Numerical solution of the acoustic wave equation by the rapid expansion method (REM) - A one step time evolution algorithm

2009 ◽  
Author(s):  
Paul L. Stoffa* ◽  
Reynam C. Pestana
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Numerical Solution ◽  
Time Evolution ◽  
Expansion Method ◽  
Rapid Expansion ◽  
Acoustic Wave Equation ◽  
One Step ◽  
Evolution Algorithm

scholarly journals ONE-STEP EXTRAPOLATION METHOD USING CHEBYSHEV’S RECURRENCE RELATION APPLIED TO SEISMIC MODELING

2016 ◽  
Vol 34 (4) ◽  
Author(s):  
Laura Lara Ortiz ◽  
Reynam C. Pestana
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Chebyshev Polynomials ◽  
Finite Difference Scheme ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
First Order ◽  
One Step

ABSTRACT. In this work we show that the solution of the first order differential wave equation for an analytical wavefield, using a finite-difference scheme in time, follows exactly the same recursion of modified Chebyshev polynomials. Based on this, we proposed a numerical...Keywords: seismic modeling, acoustic wave equation, analytical wavefield, Chebyshev polinomials. RESUMO. Neste trabalho, mostra-se que a solução da equação de onda de primeira ordem com um campo de onda analítico usando um esquema de diferenças finitas no tempo segue exatamente a relação de recorrência dos polinômios modificados de Chebyshev. O algoritmo...Palavras-chave: modelagem sísmica, equação da onda acústica, campo analítico, polinômios de Chebyshev.

Time evolution of the wave equation using rapid expansion method

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. T121-T131 ◽  
Author(s):  
Reynam C. Pestana ◽  
Paul L. Stoffa
Keyword(s):  
Wave Equation ◽  
Time Evolution ◽  
Time Derivative ◽  
Expansion Method ◽  
Pressure Response ◽  
Rapid Expansion ◽  
Reverse Time ◽  
Step Method ◽  
Time Migration ◽  
Spatially Varying

Forward modeling of seismic data and reverse time migration are based on the time evolution of wavefields. For the case of spatially varying velocity, we have worked on two approaches to evaluate the time evolution of seismic wavefields. An exact solution for the constant-velocity acoustic wave equation can be used to simulate the pressure response at any time. For a spatially varying velocity, a one-step method can be developed where no intermediate time responses are required. Using this approach, we have solved for the pressure response at intermediate times and have developed a recursive solution. The solution has a very high degree of accuracy and can be reduced to various finite-difference time-derivative methods, depending on the approximations used. Although the two approaches are closely related, each has advantages, depending on the problem being solved.

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