Method and system for processing seismic images to obtain a reference RGT surface of a geological formation
A computer-implemented method for processing a seismic image obtained from seismic measurements performed on a geological formation includes determining a relative geological time (RGT) image based on the seismic image; obtaining setpoints for the RGT image; retrieving an RGT surface of the RGT image for each of the setpoints, wherein each point of an RGT surface is defined by a vertical position and at least one horizontal position; and determining a reference RGT surface by combining the RGT surfaces determined for the setpoints. The vertical position of a point of the reference RGT surface is obtained by combining the vertical positions of the points of the RGT surfaces having the same at least one horizontal position as the considered point of the reference RGT surface. The combining of the vertical positions uses weighting coefficients.
1 . A method implemented by a computer for processing a seismic image obtained from seismic measurements performed on a geological formation, said method comprising:
determining a relative geological time (RGT) image based on the seismic image;
obtaining setpoints for the RGT image, said setpoints representing constraints to be satisfied by a reference RGT surface to be determined;
retrieving an RGT surface of the RGT image for each of the setpoints, wherein each point of an RGT surface is defined by a vertical position and at least one horizontal position; and
determining the reference RGT surface by combining the RGT surfaces determined for the setpoints, wherein a vertical position of a respective point of the reference RGT surface is obtained by combining the vertical positions of the points of the RGT surfaces having a same at least one horizontal position as the respective point of the reference RGT surface;
wherein said combining of the vertical positions uses weighting coefficients; and
wherein a value of a weighting coefficient used for the vertical position of an RGT surface decreases with a distance increasing between the at least one horizontal position of the respective point of the reference RGT surface and the at least one horizontal position of the setpoint associated with a respective RGT surface.
2 . The method according to claim 1 , wherein obtaining setpoints for the RGT image comprises obtaining a patch of points of the RGT image, said patch of points having a boundary, wherein the setpoints comprise points located on the boundary of the patch of points, and wherein the reference RGT surface between setpoints located on the boundary of the patch of points is obtained from said patch of points.
3 . The method according to claim 2 , wherein obtaining a patch of points comprises defining a seed on a seismic trace of the seismic image and propagating laterally the seed by searching for pixels of adjacent seismic traces that satisfy a predetermined criterion of similarity with the seed.
4 . The method according to claim 1 , wherein the value of the weighting coefficient used for the vertical position of an RGT surface is:
substantially equal to one if the at least one horizontal position of the respective point of the reference RGT surface is equal to the at least one horizontal position of the setpoint associated with the respective RGT surface; and
substantially equal to zero if the at least one horizontal position of the respective point of the reference RGT surface is equal to the at least one horizontal position of the setpoint associated with a different RGT surface.
5 . The method according to claim 1 , wherein the reference RGT surface is defined by:
S
ref
(
i
,
j
)
=
∑
n
=
1
N
setpoint
w
n
(
i
,
j
)
×
S
n
(
i
,
j
)
wherein:
S ref (i,j) is the vertical position of the point of the reference RGT surface S ref having the horizontal positions (i,j);
N setpoint is a total number of the setpoints;
S n is the RGT surface retrieved for the setpoint of index n;
S n (i,j) is the vertical position of the point of the RGT surface S n having the horizontal positions (i,j); and
w n (i,j) is the weighting coefficient used for the vertical position of the RGT surface S n for the horizontal positions (i,j).
6 . The method according to claim 5 , wherein the weighting coefficient used for the vertical position of the RGT surface is defined by:
{
w
n
(
i
n
,
j
n
)
=
1
and
w
n
(
i
m
,
j
m
)
=
0
∀
m
≠
n
w
n
(
i
,
j
)
=
F
n
(
i
,
j
)
F
(
i
,
j
)
if
(
i
,
j
)
≠
(
i
n
,
j
n
)
and
(
i
,
j
)
≠
(
i
m
,
j
m
)
∀
m
≠
n
wherein:
F
n
(
i
,
j
)
=
[
dist
(
(
i
,
j
)
,
(
i
n
,
j
n
)
)
]
-
α
F
(
i
,
j
)
=
∑
n
=
1
N
setpoint
F
n
(
i
,
j
)
wherein:
(i n , j n ) are the horizontal positions of the setpoint of index n;
dist((i,j), (i n ,j n )) is the distance in the horizontal plane between the point having the horizontal positions (i,j) and the horizontal positions (i n ,j n ) of the setpoint of index n; and
α>1 is a predetermined factor.
7 . The method according to claim 6 , wherein α>2 and/or α<60.
8 . The method according to claim 5 , wherein the weighting coefficient used for the vertical position of the RGT surface is defined by:
w
n
(
i
,
j
)
=
F
′
n
(
i
,
j
)
F
′
(
i
,
j
)
wherein:
F
′
n
(
i
,
j
)
=
1
exp
(
[
dist
(
(
i
,
j
)
,
(
i
n
,
j
n
)
)
]
α
)
F
′
(
i
,
j
)
=
∑
n
=
1
N
setpoint
F
′
n
(
i
,
j
)
wherein:
(i n , j n ) are the horizontal positions of the setpoint of index n;
dist((i,j), (i n ,j n )) is the distance in the horizontal plane between the point having the horizontal positions (i,j) and the horizontal positions (i n ,j n ) of the setpoint of index n; and
α>1 is a predetermined factor.
9 . The method according to claim 1 , comprising converting to frequency-domain the reference RGT surface.
10 . The method according to claim 9 , wherein the seismic image includes a plurality of seismic traces, and converting to frequency-domain the reference RGT surface comprises:
determining an intersection point between each seismic trace and the reference RGT surface;
selecting an interval of pixels of each seismic trace, said interval of pixels being centered on the intersection point; and
converting to frequency-domain the values of each interval of pixels, thereby obtaining a plurality of frequency-domain representations of the reference RGT surface associated with respective analysis frequencies.
11 . The method according to claim 10 , comprising selecting three analysis frequencies and generating a red-green-blue (RGB) image of the reference RGT surface based on three frequency-domain representations of the plurality of frequency-domain representations associated respectively with the three selected analysis frequencies.
12 . A non-transitory computer-readable storage medium comprising instructions which, when executed by at least one processor, configure said at least one processor to carry out the processing method of claim 1 .
13 . A computer system for processing a seismic image, said computer system comprising at least one processor configured to carry out the processing method of claim 1 .