Wave Field Simulation Based On Optimized Finite-differential Coefficient

In recent years,the significance and status of oil and natural gas energy are increasing.As a part of seismic exploration research,seismic wave field simulation is becoming more and more important,especially in reverse time migration and full waveform inversion.Numerical simulation of seismic wave field based on wave equation is a common wave field simulation method,which is widely used in the study of various underground media.This paper introduces the principle,implementation and error analysis of finite difference method.At the same time,some common absorption boundary methods are introduced to solve the problem that wave field simulation accuracy is affected when there is no boundary.Because the finite-difference method introduces truncation error term in principle,the result of numerical simulation accumulates will accumulate some errer,which looks like pseudo fluctuation.This is often referred to as "numerical dispersion".It is shown that the finite difference operator can be obtained by truncating the spatial convolution sequence of the pseudo-spectral method.In order to reduce the numerical dispersion,this paper proposes an optimal difference operator based on self-convolution Kaiser window truncation and verifies it under different models.The results show that this method can effectively reduce the numerical dispersion,and can replace the high-order simulation results of conventional difference operators with low-order wave field simulation,thus greatly reducing the calculation cost.In order to further simulate the real underground medium,this paper studies the two-phase medium model based on Biot theory,and applies the optimized difference operator to obtain the wave field simulation results with lower dispersion.The results show that the interaction of solid and liquid components has different effects on the shape and propagation of seismic wave field.