Two-dimensional elastic wave finite-difference simulation with adaptive mesh refinement

ZHANG Chunli; ZHANG Wei

doi:10.13471/j.cnki.acta.snus.2021D073

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Two-dimensional elastic wave finite-difference simulation with adaptive mesh refinement

Research articles | 更新时间：2023-11-01

- Two-dimensional elastic wave finite-difference simulation with adaptive mesh refinement
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 1, Pages: 125-138(2022)
- 作者机构：
  
  1.中国科学技术大学地球和空间科学学院，安徽合肥 230026
  2.南方科技大学深圳市深远海油气勘探技术重点实验室，广东深圳 518055
  3.南方科技大学地球与空间科学系，广东深圳 518055
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2021D073
  CLC： P315
- Published：25 January 2022，
  
  Published Online：22 December 2021，
  
  Received：16 October 2021，
  
  Accepted：28 October 2021
扫描看全文
张春丽,张伟.二维弹性波自适应网格有限差分模拟方法[J].中山大学学报(自然科学版),2022,61(01):125-138.

ZHANG Chunli,ZHANG Wei.Two-dimensional elastic wave finite-difference simulation with adaptive mesh refinement[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(01):125-138.
张春丽,张伟.二维弹性波自适应网格有限差分模拟方法[J].中山大学学报(自然科学版),2022,61(01):125-138. DOI： 10.13471/j.cnki.acta.snus.2021D073.

ZHANG Chunli,ZHANG Wei.Two-dimensional elastic wave finite-difference simulation with adaptive mesh refinement[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(01):125-138. DOI： 10.13471/j.cnki.acta.snus.2021D073.

摘要

弹性波数值模拟的所需的计算资源与网格点数相关。传统均匀网格有限差分方法的网格大小由复杂模型中的最小传播速度决定，导致高速区不必要的过密网格。比起已有的变网格，自适应网格（AMR，adaptive mesh refinement）灵活的结构使其可沿低速区的不规则区间使用密网格，因而计算效率提升更明显。本文将自适应网格同有限差分法结合，发展了适用于复杂模型的二维弹性波高效数值模拟算法。控制方程为一阶速度-应力方程组形式的弹性波方程，一阶空间导数采用高阶同位网格中心差分格式和显式滤波算子计算，时间积分采用四阶Runge-Kutta法。基于现有的自适应网格程序通用框架，实现自适应网格存储结构、网格生成和并行计算的负载均衡问题。数值算例表明，本文提出的方法适用于复杂速度模型的地震波传播计算，计算结果与传统均匀网格结果较一致，相位误差和幅值误差在10%左右。本文提出的方法从两个方面提高了计算效率：一是减少网格点数；二是通过增大高速区网格大小提高满足稳定性的时间步长。

Abstract

The computation resources required by elastic wave simulations are related to the number of grid points. The grid spacing for the conventional uniform grid is determined by the lowest velocity in the complex model， and thus the high-velocity zones are unnecessarily discretized to a too-small grid spacing. Adaptive Mesh Refinement（AMR） can flexibly deal with different irregular structures， using fine grids only for lower velocity zones， thus with high efficiency. We combine AMR with the finite-difference method to simulate the two-dimensional elastic wave for models with complex structures. The governing equation is the velocity-stress elastic wave equation in the first-order partial differential equation form. We calculate the spatial derivatives using high-order collocated-grid central difference schemes with an explicit filtering operator and implement the time integration with the Runge-Kutta method. We build up our implementation on an existing AMR framework to fulfill the data structure management， mesh generation， and load balance of the AMR. The results of the numerical experiments reveal that our scheme can be used for seismic wave simulations in complex velocity models. The results obtained by the proposed scheme fit well with those obtained by using a uniform grid with both phase and amplitude errors of ~10%. The proposed AMR scheme increases the computational efficiency by two folds： reducing the number of grid points and enlarging the time step as the grid spacing is increased in high-velocity regions.

关键词

弹性波数值模拟有限差分法自适应网格负载均衡

Keywords

elastic wave numerical simulationfinite-difference methodadaptive mesh refinementload balance

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