U.S. patent application number 10/412995 was filed with the patent office on 2004-10-14 for property prediction using residual stepwise regression.
Invention is credited to Brumbaugh, David L..
Application Number | 20040204858 10/412995 |
Document ID | / |
Family ID | 33097885 |
Filed Date | 2004-10-14 |
United States Patent
Application |
20040204858 |
Kind Code |
A1 |
Brumbaugh, David L. |
October 14, 2004 |
PROPERTY PREDICTION USING RESIDUAL STEPWISE REGRESSION
Abstract
A method for predicting reservoir properties at an unexplored
subterranean location based on known seismic attributes at the
unexplored subterranean location, as well as known reservoir
properties and seismic attributes at a plurality of explored
subterranean locations proximate to the unexplored subterranean
locations. The method uses residual stepwise regression to generate
a prediction equation capable of calculating predicted reservoir
properties based on multiple seismic attributes. The residual
stepwise regression involves using residual values from a previous
regression step to determine which seismic attribute will be
included in a subsequent regression step.
Inventors: |
Brumbaugh, David L.;
(Bartlesville, OK) |
Correspondence
Address: |
RICHMOND, HITCHCOCK,
FISH & DOLLAR
P.O. Box 2443
Bartlesville
OK
74005
US
|
Family ID: |
33097885 |
Appl. No.: |
10/412995 |
Filed: |
April 14, 2003 |
Current U.S.
Class: |
702/13 ;
702/14 |
Current CPC
Class: |
G01V 1/30 20130101 |
Class at
Publication: |
702/013 ;
702/014 |
International
Class: |
G01V 001/28 |
Claims
1. A method of predicting a reservoir property at an unexplored
subterranean location based on a seismic attribute pool generated
from a seismic survey and known reservoir properties at explored
subterranean locations, said seismic attribute pool including a
plurality of common seismic attributes for each explored and
unexplored location, said method comprising the steps of: (a)
performing a first regression of the known reservoir properties and
a first one of the common seismic attributes at the explored
locations, said regression yielding a first prediction equation for
calculating a first predicted reservoir property; (b) calculating
first residuals for the known reservoir properties and
corresponding first predicted reservoir properties generated with
the first prediction equation; (c) correlating the first residuals
with the common seismic attributes not used in the regression of
step (a); and (d) selecting the common seismic attribute with the
highest correlation from step (c) as a second one of the common
seismic attributes.
2. The method of claim 1; and (e) performing a second regression of
the known reservoir properties and the first one and second one of
the common seismic attributes at a plurality of the explored
locations, said second regression yielding a second prediction
equation for calculating a second predicted reservoir property.
3. The method of claim 2; and (f) determining a first correlation
value and a first prediction error for the first regression; and
(g) determining a second correlation value and a second prediction
error for the second regression.
4. The method of claim 3; and (h) comparing the second correlation
value and second prediction error with the first correlation value
and first prediction error to determine whether the second
prediction equation provides a more accurate property prediction
than the first prediction equation.
5. The method of claim 4; and (i) using the first prediction
equation to calculate the reservoir property at the unexplored
subterranean location if the second prediction equation does not
provide a more accurate property prediction than the first
prediction equation.
6. The method of claim 2; and (j) calculating second residuals for
the known reservoir properties and corresponding second predicted
reservoir properties generated with the second prediction
equation.
7. The method of claim 6; and (k) correlating the second residuals
with the common seismic attributes not used in the second
regression.
8. The method of claim 7; and (l) selecting the common seismic
attribute with the highest correlation from step (k) as a third one
of the seismic attributes.
9. The method of claim 8; and (m) performing a third regression of
the known reservoir properties and the first one, second one, and
third one of the common seismic attributes at a plurality of the
explored locations, said third regression yielding a third
prediction equation for calculating a third predicted reservoir
property.
10. The method of claim 1; and (n) prior to step (a), correlating
the known reservoir properties with each of the common seismic
attributes.
11. The method of claim 10; and (o) selecting the first one of the
common seismic attributes based on the correlation of step (n).
12. The method of claim 11, said first one of the common seismic
attributes having the best correlation from step (n).
13. The method of claim 1; and (p) selecting a common seismic
attribute different from the first one of the common seismic
attributes; and (q) repeating steps (a)-(d) using the common
seismic attribute selected in step (p) as the first one of the
common seismic attributes.
14. A stepwise regression method for predicting a reservoir
property at an unexplored subterranean location based on a seismic
attribute pool generated from a seismic survey and known reservoir
properties at explored subterranean locations, said seismic
attribute pool including a plurality of common seismic attributes
for each explored and unexplored location, said method comprising
the steps of: (a) selecting one of the common seismic attributes as
a current starting attribute and proceeding to step (b); (b) adding
the selected seismic attribute from the previous step to a
cumulative attribute set and proceeding to step (c); (c) performing
a regression of the known reservoir properties and the seismic
attribute or attributes in the cumulative attribute set, to thereby
yield a current prediction equation for calculating a predicted
reservoir property and proceeding to step (d); (d) calculating a
current correlation value, a current prediction error, and current
residuals for the known reservoir properties and corresponding
predicted reservoir properties generated with the current
prediction equation and proceeding to step (e); (e) proceeding to
step (g) if the selected seismic attribute from step (b) is the
starting seismic attribute, otherwise comparing the current
correlation value and prediction error to a prior correlation value
and prediction error and proceeding to step (f); (f) proceeding to
step 0) if the current correlation value or prediction error is
worse than the prior correlation value and prediction error,
otherwise proceeding to step (g); (g) correlating the residuals
from step (d) with each of the common seismic attributes not
currently in the cumulative attribute data set and proceeding to
step (h); (h) designating the current prediction equation,
correlation value, and prediction error as a prior prediction
equation, correlation value, and prediction error and proceeding to
step (i); (i) selecting the seismic attribute with the highest
correlation from step (g) as a next seismic attribute and returning
to step (b); and (j) designating the prior prediction equation as
an optimum prediction equation for the current starting
attribute.
15. The stepwise regression method of claim 14; and (k) subsequent
to step (j), designating one of the common seismic attributes not
selected in step (a) as the current starting attribute and
proceeding to step (b).
16. The stepwise regression method of claim 15, step (a) including
the substep of: (a1) correlating the known reservoir properties
with the common seismic attributes.
17. The stepwise regression method of claim 16, step (a) including
the substep of: (a2) designating several of the common seismic
attributes as possible starting attributes based on the correlation
of step (a1).
18. The stepwise regression method of claim 17, step (a) including
the substep of: (a3) selecting the possible starting attribute with
the highest correlation from step (a1) as the current starting
attribute.
19. The stepwise regression method of claim 18, step (k) including
the substep of: (k1) selecting the possible starting attribute with
the second highest correlation from step (a) as the current
starting attribute.
20. A method of predicting a reservoir property at an unexplored
subterranean location based on a seismic attribute pool generated
from a seismic survey and known reservoir properties at explored
subterranean locations, said seismic attribute pool including a
plurality of common seismic attributes for each explored and
unexplored location, said method comprising the steps of: (a)
correlating the known reservoir properties with the common seismic
attributes to yield a correlation value that is proportional to the
degree of correlation between the known reservoir properties and
the common seismic attributes; (b) selecting several of the common
seismic attributes with the highest correlation values as possible
starting attributes; (c) determining a prediction equation for each
possible starting attribute, each of said prediction equations
having a correlation value and prediction error associated
therewith; and (d) selecting an optimum prediction equation from
the prediction equations determined in step (c) based on the
correlation value and prediction error associated with the
prediction equations determined in step (c).
21. The method of claim 20, step (b) including selecting 3 to 6 of
the common seismic attributes with the highest correlation values
as possible starting attributes.
22. The method of claim 20, said prediction equation being operable
to calculate a predicted reservoir property based on a plurality of
the common seismic attributes.
23. The method of claim 22, step (c) including using stepwise
residual regression to determine the prediction equation.
24. The method of claim 23, step (c) including calculating
residuals for each regression of the stepwise regression, step (c)
including correlating the residuals with the common seismic
attributes not used in a previous regression.
25. The method of claim 24, step (c) including using the seismic
attribute that best correlates with the residuals as the next
seismic attribute to be used in a subsequent regression.
26. The method of claim 23, step (d) including comparing the
correlation value and prediction error of a prior regression with
the correlation value and prediction error of a current regression
to determine whether to continue with another regression.
27. The method of claim 26, step (d) including designating the
current regression as a last regression when the correlation value
or prediction error of the current regression do not improve upon
the correlation value and prediction error of the prior regression,
said optimum prediction equation being generated from the
regression conducted just prior to the last regression.
28. A method comprising the steps of: (a) extracting actual well
data from a plurality of subterranean well locations, said well
data including a target reservoir property for each well location;
(b) generating seismic data from a seismic survey of a subterranean
region of interest that includes the subterranean well locations,
said seismic data including a plurality of seismic attributes for
each well location; (c) selecting an unexplored location in the
subterranean region of interest, said unexplored location being
spaced from the well locations; (d) correlating the target
reservoir properties with the seismic attributes to yield a
correlation value that is proportional to the degree of correlation
between the target reservoir properties and the seismic attributes;
(e) selecting several of the seismic attributes with the highest
correlation values as possible starting attributes; (f) determining
a prediction equation for each possible starting attribute, each of
said prediction equations having a correlation value and prediction
error associated therewith; (g) selecting an optimum prediction
equation from the prediction equations determined in step (f) based
on the correlation value and prediction error of the prediction
equations; and (h) using the optimum prediction equation to
calculate a predicted reservoir property at the unexplored location
based on a plurality of the seismic attributes at the unexplored
location.
29. The method of claim 28, step (f) including using stepwise
residual regression to determine the prediction equation for each
starting attribute.
30. The method of claim 29, said stepwise regression starting with
a regression of one of the possible starting attributes and then
adding additional seismic attributes for subsequent
regressions.
31. The method of claim 30, step (f) including selecting the
additional seismic attributes based on a correlation of a previous
regression's residuals and the seismic attributes not used in the
previous regression.
32. A method of determining the relative significance of multiple
seismic attributes used to predict a reservoir property, said
method comprising the steps of: (a) normalizing each of the seismic
attributes; (b) generating a reservoir property prediction equation
via regression of the multiple seismic attributes and actual
reservoir properties, said prediction equation being operable to
calculate a predicted reservoir property based on the value of the
seismic attributes plugged into the prediction equation, said
prediction equation including a coefficient associated with each
normalized seismic attribute; (c) dividing the coefficient for each
normalized seismic attribute by the sum of the absolute values of
all the coefficients used in the prediction equation.
33. The method of claim 32, step (a) including calculating a mean
value and a standard deviation for each seismic attribute.
34. The method of claim 33, step (a) including subtracting the mean
value for each seismic attribute from each sample for that seismic
attribute to obtain a mean difference.
35. The method of claim 34, step (a) including dividing each mean
difference for each seismic attribute by the corresponding standard
deviation.
36. A method of determining the relative significance of multiple
seismic attributes used as variables in a reservoir property
prediction equation, said prediction equation being operable to
calculate a predicted reservoir property based on the values of the
seismic attributes plugged into the prediction equation, said
prediction equation including a coefficient associated with each
seismic attribute, said method comprising the steps of: (a)
determining a standard deviation for each seismic attribute used in
the prediction equation; (b) multiplying the standard deviation for
each seismic attribute by the coefficient for that respective
seismic attribute to yield a modified coefficient for each seismic
attribute; and (c) dividing the modified coefficient for each
seismic attribute by the sum of the absolute values of all the
modified coefficients for all the seismic attributes used in the
prediction equation.
37. A computer program stored on a computer-readable medium for
directing operation of a computer to predict a reservoir property
at an unexplored subterranean location based on a seismic attribute
pool generated from a seismic survey and known reservoir properties
at explored subterranean locations said seismic attribute pool
including a plurality of common seismic attributes for each
explored and unexplored location, said computer program comprising:
(a) a code segment operable to perform a regression of the known
reservoir properties and a first one of the common seismic
attributes at the explored locations said regression yielding a
prediction equation for calculating a predicted reservoir property;
(b) a code segment operable to calculate residuals for the known
reservoir properties and corresponding predicted reservoir
properties generated with the prediction equation; (c) a code
segment operable to correlate the residuals with the common seismic
attributes not used in the regression; and (d) a code segment
operable to select the common seismic attribute with the highest
correlation from the correlation step as a second one of the common
seismic attributes.
38. A computer program stored on a computer-readable medium for
directing operation of a computer to predict a reservoir property
at an unexplored subterranean location based on a seismic attribute
pool generated from a seismic survey and known reservoir properties
at explored subterranean locations, said seismic attribute pool
including a plurality of common seismic attributes for each
explored and unexplored location, said computer program comprising:
(a) a code segment operable to select one of the common seismic
attributes as a current starting attribute; (b) a code segment
operable to add the seismic attribute selected by code segment (a)
to a cumulative attribute set; (c) a code segment operable to
perform a regression of the known reservoir properties and the
seismic attribute or attributes in the cumulative attribute set to
thereby yield a current prediction equation for calculating a
predicted reservoir; (d) a code segment for calculating a current
correlation value, a current prediction error, and current
residuals for the known reservoir properties and corresponding
predicted reservoir properties generated with the current
prediction equation: (e) a code segment operable to initiate code
segment (g) if the selected seismic attribute employed in code
segment (b) is the starting seismic attribute, otherwise to compare
the current correlation value and prediction error to a prior
correlation value and prediction error; (f) a code segment operable
to initiate code segment (i) if the current correlation value or
prediction error is worse than the prior correlation value and
prediction error; (g) a code segment operable to correlate the
residuals calculated by code segment (d) with each of the common
seismic attributes not currently in the cumulative attribute data
set; (h) a code segment operable to designate the current
prediction equation, correlation value, and prediction error as a
prior prediction equation, correlation value, and prediction error:
(i) a code segment operable to select the seismic attribute with
the highest correlation generated by code segment (g) as a next
seismic attribute and initiate code segment (b); and (j) a code
segment operable to designate the prior prediction equation as an
optimum prediction equation for the current starting attribute.
39. A computer program stored on a computer-readable medium for
directing operation of a computer to predict a reservoir property
at an unexplored subterranean location based on a seismic attribute
pool generated from a seismic survey and known reservoir properties
at explored subterranean locations, said seismic attribute pool
including a plurality of common seismic attributes for each
explored and unexplored location, said computer program comprising:
(a) a code segment operable to correlate the known reservoir
properties with the common seismic attributes to yield a
correlation value that is proportional to the degree of correlation
between the known reservoir properties and the common seismic
attributes; (b) a code segment operable to select several of the
common seismic attributes with the highest correlation values as
possible starting attributes; (c) a code segment operable to
determine a prediction equation for each possible starting
attribute, each of said prediction equations having a correlation
value and prediction error associated therewith, and (d) a code
segment operable to select an optimum prediction equation from the
prediction equations determined by code segment (c) based on the
correlation value and prediction error associated with the
prediction equations determined by code segment (c).
40. (Canceled)
41. A computer program stored on a computer-readable medium for
directing operation of a computer to determine the relative
significance of multiple seismic attributes used to predict a
reservoir property, said computer program comprising: (a) a code
segment operable to normalize each of the seismic attributes; (b) a
code segment operable to generate a reservoir property prediction
equation via regression of the multiple seismic attributes and
actual reservoir properties, said prediction equation being
operable to calculate a predicted reservoir property based on the
value of the seismic attributes plugged into the prediction
equation, said prediction equation including a coefficient
associated with each normalized seismic attribute; (c) a code
segment for dividing the coefficient for each normalized seismic
attribute by the sum of the absolute values of all the coefficients
used in the prediction equation.
42. A computer program stored on a computer-readable medium for
directing operation of a computer to determine the relative
significance of multiple seismic attributes used as variables in a
reservoir property prediction equation, said prediction equation
being operable to calculate a predicted reservoir property based on
the values of the seismic attributes plugged into the prediction
equation, said prediction equation including a coefficient
associated with each seismic attribute, said computer program
comprising: (a) a code segment operable to determine a standard
deviation for each seismic attribute used in the prediction
equation; (b) a code segment operable to multiply the standard
deviation for each seismic attribute by the coefficient for that
respective seismic attribute to yield a modified coefficient for
each seismic attribute; and (c) a code segment operable to divide
the modified coefficient for each seismic attribute by the sum of
the absolute values of all the modified coefficients for all the
seismic attributes used in the prediction equation.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates generally to methods for using
seismic data to predict reservoir properties at unexplored
subterranean locations. In another aspect, the invention relates to
a method for predicting reservoir properties at unexplored
subterranean locations based on known reservoir properties at
explored subterranean locations and seismic attributes generated
from a seismic survey or surveys encompassing both the explored and
unexplored subterranean locations.
[0003] 2. Description of the Prior Art
[0004] Seismic surveys gather important information about the
subsurface of the earth. Data gathered from a seismic survey is
typically manipulated to yield a pool of unique seismic attributes.
Seismic attributes can be defined as analytical measurements of the
seismic expression of geologic conditions and can take a variety of
forms. Frequently, seismic attributes are measurements of a seismic
waveform's amplitude, length, area, symmetry, frequency, or phase.
In addition, seismic attributes maybe discrete classifications
(e.g., pattern assignments or facies), structural (time or depth
horizons, isochrons, or isopachs), and spatial coordinates (e.g.,
X-coordinate and Y-coordinate). Each seismic attribute responds to
particular reservoir conditions in a unique manner. Thus, seismic
attributes can be used to predict reservoir properties (e.g.,
porosity, thickness, or fluid type) of the subterranean formation.
By using multiple seismic attributes for reservoir property
prediction, noise contamination may be reduced and accuracy of the
prediction may be enhanced.
[0005] A number of conventional methods exist for using multiple
seismic attributes to predict reservoir properties of a
subterranean formation. When known reservoir properties (typically
from well logs) are available at locations within the surveyed
region, those known reservoir properties can be used to help
"calibrate" the seismic attributes. A variety of methods exist for
calibrating seismic attributes with known reservoir properties in
an effort to more accurately predict reservoir properties at
unexplored locations. One conventional calibration method performs
calculations for all possible combinations of the seismic
attributes. Such an exhaustive approach is very computationally
intensive and can require long periods of time and expensive
computers to achieve. Another conventional calibration method
involves selecting a pre-identified group of the seismic attributes
to use in the calculation. However, one can never be sure that the
pre-selected seismic attributes provide the best solution. Still
another conventional calibration method progressively adds seismic
attributes to a predetermined starting attribute. This method,
however, can result in a local answer which is not the optimal
global solution.
[0006] Typically, the above-described conventional techniques each
yield a multi-variable prediction equation that can be employed to
calculate a predicted reservoir property at a certain unexplored
location based on multiple seismic attributes at that location.
However, there is currently no procedure for quantitatively
determining the relative contribution of each seismic attribute
used in the prediction equation. Such a procedure for
quantitatively determining the predictive significance of each
seismic attribute would be helpful for selecting which seismic
attributes to extract from seismic survey data for future property
predictions.
OBJECTS AND SUMMARY OF THE INVENTION
[0007] It is therefore an object of the present invention to
provide a computationally efficient method of predicting reservoir
properties using multiple seismic attributes.
[0008] Another object of the present invention is to provide a more
accurate method of predicting reservoir properties using multiple
seismic attributes that avoids providing a local solution.
[0009] Still another object of the present invention is to provide
a quantitative method of determining the relative significance of
individual attributes used as variables in multi-variable
prediction equations.
[0010] It should be understood that the above-listed objects are
only exemplary, and not all the objects listed above need be
accomplished by the invention described and claimed herein.
[0011] In one embodiment of the present invention, there is
provided a method of predicting a reservoir property at an
unexplored subterranean location based on a seismic attribute pool
generated from a seismic survey and known reservoir properties at
explored subterranean locations. The seismic attribute pool
includes a plurality of common seismic attributes for each explored
and unexplored location. The property prediction method comprises
the steps of: (a) performing a first regression of the known
reservoir properties and a first one of the common seismic
attributes at the explored locations, with the regression yielding
a first prediction equation for calculating a first predicted
reservoir property; (b) calculating first residuals for the known
reservoir properties and corresponding first predicted reservoir
properties generated with the first prediction equation; (c)
correlating the first residuals with the common seismic attributes
not used in the regression of step (a); and (d) selecting the
common seismic attribute with the highest correlation from step (c)
as a second one of the common seismic attributes.
[0012] In another embodiment of the present invention, there is
provided a stepwise regression method for predicting a reservoir
property at an unexplored subterranean location based on a seismic
attribute pool generated from a seismic survey and known reservoir
properties at explored subterranean locations. The seismic
attribute pool includes a plurality of common seismic attributes
for each explored and unexplored location. The stepwise cumulative
regression method comprises the steps of: (a) selecting one of the
common seismic attributes as a current starting attribute and
proceeding to step (b); (b) adding the selected seismic attribute
from the previous step to a cumulative attribute set and proceeding
to step (c); (c) performing a regression of the known reservoir
properties and the seismic attribute or attributes in the
cumulative attribute set, to thereby yield a current prediction
equation for calculating a predicted reservoir property and
proceeding to step (d); (d) calculating a current correlation
value, a current prediction error and current residuals for the
known reservoir properties and corresponding predicted reservoir
properties generated with the current prediction equation and
proceeding to step (e); (e) proceeding to step (g) if the selected
seismic attribute from step (b) is the starting seismic attribute,
otherwise comparing the current correlation value and prediction
error to a prior correlation value and prediction error and
proceeding to step (f); (f) proceeding to step (j) if the current
correlation value or prediction error is worse than the prior
correlation value and prediction error, otherwise proceeding to
step (g); (g) correlating the residuals from step (d) with each of
the common seismic attributes not currently in the cumulative
attribute data set and proceeding to step (h); (h) designating the
current prediction equation, correlation value, and prediction
error as a prior prediction equation, correlation value, and
prediction error and proceeding to step (i); (i) selecting the
seismic attribute with the highest correlation from step (g) as a
next seismic attribute and returning to step (b); and (j)
designating the prior prediction equation as an optimum prediction
equation for the current starting attribute.
[0013] In still another embodiment of the present invention, there
is provided a method of predicting a reservoir property at an
unexplored subterranean location based on a seismic attribute pool
generated from a seismic survey and known reservoir properties at
explored subterranean locations. The seismic attribute pool
includes a plurality of common seismic attributes for each explored
and unexplored location. The prediction method comprises the steps
of: (a) correlating the known reservoir properties with the common
seismic attributes to yield a correlation value that is
proportional to the degree of correlation between the known
reservoir properties and the common seismic attributes; (b)
selecting several of the common seismic attributes with the highest
correlation values as possible starting attributes; (c) determining
a prediction equation for each possible starting attribute, each of
said prediction equations having a correlation value and prediction
error associated therewith; and (d) selecting an optimum prediction
equation from the prediction equations determined in step (c) based
on the correlation value and prediction error of the prediction
equations determined in step (c).
[0014] In yet another embodiment of the present invention, there is
provided a method comprising the steps of: (a) extracting actual
well data from a plurality of subterranean well locations, the well
data including a target reservoir property for each well location;
(b) generating seismic data from a seismic survey of a subterranean
region of interest that includes the subterranean well locations,
with the seismic data including a plurality of seismic attributes
for each well location; (c) selecting an unexplored location in the
subterranean region of interest, with the unexplored location being
spaced from the well locations; (d) correlating the target
reservoir properties with the seismic attributes to yield a
correlation value that is proportional to the degree of correlation
between the target reservoir properties and the seismic attributes;
(e) selecting several of the seismic attributes with the highest
correlation values as possible starting attributes; (f) determining
a prediction equation for each possible starting attribute, each of
the prediction equations having a correlation value and prediction
error associated therewith; and (g) selecting an optimum prediction
equation from the prediction equations determined in step (f) based
on the correlation value and prediction error of the prediction
equations; and (h) using the optimum prediction equation to
calculate a predicted reservoir property at the unexplored location
based on the seismic attributes at the unexplored location.
[0015] In a further embodiment of the present invention, there is
provided a method of determining the relative significance of
multiple seismic attributes used to predict a reservoir property.
The method comprises the steps of: (a) normalizing each of the
seismic attributes; (b) generating a reservoir property prediction
equation via regression of the multiple seismic attributes and
actual reservoir properties, the prediction equation being operable
to calculate a predicted reservoir property based on the value of
the seismic attributes plugged into the prediction equation, the
prediction equation including a coefficient associated with each
normalized seismic attribute; and (c) dividing the coefficient for
each normalized seismic attribute by the sum of the absolute values
of all the coefficients used in the prediction equation.
[0016] In a still further embodiment of the present invention,
there is provided a method of determining the relative significance
of multiple seismic attributes used as variables in a reservoir
property prediction equation. The prediction equation is operable
to calculate a predicted reservoir property based on the values of
the seismic attributes plugged into the prediction equation. The
prediction equation includes a coefficient associated with each
seismic attribute. The method comprises the steps of: (a)
determining a standard deviation for each seismic attribute used in
the prediction equation; (b) multiplying the standard deviation for
each seismic attribute by the coefficient for that respective
seismic attribute to yield a modified coefficient for each seismic
attribute; and (c) dividing the modified coefficient for each
seismic attribute by the sum of the absolute values of all the
modified coefficients for all the seismic attributes used in the
prediction equation.
BRIEF DESCRIPTION OF THE DRAWING FIGURES
[0017] A preferred embodiment of the present invention is described
in detail below with reference to the attached drawing figures,
wherein:
[0018] FIG. 1 is a simplified isometric view of a subterranean
region of interest, particularly illustrating a plurality of
wellbores extending downwardly to a reservoir in the subterranean
formation;
[0019] FIG. 2 is the first half of a flow chart depicting steps
involved in the property prediction method of the present
invention;
[0020] FIG. 3 is the second half of the property prediction flow
chart of FIG. 2;
[0021] FIG. 4a is a graphical illustration of the manner in which a
first one of the seismic attributes is correlated with the known
reservoir properties to yield a correlation coefficient,
particularly illustrating data for a first seismic attribute having
a correlation coefficient of 0.85;
[0022] FIG. 4b is a graphical illustration similar to that of FIG.
4a, particularly illustrating data for a second seismic attribute
having a correlation coefficient of 0.5;
[0023] FIG. 5a is a graphical illustration of the initial
regression step of the present invention, particularly illustrating
the prediction equation, correlation coefficient, prediction error,
and residuals associated with the regression;
[0024] FIG. 5b is a graphical illustration of the residual
correlation step of the present invention, particularly
illustrating that each seismic attribute not used in a previous
regression is correlated with the residual from the previous
regression to thereby determine which seismic attribute should be
selected for the next regression step; and
[0025] FIG. 5c is a graphical illustration of a subsequent
regression step employing more than one seismic attribute in the
regression, with the seismic attribute selected from the residual
correlation being included in such subsequent regression step.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
[0026] Referring initially to FIG. 1, a simplified oil field is
shown as including a plurality of wells A-E. Each well A-E extends
downwardly into a subterranean formation 10 and taps into a
reservoir 12 at explored subterranean locations a-e. Wells A-E can
be any drilling, testing, or production facility which has
penetrated subterranean formation 10 to thereby allow for actual
measurements or physical samples of reservoir 12 to be extracted at
explored subterranean locations a-e. Typically, the known reservoir
properties at explored locations a-e are generated from
conventional well log data. The known reservoir properties from
explored locations a-e can be any of a variety of reservoir
properties such as, for example, porosity, thickness, or fluid
type.
[0027] In addition to the data gathered from wells A-E, the present
invention requires that one or more seismic surveys be conducted
for subterranean formation 10 and reservoir 12. The seismic survey
can be conducted in accordance with conventional reflection seismic
survey procedures. The data from the seismic survey is manipulated
to yield a pool of unique seismic attributes. Thus, each explored
location a-e has at least one known reservoir property and a
plurality of unique seismic attributes associated therewith. The
seismic survey also covers an unexplored subterranean location x in
reservoir 12. Thus, the seismic attribute pool should also include
a plurality of unique seismic attributes associated with unexplored
location x. The present invention involves a residual stepwise
regression method that can be used to predict a reservoir property
at unexplored location x based upon the known reservoir properties
at explored locations a-e, the seismic attributes at explored
locations a-e, and the seismic attributes at unexplored location
x.
[0028] Referring to FIG. 2, in accordance with the present
invention, known reservoir property data 20 (which can include
reservoir properties from explored locations a-e in FIG. 1) and
seismic attribute pool data 22 (which can include a plurality of
common seismic attributes from explored locations a-e and
unexplored location x in FIG. 1) are correlated in step 24. In
correlation step 24, each seismic attribute at each explored
location is correlated with the known reservoir property at each
explored location to thereby yield a correlation coefficient. The
calculation of a correlation coefficient is a common procedure
known to those skilled in the art. A correlation coefficient is
typically a number between -1 and 1 which measures the degree to
which two variables are linearly related. If there is a perfect
linear relationship with positive slope between the two variables,
a correlation coefficient of 1 results. If there is a perfect
linear relationship with negative slope between the two variables,
a correlation coefficient of -1 results. If there is absolutely no
linear relationship between the two variables, a correlation
coefficient of 0 results. One common method for calculating the
correlation coefficient is known as the Pearson's Product Moment
method. The Pearson's Product Moment correlation coefficient is a
measure of the linear association between two variables that have
been measured on interval or ratio scales, such as the relationship
between a person's height in inches and weight in pounds. However,
the Pearson's Product Moment correlation coefficient can be
misleadingly small when there is a relationship between the
variables, but it is a non-linear one. Another common method for
calculating the correlation coefficient is known as the Spearman
Rank method. The Spearman Rank correlation coefficient is usually
calculated on occasions when it is not convenient, economic, or
even possible to give actual values to variables, but only to
assign a rank order to instances of each variable. The Spearman
Rank correlation coefficient may be a better indicator that a
relationship exists between two variables when the relationship is
non-linear. Various other methods suitable for calculating the
correlation coefficient in step 24 (FIG. 2) are well known in the
art.
[0029] FIGS. 4a and 4b provide a simplified graphical illustration
of correlation step 24 (FIG. 2). FIG. 4a shows the correlation of a
first seismic attribute (Seismic Attribute #1) and a known
reservoir property at 15 explored subterranean locations. Each dot
on the scatter plots of FIGS. 4a and 4b represents the seismic
attribute and reservoir property at a particular explored
subterranean location. For example, Seismic Attribute # 1 and the
reservoir property for explored subterranean location a (FIG. 1) is
depicted in FIG. 4a as having coordinates (SA.sub.1,a,RP.sub.a).
FIG. 4a shows that Seismic Attribute #1 has a correlation
coefficient of 0.85, while FIG. 4b shows that Seismic Attribute #2
has a correlation coefficient of 0.5. Although FIGS. 4a and 4b only
show correlation coefficients being calculated for Seismic
Attributes #1 and #2, correlation step 24 in FIG. 2 preferably
includes the calculation of a correlation coefficient for each of
seismic attributes in seismic attribute pool 22.
[0030] Referring again to FIG. 2, after each of the seismic
attributes has been correlated with the known reservoir properties
in correlation step 24, "X" number of the seismic attributes with
the highest correlation coefficients are selected as possible
starting attributes in starting attribute selection step 26.
Preferably, X equals 3-6, so that the seismic attributes with the
3-6 highest correlation coefficients are selected in step 26, with
Possible Starting Attribute #1 having the highest correlation
coefficient, Possible Starting Attribute #2 having the second
highest correlation coefficient, Possible Starting Attribute #3
having the third highest correlation coefficient, and so on. In
step 28, "Y" is set equal to 1. Y is used in FIGS. 2 and 3 to
identify which starting attribute is under consideration. In step
30, Possible Starting Attribute #Y is selected as the starting
attribute. So for the initial starting attribute Y is equal to 1,
while for subsequent starting attributes Y can be any number (other
than one) up to X.
[0031] In step 32, the seismic attribute selected in the previous
step is written to cumulative attribute set Y 34. In the initial
pass through the residual stepwise regression method outlined in
steps 32-52 (FIGS. 2 and 3), cumulative attribute set Y 34 contains
only the starting attribute Y. However, as other attributes are
selected for consideration in the stepwise regression, these
attributes are cumulatively added to attribute set Y 34 in a manner
discussed in detail below. Each starting attribute will have its
own unique cumulative attribute set Y 34. For example, Cumulative
Attribute Set #1 will contain only the seismic attributes used in
the residual stepwise regression associated with Starting Attribute
#1, Cumulative Attribute Set #2 will contain only the seismic
attributes used in the residual stepwise regression associated with
Starting Attribute #2, and so on. After the selected attribute has
been written to cumulative attribute set Y 34 in step 32, a
regression step 36 is performed.
[0032] In step 36, a regression of known reservoir properties 20
with the seismic attribute(s) in cumulative attribute set Y 34 is
conducted. This regression yields a prediction equation that can be
used to calculate a predicted reservoir property based on a given
seismic attribute or attributes. FIG. 5a graphically illustrates
regression step 36 (FIG. 2) for the initial regression with only
one seismic attribute (i.e., Starting Attribute #1) present in
cumulative attribute set Y 34. FIG. 5a shows the prediction
equation expressed as follows: RP=m.sub.1(SA.sub.1)+b.sub.1,
wherein RP is the predicted reservoir property, m, is a first
coefficient, SA, is a first seismic attribute, and b.sub.1 is a
first constant. Thus, the initial regression step utilizing only
one seismic attribute results in a single-variable prediction
equation. Although the prediction equation expressed in FIG. 5a is
a linear equation, it is entirely within the ambit of the present
invention for regression step 36 (FIG. 2) to be a non-linear
regression yielding a non-linear prediction equation.
[0033] Referring again to FIG. 2, in step 38, the prediction
equation is used to determine predicted reservoir properties. As
shown in FIG. 5a, the predicted reservoir properties lie along the
prediction line defined by the prediction equation. In step 40
(FIG. 2), the correlation value (e.g., correlation coefficient),
prediction error, and residual of the data associated with the
prediction equation generated in step 36 are determined. The
correlation value determined in step 40 can simply be the
correlation coefficient for the seismic attributes in cumulative
attribute set Y 34 and the known reservoir properties. FIG. 5a
shows that the data used for the initial regression step has a
correlation coefficient (CC) of 0.85. As shown in FIG. 5a, the
prediction error can be the maximum difference between the actual
reservoir property and the predicted reservoir property determined
in step 38. Alternatively, the prediction error can be the average
difference between the actual reservoir property and the predicted
reservoir property determined in step 38. FIG. 5a shows a maximum
prediction error (PE) for the initial regression step of 10. FIG.
5a also shows that the residual calculated in step 40 is simply the
difference between each known reservoir property and the
corresponding predicted reservoir property. Thus, each data point
on the scatter plot of FIG. 5a has a unique residual value
associated therewith, while the entire scatter plot of FIG. 5a has
only one prediction error and correlation value associated
therewith.
[0034] Referring now to FIG. 3, in step 42, a determination is made
as to whether cumulative attribute set Y 34 (FIG. 2) contains only
the starting attribute Y. If cumulative attribute set Y 34 contains
only starting attribute Y, step 44 writes the correlation value
(from step 40), prediction error (from step 40), and associated
prediction equation (from step 36) to non-cumulative data set 46.
In step 50 (FIG. 3), the residuals calculated in step 40 are
correlated with each attribute in seismic attribute pool 22, except
for seismic attributes already written to cumulative attribute set
Y 34. FIG. 5b provides a simplified graphical illustration of the
correlation of one seismic attribute (Z) with the residuals from
FIG. 5a. In step 52 (FIG. 3), the seismic attribute with the best
correlation in step 50 is selected as the next seismic attribute.
Thus, the correlation of the residual with the seismic attributes
not already in the cumulative attribute data set is used to select
which of the seismic attributes will be added to the next iteration
of the stepwise regression. Therefore, as used herein, the term
"residual stepwise regression" shall denote a stepwise regression
method wherein the next variable to be used in the next regression
step is selected based on the residual from the previous regression
step.
[0035] Referring to FIGS. 2 and 3, once the next seismic attribute
has been selected in step 52 (FIG. 3), the selected seismic
attribute is written to cumulative attribute set Y 34 (FIG. 2) in
step 32 (FIG. 2). Steps 36, 38, and 40 (FIG. 2) are then repeated
for cumulative attribute set Y 34, which now contains more than one
seismic attribute. FIG. 5c provides a simplified graphical
illustration of regression step 36 (FIG. 2) utilizing two seismic
attributes (e.g., Seismic Attributes #1 and #4). FIG. 5c makes the
assumption that Seismic Attribute #4 had the highest correlation
with the residual in step 50 (FIG. 3) and was, therefore, added to
cumulative attribute set Y 34. Thus, the prediction equation for
the multi-variable regression performed in step 36 (FIG. 2)
includes more than one seismic attribute variable. An example of
such a multi-variable prediction equation is illustrated in FIG. 5c
as follows: RP=m.sub.1(SA.sub.1)+m.sub.4(SA.sub.4)+b.sub.2. FIG. 5c
also shows that the correlation coefficient (CC) and prediction
error (PE) associated with the second regression step are 0.90 and
8, respectively.
[0036] Referring again to FIG. 3, when cumulative attribution set Y
34 (FIG. 2) contains an attribute other than just the starting
attribute, the method of the present invention proceeds from step
42 to comparison step 54. In step 54, the current correlation value
and prediction error determined in steps 38 and 40 (FIG. 2) are
compared with the prior correlation value and prediction error
written to non-cumulative data set 46 (FIG. 3) in the previous
iteration of the stepwise regression. In step 56, the method asks
whether the current correlation value and prediction error are
better than the prior correlation value and prediction error.
Typically, a "better" correlation value is represented by a
correlation coefficient having a higher absolute value than the
previous correlation coefficient, while a "better" prediction error
is a prediction error having a smaller value than the previous
prediction error. If both the current correlation value and
prediction error are better than the prior correlation value and
prediction error, the method proceeds from step 56 to step 44 where
the current correlation value, prediction error, and associated
prediction equation are written to non-cumulative data set 46,
thereby replacing the previous data written to data set 46. If the
current correlation value is worse than the prior correlation value
or the current prediction error is worse than the prior prediction
error, step 58 writes the prior correlation value, prediction
error, and associated prediction equation for starting attribute Y
to data set 60 and proceeds to step 62. Thus, the inventive method
includes a stepwise regression that continues to add seismic
attributes to the analysis until no improvement is provided by the
inclusion of more seismic attributes in the regression.
[0037] In step 62 (FIG. 3), the inventive method asks whether Y is
equal to X. If Y is equal to X, this means that all of the possible
starting attributes (selected in step 26 of FIG. 2) have been
addressed in the residual stepwise regression of steps 32-56. If Y
is not equal to X, this means that one or more possible starting
attributes has not yet been addressed. Thus, if Y is not equal to
X, the method proceeds to step 64 (FIG. 2) where Y is set equal to
Y+1, thereby selecting the next starting attribute in step 30.
After the next starting attribute is selected, steps 32 through 62
are repeated until the residual stepwise regression has been
performed for all of the possible starting attributes selected in
step 26 (FIG. 2).
[0038] Referring again to FIG. 3, once all possible starting
attributes have been addressed in residual stepwise regression
steps 32-62, step 66 compares the correlation value and prediction
error associated with each starting attribute from data set 60. In
step 68, the prediction equation corresponding to the starting
seismic attribute having the best correlation value and prediction
error is selected. This optimum prediction equation is typically a
multi-variable equation which can calculate a predicted reservoir
property based on the value of various unique seismic attributes.
Referring to FIG. 1, for example, the optimum prediction equation
from step 68 (FIG. 3) can be used to calculate a predicted
reservoir property at unexplored location x based on a plurality of
seismic attributes corresponding to unexplored location x.
[0039] In another embodiment of this invention, a method is
provided for determining the relative significance of multiple
seismic attributes used as variables in a reservoir property
prediction equation. This embodiment of the invention can be
applied to the reservoir property prediction equation generated
from the method outlined in FIGS. 2 and 3. Alternatively, this
embodiment of the invention can be employed separately from the
method outlined in FIGS. 2 and 3. Generally, reservoir property
prediction equations will have the following form:
Reservoir Property=W.sub.1A.sub.1+W.sub.2A.sub.2+W.sub.3A.sub.3+ .
. . +B
[0040] wherein A.sub.i is a unique seismic attribute, W.sub.i is a
unique coefficient for attribute i, and B is a constant. It has
been discovered that the order of significance of the seismic
attributes can be determined by multiplying each attribute's
coefficient (W.sub.i) by that attribute's standard deviation
(.sigma..sub.i) to give a modified coefficient (M.sub.i). The
attribute significance can then be determined by dividing the
modified coefficient (M.sub.i) by the sum of the absolute value of
all of the modified coefficients. Thus, the attribute significance
can be expressed as follows: 1 Attribute Significance = W i * i / W
i i = 1 n * i
[0041] In accordance with another embodiment of the invention, the
significance of seismic attributes in a prediction equation can be
determined by normalizing each attribute prior to determining the
prediction equation. To normalize each attribute, the mean of that
attribute must be subtracted from each sample of the attribute, and
this result divided by the standard deviation of the attribute. The
prediction equation can then be generated using the normalized
attribute in a conventional regression process or the inventive
regression process described herein. The resulting prediction
equation can then be analyzed for each attribute's contribution
significance. This is done by dividing the coefficient of the
attribute by the sum of the absolute value of all the coefficients
involved in the prediction equation. A negative result means that
the attribute is inversely related to the property being predicted,
whereas a positive result means they are directly related. After
the significance of the seismic attribute used in a reservoir
property prediction equation has been determined, this information
can be used to ensure that the most significant attributes are
extracted from future seismic survey data.
[0042] It will be appreciated that the various steps of the method
may be implemented using software, firmware, hardware, or any
combination thereof. In a preferred implementation, the various
steps are encoded as instructions in one or more routines,
subroutines, or code segments of a computer program stored on a
memory media and executable by a computing device. The computing
device may take the form of any conventional personal computer,
whether desktop or portable in nature, or any of a variety of
smaller hand-held devices having sufficient processing and other
computing resources to execute the computer program in the manner
desired. In an equally preferred alternative implementation, the
various steps are implemented in the electronic logic hardware of a
substantially electronic device.
[0043] The preferred forms of the invention described above are to
be used as illustration only and should not be used in a limiting
sense to interpret the scope of the present invention. Obvious
modifications to the exemplary embodiments, set forth above, could
be readily made by those skilled in the art without departing from
the spirit of the present invention.
[0044] The inventor hereby states his intent to rely on the
Doctrine of Equivalents to determine and assess the reasonably fair
scope of the present invention as it pertains to any apparatus not
materially departing from but outside the literal scope of the
invention as set forth in the following claims.
* * * * *