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3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

Petroleum Science 2020年第4期17卷 967-989页

作者： Qiang Zou Jian-Ping Huang Peng Yong Zhen-Chun Li School of Geosciences China University of Petroleum(East China)Qingdao 266580ShandongChina Tarim Oilfeld Branch CNPCKorla 841000XinjiangChina

Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and ***,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency *** develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave *** the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) *** the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion *** coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration ***,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning *** dispersion analyses show that the presented method produces less modeling errors than the traditional ESG *** synthetic examples demonstrate the effectiveness and superiority of the presented method.

关键词： 3D elastic wave equation Optimized equivalent staggered-grid Numerical dispersion Newton iteration method plane wave solution

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Instability of Two Interacting Quasi-Monochromatic waves in Shallow Water

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China Ocean Engineering 2007年第3期21卷 451-460页

作者：汤叔楩韦立新徐援 School of Sciences Hebei University of Science and Technology The Survey Bureau of Hydrology and Water Resaurces of Lower Reaches of Changjiang River CWRC Collage of Sciences Hohai University

The nonlinear interactions of waves with a double-peaked power spectrum have been studied in shallow water. The starting point is the prototypical equation for nonlinear unidirectional waves in shallow water, i.e. the Korteweg de Vries equation. By means of a multiple-scale technique two defocusing coupled Nonlinear SchrCMinger equations are derived. It is found analytically that plane wave solutions of such a system are unstable for small perturbations, showing that the existence of a new energy exchange mechanism which can influence the behavior of ocean waves in shallow water.

关键词： instability ocean wave Korteweg de Vries equation coupled nonlinear Schrodinger equation plane wave solution

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A Compact Finite Difference Schemes for Solving the Coupled Nonlinear Schrodinger-Boussinesq Equations

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Applied Mathematics 2016年第7期7卷 605-615页

作者： M. S. Ismail H. A. Ashi Department of Math College of Science King Abdulaziz University Jeddah Saudi Arabia

In this paper we are going to derive two numerical methods for solving the coupled nonlinear Schrodinger-Boussinesq equation. The first method is a nonlinear implicit scheme of second order accuracy in both directions time and space;the scheme is unconditionally stable. The second scheme is a nonlinear implicit scheme of second order accuracy in time and fourth order accuracy in space direction. A generalized method is also derived where the previous schemes can be obtained by some special values of l. The proposed methods will produced a coupled nonlinear tridiagonal system which can be solved by fixed point method. The exact solutions and the conserved quantities for two different tests are used to display the robustness of the proposed schemes.

关键词： Coupled Nonlinear Schrodinger-Boussinesq Equation Conserved Quantities Soliton plane wave solution Fixed Point Method

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