U.S. patent application number 13/450477 was filed with the patent office on 2016-04-07 for systems and methods for optimizing low frequency output from airgun source arrays.
The applicant listed for this patent is Jon-Fredrik Hopperstad, Robert Laws, John Richard Tulett. Invention is credited to Jon-Fredrik Hopperstad, Robert Laws, John Richard Tulett.
Application Number | 20160097869 13/450477 |
Document ID | / |
Family ID | 46718926 |
Filed Date | 2016-04-07 |
United States Patent
Application |
20160097869 |
Kind Code |
A9 |
Hopperstad; Jon-Fredrik ; et
al. |
April 7, 2016 |
Systems and Methods for Optimizing Low Frequency Output from Airgun
Source Arrays
Abstract
A technique provides a source design and method for increasing
low frequency output of a marine source array. The approach
comprises providing a plurality of airguns. At least some of the
airguns are activated to generate an effective bubble energy. The
effective bubble energy may be optimized through use, preparation
and/or arrangement of the airguns.
Inventors: |
Hopperstad; Jon-Fredrik;
(Cambridge, GB) ; Laws; Robert; (Cambridge,
GB) ; Tulett; John Richard; (Yokohama-shi,
JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Hopperstad; Jon-Fredrik
Laws; Robert
Tulett; John Richard |
Cambridge
Cambridge
Yokohama-shi |
|
GB
GB
JP |
|
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20120218869 A1 |
August 30, 2012 |
|
|
Family ID: |
46718926 |
Appl. No.: |
13/450477 |
Filed: |
April 19, 2012 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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|
13112869 |
May 20, 2011 |
9025417 |
|
|
13450477 |
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61376464 |
Aug 24, 2010 |
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61568655 |
Dec 9, 2011 |
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Current U.S.
Class: |
367/144 |
Current CPC
Class: |
G01V 1/137 20130101;
G01V 2210/1293 20130101; G01V 1/3861 20130101; G01V 2210/127
20130101; G01V 2210/1212 20130101 |
International
Class: |
G01V 1/137 20060101
G01V001/137 |
Claims
1. A system for increasing low frequency output of a marine source
array, comprising: a plurality of airguns arranged such that the
airguns are held by a framework in sufficiently close proximity to
one another to generate an effective bubble energy of more than
400010.sup.3 psiin.sup.3 for at least some of the airguns.
2. A system according to claim 1, wherein bubbles emitted by the
airguns when activated are substantially frequency-locked.
3. A system according to claim 1, wherein the effective bubble
energy of the largest bubble emitted by the airguns is at least one
third of the total potential bubble energy with respect to each
shot of the airguns.
4. A system according to claim 1, further comprising a
high-pressure reservoir coupled to the plurality of airguns via at
least two high-pressure hoses.
5. A system according to claim 1, wherein at least some of the
airguns are charged with a different firing pressure level than
other airguns of the plurality of airguns.
6. A system according to claim 1, wherein at least some of the
airguns generate multiple substantially frequency-locked bubbles
such that the largest effective bubble energy is greater than
1000010.sup.3 psiin.sup.3.
7. A system according to claim 1, wherein the airguns generate an
effective bubble energy such that the largest bubble has an
effective bubble energy greater than 300010.sup.3 psiin.sup.3,
further wherein the largest bubble comprises multiple substantially
frequency-locked bubbles, and wherein the effective bubble energy
of the largest bubble is between 33% and 74% of the total potential
bubble energy fired at each shot.
8. A system according to claim 1, wherein the effective bubble
energy can be calculated by the formula: Q eff = k 3 ( 1 + d 10 )
15 6 f obs 3 . ##EQU00008## where Q.sub.eff is the effective bubble
energy, fobs is the observed bubble frequency, d is the source
depth, and k is an empirical constant.
9. A method for increasing low frequency output of a marine source
array, comprising: providing a plurality of airguns; identifying a
largest effective bubble energy for the marine source array;
arranging at least some of the airguns in such a way that the
largest effective bubble energy is substantially achieved upon
activation of the airguns; and activating the airguns.
10. A method according to claim 9, further comprising increasing
airgun chamber volume to achieve the largest effective bubble
energy with respect to the plurality of airguns.
11. A method according to claim 9, further comprising increasing
pressure supplied to the plurality of airguns to achieve the
largest effective bubble energy with respect to the plurality of
airguns.
12. A method according to claim 9, wherein activating comprises
activating at least some of the airguns to generate an effective
bubble energy of more than 400010.sup.3 psiin.sup.3.
13. A method according to claim 9, wherein activating comprises
generating an effective bubble energy of the largest bubble that is
at least one third of the total potential bubble energy with
respect to each shot of the airguns.
14. A method according to claim 9, further comprising charging at
least some of the airguns from a high-pressure reservoir via at
least two high-pressure hoses.
15. A method according to claim 9, further comprising charging at
least some of the airguns with a different firing pressure level
than other airguns of the plurality of airguns.
16. A method for increasing low frequency output of a marine source
array, comprising: providing a plurality of airguns; arranging the
airguns in close proximity to one another; optimizing an effective
bubble energy of at least some of the plurality of airguns by
achieving a selected ratio of the effective bubble energy and the
total potential bubble energy; and activating the airguns to
substantially frequency-lock the bubbles emitted by the
airguns.
17. A method according to claim 16, wherein optimizing comprises
increasing airgun volume of at least some airguns.
18. A method according to claim 16, wherein optimizing comprises
increasing the number of airguns.
19. A method according to claim 16, wherein optimizing comprises
increasing the firing pressure of at least some airguns.
20. A method according to claim 16, wherein optimizing comprises
decreasing the spacing between at least some airguns.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. Provisional
Patent Application No. 61/568,655, filed Dec. 9, 2011, and U.S.
patent application Ser. No. 13/112,869, filed May 20, 2011, which,
in turn, claims the benefit of U.S. Provisional Patent Application
No. 61/376,464, filed Aug. 24, 2010, which are incorporated herein
by reference in their entirety.
TECHNICAL FIELD
[0002] The present disclosure relates in general to seismic source
arrays, and more particularly to systems and methods for optimizing
low frequency output of such source arrays.
BACKGROUND
[0003] In seismic applications, airgun source arrays are often used
to generate acoustic output, which when reflected off of subsurface
formations may be detected by associated seismic receivers. Such
data may be used to build up an image of subsurface formations for
assessing the likelihood of hydrocarbon production.
[0004] The low frequency output of marine airgun seismic sources is
limited by the resonance frequency of the largest airgun bubble
volume in the source array. This oscillation frequency, also
referred to as the fundamental bubble frequency, is given by the
well-known Rayleigh-Willis formula:
f = k ( 1 + d 10 ) 5 6 ( P V ) 1 3 ( 1 ) ##EQU00001##
Where f is the bubble frequency measured in Hertz, d is the source
depth in meters, P is the firing pressure in psi (pound per square
inch), V is the airgun chamber volume in cubic inches and k is an
empirical constant; k=506 matches well with measurements of
conventional airguns.
[0005] Decreasing the bubble frequency requires a bigger bubble
volume. The volume increase should be substantial since the bubble
frequency is inversely proportional to the cube-root of the airgun
chamber volume. Some have recommended increasing the largest bubble
volume as a way to increase the low frequency source output.
[0006] When airguns fire in a cluster, the resulting bubble
frequency substantially equals that of a single gun of the combined
volume. Earlier work on cluster design focused on maximizing the
primary-to-bubble ratio of the resulting source signature. Such is
the airgun cluster design in use today, where the clustered airguns
are typically separated by less than one metre, and where the
airgun bubbles coalesce into one non-spherical bubble. Other
airguns in the source array are only weakly interacting, and the
volume of these guns is normally chosen to achieve maximum
destructive interference of the bubble amplitude of the overall
source signature. This is known as a `tuned array`.
SUMMARY
[0007] The present disclosure describes a source design and method
for increasing low frequency output of a marine source array. The
approach comprises providing a plurality of airguns. At least some
of the airguns are activated to generate an effective bubble energy
that may be optimized through specific use, preparation and/or
arrangement of the airguns.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] The foregoing and other features and aspects of the present
disclosure will be best understood with reference to the following
detailed description of specific embodiments of the disclosure,
when read in conjunction with the accompanying drawings,
wherein:
[0009] FIG. 1 is a schematic diagram of a marine seismic data
acquisition system according to an embodiment of the
disclosure;
[0010] FIG. 2 is a schematic diagram of a VSP arrangement according
to an embodiment of the disclosure;
[0011] FIG. 3 is a graphical depiction of a source signature of
conventional gun arrangements;
[0012] FIG. 4 is a schematic depiction of a tuned conventional
source array;
[0013] FIG. 5 is a schematic depiction of a source array designed
to optimize low frequency output according to the principles of the
present disclosure;
[0014] FIG. 6 is a schematic depiction of another source array
designed to optimize low frequency output according to the
principles of the present disclosure;
[0015] FIG. 7 is a graphical depiction comparing the optimized low
frequency output source arrays of FIGS. 5 and 6 with the
conventional source array of FIG. 4;
[0016] FIG. 8 is a process flow chart for designing a source array
to optimize low frequency output;
[0017] FIG. 9 is a schematic depiction of another source array
designed to optimize low frequency output according to the
principles of the present disclosure;
[0018] FIG. 10 is a graphical depiction of an estimated far field
spectrum of the source array of FIG. 9;
[0019] FIGS. 11a and 11b are a comparison of a conventional source
array (FIG. 11a) and such source array redesigned to optimize low
frequency output according to the principles of the present
disclosure (FIG. 11b);
[0020] FIG. 12 is a flowchart demonstrating a design application
for a low frequency source array;
[0021] FIG. 13 is a schematic depiction of a source having a
plurality of suspended airguns;
[0022] FIG. 14 is a graphical depiction of a measured far field
spectrum of the source configuration of FIG. 13;
[0023] FIG. 15 is a graphical depiction of a measured far field
spectrum of the source configuration of FIG. 13 in which at least
some of the airguns of the source array are operated at higher
firing pressure; and
[0024] FIG. 16 is a graphical depiction of a measured far field
spectrum of the source configuration of FIG. 13 in which at least
some of the airguns of the source array are charged to a higher
pressure level than other airguns of the source array.
DETAILED DESCRIPTION
[0025] Refer now to the drawings wherein depicted elements are not
necessarily shown to scale and wherein like or similar elements are
designated by the same reference numeral through the several
views.
[0026] FIG. 1 depicts an embodiment 10 of a marine seismic data
acquisition system in accordance with some embodiments of the
disclosure. In the system 10, a survey vessel 12 tows one or more
seismic streamers 14 (one example of streamers 14 being depicted in
FIG. 1). The seismic streamers 14 may be several thousand meters
long and may contain various support cables (not shown), as well as
wiring and/or circuitry (not shown) that may be used to support
communication along the streamers 14. In general, each streamer 14
includes a primary cable into which is mounted seismic sensors 16
that record seismic signals. It is to be appreciated that the
sensors 16 are illustrated schematically for emphasis in FIG. 1,
and that in practice, the sensors 16 may be disposed within the
streamer cable 14. The seismic sensors 16 may include pressure
sensors (e.g., hydrophones) and/or particle motion sensors (e.g.,
accelerometers).
[0027] The marine seismic data acquisition system 10 includes a
seismic source 20 that typically takes the form of an array of
airguns. In some embodiments of the disclosure, the seismic source
20 may be towed by the survey vessel 12. In other embodiments, the
seismic source 20 may operate independently of the survey vessel
12, in that the seismic source may be coupled to other vessels,
buoys or rigs, as just a few examples.
[0028] As the seismic streamers 14 are towed behind the survey
vessel 12, acoustic signals 18 (an example of an acoustic signal 18
is depicted in FIG. 1) are produced by the seismic source 20 and
are directed down through a water column 22 into strata 24 and 26
beneath a water bottom surface 28. The acoustic signals 18 are
reflected from the various subterranean geological formations, such
as an exemplary formation 30 that is depicted in FIG. 1. The
incident acoustic signals 18 produce corresponding reflected
acoustic signals, or pressure waves 32, which are sensed by the
seismic sensors 16.
[0029] The seismic acquisition enables the buildup of an image of a
survey area for purposes of identifying subterranean geological
formations, such as the exemplary geological formation 30.
Subsequent analysis of the representation may reveal probable
locations of hydrocarbon deposits in subterranean geological
formations. Depending on the particular embodiment of the
disclosure, portions of the analysis of the representation may be
performed on the seismic survey vessel 12, such as by a signal
processing unit 34.
[0030] In addition to towed marine applications, the present
disclosure also is applicable to VSP surveys. A vertical seismic
profile (VSP) is a class of borehole seismic measurements used for
correlation between surface seismic receivers and wireline logging
data. VSPs can be used to tie surface seismic data to well data,
providing a useful tie to measured depths. Typically VSPs yield
higher resolution data than surface seismic profiles provide. VSPs
enable converting seismic data to zero-phase data and enable
distinguishing primary reflections from multiples. In addition, a
VSP often is used for analysis of portions of a formation ahead of
the drill bit. Referring to FIG. 2, a simplified view of an
offshore rig 36 positioned over a subsea borehole 37 is shown. The
borehole 37 contains a plurality of spaced receivers 38 to
facilitate, for example, a VSP acquisition. The receivers 38 can be
deployed in the borehole 37 with a variety of methods and systems,
including a wireline cable; a downhole assembly, e.g. drill
collars; permanent fixation to a side of the borehole; or with
other suitable techniques. The rig 36 is shown supporting a
conventional seismic survey apparatus designated generally as 39.
The survey apparatus 39 includes a source 40, which takes the form
of an air-gun or guns suspended below the surface by a float 41. An
analog hydrophone 42 is suspended below the air guns 40 and may
provide information for correcting time break errors (errors
attributable to time differences for swells, irregular source
firings, etc.).
[0031] One or more analog lines 43 form part of an umbilical 44
that may also include an airline. The analog lines 43 traverse a
handling system, such as a crane 45. The analog lines 43 provide an
analog communications/control link between the guns 40, the
hydrophone 42, a gun controller 46, and a computer processor
47.
[0032] Having generally described an example of a seismic data
acquisition process and a VSP technique, attention is now directed
to the seismic source 20 (FIG. 1), 40 (FIG. 2), which may take the
form of an airgun cluster. In VSP applications, seismic sources are
normally comprised of airgun clusters; e.g. one to four clusters,
wherein each cluster includes, for example, two to four airguns.
Airgun clusters also are prevalent in source arrays for towed
marine, seabed seismic and some borehole seismic applications. The
teachings of the present disclosure may be utilized in any of the
aforementioned settings.
[0033] The widespread use of airgun clusters can be attributed to
two main characteristics. First, clustering of medium sized airguns
can achieve the same bubble frequency as a large single airgun with
the same total volume. Airgun clusters are considered more robust
and easier to handle than large single airguns. Secondly, airgun
clusters have a higher peak-to-bubble ratio than the equivalently
sized single airgun, and are therefore well-suited for tuned
arrays.
[0034] The higher peak-to-bubble ratio associated with airgun
clusters is illustrated in the top panel of FIG. 3, which compares
a single airgun of about 600 in.sup.3 with a three-gun cluster with
the same total volume; the measurement bandwidth is 0-500 Hz. The
three-gun cluster has a primary-to-bubble ratio of
1.00/0.26.apprxeq.3.9, while the single airgun has a
primary-to-bubble ratio of 0.55/0.35.apprxeq.1.6. The higher
peak-to-bubble ratio manifests itself in a flatter spectrum in the
bottom panel of FIG. 3.
[0035] The spectral comparison also indicates that the output at
the bubble frequency, i.e. 6.8 Hz, is substantially identical. It
has been found that no matter how you arrange the cluster to
release the air, the spectral level at the bubble frequency is
substantially the same. In accordance with this observation, an
initial embodiment of the present disclosure seeks to optimize low
frequency output by implementing large airgun cluster(s), whose
volume is larger than what is considered practical for a single
airgun.
[0036] The low frequency output of airgun sources is limited by the
resonance frequency of the largest bubble volume in the array. In
conventional seismic sources, and especially for source arrays used
in towed marine, the volume of the largest bubble is small compared
with the total source volume. Accordingly, there is scope for
increasing the low frequency output, without increasing the total
gas volume, by shifting the bubble frequency towards zero. The
lower resonance frequency is achieved by releasing a larger amount
of gas into one big bubble or multiple frequency locked
bubbles.
[0037] Airgun bubbles can exhibit cluster-type oscillation
frequency even at non-coalescing distances. For example, the
bubbles from two closely spaced airguns of different volume may
oscillate with the same frequency (the frequency of the combined
volume), even though the bubbles are not coalescing. In fact, they
may not even be touching. The bubble interaction is entirely
through the pressure field. This phenomenon is known as frequency
locking. Bubbles are `fully frequency locked` when their bubble
frequency substantially equals that associated with the combined
volume. Not fully interacting bubbles are commonly referred to as
`partially frequency locked`, and as `non-interacting` when the
presence of the other bubbles do not affect the oscillation
frequency.
[0038] FIG. 4 depicts an example of a typical prior art airgun
array 48 in which single and clustered airguns are spaced at 3
meters in the in-line direction. The largest cluster 49 in the
array 48 has a volume of 2.times.290 in.sup.3=580 in.sup.3. The two
cluster bubbles are fully frequency locked to each other, and
partially frequency locked to an adjacent cluster 50, which has a
volume of 2.times.195 in.sup.3. Accordingly, the 2.times.290
in.sup.3 bubbles oscillate with a frequency corresponding to an
effective volume of about 750 in.sup.3. The array 48 further
includes single airguns 51, 52, 53, 54 with volumes 280 in.sup.3,
195 in.sup.3, 145 in.sup.3, 105 in.sup.3, respectively, resulting
in a total volume of each string/subarray of 1695 in.sup.3 and a
total source array volume of 5085 in.sup.3. Thus, the largest
bubble in array 48 uses only 750/1695.apprxeq.44% of the available
subarray volume, and only 750/5085.apprxeq.15% of the total source
volume available. "Source volume" as used in the present disclosure
means the total volume of airguns fired at each shot and excludes
volumes that could be generated by guns (e.g., spare guns) not used
during the shot. These numbers are quite typical for prior art
source arrays. The total high pressure gas capacity available is
used to generate many weakly interacting bubbles, and the largest
bubble is small compared with the total source volume.
[0039] In contrast, source designs according to the present
disclosure aim to optimize the use of available high pressure gas
capacity for generating very low frequencies. To extend the source
bandwidth as much as possible towards zero Hertz, substantially all
of the available high pressure gas should be released into one huge
bubble oscillation. This can be achieved with an airgun cluster
wherein some or all cluster bubbles are fully frequency locked,
i.e., the cluster bubbles oscillate with the frequency associated
with the total cluster volume. Various examples of implementing the
teachings of the present disclosure will now be described. It is to
be appreciated, however, that these are merely examples and other
methods and arrangements of achieving full frequency locking of
cluster bubbles are contemplated as falling within the scope of the
present disclosure.
Example 1
Source Array Wherein the Largest Bubble is One-Third of the Total
Source Volume
[0040] In an embodiment of the present disclosure, the largest
quantity of high pressure gas possible is released into one
location to maximize the very low frequency output. There might be
several factors limiting the largest bubble in an array, e.g. the
total source volume may be limited by the onboard compressor
capacity and the seismic shot interval. The total source volume
also may be limited by the flow capacity of the conduits (e.g.,
hoses) connecting the source and the onboard compressor or onboard
high pressure reservoir, or it may be limited by the number of high
pressure hoses the ship can tow.
[0041] Similarly, the largest bubble in the source array might be
limited by how much of the total source volume can be released into
substantially one location. FIG. 5 depicts one embodiment of the
present disclosure in which the largest bubble is limited by the
flow capacity of the high pressure hoses that connect the source to
the vessel. A vessel 60 tows a source array 62, which includes a
pair of substantially identical subarrays 64 disposed about another
subarray 66 (which includes a pair of single airguns 67 disposed
about a cluster 68 in the in-line direction). The cross-line
spacing between subarrays 64 and 66 is, for example, 6 meters and
the in-line spacing between each of the single airguns 67 and the
cluster 68 is, for example, 6 meters. In this embodiment, each
subarray 64, 66 is charged by a shipborne high pressure reservoir
via one high pressure hose, whose flow capacity is approximately
2100 in.sup.3 per shot. In this example, the source array 62 is
further limited by how close one can place two hoses, and
consequently it may not be possible to frequency lock the bubbles
from different subarrays. Hence, the largest bubble may be 2100
in.sup.3. The bubble frequency associated with 2100 in.sup.3 is
achieved by fully frequency locking six 350 in.sup.3 airgun
bubbles, while the bubble frequency associated with 1050 in.sup.3
is achieved by fully frequency locking two 525 in.sup.3 airgun
bubbles. The dashed lines indicate the regions with full frequency
locking. The interaction between the regions is negligible, and it
is also negligible between any region and any of the single airgun
bubbles.
[0042] The effective bubble volume of the subarrays 64 is
substantially 2100 in.sup.3, while the subarray 66 has two distinct
bubble frequencies: the frequencies associated with a bubble
volumes of 1050 in.sup.3 and 525 in.sup.3. These volumes result in
bubble frequencies that are 1/3 and 2/3 of an octave higher than
the lowest bubble frequency. In this example, the outer subarrays
64 have been optimized according to the present disclosure, while
the subarray 66 is used to fill-in the bubble notch frequencies in
order to flatten the spectrum. In this example, the largest
effective bubble volume is approximately 33.3% of the total source
volume, i.e. 2100 in.sup.3 out of 6300 in.sup.3 total volume.
Example 2
Source Array Wherein the Largest Bubble Equals the Total Source
Volume
[0043] FIG. 6 depicts a schematic view of another source somewhat
different than that disclosed in Example 1 and wherein all of the
released gas is frequency locked into one very large airgun bubble.
In the embodiment of FIG. 6, a source 70 comprises, for example,
twenty-one 300 in.sup.3 airgun bubbles arranged on a hexagonal grid
in three layers. The airguns are connected to a plurality of high
pressure hoses 72, which extend from a vessel 74. In this
arrangement, the high pressure hoses 72 terminate at substantially
the same location, thus enabling the guns to be positioned within
full frequency locking distance. All twenty-one airgun bubbles are
fully frequency locked and oscillate with the period associated
with the combined volume, e.g. 6300 in.sup.3. Thus, the volume of
the largest effective bubble equals the total source volume.
Although a specific number of airguns with specific bubble volumes
are described in this example, it is to be appreciated that such
numbers and volumes may be altered while still enabling full
frequency locking of the array.
[0044] FIG. 7 compares the modeled spectra of the conventional
source in FIG. 4 (dotted curve) wherein the largest effective
bubble volume is 15% of the total source volume; the new source
illustrated in FIG. 5 (dashed curve) wherein the largest effective
bubble volume is approximately 33% of the total source volume; and
the new source shown in FIG. 6 (solid curve) wherein the effective
bubble volume is 100% of the total source volume. The comparison of
FIG. 7 demonstrates how the low frequency output increases with the
size of the effective bubble volume as both the dashed and the
solid curves have significantly more low frequency output than the
conventional reference spectrum (dotted curve).
Example 3
Array Wherein the Largest Bubble Equals Half of the Total Source
Volume
[0045] In some embodiments, additional gas for tuning the source
array by creating other distinct bubble frequencies may be desired.
Accordingly, FIG. 8 depicts a flow chart 80 showing how a source
can be designed, or re-designed, to take this into account. That
is, an optimum low frequency source may be designed, while
maintaining some spectral flatness given design restrictions
imposed by the available equipment.
[0046] In block 82, the desired relative size of the largest
effective bubble volume relative to the total source volume is
determined. This desired ratio of the volume of the largest bubble
in the array to the total array volume affects the trade-off
between maximizing the low frequency output and flattening the
spectrum by introducing additional bubble frequencies to fill-in
the spectral notches. In this example, the desired size of the
largest effective bubble is half of the total source volume
available per shot. This ratio is 1/3 in Example 1; 1/1 in Example
2; and about 0.74 in Example 4. The ratio illustrated in block 82
is equivalent to "the desired ratio Qeff/Qtotal" of block 137 in
FIG. 12.
[0047] Block 84 establishes the largest effective bubble volume
that may be practically achieved given the restrictions imposed by
the available equipment. For example, the total source volume per
shot is limited by the flow capacity per high pressure gas hose and
the number of hoses available. Referring to FIG. 9, which
illustrates one implementation, only two gas hoses 90, 92 from a
high pressure reservoir, e.g. the shipboard compressor, and a
submerged source array 94 are available, with each hose having a
flow capacity of, for example, 1680 in.sup.3 per shot. Thus, in
this example, the desired effective volume of the largest bubble is
(1680+1680)2/3=2240 in.sup.3. However, in this example, the largest
effective bubble volume is further limited by how close the two
strings can be positioned to avoid tangling of the equipment while
towing, so it is not possible to frequency lock gas bubbles from
different strings. Consequently, the actual effective volume of the
largest bubble may be 1680 in.sup.3. In order to optimize the
bubble volume in the array (e.g., achieve as large bubble volume as
practically possible), several factors can be considered, such as
shown by the side blocks pointing toward block 84. For example, the
largest bubble volume may be affected by the supply reservoir
capacity. In other words, the output capacity of the compressor per
shot may be increased to achieve maximum actual bubble volume. The
largest bubble volume may also be affected by the flow capacity of
each hose between the supply and source. In other words, the
cross-sectional flow area of the hoses feeding the source may be
increased to allow enough compressed air to be delivered to the
source within a shot-recharge-cycle. To circumvent flow
restriction, several gas hoses may be used in parallel so as to
increase the total feed capacity. Adjacent subarrays can be
suitably designed and/or arranged within locking distance such that
the air released from airguns that are located on different
subarrays being fed by separate hoses may be frequency-locked so as
to creat the maximum bubble volume. The conduits between the high
pressure supply and the airgun should contain no or minimum
branched network of hoses and pipes so that there is no or
insignificant restriction on the total volume of released air that
can be frequency-locked.
[0048] Referring again to FIG. 8, block 86 contemplates design of
an airgun cluster arrangement 96 (FIG. 9) to achieve the largest
frequency-locked bubble, i.e. the one that results in the 1680
in.sup.3 effective bubble volume, which corresponds to the total
volume available from one gas hose. In this example, the desired
bubble frequency is achieved with six 280 in.sup.3 airguns in close
proximity.
[0049] Block 88 of the flow chart contemplates design of other
bubble frequencies in the array so as to facilitate
frequency-locking of other smaller bubbles in the array. For
example, instead of maximizing the low frequency output by
duplicating the airgun arrangement in block 86, another airgun
subarray 98 may be arranged to use the remaining gas to flatten the
spectrum. In this example, three additional bubble frequencies may
be uniformly distributed, on a linear frequency scale, between the
first bubble frequency and its first harmonic. The Rayleigh-Willis
formula in Equation 1 gives the effective bubble volume of these
other bubble frequencies: V.sub.2=1680/(1.25).sup.3.apprxeq.860
in.sup.3, V.sub.3=1680/(1.50).sup.3.apprxeq.498 in.sup.3,
V.sub.4=1680/(1.75).sup.3.apprxeq.313 in.sup.3. In this example,
the second largest effective bubble volume, V.sub.2, is created by
a three gun cluster having two 250 in.sup.3 guns and one 360
in.sup.3 gun. Similarly, V.sub.3 is created by a two gun cluster
having two 250 in.sup.3 guns, and V.sub.4 is a single airgun of 310
in.sup.3.
[0050] Accordingly, the design of FIG. 9 achieves a largest
effective bubble volume that is 50% of the total source volume,
while also achieving spectral flattening using three additional
bubble frequencies that are uniformly distributed between the
frequency of the largest bubble and its first harmonic. The
spectral flattening of this array is illustrated in FIG. 10.
Example 4
Redesign of a Conventional Cluster Source
[0051] The teachings of the present disclosure provide useful
methods for redesigning existing cluster arrays to optimize low
frequency output. FIG. 11A depicts the layout of a conventional
cluster source deployed in dual mode as described in U.S. Pat. No.
4,956,822. The prior art cluster source has been designed for
enhanced spectral flatness, i.e. high primary-to-bubble ratio, with
little regard for the very low frequency source output.
[0052] The value of the effective bubble volume, V.sub.eff, can be
calculated by solving the Rayleigh-Willis formula in Equation 1 for
the bubble volume, V, and inputting values for air pressure (e.g.,
2000 psi), source depth (e.g, 10 ft) and bubble frequency (e.g.
1/196.5 ms.apprxeq.5.089 Hz).
V eff = k 3 ( 1 + d 10 ) 15 6 P f 3 ( 2 ) ##EQU00002##
Accordingly, use of these values leads to a maximum effective
bubble volume of only 956 in.sup.3, i.e. 40% of the total source
volume of 2400 in.sup.3. Although the listed values were used to
define the maximum effective bubble volume of the configuration of
FIG. 11A, it is to be appreciated that this definition can be used
to quantify the effective bubble volume(s) of any prior art
source.
[0053] According to the principles of the present disclosure, such
source can be redesigned to maximize the low frequency output while
using the same total amount of compressed air and maintaining some
spectral flatness. Assuming that the firing pressure is the same,
i.e. 2000 psi, the source depth is the same, i.e. 10 ft, and that
the total volume cannot exceed 2400 in.sup.3 and that there are no
other restrictions on how the total volume can be distributed, the
source can be redesigned to have two distinct bubble frequencies.
The first bubble frequency may be defined as low as possible and
the second bubble frequency may be designed as being half an octave
higher than the first bubble frequency, such that the second bubble
frequency will coincide with the bubble notch of the first bubble
frequency. This restriction can be expressed as
V.sub.bub,max(1+2.sup.-3/2)=V.sub.tot (3)
[0054] In other words, the largest effective bubble may be
approximately 74% of the total source volume. Consequently, the
first bubble may oscillate with a frequency associated with 1773
in.sup.3 and the second bubble may oscillate with a frequency
associated with 627 in.sup.3. Similar to the other examples
disclosed herein, such bubble oscillations are obtained by fully
frequency locking multiple airgun bubbles in close proximity.
[0055] The redesigned low frequency source is depicted in FIG. 11B
as having a pair of cluster units 100, 102, including a 1773
in.sup.3 bubble, which may be constructed from six 295.5 in.sup.3
guns, and a 627 in.sup.3 bubble, which may be constructed from two
313.5 in.sup.3 guns. The two cluster units are well separated such
that the interaction between the cluster units is negligible.
Redesigning the prior art cluster according to the principles
disclosed herein increases the effective bubble volume from 956
in.sup.3 to 1773 in.sup.3, which at 10 ft depth corresponds to a
bubble frequency of 5.1 and 4.1 Hz respectively. Accordingly, the
bubble frequency has been shifted by 0.3 octave by redesigning the
cluster source layout.
[0056] In the embodiments described above, the source array can be
selectively redesigned to emit more low frequency output by
clustering several airguns to create a large bubble. In another
embodiment, an approach is used to optimize low frequency output
from airgun source arrays by, for example, increasing the firing
pressure, thereby enabling an even lower bubble resonance
frequency. In the embodiments described above, description is
provided regarding how to create a bigger bubble by frequency
locking the oscillation from multiple airgun bubbles. When airguns
fire in close proximity the resulting bubble oscillates with the
frequency associated with the total cluster volume. In the
embodiments discussed below, the approach is generalized to also
account for the firing pressure. The embodiments also may be
combined to utilize, for example, larger bubbles and/or more
optimized firing pressure to further optimize low frequency
output.
[0057] As discussed above, to maximise the very low frequency
output the largest quantity of high pressure gas possible may be
released into one location. There may be several factors limiting
the largest bubble in the array, e.g. the total source volume may
be limited by the onboard compressor capacity and the seismic shot
interval; the total source volume also may be limited by the flow
capacity of the hoses connecting the source and the onboard
compressor or onboard high pressure reservoir, or it may be limited
by the number of high pressure hoses that a ship can tow. In the
previous embodiments, an assumption was made that the supply
pressure was already operating at maximum capacity, while here we
also consider the case of increasing the supply pressure level.
[0058] In its original form (see e.g. Kramer et al., 1969), the
Rayleigh-Willis formula was expressed as a function of the
potential bubble energy, Q, here defined as the product of firing
pressure and the airgun chamber volume. Replacing PV in Equation 1
with Q gives:
f = k ( 1 + d 10 ) 5 6 Q 1 3 ( 4 ) ##EQU00003##
Where, as before, f is the bubble frequency measured in Hertz and d
is the source depth in metres. Furthermore, Q is referred to as the
"bubble energy" and measured in the awkward, yet convenient, unit
psiin.sup.3 (pound-per-square-inch times cubic-inches); 1
psiin.sup.3.apprxeq.0.1130 Joules. The empirical constant k is the
same as before.
[0059] This generalized version of the Rayleigh-Willis formula can
be used to calculate the bubble frequency for fully frequency
locked bubbles wherein the individual airguns have been charged
with different firing pressure. For this case the combined bubble
energy of the frequency locked bubbles is the sum of the product of
the individual airgun volume and its firing pressure:
Q = n P n V n ( 5 ) ##EQU00004##
In this context we can describe bubble frequency locking in a more
general way: when airguns fire in close proximity the airgun
bubbles are frequency locked when the resulting bubble(s)
oscillates with the frequency associated with the total cluster
bubble energy Q. For example, creating a 5.1 Hz bubble oscillation
at 6 metres depth requires a bubble energy of Q=400010.sup.3
psiin.sup.3. This can be achieved in several ways, for example: one
can frequency lock 2000 in.sup.3 of air fired at 2000 psi, or one
can frequency lock about 1333 in.sup.3 of air fired at 3000 psi, or
as a third example, one can frequency lock 1000 in.sup.3 of air
fired at 2000 psi with 800 in.sup.3 of air fired at 2500 psi. All
three examples have the same cluster bubble energy: Q=400010.sup.3
psiin.sup.3.
[0060] Furthermore, the generalized version of the Rayleigh-Willis
formula also allows us to compare the low frequency utilization of
source configurations operated at different pressure levels. By
rearranging Equation 4 for the bubble energy, Q, we obtain a metric
that describes the "effective bubble energy", Q.sub.eff, of an
array:
Q eff = k 3 ( 1 + d 10 ) 15 6 f obs 3 ( 6 ) ##EQU00005##
Where f.sub.obs is the observed bubble frequency from source
signature measurements. This definition can be used to quantify the
effective bubble energy of the largest bubble in any prior art
source, thereby quantifying to what degree the individual bubbles
frequency lock.
Example 5
Quantifying the Effective Bubble Energy of a Source
[0061] The effective bubble energy, as defined by Equation 6, can
be used to evaluate the low frequency utilization of any
source.
[0062] Assume, for example, a source configuration comprising
multiple airguns. For this configuration the inter-gun distance is
small enough for bubble frequency locking to occur, but it is not
clear how many bubbles frequency lock and whether they fully
frequency lock; i.e. oscillate with the frequency associated with
the combined bubble energy. Furthermore, assume the airguns have a
total volume of 2400 in.sup.3, and that it has been tested at 3 m
source depth at two different pressure levels with the following
results:
TABLE-US-00001 Source firing pressure 2000 psi 3000 psi Observed
bubble frequency 5.10 Hz 4.06 Hz
Using Equation 6, one can calculate the effective bubble energy and
thereby quantify the degree of frequency locking of the source.
[0063] When fired at 2000 psi, the total bubble energy of the
source is Q.sub.total=20002400=480010.sup.3 psiin.sup.3, while the
effective bubble energy is:
Q eff = 506 3 ( 1 + 3 10 ) 15 6 5.1 3 .apprxeq. 1882 10 3 psi in 3
##EQU00006##
which is 1882e3/(20002400).apprxeq.39% of the total potential
bubble energy if all the individual bubbles had fully frequency
locked.
[0064] Similarly, at 3000 psi the total bubble energy of the source
is Q.sub.total=30002400=720010.sup.3 psiin.sup.3, while the
effective bubble energy is:
Q eff = 506 3 ( 1 + 3 10 ) 15 6 4.06 3 .apprxeq. 3730 10 3 psi in 3
##EQU00007##
which is 3730e3/(30002400).apprxeq.52% of the total potential
bubble energy.
[0065] Consequently, even though the source exhibits a larger
degree of frequency locking at 3000 psi than at 2000 psi firing
pressure--52% compared with 38%--the source only utilized about
half of the total bubble energy to create its largest bubble.
Example 6
Source Configuration Limited by the Supply Pressure
[0066] Referring generally to the flowchart of FIG. 12, an example
is provided for designing a source which is limited by a given
firing pressure, e.g. 2000 psi firing pressure. As illustrated, an
initial setup procedure may be performed in which airgun source
parameters are obtained, as indicated by block 110. The setup may
comprise obtaining initial hardware parameters, e.g. air guns
(type, number, chamber volume, firing pressure) and source geometry
(airgun to airgun spacings), as indicated by block 112. Following
setup, the total bubble energy achievable may be calculated, as
indicated by block 114. A variety of processes may be employed to
maximize the total possible bubble energy, as indicated by block
116.
[0067] For example, a determination may be made whether airgun
volume can be increased, as represented by decision block 118. If
the volume can be increased, a larger chamber is selected, as
indicated by block 120, and this updated information is used in
updating the energy calculations (see block 114). Another
determination may be whether the number of airguns can be
increased, as represented by decision block 122. If the number of
airguns can be increased, a larger number is selected as indicated
by block 124. Again, this updated information may be used in
updating the energy calculations at block 114. Another example of a
determination for maximizing total bubble energy may comprise
evaluating whether the firing pressure can be increased, as
indicated by decision block 126. If the firing pressure can be
increased, the increased pressure parameters are determined, as
indicated by block 128. This updated information also may be used
to update the overall energy calculations at block 114.
[0068] If the various parameter values can no longer be increased,
the final selected parameter values may be used to facilitate
assembly of a desired airgun source array, as indicated by block
130. In-sea tests may then be conducted, as indicated by block 132.
For example, the airgun source may be placed in-sea to enable
firing of the airguns and obtaining of desired measurements, e.g.
signatures, bubble frequencies, and depth. The data is used to
calculate an effective bubble energy, as indicated by block 134.
This allows determination of whether the ratio of effective bubble
energy to total bubble energy achievable is desirable, as indicated
by decision block 136. The desired ratio of effective bubble energy
to total bubble energy may be input, as indicated by block 137. If
the desired ratio is achieved, the design is validated, as
indicated by block 138. However, if the desired ratio is not
achieved, additional evaluations can be performed. For example, a
determination may be made as to whether airgun spacings can be
decreased, as indicated by decision block 139. If the airgun
spacings can be decreased, another source geometry can then be
determined, as indicated by block 140. The new source geometry may
be used to facilitate assembly of another source array, as
indicated by block 130. However, if the additional evaluations do
not suggest a new source geometry, the specific design may be
terminated, as indicated by block 142.
[0069] FIG. 13 illustrates a source configuration that has been
designed according to a present embodiment. In this example, a
source 144 (which may be part of a larger source array or may
comprise the entire source array) has a total volume of 1500
in.sup.3, and comprises six 250 in.sup.3 airguns 146 mounted in
close proximity. For example, a group of three airguns 146 may be
mounted on the first side of a framework 148 and a second group of
three airguns 146 may be mounted on a second side of the framework
148. However, the number and arrangement of airguns 146 may be
adjusted/changed depending on the parameters of a given
application. In the example illustrated, the airguns 146 are
suspended from a float 150 via suitable suspension lines 152. When
operated with 2000 psi firing pressure at 7 metres depth, for
example, and assuming the individual bubbles fully frequency lock,
Equation 1 predicts the resulting bubble will oscillate at 5.5
Hz.
[0070] With conventional airguns having maximum firing pressure
limited to 2000 psi, any attempt to exceed the airgun
manufacturer's working pressure rating of 2000 psi poses a
potential for problems with respect to equipment and personnel.
[0071] By employing a higher flow rate compressor or a high
pressure supply reservoir that has the capacity to deliver
increased air flow, increasing the volume of the airgun chambers
becomes an effective way of further reducing the bubble frequency
for seismic source systems. Equation 1 shows that the bubble
frequency is inversely proportional to the cube-root of the product
of the firing pressure and the airgun chamber volume. Equation 5
shows that the bubble energy is proportional to the firing pressure
and volume of the airgun source. Consequently, increasing the
airgun chamber volumes from 250 in.sup.3 to 350 in.sup.3 is
equivalent to increasing the total bubble energy by 40%.
[0072] FIG. 14 shows measured far-field spectra of the 1500
in.sup.3 source (illustrated in FIG. 13) operated with 2000 psi
firing pressure at 7 metres depth. The vertical dashed line
indicates the theoretical bubble resonance frequency calculated
with Equation 4. The figure confirms that the six bubbles fully
frequency lock at 2000 psi, i.e. the bubbles oscillate with the
frequency associated with the total bubble energy.
[0073] This low frequency source, with an initial total volume of
1500 in.sup.3 subsequently increased to 2100 in.sup.3, is the
result of the disclosed design method described in FIG. 12. The
result of the design process is creation of the largest bubble
possible using available airgun chambers to increase the low
frequency output and to maximize the total bubble energy, i.e. to
maximize Q.sub.total.
[0074] Referring to the flow chart in FIG. 12 and the table below,
one example provides initial hardware parameters having a total
bubble energy for the source array of Q.sub.total=300010.sup.3
psiin.sup.3. This initial design example was limited by the total
source volume (1500 in.sup.3) and the maximum number of airguns
(six) within the frame design. However, after reassessing the
hardware parameters through the `process to maximize Q.sub.total`
loop in FIG. 12 it was found that total source bubble energy could
be increased to 420010.sup.3 psiin.sup.3 by fitting larger airgun
chamber volumes. The final design in this example is limited by the
maximum number of airguns in the frame and the maximum safe firing
pressure of the airguns.
TABLE-US-00002 Initial parameters After maximizing Q.sub.total
Number of airguns 6 6 Airgun chamber volumes 6 250 = 1500 in.sup.3
6 350 = 2100 in.sup.3 Max safe airgun operating 2000 psi 2000 psi
pressure Q.sub.total 3000 10.sup.3 psi in.sup.3 4200 10.sup.3 psi
in.sup.3
This design process has maximized the total bubble energy
available.
Example 7
Increasing the Effective Bubble Energy by Increasing the Firing
Pressure
[0075] In another example, FIG. 13 may again be used to illustrate
a configuration embodiment of the present disclosure. In this
example, the source 144 again has a total volume of 1500 in.sup.3
and comprises six 250 in.sup.3 airguns 146 mounted in close
proximity. When operated with 2000 psi firing pressure at 7 metres
depth, and assuming the individual bubbles fully frequency lock,
Equation 1 predicts the resulting bubble will oscillate at 5.5
Hz.
[0076] A majority of seismic surveys operate airgun sources with
about 2000 psi firing pressure. This is sometimes considered an
industry standard. However, some modern airguns have been designed
to operate with 3000 psi maximum firing pressure. The 2000 psi
pressure level has traditionally been preferred because of limited
compressor capacity, reduced HSE risk and longer service
intervals.
[0077] Despite this, increasing the source firing pressure is an
effective way of further reducing the bubble frequency for seismic
source systems that have additional compressor capacity or
additional high pressure supply reservoir capacity. Equation 1
shows that the bubble frequency is inversely proportional to the
cube-root of the product of the firing pressure and the airgun
chamber volume. Consequently, increasing the firing pressure from
2000 to 3000 psi is equivalent to increasing the total bubble
energy by 50%, i.e. increasing P from 2000 to 3000 psi in Equation
5.
[0078] FIG. 15 shows measured far field spectra of the 1500
in.sup.3 source 144, illustrated in FIG. 13, operated with 3000 and
2000 psi firing pressure at 7 metres depth. The vertical dashed
lines indicate the theoretical bubble resonance frequency
calculated with Equation 4. The figure confirms that the six
bubbles fully frequency lock at both 2000 and 3000 psi, i.e. the
bubbles oscillate with the frequency associated with the total
bubble energy. Furthermore, the figure shows that the bubble
frequency is significantly lower by increasing the firing pressure
from 2000 to 3000 psi.
[0079] This low frequency source, with a total volume of 1500
in.sup.3 and fired at 3000 psi, is the result of implementing the
disclosed design method described in FIG. 12. This design also
creates the largest bubble possible within operational constraints
to increase the low frequency output. In other words, the design
provides a bubble oscillation where the effective bubble energy
equals the total bubble energy, and for which the total bubble
energy is maximized, i.e., maximize Q.sub.total and design the
source such that Q.sub.eff/Q.sub.total=1. This result is quite
different from the results of prior art source designs. For
conventional sources the inter-gun spacing and the distribution of
bubble frequencies are normally chosen to achieve maximum spectral
flatness, while in this case we aim to emit only one bubble
frequency: the oscillation frequency associated with the total air
supply capacity available.
[0080] Referring to the flow chart in FIG. 12 and the table below,
the initial hardware parameters provide a total bubble energy for
the source array of Q.sub.total=240010.sup.3 psiin.sup.3. The
initial design was limited by the total source volume (1200
in.sup.3) and the maximum operating pressure for the chosen airgun
type (2000 psi). However, after reassessing the hardware parameters
through the `process to maximize Q.sub.total` loop in FIG. 12 it
was found that total source bubble energy could be increased to
450010.sup.3 psiin.sup.3 by replacing the airgun type with one that
is designed to safely operate at 3000 psi and by increasing the
airgun chamber volumes. The final design may be limited by the
number of airguns and the maximum airgun chamber volume
considered.
TABLE-US-00003 Initial parameters After maximizing Q.sub.total
Number of airguns 6 6 Airgun chamber volumes 3 250 + 3 150 = 6 250
= 1500 in.sup.3 1200 in.sup.3 Max safe airgun operating 2000 psi
3000 psi pressure Available air supply 2000 in.sup.3 at 3000 psi
2000 in.sup.3 at 3000 psi capacity Q.sub.total 2400 10.sup.3 psi
in.sup.3 4500 10.sup.3 psi in.sup.3
[0081] The first part of the design process aims to maximize the
total bubble energy available, while the second part of the design
process aims to release all the bubble energy available into one
bubble frequency. This is achieved by fully frequency locking the
bubble oscillation for the air released from the six airguns 146
which may require compact source geometry. The table below shows
how the outer dimensions of the source shrunk following the second
part of the design process outlined in FIG. 12:
TABLE-US-00004 Initial design Final design Source outer dimensions
0.9 .times. 0.8 .times. 3.0 0.9 .times. 0.8 .times. 1.5 in metres
Q.sub.eff <Q.sub.total 4500 10.sup.3 psi in.sup.3
Example 8
Clustering Airguns Charged with Different Firing Pressure
[0082] In this example, the airguns 146 illustrated in FIG. 13
provide a special cluster configuration. It is the result of
optimizing the low frequency output when only specific airguns are
available and with limited high pressure air supply capacity.
[0083] For this example, an assumption can be made that the high
pressure reservoir has a maximum output capacity of 1200 in.sup.3
at 2000 psi per shot and that only six 250 in.sup.3 airguns are
available to use in our source design. Additionally, the desired
optimization of low frequency output in this example is to maximize
the low frequency output.
[0084] To maximize the low frequency output the largest possible
bubble is created and this can be achieved by frequency locking as
many of the 250 in.sup.3 airguns as possible. However, in this
example we are limited by air supply capacity: the total potential
bubble energy available from the supply is 20001200=240010.sup.3
psiin.sup.3. Consequently, if one charges the airguns with 2000 psi
one can only fire four 250 in.sup.3 airguns before running out of
air supply (2000 psi250 in.sup.34=200010.sup.3 psiin.sup.3).
[0085] Therefore, to utilize the full air supply capacity, it is
better to charge all six 250 in.sup.3 airguns with 1600 psi, such
that the total bubble energy of the array is 1600 psi250
in.sup.36=240010.sup.3 psiin.sup.3. In this particular example,
however, three of the airguns (e.g. left side in FIG. 13) are fired
at 2000 psi and the other three (e.g. right side in FIG. 13) at
1200 psi, which gives the equivalent total bubble energy:
20002503+12002503=240010.sup.3 psiin.sup.3.
[0086] FIG. 16 shows a measured farfield spectrum of the resulting
source. (See FIG. 13 and the resulting source example described in
the preceding paragraph. For this example, FIG. 16 graphically
illustrates measured farfield spectrum of the source configuration
described in the preceding paragraph in which the source depth is 7
meters.) The dashed vertical line indicates the theoretical bubble
frequency for Q=240010.sup.3 psiin.sup.3 at the deployed source
depth (7 metres). The fundamental bubble frequency of the measured
spectrum coincides well with the theoretical prediction, which
demonstrates that the source 144 is utilizing the full air flow
capacity in the resulting bubble oscillation as desired.
Example 9
Source Array Wherein the Largest Bubble is One-Third of the Total
Source Volume
[0087] Example 9 is similar to Example 1 discussed above, but the
present example incorporates the effective bubble energy framework.
In Example 9, one aspect is release of the largest quantity of high
pressure gas possible into one location to maximize the very low
frequency output. There may be several factors limiting the largest
bubble in an array. For example, the total source volume may be
limited by the onboard compressor capacity and the seismic shot
interval. The total source volume also may be limited by the flow
capacity of the conduits (e.g., hoses) connecting the source and
the onboard compressor or onboard high pressure reservoir, or it
might be limited by the number of high pressure hoses the ship can
tow.
[0088] Similarly, the largest bubble in the source array might be
limited by how much of the total source volume can be released into
substantially one location. FIG. 5 may again be referenced as
depicting an embodiment of the present disclosure where the largest
bubble is limited by the flow capacity of the high pressure hoses
that connects the source to the vessel 60. As described in the
previous embodiment, vessel 60 tows a source array 62, which
includes the pair of substantially identical subarrays 64 disposed
about another subarray 66 (which includes the pair of single
airguns 67 disposed about cluster 68 in the in-line direction). The
cross-line spacing between subarrays 64 and 66 is, for example, 6
meters and the in-line spacing between each of the single airguns
67 and the cluster 68 is, for example, 6 meters. In the present
embodiment, each subarray 64, 66 is charged by a shipborne high
pressure reservoir via one high pressure hose, whose flow capacity
is approximately 2100 in.sup.3 at 2000 psi per shot. The subarrays
64, 66 are charged to the same pressure level, and the source array
62 may be further limited by how close one can place two hoses, and
consequently it may not be possible to frequency lock the bubbles
from different subarrays. Hence, the largest bubble is 2100
in.sup.3. The bubble frequency associated with 2100 in.sup.3 is
achieved by fully frequency locking six 350 in.sup.3 airgun
bubbles, while the bubble frequency associated with 1050 in.sup.3
is achieved by fully frequency locking two 525 in.sup.3 airgun
bubbles. The dashed lines indicate the regions with full frequency
locking. The interaction between the regions is negligible, and it
is also negligible between any region and any of the single airgun
bubbles.
[0089] The effective bubble energy of the subarrays 64 is
substantially 2000 psi2100 in.sup.3=420010.sup.3 psiin.sup.3, while
the subarray 66 has two distinct bubble frequencies: the
frequencies associated with bubble volumes of 1050 in.sup.3 and 525
in.sup.3. These volumes result in bubble frequencies that are 1/3
and 2/3 of an octave higher than the lowest bubble frequency. In
this example, the outer subarrays 64 have been optimized according
to the present disclosure, while the subarray 66 is used to fill-in
the bubble notch frequencies in order to flatten the spectrum in a
conventional manner. In this example, the effective bubble energy
of the largest bubble is approximately 33.3% of the total potential
bubble energy, i.e. 20002100=420010.sup.3 psiin.sup.3 out of a
total of 20006300=1260010.sup.3 psiin.sup.3.
Example 10
Source Array Wherein the Largest Bubble Equals the Total Source
Volume
[0090] Example 10 is similar to Example 2 discussed above, but the
present example incorporates the effective bubble energy framework.
Referring again to FIG. 6, this figure depicts a schematic view of
another type of source relative to that disclosed in Example 8,
wherein all of the released gas is frequency locked into one very
large airgun bubble. In FIG. 6, the source 70 comprises twenty-one
300 in.sup.3 airgun bubbles arranged on a hexagonal grid in three
layers. In this example, the airguns are again connected to the
plurality of high pressure hoses 72, which extend from vessel 74.
With this arrangement, the high pressure hoses 72 terminate at
substantially the same location, thus enabling the guns to be
positioned within full frequency locking distance. All twenty-one
airgun bubbles are fully frequency locked and oscillate with the
period associated with the combined volume, e.g. 6300 in.sup.3.
Thus, the volume of the largest effective bubble equals the total
source volume. Although a specific number of airguns with specific
bubble volumes are described in this example, it is to be
appreciated that such numbers and volumes may be altered while
still enabling full frequency locking of the array.
[0091] FIG. 7 compares the modeled spectra of a conventional source
and two of the new sources designed according to the present
invention. The firing pressure is 2000 psi for all three cases.
FIG. 7 compares the conventional source illustrated in FIG. 4
(dotted curve), in which the effective bubble energy of the largest
bubble is 15% of the total bubble energy of the array; the new
source illustrated in FIG. 5 (dashed curve), in which the effective
bubble energy of the largest bubble is approximately 33% of the
total bubble energy of the array; and the new source shown in FIG.
6 (solid curve), in which the effective bubble energy is 100% of
the total bubble energy of the array.
[0092] For the purposes of this embodiment, the comparison of FIG.
7 further demonstrates how the low frequency output increases with
the effective bubble energy as both the dashed and the solid curves
have significantly more low frequency output than the conventional
reference spectrum (dotted curve).
Example 11
Source Array Wherein the Largest Bubble Equals Half of the Total
Source Volume
[0093] Example 11 is similar to Example 3 discussed above, but the
present example incorporates the effective bubble energy framework.
In some embodiments, additional gas for tuning the source array by
creating other distinct bubble frequencies may be desired. The
flowchart of FIG. 12 shows how a source can be designed, or
re-designed, to take this into account. That is, an optimum low
frequency source may be designed, while maintaining some spectral
flatness given design restrictions imposed by the available
equipment.
[0094] In block 137 `Desired Ratio` of FIG. 12, the desired ratio
of the effective bubble energy of the largest bubble to the total
source bubble energy is determined. This ratio affects the
trade-off between maximizing the low frequency output and
flattening the spectrum by introducing additional bubble
frequencies to fill-in the spectral notches. In this example, the
desired effective bubble energy of the largest bubble is two-thirds
of the total source bubble energy available per shot.
[0095] In block 134 `Calculate Q.sub.effective` of FIG. 12, the
design procedure establishes the largest effective bubble energy
that may be practically achieved given the restrictions imposed by
the available equipment. For example, the total source bubble
energy per shot is limited by the flow capacity per high pressure
gas hose and by the number of hoses available. Referring to the
source layout of FIG. 9, for example, an implementation is
illustrated in which only two gas hoses 90, 92 from a high pressure
reservoir, e.g. the shipboard compressor, and a submerged source
array 94 are available. Each hose has a flow capacity of, for
example, 1680 in.sup.3 at 2000 psi per shot. Thus, in this example,
the desired effective energy of the largest bubble is
2000(1680+1680)2/3=20002240=448010.sup.3 psiin.sup.3. However, in
this example, the largest effective bubble energy is further
limited by how close the two strings can be positioned to avoid
tangling of the equipment while towing, so it is not possible to
frequency lock gas bubbles from different strings. Consequently,
the actual effective energy of the largest bubble may be
20001680=336010.sup.3 psiin.sup.3.
[0096] Referring again to FIG. 12, block 130 `Assembly`
contemplates design of an airgun cluster arrangement 96 (see FIG.
9) to achieve the largest bubble energy (i.e. the one that results
in the 20001680=336010.sup.3 psiin.sup.3 effective bubble energy)
which corresponds to the total bubble energy available from one gas
hose. In this example, the desired bubble frequency is achieved
with six 280 in.sup.3 airguns in close proximity.
[0097] Block 130 `Assembly` also can be used to design other bubble
frequencies in the array. For example, instead of maximizing the
low frequency output by duplicating the airgun arrangement
described above, another airgun subarray 98 may be arranged to use
the remaining gas to flatten the spectrum. In this example, three
additional bubble frequencies may be uniformly distributed, on a
linear frequency scale, between the first bubble frequency and its
first harmonic. The Rayleigh-Willis formula in Equation 1 gives the
effective bubble volume of these other bubble frequencies:
V.sub.2=1680/(1.25).sup.3.apprxeq.860 in.sup.3,
V.sub.3=1680/(1.50).sup.3.apprxeq.498 in.sup.3,
V.sub.4=1680/(1.75).sup.3.apprxeq.313 in.sup.3. All airguns may be
fired at 2000 psi. In this example, the second largest bubble
volume, V.sub.2, is created by a three gun cluster having two 250
in.sup.3 guns and one 360 in.sup.3 gun. Similarly, V.sub.3 is
created by a two gun cluster having two 250 in.sup.3 guns, and
V.sub.4 is a single airgun of 310 in.sup.3. The desired bubble
energy ratio for the four bubbles is: 20001680/(672010.sup.3)=0.5
for the largest bubble, 2000860/(672010.sup.3).apprxeq.0.26 for the
second bubble, 2000500/(672010.sup.3).apprxeq.0.15 for the third
bubble, and 2000310/(672010.sup.3).apprxeq.0.09 for the fourth
bubble. Referring again to FIG. 12, each of the frequency locked
bubbles can be designed via the second part of the flow chart by
inputting the respective bubble energy ratio in block 137 `Desired
ratio`.
[0098] Accordingly, the design of the layout in FIG. 9 achieves a
largest effective bubble energy that is 50% of the total bubble
energy of the source, while also achieving spectral flattening
using three additional bubble frequencies that are uniformly
distributed between the frequency of the largest bubble and its
first harmonic. The spectral flattening of this array is
illustrated in FIG. 10.
Example 12
Redesign of a Conventional Cluster Source
[0099] Example 12 is similar to Example 4 discussed above, but the
present example again incorporates the effective bubble energy
framework. In this example, useful methods are provided for
redesigning existing cluster arrays to optimize low frequency
output. FIG. 11A depicts the layout of a conventional cluster
source deployed in dual mode as described in U.S. Pat. No.
4,956,822. The prior art cluster source has been designed for
enhanced spectral flatness, i.e. high primary-to-bubble ratio, with
little regard for the very low frequency source output.
[0100] The value of the effective bubble energy, Q.sub.eff, can be
calculated using the formula in Equation 6 and inputting values for
air pressure (e.g., 2000 psi), source depth (e.g, 10 ft) and bubble
frequency (e.g. 1/196.5 ms.apprxeq.5.089 Hz).
[0101] Accordingly, use of these exemplary values leads to a
maximum effective bubble energy of only 189410.sup.3 psiin.sup.3,
i.e. 39% of the total bubble energy of the array
(20002400=480010.sup.3 psiin.sup.3). Although exemplary values were
used to define the maximum effective bubble volume of the
configuration of FIG. 11A, it is to be appreciated that this
definition can be used to quantify the effective bubble energy of
any prior art source.
[0102] According to the principles of the present disclosure, such
source can be redesigned to maximize the low frequency output while
using the same total amount of compressed air and maintaining some
spectral flatness. Assuming that the firing pressure is the same,
i.e. 2000 psi, the source depth is the same, i.e. 10 ft, and that
the total volume cannot exceed 2400 in.sup.3 and that there are no
other restrictions on how the total volume can be distributed, the
source can be redesigned to have two distinct bubble frequencies.
The first bubble frequency may be defined as low as possible and
the second bubble frequency may be designed as being half an octave
higher than the first bubble frequency, such that the second bubble
frequency will coincide with the bubble notch of the first bubble
frequency. This restriction can be expressed as
Q.sub.eff,max(1+2.sup.-3/2)=Q.sub.tot (3)
In other words, the effective bubble energy of the largest bubble
may be approximately 74% of the total bubble energy of the source.
The firing pressure in the present source embodiment may be similar
to that of previous embodiments (e.g. 2000 psi). Consequently, at
2000 psi, the first bubble may oscillate with a frequency
associated with 1773 in.sup.3 (about 74% of 2400) and the second
bubble may oscillate with a frequency associated with 627 in.sup.3
(about 26% of 2400). Similar to the other examples disclosed
herein, such bubble oscillations are obtained by fully frequency
locking multiple airgun bubbles in close proximity.
[0103] The redesigned low frequency source is depicted in FIG. 11B
as having a pair of cluster units 100, 102, including: a 1773
in.sup.3 bubble, which may be constructed from six 295.5 in.sup.3
guns, and a 627 in.sup.3 bubble, which may be constructed from two
313.5 in.sup.3 guns. The two cluster units are well separated such
that the interaction between the cluster units is negligible.
Redesigning clusters according to the principles disclosed herein
increases the effective bubble energy from 189410.sup.3 psiin.sup.3
to 20001773=354610.sup.3 psiin.sup.3, which at 10 ft depth and 2000
psi firing pressure corresponds to a bubble frequency of 5.1 and
4.1 Hz respectively. Accordingly, the bubble frequency has been
shifted by 0.3 octave by redesigning the cluster source layout.
[0104] As described above, sources and source arrays may be used,
arranged, and/or positioned to optimize low frequency output. For
example, the bubble size and/or pressures applied may be selected
individually or in combination to optimize low frequency output
from airgun source arrays. In some applications, the methodology
comprises deploying a plurality of air guns and activating at least
some of the airguns to generate an effective bubble energy as
described in the embodiments above. For example, the airguns may be
activated to generate an effective bubble energy of more than
400010.sup.3 psiin.sup.3. In other applications, at least some of
the airguns may be activated to generate multiple frequency locked
bubbles such that the largest effective bubble energy is greater
than 1000010.sup.3 psiin.sup.3. As described herein, the activating
also may comprise generating effective bubble energy in which the
largest bubble has effective bubble energy greater than
300010.sup.3 psiin.sup.3 and in which the largest bubble comprises
multiple frequency locked bubbles. In this example, the effective
bubble energy of the largest bubble is between 33% and 74% of the
total potential bubble energy fired at each shot. However, the
largest bubble effective bubble energy and the ratio of the largest
bubble effective bubble energy to the total potential bubble energy
may vary depending on the parameters of a specific application.
[0105] In similar applications, the methodology comprises providing
a plurality of air guns and identifying a largest effective bubble
energy for a marine source array. At least some of the airguns may
be arranged to achieve the largest effective bubble energy upon
activation of those airguns. However, the effective bubble energy
of at least some of the plurality of airguns may be optimized
according to other parameters. Additionally, the airguns may be
arranged in close proximity to one another and the airguns may be
activated to fully frequency lock the bubbles emitted by the
airguns. In any of these applications, the effective bubble energy
and the ratio of effective bubble energy to potential bubble energy
may be selected according to the needs/parameters of the seismic
application. In a variety of these examples, at least some of the
airguns may be activated to generate an effective bubble energy of
more than 400010.sup.3 psiin.sup.3 and/or those airguns may be
activated to generate multiple frequency locked bubbles such that
the largest effective bubble energy is greater than 1000010.sup.3
psiin.sup.3 as discussed above. Similarly, the activating also may
comprise generating effective bubble energy where the largest
bubble has effective bubble energy greater than, for example,
300010.sup.3 psiin.sup.3 and in which the largest bubble comprises
multiple frequency locked bubbles. By way of example, the effective
bubble energy of the largest bubble in these latter examples may
similarly be between 33% and 74% of the total potential bubble
energy fired at each shot. Again, however, these values are
provided as examples and the effective bubble energy values and
ratio values can change depending on the parameters of a given
seismic application.
[0106] Although specific embodiments of the invention have been
disclosed herein in some detail, this has been done solely for the
purposes of describing various features and aspects of the
invention, and is not intended to be limiting with respect to the
scope of the invention. For example, although many of the drawings
depict the use of towed source arrays, the teachings of the present
disclosure are also applicable to source designs for vertical
seismic profiling (VSP) surveys in which substantially stationary
source arrays may be substituted for towed source arrays. In VSP
applications, receivers can be deployed in the borehole with a
variety of methods and systems, including a wireline cable; a
downhole assembly, e.g. drill collars; permanent fixation to a side
of the borehole; or with other suitable techniques. It is therefore
contemplated that various substitutions, alterations, and/or
modifications, including but not limited to those implementation
variations which may have been suggested herein, may be made to the
disclosed embodiments without departing from the spirit and scope
of the invention as defined by the appended claims which
follow.
* * * * *