Hybrid absorbing boundary condition for piecewise smooth curved boundary in 2D acoustic finite difference modelling
Bei Li 1 2 Yang Liu 1 2 3 Yumin Zhao 1 2 Xin Liu 1 2
+ Author Affiliations
- Author Affiliations
1 State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum, Beijing 102249, China.
2 CNPC Key Laboratory of Geophysical Prospecting, China University of Petroleum, Beijing 102249, China.
3 Corresponding author. Email: wliuyang@vip.sina.com
Exploration Geophysics 49(4) 469-483 https://doi.org/10.1071/EG17012
Submitted: 15 January 2017 Accepted: 20 June 2017 Published: 18 August 2017
Abstract
Flexible computational domains and their corresponding irregular absorbing boundary conditions (ABCs) have previously been shown to improve the efficiency of finite difference (FD) modelling. However, these proposed ABCs for irregular boundaries are based on irregular grid methods. Although they can improve geometric flexibility of FD modelling, irregular grid methods are still complex to implement due to computationally expensive meshing process. To avoid complex mesh generation, FDs in mesh-free discretisation have been developed for nontrivial geometric settings, where scattered nodes can be placed suitably with respect to irregular boundaries and arbitrarily shaped anomalies without coordinate mapping or mesh-element forming. Radial-basis-function-generated FD (RBF-FD) has been proven successful in modelling seismic wave propagation based on mesh-free discretisation. Using RBF-FD, we develop a hybrid ABC for piecewise smooth curved boundary in 2D acoustic wave modelling based on straightforward expanding strategies for sampled boundary and corner nodes. The whole irregular computational domain is combined by an objective zone and a transition zone separated by piecewise smooth curved boundary. Nodal distribution in the objective zone is adaptive to the model structure through special alignment and varying density of nodes, while the transition zone are designed for solving one way wave equation more easily and accurately in the presence of piecewise smooth curved boundary. Modelling examples for homogenous and heterogeneous models with differently shaped computational domains demonstrate the effectiveness of our proposed method.
Key words: acoustic wave equation, hybrid absorbing boundary condition, mesh-free method, numerical modelling, one way wave equation, piecewise smooth curved boundary, radial-basis-function-generated finite difference.
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