Open AccessStructure‐preserving modelling of elastic waves: a symplectic discrete singular convolution differentiator method
Author(s) -
Li Xiaofan,
Wang Wenshuai,
Lu Mingwen,
Zhang Meigen,
Li Yiqiong
Publication year - 2012
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2011.05344.x
Subject(s) - differentiator , discretization , symplectic geometry , classification of discontinuities , convolution (computer science) , truncation (statistics) , numerical analysis , mathematics , dispersion (optics) , mathematical analysis , computer science , physics , artificial neural network , statistics , machine learning , optics , computer network , bandwidth (computing)
SUMMARY In this paper, we introduce the so‐called symplectic discrete singular convolution differentiator (SDSCD) method for structure‐preserving modelling of elastic waves. In the method presented, physical space is discretized by the DSCD, whereas an explicit third‐order symplectic scheme is used for the time discretization. This approach uses optimization and truncation to form a localized operator. This preserves the fine structure of the wavefield in complex media and avoids non‐causal interaction when parameter discontinuities are present in the medium. Theoretically, the approach presented is a structure‐preserving algorithm. Also, some numerical experiments are shown in this paper. Elastic wavefield modelling experiments on a laterally heterogeneous medium with high parameter contrasts demonstrate the superior performance of the SDSCD for suppression of numerical dispersion. Long‐term computational experiments exhibit the remarkable capability of the approach presented for long‐time simulations. Promising numerical results suggest the SDSCD is suitable for high‐precision and long‐time numerical simulations, as it has structure‐preserving property and it can suppress effectively numerical dispersion when coarse grids are used.