Viscoacoustic wave equation has been widely applied to describe the viscoelasticity of subsurface media and the wave propagation characteristics. The finite difference frequency domain (FDFD) method is a practical approach for the simulation of viscoacoustic and viscoelastic wavefields. At present, the second-order five-point FDFD method and optimal nine-point FDFD method commonly used in viscoacoustic wave simulation exhibit large errors when the number of points per wavelength is smaller than 4. By adjusting the FDFD coefficients adaptive to the number of points per wavelength for improving the accuracy of FDFD method, we propose a general adaptive-coefficient FDFD method for viscoacoustic wave simulation with different ratios of spatial grid sizes. Furthermore, to verify the validity of the adaptive-coefficient FDFD method for general viscoacoustic wave models, we adopt the analytic solution as well as high-order FDFD as reference solutions for the three typical viscoacoustic models. The FDFD scheme in the proposed method is obtained by introducing some correction terms to the conventional second-order FDFD scheme, where the correction terms are selected based on the distance between grid point and central point. The adaptive coefficients of correction terms are related to both the ratio of spatial grid sizes and the number of points per wavelength. The required adaptive coefficients can be efficiently determined by applying the acoustic numerical dispersion relation and lookup table. Numerical dispersion analysis shows that within a phase velocity error of 1% , the number of points per wavelength required by the proposed general adaptive-coefficient method can be less than 2. 5 for both equal and unequal spatial grid sizes. Numerical simulation results show that for the different ratios of spatial grid sizes, compared to the commonly used second-order five-point FDFD and optimal nine-point FDFD, the general adaptive-coefficient FDFD method can effectively improve the accuracy of viscoacoustic wave simulation, while requiring the similar computational cost and computer memory.
General adaptive-coefficient finite-difference frequency-domain method for wavefield simulation of viscoacoustic equation
Carcione J. M.;
2024-01-01
Abstract
Viscoacoustic wave equation has been widely applied to describe the viscoelasticity of subsurface media and the wave propagation characteristics. The finite difference frequency domain (FDFD) method is a practical approach for the simulation of viscoacoustic and viscoelastic wavefields. At present, the second-order five-point FDFD method and optimal nine-point FDFD method commonly used in viscoacoustic wave simulation exhibit large errors when the number of points per wavelength is smaller than 4. By adjusting the FDFD coefficients adaptive to the number of points per wavelength for improving the accuracy of FDFD method, we propose a general adaptive-coefficient FDFD method for viscoacoustic wave simulation with different ratios of spatial grid sizes. Furthermore, to verify the validity of the adaptive-coefficient FDFD method for general viscoacoustic wave models, we adopt the analytic solution as well as high-order FDFD as reference solutions for the three typical viscoacoustic models. The FDFD scheme in the proposed method is obtained by introducing some correction terms to the conventional second-order FDFD scheme, where the correction terms are selected based on the distance between grid point and central point. The adaptive coefficients of correction terms are related to both the ratio of spatial grid sizes and the number of points per wavelength. The required adaptive coefficients can be efficiently determined by applying the acoustic numerical dispersion relation and lookup table. Numerical dispersion analysis shows that within a phase velocity error of 1% , the number of points per wavelength required by the proposed general adaptive-coefficient method can be less than 2. 5 for both equal and unequal spatial grid sizes. Numerical simulation results show that for the different ratios of spatial grid sizes, compared to the commonly used second-order five-point FDFD and optimal nine-point FDFD, the general adaptive-coefficient FDFD method can effectively improve the accuracy of viscoacoustic wave simulation, while requiring the similar computational cost and computer memory.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
