| In recent years,acoustic anisotropy-based seismic exploration has been used in the pre-drilling surveys of oil and gas resources in several large-scale oil and gas fields,such as the North sea oil field and the Gulf of Mexico oil field.In these known fields,most of the shallow conventional reservoirs have already been located.The current exploration targets are the unconventional reservoirs in the deeper complex structures,such as shale oil and gas and coal-seam methane.In terms of seismic exploration,the seismic waves travel through numerous sedimentary layers before reaching such deep reservoirs,where some physical mechanisms can induce seismic anisotropy,such as shales,thin layers,and natural fracture systems,which means that the velocity of seismic waves depends on the direction of propagation.Neglecting this property may lead to significant distortions in the seismic data processing results,such as blurred reverse time migration results,dislocation of the reservoirs,and anomalous reflection coefficients.As the engine of seismic data processing technologies,the seismic wave extrapolation in anisotropic media can be performed by solving the elastic wave equation.However,the anisotropic extrapolation of elastic waves involves multiple parameters and has low computational efficiency.Meanwhile,useful information about the subsurface structures mainly comes from the P-wave component.Therefore,according to the acoustic approximation,the vertical S-wave velocity in transversely isotropic media with a vertical symmetry axis(VTI media)is set to constant zero to suppress the SV-wave propagation,thus the elastic seismic wave is reduced to the acoustic wave.Compared to the elastic case,solving the acoustic wave equation in VTI media involves fewer parameters and has higher computational efficiency.The acoustic approximation can also be used to implement the acoustic wave extrapolation in transversely isotropic media with a tilted symmetry axis(TTI media)and orthorhombic(ORT)media.However,under the acoustic approximation,the S-wave energy is not eliminated as expected but exists as coupled S-wave artifacts in the acoustic wavefield,which leads to instability issues.This paper proposes a decoupling approximation method for the P-wave phase velocity in anisotropic media and,on this basis,derives the acoustic wave equations in VTI media,TTI media,and 3D ORT media,respectively.Since this method avoids the S-wave artifacts caused by the acoustic approximation,it can be used for accurate and stable anisotropic extrapolation of acoustic waves.This paper also optimizes the computational efficiency of the mixed-domain acoustic wave equation in TTI media and uses it for reverse time migration in 2D TTI models.The specific studies are as follows:It is observed that the P-wave propagation in acoustic VTI media is always reasonably accurate regardless of the accuracy of the SV-wave phase velocity.Based on such fact,in the P-wave phase velocity expression in VTI media,this paper defines an algebraic expression representing the SV-wave phase velocity.Sensitivity analysis shows that this algebraic expression plays a negligible role in the P-wave phase velocity expression.Therefore,the algebraic expression is replaced by a phase angle-related variable.Doing so can greatly simplify the P-wave phase velocity expression and naturally removes the inherent coupling between the P-and SV-waves.This decoupling approximation generates an independent expression for the P-wave phase velocity.It has sound accuracy performance and involves only three anisotropy parameters.This paper derives the corresponding second-order acoustic wave equation in VTI media and provides three alternative solutions involving spectral methods.Numerical experiments show that the proposed decoupling approximation can be used for accurate and stable acoustic wave extrapolation and reverse time migration in the complex Hess VTI model.There are no coupled SV-wave artifacts in the corresponding acoustic wavefields.By rotating the axial wavenumbers in the P-wave dispersion relation,the decoupling approximate acoustic wave equation is extended from VTI media to TTI media.Similarly,it has good accuracy performance and involves only three anisotropy parameters.However,when solving this acoustic wave equation in TTI media by the hybrid method,10 fast Fourier transforms are required at each time step to calculate the multiple wavenumbers in it.This computational cost is extremely high.According to the linear nature of the Fourier transform,this paper proposes an optimization strategy to reduce the number of wavenumbers in such mixed-domain wave equations.It allows the decoupling approximate acoustic wave equation in TTI media to be computationally optimal,where the number of fast Fourier transforms reduces to three.Solving this improved acoustic wave equation can generate accurate and stable acoustic wavefields without any coupled SV-wave artifacts.This decoupling approximate acoustic wave extrapolation is computationally efficient and suitable for the acoustic reverse time migration in large-scale TTI media.In the numerical experiments,this paper obtains good reverse time migration results of the BP 2007 benchmark TTI model.Similarly,the P-wave propagation in acoustic ORT media is always reasonably accurate regardless of the accuracy of the S1-and S2-wave phase velocities.Therefore,the decoupling approximation theory can also be applied in 3D ORT media.This paper starts with a cubic approximation of the P-wave phase velocity expression in ORT media and then defines two algebraic expressions representing the S1-and S2-wave phase velocities in it.Numerical tests show that both play a negligible role in the P-wave phase velocity expression.Based on such insensitivity,the two algebraic expressions are replaced with a designed variable and constant zero to eliminate the complex trigonometric functions and root terms in the P-wave phase velocity expression.Doing so can remove the inherent coupling between the P-and S-waves.The corresponding independent expression of the P-wave phase velocity involves only six anisotropy parameters but is reasonably accurate.This paper derives the corresponding second-order acoustic wave equation in 3D ORT media and provides a low-rank solver and a Gaussian elimination-based finite-difference solution.Numerical experiments show that the proposed decoupling approximation can be used for accurate and stable acoustic wave extrapolation in complex ORT models.There are no coupled S1-or S2-wave artifacts in the corresponding acoustic wavefields. |
PDF Full Text Request