Enhanced Difference Algorithm for Seismic Modeling Based on Fruit Fly Optimization

Abstract

The acoustic wave equation is an important basis for seismic wave propagation, imaging, and migration. This equation has led to the development of finite difference methods, but these methods are prone to numerical instability and grid dispersion problems, with the issue of dispersion being the most vital. Optimization methods can improve the accuracy across a large range of wavenumbers or frequencies. In this paper, we present a novel evolutionary optimization scheme for the acoustic wave equation. Our approach involves combining the fruit fly optimization algorithm (FOA) and sampling approximation (SA) to obtain the optimal difference operator for a wide range of wavenumbers. The difference coefficients are optimized to be extracted by the FOA, and the function of fitness, which is used to introduce an iterative process to determine the best smells, is evaluated by acoustic wave simulations. Based on the space-domain dispersion relation, we prove that the accuracy with which the absolute error is minimized is the same as that of the relative error. Within a given range of wavenumbers, we propose a fitness function by minimizing the absolute errors of the space-domain dispersion relation, and the dispersion analysis reveals that this scheme is superior to the Taylor-expansion scheme. We conduct two experiments by applying homogeneous and complex models, respectively. Further, the modeling results indicate that the fruit fly optimization approach in conjunction with sampling approximation preserve a higher accuracy for a small operator length and reduce the numerical artifacts.

Novel Optimal Staggered Grid Finite Difference Scheme Based on Gram–Schmidt Procedure for Acoustic Wave Modelling

“…Under the condition of same operator length and wavenumber range, the accuracy of the SGFD coefficients calculated using the different methods can be compared using the generated error. Zhang et al (2017) proved that the comparison accuracy based on the absolute and relative errors was consistent.…”

“…Compared with that based on the common rectangular standard grid, the finite difference method based on a staggered grid (SGFD) has higher computational stability and accuracy. However, when the SGFD method is used for numerical simulation of seismic wave propagation, researchers encounter the inevitable problem of numerical dispersion (Virieux 1986;Robertsson 1996;Saenger and Shapiro 2002;Liu and Sen 2013;Yang et al, 2015Yang et al, , 2016Zhang et al, 2017;Ren and Li 2019). This is because the existence of large grids or high-frequency components leads to a reduction in the spatial sampling points, resulting in redundant wave artifacts, which can be clearly displayed in the wavefield snapshot and single-shot record.…”