Methods and computer-readable medium to implement computing the propagation velocity of seismic waves
The invention relates to methods and computer-readable medium for computing the propagation velocity of seismic waves in the earth. The invention computes the true propagation velocity of seismic waves in the earth, which is a condition of obtaining an accurate image of subsurface geology that can be used to prospect for oil and gas deposits. In an embodiment, the method of computing the propagation velocity of seismic waves in earth, includes providing an estimate of the propagation velocity, generating a time shift gather using a depth migration at a plurality of locations of the earth, converting each of the time shift gathers to a semblance gather, transforming each semblance gather into a velocity gather whose energy peaks represent a root-mean-square average of the propagation velocity along the forward and backward path between earth's surface and a point of the subsurface geology, and converting the energy peaks to the propagation velocity.
1. A computer implemented method of determining a propagation velocity of seismic waves in earth, comprising:
using a processor;
using a memory holding program instructions executable by the processor to implement:
inputting an estimate of the propagation velocity;
generating a time shift gather using a depth migration and the propagation velocity at a plurality of locations of the earth;
converting each of the time shift gathers to a semblance gather;
transforming each semblance gather into a velocity gather, whose energy peaks represent a root-mean-square average of the propagation velocity along a forward and backward path between earth's surface and a point of a subsurface geology;
converting the energy peaks to the propagation velocity; and
storing the propagation velocity.
2. The method of claim 1 , wherein converting each of the time shift gathers to a semblance gather includes:
(a) computing an amplitude squared time shift gather, and
(b) counting shot images contributing to each time shift gather.
3. The method of claim 1 , wherein the step of transforming each semblance gather into a velocity gather includes associating a migration time-shift parameter, τ, with a residual travel time, Δt, from the depth migration using the estimate of the propagation velocity.
4. The method of claim 3 , wherein the migration time-shift parameter, τ, on the semblance gather relates to a root-mean-square average of the propagation velocity change, Δv(t), along the forward and backward path between earth's surface and the point of the subsurface geology.
5. The method of claim 4 , wherein the migration time-shift parameter, τ, on the semblance gather relates to the root-mean-square average of the propagation velocity change, Δv(t), by the following formula:
τ
t
=
-
1
+
1
+
2
Δ
v
(
t
)
v
(
t
)
(
1
-
Δ
v
(
t
)
2
v
(
t
)
)
(
1
-
Δ
v
(
t
)
v
(
t
)
)
2
.
6. The method of claim 5 , wherein transforming each semblance gather into a velocity gather includes interpolating between the migration time-shift parameter, τ, and the root-mean-square average of the propagation velocity change, Δv(t).
7. The method of claim 6 , further comprising selecting a maxima of each of the energy peaks on the velocity gather.
8. The method of claim 7 , further comprising updating the propagation velocity, using the selected energy maxima.
9. The method of claim 5 , wherein transforming each semblance gather into a velocity gather includes interpolating between the migration time-shift parameter, τ, and the root-mean-square average of the propagation velocity change, Δv(t), plus the estimate of the propagation velocity.
10. The method of claim 9 , further comprising selecting a maxima of each of the energy peaks on the velocity gather.
11. The method of claim 10 , further comprising updating the propagation velocity, using the selected energy maxima.
12. The method of claim 6 , wherein selecting a maxima of each of the energy peaks is performed by a computer.
13. The method of claim 4 , wherein the migration time-shift parameter, τ, on the semblance gather relates to the root-mean-square average of the propagation velocity change, Δv(t), by the following formula:
τ
t
≈
Δ
v
(
t
)
v
(
t
)
(
1
+
Δ
v
(
t
)
v
(
t
)
)
.
14. The method of claim 4 , wherein the migration time-shift parameter, τ, on the semblance gather relates to the root-mean-square average of the propagation velocity change, Δv(t), by the following formula:
Δ
v
(
t
)
v
(
t
)
≈
τ
t
.
15. A computer implemented method of determining a propagation velocity of seismic waves in earth, comprising:
providing an estimate of the propagation velocity;
generating a time shift gather using a depth migration and the propagation velocity at a plurality of locations of the earth;
transforming each time shift gather into a velocity gather, whose energy peaks represent a root-mean-square average of the propagation velocity along a forward and backward path between earth's surface and a point of a subsurface geology;
converting the energy peaks to the propagation velocity; and
storing the propagation velocity.
16. The method of claim 15 , wherein the step of transforming each time shift gather into a velocity gather includes associating a migration time-shift parameter, τ, with a residual travel time, Δt, from the depth migration using the estimate of the propagation velocity.
17. The method of claim 16 , wherein the migration time-shift parameter, τ, on the time shift gather relates to the root-mean square average of the propagation velocity change, Δv(t).
18. The method of claim 17 , wherein the migration time-shift parameter, τ, relates to the root-mean-square average of the propagation velocity change, Δv(t), by the following formula:
τ
t
=
-
1
+
1
+
2
Δ
v
(
t
)
v
(
t
)
(
1
-
Δ
v
(
t
)
2
v
(
t
)
)
(
1
-
Δ
v
(
t
)
v
(
t
)
)
2
.
19. The method of claim 18 , wherein transforming each time shift gather into the velocity gather includes interpolating between the migration time-shift parameter, τ, and the root-mean-square average of the propagation velocity change, Δv(t).
20. The method of claim 19 , further comprising selecting a maxima of each of the energy peaks on the velocity gather.
21. The method of claim 20 , further comprising updating the propagation velocity, using the selected energy maxima.
22. The method of claim 18 , wherein transforming each time shift gather into the velocity gather includes interpolating between the migration time-shift parameter, τ, and the root-mean-square average of the propagation velocity change, Δv(t), plus the estimate of the propagation velocity.
23. The method of claim 22 , further comprising selecting a maxima of each of the energy peaks on the velocity gather.
24. The method of claim 23 , further comprising updating the propagation velocity, using the selected energy maxima.
25. The method of claim 23 , wherein selecting the maxima of each of the energy peaks is performed by a computer.
26. The method of claim 17 , wherein the migration time-shift parameter, τ, relates to the root-mean-square average of the propagation velocity change, Δv(t), by the following formula:
τ
t
≈
Δ
v
(
t
)
v
(
t
)
(
1
+
Δ
v
(
t
)
v
(
t
)
)
.
27. The method of claim 17 , wherein the migration time-shift parameter, τ, relates to the root-mean-square average of the propagation velocity change, Δv(t), by the following formula:
Δ
v
(
t
)
v
(
t
)
≈
τ
t
.
28. A non-transitory computer-readable medium storing program instructions that cause a computer to perform steps, comprising:
inputting an estimate of a propagation velocity;
generating a time shift gather using a depth migration and the propagation velocity at a plurality of locations of the earth;
converting each of the time shift gathers to a semblance gather;
transforming each semblance gather into a velocity gather, whose energy peaks represent a root-mean-square average of the propagation velocity along a forward and backward path between earth's surface and a point of a subsurface geology;
converting the energy peaks to the propagation velocity; and
storing the propagation velocity.
29. The non-transitory computer-readable medium of claim 28 , wherein converting each of the time shift gathers to a semblance gather includes:
(a) computing an amplitude squared time shift gather, and
(b) counting shot images contributing to each time shift gather.
30. The non-transitory computer-readable medium of claim 28 , wherein the step of transforming each semblance gather into a velocity gather includes associating a migration time-shift parameter, τ, with a residual travel time, Δt, from the depth migration using the estimate of the propagation velocity.
31. The non-transitory computer-readable medium of claim 30 , wherein the migration time-shift parameter, τ, on the semblance gather relates to a root-mean-square average of the propagation velocity change, Δv(t), along the forward and backward path between earth's surface and the point of the subsurface geology.
32. The non-transitory computer-readable medium of claim 31 , wherein the migration time-shift parameter, τ, on the semblance gather relates to the root-mean-square average of the propagation velocity change by the following formula:
τ
t
=
-
1
+
1
+
2
Δ
v
(
t
)
v
(
t
)
(
1
-
Δ
v
(
t
)
2
v
(
t
)
)
(
1
-
Δ
v
(
t
)
v
(
t
)
)
2
.
33. The non-transitory computer-readable medium of claim 32 , wherein transforming each semblance gather into a velocity gather includes interpolating between the migration time-shift parameter, τ, and the root-mean-square average of the propagation velocity change, Δv(t).
34. The non-transitory computer-readable medium of claim 33 , further comprising selecting a maxima of each of the energy peaks on the velocity gather.
35. The non-transitory computer-readable medium of claim 34 , further comprising updating the propagation velocity, using the selected energy maxima.
36. The non-transitory computer-readable medium of claim 33 , wherein selecting a maxima of each of the energy peaks is performed by a computer.
37. The non-transitory computer-readable medium of claim 32 , wherein transforming each semblance gather into a velocity gather includes interpolating between the migration time-shift parameter, τ, and the root-mean-square average of the propagation velocity change, Δv(t), plus the estimate of the propagation velocity.
38. The non-transitory computer-readable medium of claim 37 , further comprising selecting a maxima of each of the energy peaks on the velocity gather.
39. The non-transitory computer-readable medium of claim 38 , further comprising updating the propagation velocity, using the selected energy maxima.
40. The non-transitory computer-readable medium of claim 31 , wherein the migration time-shift parameter, τ, on the semblance gather relates to the root-mean-square average of the propagation velocity change by the following formula:
τ
t
≈
Δ
v
(
t
)
v
(
t
)
(
1
+
Δ
v
(
t
)
v
(
t
)
)
.
41. The non-transitory computer-readable medium of claim 31 , wherein the migration time-shift parameter, τ, on the semblance gather relates to the root-mean-square average of the propagation velocity change by the following formula:
Δ
v
(
t
)
v
(
t
)
≈
τ
t
.