A Finite-Difference Seismic Wavefield Simulation Method with Deep Uniform Sampling Trapezoidal Grid

Abstract

A finite difference seismic wave field simulation method adopting depth uniform sampling trapezoid grids comprises the steps as follows: firstly, the transformational relation between the coordinationpositions under a trapezoid coordinate system and coordinate positions under a rectangular coordinate system is determined, then, the expression form of a 2D wave equation in the trapezoid coordinatesystem is derived, and finally, as the wave equation in the trapezoid coordinate system has space mixed partial derivation, the mixed partial derivation is solved into non-mixed partial derivatives through coordinate rotation transformation, then, the wave equation under the trapezoid coordinate system is solved, and a simulation wave field is obtained. By means of the method, false reflection produced by transition of different sizes of grid areas can be avoided, and oversampling of traditional fixed grid finite difference for deep high-speed areas can be effectively reduced. The shallow simulation accuracy of the trapezoid coordinate system wave field is high, the deep horizontal response range is wide, and the number of finite difference grids can be effectively reduced.

Description

technical field [0001] The invention belongs to the technical field of seismic exploration, and relates to a seismic wave field forward modeling method, in particular to a depth uniform sampling trapezoidal grid finite difference seismic wave field simulation method. Background technique [0002] Seismic wave field simulation provides the response information of the subsurface medium within a period of time after the source is excited by solving the wave equation, which is an important means to understand the propagation characteristics of seismic waves in complex media. Accurate and efficient solution of the wave equation is crucial in many seismic exploration applications, such as observation system design, multiple wave suppression, seismic data interpretation, high-precision imaging and modeling, etc. (Etgen and O'Brien, 2007; Ren et al., 2011). At present, seismic wave field simulation is mainly divided into finite difference method, finite element method, pseudospectr...

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Problems solved by technology

The interpolation-based variable grid finite difference interpolation gives the required additional grid point information near the interface between coarse and fine grids. The additional calculation is small and the implementation is simple, but the interpolation is easy to cause false reflections and wave field recursion instability (Hayashi and Burns,1999)

The variable grid finite difference based on neighborhood difference approximation approximates the continuous partial derivative as a linear combination of the center point and its neighborhood grid points. The placement of grid points is free and flexible, but the grid point difference coefficient generally needs to be passed through the medium model. Calculation, adding a lot of additional calculations (Chen et al., 2016)

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