Frequency Space Domain Seismic Forward Modeling Based On The Implicit Finite Difference Scheme

The frequency space domain (denoted as’frequency domain’) seismic forward modeling method, compared with that in time domain, has the advantages of high computing efficiency for multiple-source modeling, easily stimulating the attenuation effect, etc. It is also the kernel algorithm of the full waveform inversion in the frequency domain. However, its explicit conventional algorithms suffer from the problems that the finite difference (FD) operator is not compact enough and may not make full use of the information of the surrounding points around the current calculation point, and the implicit coefficients of the current implicit FD algorithms are difficult to be optimized. This thesis presents a generalized implicit FD operator. More accurate simulation results can be obtained by applying this operator to the forward modeling of scalar wave equation and the elastic wave equation.Firstly, the differences in the optimization of implicit coefficients and the other aspects between the implicit FD operators based on the Pade approximation and the Taylor expansion are compared in detail. The generalized implicit FD operators based on Taylor expansion are derived for the second derivatives, first derivatives and staggered-grid first derivatives. The implicit coefficients in a FD operator can be easily optimized.Second, the generalized implicit FD operators of second derivatives are applied to the forward modeling of frequency domain scalar wave equation. The implicit FD schemes of center calculation area, the second-order Absorbing Boundary Conditions and PML boundary conditions are derived. The implicit coefficients are optimized based on the minimum error of dispersions.Finally, the thesis applies the generalized implicit FD operators of second derivatives and first derivatives to forward modeling of the frequency domain elastic wave equation. The accuracy between the explicit and implicit schemes is compared through the dispersion relations, and the implicit coefficients are also optimized for the frequency domain elastic wave equation.The generalized implicit FD operator presented in this thesis has the same accuracy with that based on Pade approximation, but it is easier to improve the accuracy of FD forward modeling by optimizing the FD coefficients. The numeric experiments demonstrate that more accurate results can be obtained by the forward modeling of frequency domain wave equation with the optimized FD coefficients.