Processes and systems for generating a high-resolution velocity model of a subterranean formation using iterative full-waveform inversion
This disclosure describes processes and systems for generating a high-resolution velocity model of a subterranean formation from recorded seismic data gathers obtained in a marine seismic survey of the subterranean formation. A velocity model is computed by iterative FWI using reflections, resolving the velocity field of deep subterranean targets without requiring ultralong offsets. The processes and systems use of an impedance sensitivity kernel to characterize reflections in a modeled wavefield, and then use the reflections to compute a velocity sensitivity kernel that is used to produce low-wavenumber updates to the velocity model. The iterative process is applied in a cascade such that position of reflectors and background velocity are simultaneously updated. Once the low-wavenumber components of the velocity model are updated, the velocity model is used as an input of conventional FWI to introduce missing velocity components (i.e., high-wavenumber) to increase the resolution of the velocity model.
1. In a computer-implemented process that generates a velocity model of a subterranean formation located beneath a body of water using recorded seismic data that was recorded during a marine survey, the improvement comprising:
iteratively
applying forward modeling to a source wavefield and velocity and density models of the subterranean formation to generate updated synthetic seismic data,
computing a residual between the synthetic seismic data and the recorded seismic data,
applying adjoint migration to the residual to obtain a migrated residual,
computing an impedance gradient that suppresses low-wavenumber components of the density model based on the source wavefield and the migrated residual,
computing a velocity gradient that suppresses high-wavenumber components of the velocity model based on the source wavefield and the migrated residual,
updating the density model based on the impedance gradient,
updating the velocity model based on the velocity gradient, and
computing a residual magnitude of the residual until the residual magnitude is less than a residual magnitude threshold; and
applying full-waveform inversion to the velocity model to generate a final velocity model containing low-wavenumber and high-wavenumber components, thereby generating a final velocity model of the subterranean formation with improved resolution.
2. The process of claim 1 further comprises using the final velocity model to generate an image of the subterranean formation, the image providing a visual representation of subsurface features and layers within the subterranean formation.
3. The process of claim 1 , wherein computing the impedance gradient comprises:
computing a weighted bulk modulus sensitivity kernel based on a product of a time derivative of the source wavefield and a time derivative of the migrated residual;
computing a weighted density sensitivity kernel based on a scalar product of a gradient of the source wavefield and a gradient of the migration residual; and
subtracting the weighted density sensitivity kernel from the weighted bulk modulus sensitivity kernel to obtain the impedance gradient.
4. The process of claim 1 , wherein the computing the velocity gradient comprises:
computing a weighted bulk modulus sensitivity kernel based on a product of a time derivative of the source wavefield and a time derivative of the migrated residual;
computing a weighted density sensitivity kernel based on a scalar product of a gradient of the source wavefield and a gradient of the migration residual; and
adding the weighted bulk modulus sensitivity kernel and the weighted density sensitivity kernel to obtain the velocity gradient.
5. The process of claim 1 , wherein updating the density model comprises: for each point in the density model, linearly combining an impedance gradient value of the impedance gradient with a previous density to obtain an updated density.
6. The process of claim 1 , wherein updating the velocity model comprises: for each point in the velocity model, linearly combining a velocity gradient value of the velocity gradient with a previous wave speed obtain an updated wave speed.
7. A computer system for generating a velocity model of a subterranean formation from recorded seismic data recorded in a marine seismic survey of the subterranean formation, the system comprising:
one or more processors;
one or more data-storage devices; and
machine-readable instructions stored in the one or more data-storage devices that when executed using the one or more processors controls the system to execute operations comprising:
applying forward modeling to a source wavefield and initial velocity and density models of the subterranean formation to generate synthetic seismic data;
computing a residual between the updated synthetic seismic data and the recorded seismic data;
iteratively
applying adjoint migration to the residual to obtain a migrated residual,
computing an impedance gradient that suppresses low-wavenumber components of the density model based on the source wavefield and the migrated residual,
computing a velocity gradient that suppresses high-wavenumber components of the velocity model based on the source wavefield and the migrated residual,
updating the density model based on the impedance gradient,
updating the velocity model based on the velocity gradient,
applying forward modeling to the source wavefield and the velocity and density models to generate updated synthetic seismic data,
computing a residual between the updated synthetic seismic data and the recorded seismic data, and
computing a residual magnitude of the residual until the residual magnitude is less than a residual magnitude threshold; and
applying full-waveform inversion to the velocity model to generate a final velocity model containing low-wavenumber and high-wavenumber components.
8. The system of claim 7 further comprises using the final velocity model to generate an image of the subterranean formation, the image providing a visual representation of subsurface features and layers within the subterranean formation.
9. The system of claim 7 , wherein computing the impedance gradient comprises:
computing a weighted bulk modulus sensitivity kernel based on a product of a time derivative of the source wavefield and a time derivative of the migrated residual;
computing a weighted density sensitivity kernel based on a scalar product of a gradient of the source wavefield and a gradient of the migration residual; and
subtracting the weighted density sensitivity kernel from the weighted bulk modulus sensitivity kernel to obtain the impedance gradient.
10. The system of claim 7 , wherein the computing the velocity gradient comprises;
computing a weighted bulk modulus sensitivity kernel based on a product of a time derivative of the source wavefield and a time derivative of the migrated residual;
computing a weighted density sensitivity kernel based on a scalar product of a gradient of the source wavefield and a gradient of the migration residual; and
adding the weighted bulk modulus sensitivity kernel and the weighted density sensitivity kernel to obtain the velocity gradient.
11. The system of claim 7 , wherein updating the density model comprises: for each point in the density model, linearly combining an impedance gradient value of the impedance gradient with a previous density to obtain an updated density.
12. The system of claim 7 , wherein updating the velocity model comprises: for each point in the velocity model, linearly combining a velocity gradient value of the velocity gradient with a previous wave speed obtain an updated wave speed.
13. A non-transitory computer-readable medium encoded with machine-readable instructions that cause one or more processors of a computer system to execute operations comprising:
iteratively
applying forward modeling to a source wavefield and velocity and density models of the subterranean formation to generate updated synthetic seismic data,
computing a residual between the synthetic seismic data and the recorded seismic data,
applying adjoint migration to the residual to obtain a migrated residual,
computing an impedance gradient that suppresses low-wavenumber components of the density model based on the source wavefield and the migrated residual,
computing a velocity gradient that suppresses high-wavenumber components of the velocity model based on the source wavefield and the migrated residual,
updating the density model based on the impedance gradient,
updating the velocity model based on the velocity gradient, and
computing a residual magnitude of the residual until the residual magnitude is less than a residual magnitude threshold; and
applying full-waveform inversion to the velocity model to generate a final velocity model containing low-wavenumber and high-wavenumber components.
14. The medium of claim 13 further comprises using the final velocity model to generate an image of the subterranean formation, the image providing a visual representation of subsurface features and layers within the subterranean formation.
15. The medium of claim 13 , wherein computing the impedance gradient comprises:
computing a weighted bulk modulus sensitivity kernel based on a product of a time derivative of the source wavefield and a time derivative of the migrated residual;
computing a weighted density sensitivity kernel based on a scalar product of a gradient of the source wavefield and a gradient of the migration residual; and
subtracting the weighted density sensitivity kernel from the weighted bulk modulus sensitivity kernel to obtain the impedance gradient.
16. The medium of claim 13 , wherein the computing the velocity gradient comprises:
computing a weighted bulk modulus sensitivity kernel based on a product of a time derivative of the source wavefield and a time derivative of the migrated residual;
computing a weighted density sensitivity kernel based on a scalar product of a gradient of the source wavefield and a gradient of the migration residual; and
adding the weighted bulk modulus sensitivity kernel and the weighted density sensitivity kernel to obtain the velocity gradient.
17. The medium of claim 13 , wherein updating the density model comprises: for each point in the density model, linearly combining an impedance gradient value of the impedance gradient with a previous density to obtain an updated density.
18. The medium of claim 13 , wherein updating the velocity model comprises:
for each point in the velocity model, linearly combining a velocity gradient value of the velocity gradient with a previous wave speed obtain an updated wave speed.
19. Apparatus for generating a velocity model of a subterranean formation from recorded seismic data collected in a marine seismic survey of the subterranean formation, the apparatus comprising:
means for applying forward modeling to a source wavefield and initial velocity and density models of the subterranean formation to generate synthetic seismic data;
means for computing a residual between the updated synthetic seismic data and the recorded seismic data;
means for iteratively
applying adjoint migration to the residual to obtain a migrated residual,
computing an impedance gradient that suppresses low-wavenumber components of the density model based on the source wavefield and the migrated residual,
computing a velocity gradient that suppresses high-wavenumber components of the velocity model based on the source wavefield and the migrated residual,
updating the density model based on the impedance gradient,
updating the velocity model based on the velocity gradient,
applying forward modeling to the source wavefield and the velocity and density models to generate updated synthetic seismic data,
computing a residual between the updated synthetic seismic data and the recorded seismic data, and
computing a residual magnitude of the residual until the residual magnitude is less than a residual magnitude threshold; and
applying full-waveform inversion to the velocity model to generate a final velocity model containing low-wavenumber and high-wavenumber components.
20. The apparatus of claim 19 further comprises means for using the final velocity model to generate an image of the subterranean formation, the image providing a visual representation of subsurface features and layers within the subterranean formation.
21. The apparatus of claim 19 , wherein the means for iteratively computing the impedance gradient comprises:
computes a weighted bulk modulus sensitivity kernel based on a product of a time derivative of the source wavefield and a time derivative of the migrated residual;
computes a weighted density sensitivity kernel based on a scalar product of a gradient of the source wavefield and a gradient of the migration residual; and
subtracts the weighted density sensitivity kernel from the weighted bulk modulus sensitivity kernel to obtain the impedance gradient.
22. The apparatus of claim 19 , wherein the means for iteratively computing the velocity gradient comprises:
computes a weighted bulk modulus sensitivity kernel based on a product of a time derivative of the source wavefield and a time derivative of the migrated residual;
computes a weighted density sensitivity kernel based on a scalar product of a gradient of the source wavefield and a gradient of the migration residual; and
adds the weighted bulk modulus sensitivity kernel and the weighted density sensitivity kernel to obtain the velocity gradient.
23. The apparatus of claim 19 , wherein the means for iteratively updating the density model comprises: for each point in the density model, linearly combines an impedance gradient value of the impedance gradient with a previous density to obtain an updated density.
24. The apparatus of claim 19 , wherein the means for iteratively updating the velocity model comprises: for each point in the velocity model, linearly combines a velocity gradient value of the velocity gradient with a previous wave speed obtain an updated wave speed.
25. A method of manufacturing a geophysical data product, the method comprising:
iteratively
applying forward modeling to a source wavefield and velocity and density models of the subterranean formation to generate updated synthetic seismic data,
computing a residual between the synthetic seismic data and the recorded seismic data,
applying adjoint migration to the residual to obtain a migrated residual,
computing an impedance gradient that suppresses low-wavenumber components of the density model based on the source wavefield and the migrated residual,
computing a velocity gradient that suppresses high-wavenumber components of the velocity model based on the source wavefield and the migrated residual,
updating the density model based on the impedance gradient,
updating the velocity model based on the velocity gradient, and
computing a residual magnitude of the residual until the residual magnitude is less than a residual magnitude threshold; and
applying full-waveform inversion to the velocity model to generate a final velocity model containing low-wavenumber and high-wavenumber components.