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Algorithms for staggered‐grid computations for poroelastic, elastic, acoustic, and scalar wave equations [Note 1. Received April 1995, revision accepted July 1996. ...]
Author(s) -
Özdenvar Turgut,
McMechan George A.
Publication year - 1997
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 - 10.1046/j.1365-2478.1997.390275.x
Subject(s) - poromechanics , biot number , scalar (mathematics) , computation , wave equation , grid , wave propagation , mathematical analysis , porous medium , physics , mathematics , mechanics , algorithm , geometry , geology , porosity , optics , geotechnical engineering
Heterogeneous wave equations are more complicated numerically than homogeneous wave equations, but are necessary for physical validity. A wide variety of numerical solutions of seismic wave equations is available, but most produce strong numerical artefacts and local instabilities where model parameters change rapidly. Accuracy and stability of heterogeneous equations is achieved through staggered‐grid formulations. A new pseudospectral staggered‐grid algorithm is developed for the poroelastic (Biot) equations. The algorithm may be reduced to handle the elastic and acoustic limits of the Biot equations. Comparisons of results from poroelastic, elastic, acoustic and scalar computations for a 2D model show that porous medium parameters may affect amplitudes significantly. The use of homogeneous wave equations for modelling of a heterogeneous medium, or of a centred rather than a staggered grid, or of simplified (e.g. acoustic) wave equations when elastic or poroelastic media are synthesized, may produce erroneous or ambiguous interpretations.