is led to believe that adding more
traces to the computation can increase the signal-to-noise ratio.
In general, the signal to noise ratio increases as we increase the
size of the analysis window. However, the overall coherency
decreases somewhat (one sees less white), since the approximation
of a possibly curving reflector by a constant (p,q) planar event
breaks down as we increase the window size. In general, the
signal-to-noise ratio of dip/azimuth estimates increases with the
number of traces in the calculation, until a point is reached
whereby the locally planar reflector approximation no longer
holds.
Conclusions
The 3D semblance technique presented in this patent application
provides an excellent measurement of seismic coherency. By using an
arbitrary size analysis window, we are able to balance the
conflicting requirements of maximizing lateral resolution and
signal-to-noise ratio that is not possible when using a fixed three
trace cross correlation technique. Accurate measurements of
coherency can be achieved by using a short temporal (vertical)
integration window that is on the order of the shortest period in
the data, whereas a zero mean cross correlation technique
preferably is used with an integration window that is greater than
the longest period in the data. Thus, the semblance process results
in less vertical smearing of geology than a cross correlation
process, even for large spatial analysis windows (See FIGS. 15A and
15B). Equally important to the coherence estimate, the semblance
process provides a direct means of estimating the 3D solid angle
(dip and azimuth) of each reflector event. These solid angle maps
may or may not be related to conventional time structure maps
defining formation boundaries. Like the basic coherency process of
Bahorich and Farmer (e.g., cross correlation), estimation of the
instantaneous dip/azimuth cube can be achieved prior to any
interpretation of the data for use in a gross overview of the
geologic setting. In this reconnaissance mode, the coherency and
instantaneous dip/azimuth cubes allow the user to pick key dip and
strike lines crossing important structural or sedimentologic
features very early in the interpretation phase of a project. In an
interpretation mode, these dips and azimuths may be related to
formation and/or sequence boundaries, such that one can map
progradation and transgression patterns of the internal structure
in 3D. Finally, having estimated the instantaneous dip and azimuth
at every point in the data cube, one can apply conventional seismic
trace attributes to locally planar reflectors, thereby greatly
increasing signal-to-noise ratios.
From the foregoing description, it will be observed that numerous
variations, alternatives and modifications will be apparent to
those skilled in the art. Accordingly, this description is to be
construed as illustrative only and is for the purpose of teaching
those skilled in the art the manner of carrying out the invention.
Other algorithms may be used to measure the similarity of nearby
regions of seismic data or to generate the "discontinuity cube."
Moreover, equivalent computations may be substituted for those
illustrated and described. For example, instead of a search over
apparant dips p and q, one could search over dip and azimuth (d,
.phi.). The inverse of the computed semblance may be used so as to
obtain a display analogous to the negative of a photograph. Also
certain features of the invention may be used independently of
other features of the invention. For example, after the solid angle
(dip and azimuth) has been estimated, a smoother and more robust
multitrace estimate of the conventional complex trace attributes
(Taner, M. T., Koehler, F., and Sheriff, R. E.; 1979; "Complex
Seismic Trace Analysis;" Geophysics, 44, 1041-1063) may be
obtained. Instead of calculating these attributes on a single
trace, one can calculate attributes of the angle stack of traces
within the analysis window. That is, one can calculate:
##EQU7##
and ##EQU8##
where ##EQU9##
(See the numerator of equation 1); U.sup.H (.tau.,p,q) is the
Hilbert transform, or quadrature component of U(.tau., p, q);
a.sub.i (.tau.,p,q) is the envelope, or instantaneous amplitude;
.PSI..sub.i (.tau.,p,q) is the instantaneous phase; f.sub.i
(.tau.,p,q) is the instantaneous frequency; and b.sub.i (.tau.,p,q)
is the instantaneous bandwidth (See Cohen, L.; 1993; "Instantaneous
Anything;" Proc. IEEE Int. Conf. Acoust. Speech Signal Processing,
4, 105-109).
In addition to these "instantaneous" attributes, other attributes
are suggested to characterize the signal within a given lobe of the
trace envelope to be that of the attribute at the peak of the
envelope .tau..sub..theta.. These include (See Bodine, J. H.; 1994;
"Waveform Analysis with Seismic Attributes;" presented in the 54th
Ann. Intl. Mtg. SEG. Atlanta, Ga., USA): the wavelet envelope:
as well as skewness, rise time, and response length. Since mixing
occurs along the true dip direction, slowly varying amplitude,
phase, frequency, and bandwidth components of the event will be
preserved. Moreover, the computation of
coherency/semblance/similarity allows one to perform "texture
analysis" of similar seismic regions. Texture analysis combined
with "cluster analysis" leads to segmentation analysis. Among other
things, this allows one to make geologic correlations and
extrapolate the geological character of the subsurface. In
addition, determination of the coherency may be used to impose a
priori constraints for both post-stack and pre-stack seismic
inversion. Thus, it will be appreciated that various modifications,
alternatives, variations, and changes may be made without departing
from the spirit and scope of the invention as defined in the
appended claims. It is, of course, intended to cover by the
appended claims all such modifications involved within the scope of
the claims.
APPENDIX 1 MULTIATTRIBUTE HLS CALIBRATION direction .phi. (hue)
Crayola Color The hues are pure, or 100% saturated colors, and
correspond to the following 1994 non-toxic 96 crayon "Crayola"
standard: N 0 blue NNE 30 plum ENE 60 magenta E 90 salmon ESE 120
red SSE 150 orange-red S 180 yellow SSW 210 lime-green WSW 240
green W 270 forest-green WNW 300 cyan NNW 330 cerulean N 360 blue
Partial 50% saturation corresponds to "dirtier" or "muddier"
colors: N 0 cadet blue NE 45 fuscia E 90 maroon SE 135 sepia S 180
gold SW 225 olive W 270 sea green NW 315 steel blue N 360 cadet
blue 0% saturation corresponds to no color pigment: N 0 gray E 90
gray S 180 gray W 270 gray N 360 gray Low values of lightness
correspond to "dark" colors; intermediate values of lightness
correspond to "deep" colors, and high values of lightness
correspond to "pastel" colors.
APPENDIX 2 SYNOPSIS .backslash.semb3d [-Nfile_in] [-Ofile_out]
[-hisfile_his] [-tstarttstart] [-tendtend] [-ildmdx] [-cldmdy]
[-aplengthaplength] [-apwidthapwidth] [-apheightapheight]
[-apazimapazim] [-llazlmxazim] [-clazimyazim] [-dzdz] [-smaxsmax]
[-pminpmin] [-pmaxpmax] [-qminqmin] [-qmaxqmax] [-threshthresh]
[-freffref] [-startlinestartline] [-endlineendline] [-exppower]
[-min] [-int] [-R] DESCRIPTION semb3d reads in 3D seismic post
stack time or depth data and generates semblance, dip and azimuth
outputs. COMMAND LINE ARGUMENTS semb3d gets all its parameters from
command line arguments. These arguments specify the input, output,
spatial analysis window, and dip discretization parameters. The
following command line arguments have been used in one embodiment
of the invention. -Nfile_ in Enter the input data set name or file
immediately after typing -N. This input file should include the
complete path name if the file resides in a different directory.
Example: -N/export/data2/san_ juan/time_ stack tells the program to
look for file `time_ stack` in directory `/export/data2/san_ juan`.
For this program, the data is stored as a rectangular grid of
regularly binned data. The number of traces (denoted by lineheader
word `NumTrc`) defines the number of traces in the `x` direction.
The number of records (seismic lines denoted by lineheader word
`NumRec`) defines the number of traces in the `y` direction.
Missing data padded in with dead traces flagged by a dead trace
header flag. -Ofile_ out Enter the output multi-attribute data set
name or file immediately after typing -O. Attributes will be output
back to back, line by line. Without scaling the semblance c will
range between 0.0 and 1.0. The values of dip will range between 0
and smax and will always be positive (pointing down). Units are in
msec/m (msec/ft) for time data, or m/m (ft/ft) for depth data. The
azimuth .phi. is perpendicular to strike and points in the
direction of maximum positive dip (pointing down). The values of
azimuth will range between 0 and 360 degrees. Properly defined, an
output azimuth of 0. degrees corresponds to North, while an output
azimuth of 90 degrees corresponds to East. The values of OMEGA =
(d, .phi.) can be chosen such that (when converted to an 8 bit
integer) the left most 6 bits correspond to a valid Seisworks color
table. This color table corresponds to the HLS color model
previously described and is generated using a program that maps the
angles scanned into an HLS (hue, lightness, saturation) color map
of OMEGA = (d, .phi.). -hls file_ hls Enter -hls followed by the
hls table file name to output an ascii flat file containing the
hue, lightness and saturation of each sample contained in the
output. This file is input to a program to generate a RGB (red,
green, blue) color lookup table needed for a proper display on
certain workstations. -tstarttstart Enter -tstart followed by the
beginning of the analysis window in msec. -tendtend Enter -tend
followed by the end of the analysis window in msec. The output
record will be (tend - tstart) msec long. -ildmdx After -ildm enter
the in-line distance measure (trace separation) in m (ft). -cldmdy
After -cldm enter the cross-line distance measure (line separation)
in m (ft). -dzdz After -dz enter the vertical depth sample
increment in m (ft). A value of dz >0 indicates the data are in
depth. -aplengthaplength After -aplength enter the half aperture
length (in meters or feet) along the azimuth of the elliptical
analysis window to be used. Increasing the analysis window by
increasing aplength, apwidth will result in: (1) increased angular
resolution, (2) decreased spatial resolution, (3) increased
computational cost; and (4) decreased overall coherency (since the
plane wave approximation is less valid. -apwidthapwidth After
-apwidth enter the half half aperture width (in meters or feet)
perpendicular to the azimuth of the elliptical analysis window to
be used. -apheightapheight After -apheight enter the half length in
milliseconds (or meters or feet) of the running time (depth)
integration window applied over the semblance. Example = .+-.2
samples. Increasing the temporal integration window apheight will
result in: (1) a smoothed, less noisy response, (2) decreased
vertical resolution, and (3) no change in computational cost.
-apazimapazim After -apazim enter the azimuth of the elliptical
analysis window (with 0 being North and 90 being East). -smaxsmax
After -smax enter the maximum dip to be tested in msec/m (msec/ft)
for time data, or in m/m (ft/ft) for depth data. This is
recommended when there is no preferential strike direction in the
data. This value can be read directly from a section display of the
data. smax will be on the order of .30 msec/m (10 msec/ft) for time
data. Increasing the value of smax beyond any true dips results in
significantly increased computational cost for an identical result.
-pminpmin After -pmin enter the minimum inline (increasing trace
number) dip to be tested in msec/m (msec/ft) for time data, or in
m/m (ft/ft) for depth data. This is recommended when there is a
predominant strike direction parallel or perpendicular to the data
acquisition lines. This value can be read directly from a section
display of the data. -pmaxpmax After -pmax enter the maximum
in-line (increasing trace number) dip to be tested in msec/m
(msec/ft) for time data, or in m/m (ft/ft) for depth data. This is
recommended when there is a predominant strike direction parallel
or perpendicular to the data acquisition lines. This value can be
read directly from a section display of the data. Enter this
command line argument to define a rectangular (2*aplength by
2*apwidth) vs. elliptical analysis window oriented along the
azimuth axis. -qminqmin After -qmin enter the minimum cross-line
(increasing line number) dip to be tested in msec/m (msec/ft) for
time data, or in m/m (ft/ft) for depth data. This is recommended
when there is a predominant strike direction parallel or
perpendicular to the data acquisition lines. This value can be read
directly from a section display of the data. -qmaxqmax After -qmax
enter the maximum cross-line (increasing line number) dip to be
tested in msec/m (msec/ft) for time data, or in m/m (ft/ft) for
depth data. This is recommended when there is a predominant strike
direction parallel or perpendicular to the data acquisition lines.
This value can be read directly from a section display of the data
-threshthresh After -thresh enter the threshhold or cutoff
semblance value, below which dip and azimuth are considered to be
valid measures; below this value shades of gray will be displayed.
Some display software limits the number of colors available for
display. -freffref After -fref enter the reference frequency in
cycles/sec (Hz) for time data, or in cycles/km (cycles/kft) used in
determining the number of dips to be searched (e.g., fref = 60 Hz
for time data, 30 cycles/km for depth data). -ilazimilazim After
-ilazim enter the in-line azimuth (0 degrees being North, 90
degrees being East) that is the azimuth of increasing trace number.
This value is used to calibrate a solid angle output file, if used.
-clazimclazim After -clazim enter the cross-line azimuth (0 degrees
being North, 90 degrees being East) that is the azimuth of
increasing line numbers. This value is used to calibrate the solid
angle output file, if used. -exppower After -exp enter the exponent
to be applied for non-linear scaling of the semblance. In general,
most semblance/coherency values will be between 0.8 and 1.0.
Scaling with power = 2.0 would map these values between .64 and
1.0, scaling with power = 4.0 would map these values between .41
and 1.0, and so forth. This is useful for loading data to an
interpretive workstation. -startlinestartline After -startline
enter the first output line to be generated. -endlineendline After
-endline enter the last output line to be generated. -min After
-min enter this command line argument to extract the dip, azimuth,
and semblance corresponding to the minimum semblance of the angles
searched. (As a default, the program searches for the maximum
semblance or coherency). -int Enter this command line argument to
scale output such that it can be represented by an 8 bit integer
ranging between -128 and +127. Useful for loading data to an
interpretive workstation.
* * * * *