Elastic Wave Equation Forward Modeling Based on Precise Integration Method

2012 ◽  
Author(s):  
Yuting Duan ◽  
Tianyue Hu
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Integration Method ◽  
Forward Modeling ◽  
Elastic Wave Equation ◽  
Precise Integration ◽  
Precise Integration Method

scholarly journals Spatial Mesh Refinement using Cubic Smoothing Spline Interpolation in Simulation of 2-D Elastic Wave Equation: Forward Modeling of Full-waveform Inversion

2021 ◽  
pp. 66-83
Author(s):  
Amila Sudu Ambegedara ◽  
U. G. I. G. K. Udagedara ◽  
Erik M. Bollt
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Spline Interpolation ◽  
Waveform Inversion ◽  
Mesh Refinement ◽  
Forward Modeling ◽  
Smoothing Spline ◽  
Small Scale ◽  
Elastic Wave Equation ◽  
Full Waveform

Full-waveform inversion (FWI) is a non-destructive health monitoring technique that can be used to identify and quantify the embedded anomalies. The forward modeling of the FWI consists of a simulation of elastic wave equation to generate synthetic data. Thus the accuracy of the FWI method highly depends on the simulation method used in the forward modeling. Simulation of a 3-D seismic survey with small-scale heterogeneities is impossible with the classic finite difference approach even on modern super computers. In this work, we adopted a mesh refinement approach for simulation of the wave equation in the presence of small-scale heterogeneities. This approach uses cubic smoothing spline interpolation for spatial mesh refinement step in solving the wave equation. The simulation results for the 2-D elastic wave equation are presented and compared with the classic finite difference approach.

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

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