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Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE

Perfectly matched layer on curvilinear grid for the second-order seismic acoustic wave equation

Sanyi Yuan 1 Shangxu Wang 1 4 Wenju Sun 1 Lina Miao 2 Zhenhua Li 3
+ Author Affiliations
- Author Affiliations

1 State Key Laboratory of Petroleum Resource and Prospecting, CNPC Key Laboratory of Geophysical Exploration, China University of Petroleum, Beijing 102249, China.

2 Department of Earth, Ocean and Atmospheric Sciences, The University of British Columbia, Vancouver V6T 1Z4, Canada.

3 Department of Physics, University of Alberta, CEB, Edmonton, Alberta T6G 2E1, Canada.

4 Corresponding author. Email: wangsx@cup.edu.cn

Exploration Geophysics 45(2) 94-104 https://doi.org/10.1071/EG13066
Submitted: 4 August 2013  Accepted: 30 January 2014   Published: 11 March 2014

Abstract

A curvilinear-grid perfectly matched layer (PML) absorbing boundary condition for the second-order seismic acoustic wave equation is presented in this paper. The rectangular grids are transformed into curvilinear grids by using a mathematical mapping to fit the curvilinear boundary, and the original wave equation is reformulated under the curvilinear coordinate system. Based on the reformulated wave equation, theoretical expressions and analysis of the curvilinear-grid PML are given. Furthermore, PML model 1 with symmetric form and PML model 2 with asymmetric form are derived from the same acoustic wave equation. By combination with the finite difference (FD) method, these two models are applied to seismic wave modelling with surface topography. The results show that the absorption effect of these two models discretised by the same second-order time difference and second-order space difference are different, and the symmetric-form PML yields better modelling results than the asymmetric-form.

Key words: acoustic wave equation, finite difference, perfectly matched layer, seismic modeling, surface topography.


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