The Optimum Nearly Analytic Discrete Method And Elastic Wave Numerical Simulations

Nearly analytic discrete method (NADM) is a new numerical simulation method. This method not only combines the basic idea of classical numerical methods, but also considers these partial derivatives with various orders including in the source equation and its branch equations as we solve the partial differential equation. By this way it can reduce effectively the loss of the seismic information of the source equation and improve numerical accuracy and computational stability. To do this, the basic thought of the NADM method is to use a truncated Taylor series expansion to approximate the time derivatives and an interpolation function constructed by higher-order truncated Taylor series to obtain the spatial high-order derivatives using some connection relations.However there are some disadvantages of the NADM, such as it needs more storage spaces for the computer code and the efficiency of the computation is not high as compared with that of the FDM. The NADM is improved and an optimum nearly analytic discrete method (ONADM) is presented in this study. Comparing relative errors of the ONADM with those of the LWC and the NADM for the 1-D initial problem and with those of the FDM and the NADM for the 2-D case illustrate that the ONADM have higher accuracy . The basic formulas of the ONADM for the 3-D case are also obtained in the present study. In addition, the validity of the 4-times decoupled absorbing boundary condition, incorporated in the ONADM, is investigated by simulating three-component synthetic VSP seismograms in three layers transversely isotropic homogeneous. Besides, the numerical simulation of elastic wave fields for 2-D and 3-D homogeneous cases and the inhomogeneous case are also presented in the study.Theory analyses and numerical results illustrate that the ONADM has higher accuracy and better stability and can reduce storage space about 53 percent and computational costs about 30 percent compared with the original NAMD. Moreover the accuracy of the modified NAMD in time increases to 4-order from 2-order of the original NADM. Numerical results suggest that the modified NADM is more suitable to wave-field modeling of large scale models because the modified method has little numerical dispersions even when too-coarse grids are used.