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NUMERICAL SOLUTION OF THE ACOUSTIC AND ELASTIC WAVE EQUATIONS BY A NEW RAPID EXPANSION METHOD 1
Author(s) -
KOSLOFF DAN,
FILHO ANIBAL QUEIROZ,
TESSMER EKKEHART,
BEHLE ALFRED
Publication year - 1989
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1989.tb02212.x
Subject(s) - acoustic wave equation , wave equation , elasticity (physics) , chebyshev filter , grid , fourier transform , mathematical analysis , numerical analysis , chebyshev polynomials , finite difference , acoustics , computer science , acoustic wave , mathematics , physics , geometry , thermodynamics
A bstract We present a new rapid expansion method (REM) for the time integration of the acoustic wave equation and the equations of dynamic elasticity in two spatial dimensions. The method is applicable to spatial grid methods such as finite differences, finite elements or the Fourier method. It is based on a Chebyshev expansion of the formal solution to the appropriate wave equation written in operator form. The method yields machine accuracy yet it is faster than methods based on temporal differencing. Its disadvantages are that it does not apply to all types of material rheology, and it can also require much storage when many snapshots and time sections are desired. Comparisons between numerical and analytical solutions for simple acoustic and elastic problems demonstrate the high accuracy of the REM.