System and method for elastic full waveform inversion and imaging
A method for seismic imaging of a subsurface using a full waveform inversion, FWI, includes the steps of obtaining an initial P-velocity model that describes how a seismic wave propagates through the subsurface, generating an S-velocity model based on the initial P-velocity model, generating an elastic synthetic dataset p based on the initial P-velocity model and the S-velocity model, receiving a recorded seismic dataset d of the subsurface, updating the P-velocity model based on a comparison between the synthetic dataset p and the recorded seismic dataset d, updating a reflectivity at various locations in the subsurface based on the updated P-velocity model, and generating an image of the subsurface based on the reflectivity.
1. A method for seismic imaging of a subsurface using a full waveform inversion, FWI, the method comprising:
obtaining an initial P-velocity model that describes how a seismic wave propagates through the subsurface;
generating an S-velocity model based on the initial P-velocity model;
generating an elastic synthetic dataset p based on the initial P-velocity model and the S-velocity model;
receiving a recorded seismic dataset d of the subsurface;
updating the P-velocity model based on a comparison between the synthetic dataset p and the recorded seismic dataset d;
updating a reflectivity at various locations in the subsurface based on the updated P-velocity model; and
generating an image of the subsurface based on the reflectivity.
2. The method of claim 1 , further comprising:
updating the S-velocity model based on the updated P-velocity model and updated reflectivity,
wherein the synthetic dataset p includes pressures.
3. The method of claim 1 , wherein the elastic synthetic dataset p is calculated based on Hooke's law, which links a stress vector describing the subsurface to a strain vector that describes the subsurface.
4. The method of claim 1 , wherein the elastic synthetic dataset p is calculated based on (1) a stress vector describing the subsurface and (2) a strain vector describing the subsurface.
5. The method of claim 1 , wherein the elastic synthetic dataset p is calculated based on an elastic wave equation.
6. The method of claim 1 , wherein the elastic synthetic dataset p is equal to an average of the first three diagonal terms of the stress vector for the subsurface.
7. The method of claim 1 , further comprising:
updating the initial P-velocity model with a cost function based on time-shifts between the elastic synthetic dataset p and the recorded seismic dataset d.
8. The method of claim 7 , wherein the cost function is a sum of squared time-shifts multiplied by weighs c, respectively, for all sources r and all sensors s for given windows w, which are frequency-dependent time windows.
9. The method of claim 1 , further comprising:
generating an adjoint source dataset using the cost function;
calculating a gradient using the adjoint source dataset; and
updating the initial P-velocity model based on the gradient.
10. The method of claim 1 , further comprising:
measuring time-shifts between the elastic synthetic dataset p and the recorded seismic dataset d;
calculating correlation coefficients between the elastic synthetic dataset p and the measured dataset d;
applying the correlation coefficients to weight the measured time-shifts;
generating an adjoint source dataset based on weighted time-shifts;
calculating a gradient using the adjoint source dataset; and
updating the initial P-velocity model based on the gradient.
11. A computing device for seismic imaging of a subsurface using a full waveform inversion, FWI, the computing device comprising:
an interface configured to receive an initial P-velocity model that describes how a seismic wave propagates through the subsurface; and
a processor connected to the interface and configured to,
generate an S-velocity model based on the initial P-velocity model;
generate an elastic synthetic dataset p based on the initial P-velocity model and the S-velocity model;
receive a recorded seismic dataset d of the subsurface;
update the P-velocity model based on a comparison between the elastic synthetic dataset p and the recorded seismic dataset d;
update a reflectivity at various locations in the subsurface based on the updated P-velocity model; and
generate an image of the subsurface based on the reflectivity.
12. The computing device of claim 11 , wherein the processor is further configured to,
update the S-velocity model based on the updated P-velocity model and the updated reflectivity,
wherein the elastic synthetic dataset p includes pressures.
13. The computing device of claim 11 , wherein the elastic synthetic dataset p is calculated based on the Hooke's law, which links a stress vector describing the subsurface to a strain vector that describes the subsurface.
14. The computing device of claim 11 , wherein the elastic synthetic dataset p is calculated based on (1) a stress vector describing the subsurface and (2) a strain vector describing the subsurface.
15. The computing device of claim 11 , wherein the elastic synthetic dataset p is calculated based on an elastic wave equation.
16. The computing device of claim 11 , wherein the elastic synthetic dataset p is equal to an average of the first three diagonal terms of the stress vector for the subsurface.
17. The computing device of claim 11 , wherein the processor is further configured to:
update the initial P-velocity model with a cost function based on time-shifts between the elastic synthetic dataset p and the recorded seismic dataset d,
wherein the cost function is a sum of squared time-shifts multiplied by weighs c, respectively, for all sources r and all sensors s for given windows w, which are frequency-dependent time windows.
18. The computing device of claim 11 , wherein the processor is further configured to:
generate an adjoint source dataset using the cost function;
calculate a gradient using the adjoint source dataset; and
update the initial P-velocity model based on the gradient.
19. The computing device of claim 11 , wherein the processor is further configured to:
measure time-shifts between the elastic synthetic dataset p and the recorded seismic dataset d;
calculate correlation coefficients between the elastic synthetic dataset p and the measured dataset d;
apply the correlation coefficients to weight the measured time-shifts;
generate an adjoint source dataset based on weighted time-shifts;
calculate a gradient using the adjoint source dataset; and
update the initial P-velocity model based on the gradient.
20. A non-transitory computer readable medium including computer executable instructions, wherein the instructions, when executed by a processor, implement a method of seismic imaging of a subsurface using a full waveform inversion, FWI, the medium comprising instructions for:
obtaining an initial P-velocity model that describes how a seismic wave propagates through the subsurface;
generating an S-velocity model based on the initial P-velocity model;
generating an elastic synthetic dataset p based on the initial P-velocity model and the S-velocity model;
receiving a recorded seismic dataset d of the subsurface;
updating the P-velocity model based on a comparison between the synthetic dataset p and the recorded seismic dataset d;
updating a reflectivity at various locations in the subsurface based on the updated P-velocity model; and
generating an image of the subsurface based on the reflectivity.