Directional Q compensation with sparsity constraints and preconditioning
A method for directional Q compensation of seismic data may comprise calculating angle-dependent subsurface travel times; applying directional Q compensation to the prestack seismic data to obtain Q-compensated data in time-space domain, wherein the directional Q compensation is based on the angle-dependent subsurface travel times; and using the Q-compensated data to generate an image of the subsurface. Directional Q compensation may comprise determining an angle-dependent forward E operator and an angle-dependent adjoint E* operator using the angle-dependent subsurface travel times; and applying a sparse inversion algorithm using the angle-dependent operators to obtain a model of Q-compensated data. The angle-dependent operators may be preconditioned by introducing ghost and source effects in a wavelet matrix and a transpose of the wavelet matrix, respectively, such that applying a sparse inversion algorithm using the preconditioned angle-dependent operators is used to obtain a model of Q-compensated, deghosted data without source effects.
1. A method for directional Q compensation of seismic data with Q effects related to a subsurface of a survey area, the method comprising:
receiving, with a computer, prestack seismic data from the survey area;
calculating, with the computer, angle-dependent subsurface travel times associated with the survey area;
applying, with the computer, directional Q compensation to the prestack seismic data to obtain Q-compensated data in time-space domain, wherein the directional Q compensation is based on the angle-dependent subsurface travel times;
using the Q-compensated data to generate, with the computer, an image of the subsurface; and
managing hydrocarbons in the subsurface using the image of the sub surface;
wherein applying directional Q compensation to the prestack seismic data comprises:
determining an angle-dependent forward E operator and an angle-dependent adjoint E* operator using the angle-dependent subsurface travel times; and
applying a sparse inversion algorithm to the prestack seismic data using the angle-dependent forward E operator and the angle-dependent adjoint E* operator to obtain a model of Q-compensated data.
2. The method of claim 1 , wherein applying directional Q compensation to the prestack seismic data comprises:
designing a multi-dimensional filter using the angle-dependent subsurface travel times; and
applying the multi-dimensional filter to the prestack seismic data to obtain the Q-compensated data in time-space domain.
3. The method of claim 1 , further comprising mapping the model to obtain Q-compensated data in time-space domain.
4. The method of claim 1 , wherein the prestack seismic data includes at least one of pressure, pressure gradient, velocity, acceleration, and other particle motion data.
5. The method of claim 1 , wherein directional Q compensation is applied to the prestack seismic data on time-space patches of the prestack seismic data.
6. A method for directional Q compensation of seismic data with Q effects related to a subsurface of a survey area, the method comprising:
receiving, with a computer, prestack seismic data from the survey area;
calculating, with the computer, angle-dependent subsurface travel times associated with the survey area;
applying, with the computer, directional Q compensation to the prestack seismic data to obtain Q-compensated data in time-space domain, wherein the directional Q compensation is based on the angle-dependent subsurface travel times;
using the Q-compensated data to generate, with the computer, an image of the subsurface; and
managing hydrocarbons in the subsurface using the image of the subsurface;
wherein applying directional Q compensation to the prestack seismic data comprises:
determining a preconditioned angle-dependent forward E operator and a preconditioned angle-dependent adjoint E* operator using the angle-dependent subsurface travel times; and
applying a sparse inversion algorithm to the prestack seismic data using the preconditioned angle-dependent forward E operator and the preconditioned angle-dependent adjoint E* operator to obtain a model of Q-compensated, deghosted data without source effects.
7. The method of claim 6 , further comprising mapping the model to obtain Q-compensated data, deghosted data without source effects in time-space domain.
8. The method of claim 6 , wherein determining a preconditioned angle-dependent forward E operator and a preconditioned angle-dependent adjoint E* operator comprises, respectively, introducing ghost and source effects in a wavelet matrix and a transpose of the wavelet matrix.
9. The method of claim 8 , further comprising reintroducing ghost and source effects in the model.
10. The method of claim 9 , further comprising mapping the model to obtain Q-compensated data in time-space domain.
11. The method of claim 6 , wherein applying directional Q compensation to the prestack seismic data comprises:
designing a multi-dimensional filter using the angle-dependent subsurface travel times; and
applying the multi-dimensional filter to the prestack seismic data to obtain the Q-compensated data in time-space domain.
12. The method of claim 6 , wherein the prestack seismic data includes at least one of pressure, pressure gradient, velocity, acceleration, and other particle motion data.
13. The method of claim 6 , wherein directional Q compensation is applied to the prestack seismic data on time-space patches of the prestack seismic data.