High-order finite-difference approximations to solve pseudoacoustic equations in 3D VTI media

Abstract

Pseudoacoustic algorithms are very fast in comparison with full elastic ones for vertical transversely isotropic (VTI) modeling, so they are suitable for many applications, especially reverse time migration. Finite differences using simple grids are commonly used to solve pseudoacoustic equations. We have developed and implemented general high-order 3D pseudoacoustic transversely isotropic formulations. The focus is the development of staggered-grid finite-difference algorithms, known for their superior numerical properties. The staggered-grid schemes based on first-order velocity-stress wave equations are developed in detail as well as schemes based on direct application to second-order stress equations. This last case uses the recently presented equivalent staggered-grid theory, resulting in a staggered-grid scheme that overcomes the problem of large memory requirement. Two examples are presented: a 3D simulation and a prestack reverse time migration application, and we perform a numerical analysis regarding computational cost and precision. The errors of the new schemes are smaller than the existing nonstaggered-grid schemes. In comparison with existing staggered-grid schemes, they require 25% less memory and only have slightly greater computational cost.

Propagação de ondas em meios anisotrópicos aplicadas ao mapeamento de estruturas

“…As onda compressionais são denominada de quase-P , assim como feito para o modo cisalhante de onda quase-S porque não se caracterizam como perturbações nas direções longitudinal e transversal à direção de propagação, em virtude da diferença entre velocidade de fase e velocidade de grupo [11] no caso anisotrópico. Será visto que tais equações para meios "pseudoacústicos" VTI podem ser obtidas por meio de uma abordagem simples e direta [18] tomando por base as equações vistas anteriormente e aplicando-se uma simplificação adequada, na qual o meio é considerado como "acústico", embora anisotrópico. Empregá-se a palavra "pseudo-acústico" com o objetivo apenas de deixar claro que o interesse é em descrever o modo de onda compressional, muito embora fisicamente meios anisotrópicos não sejam acústicos, mas sim elásticos.…”

High temporal accuracy elastic wave simulation with new time–space domain implicit staggered‐grid finite‐difference schemes

“…The finite‐difference (FD) methods for seismic wave simulation play an important role in computational seismology, owing to the low computational complexity and consumption, also economical for memory storage (e.g. Robertsson et al., 1994; Carcione et al., 2002; Etgen & O'Brien, 2007; Di Bartolo et al., 2012, 2017; Moczo et al., 2014; Fang et al., 2014; Zhou et al., 2021). One of the key issues faced by FD methods is the numerical spatial and temporal dispersion errors caused by approximating the corresponding continuous derivatives with discrete difference operators.…”