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Using the pseudospectral technique on curved grids for 2D acoustic forward modelling 1
Author(s) -
Nielsen Per,
If Flemming,
Berg Per,
Skovgaard Ove
Publication year - 1994
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.1365-2478.1994.tb00213.x
Subject(s) - curvilinear coordinates , grid , cartesian coordinate system , pseudo spectral method , computer science , computational science , regular grid , spurious relationship , geometry , computational fluid dynamics , mesh generation , fourier transform , fourier analysis , mechanics , mathematical analysis , mathematics , physics , finite element method , machine learning , thermodynamics
The Fourier pseudospectral method has been widely accepted for seismic forward modelling because of its high accuracy compared to other numerical techniques. Conventionally, the modelling is performed on Cartesian grids. This means that curved interfaces are represented in a ‘staircase fashion‘causing spurious diffractions. It is the aim of this work to eliminate these non‐physical diffractions by using curved grids that generally follow the interfaces. A further advantage of using curved grids is that the local grid density can be adjusted according to the velocity of the individual layers, i.e. the overall grid density is not restricted by the lowest velocity in the subsurface. This means that considerable savings in computer storage can be obtained and thus larger computational models can be handled. One of the major problems in using the curved grid approach has been the generation of a suitable grid that fits all the interfaces. However, as a new approach, we adopt techniques originally developed for computational fluid dynamics (CFD) applications. This allows us to put the curved grid technique into a general framework, enabling the grid to follow all interfaces. In principle, a separate grid is generated for each geological layer, patching the grid lines across the interfaces to obtain a globally continuous grid (the so‐called multiblock strategy). The curved grid is taken to constitute a generalised curvilinear coordinate system, where each grid line corresponds to a constant value of one of the curvilinear coordinates. That means that the forward modelling equations have to be written in curvilinear coordinates, resulting in additional terms in the equations. However, the subsurface geometry is much simpler in the curvilinear space. The advantages of the curved grid technique are demonstrated for the 2D acoustic wave equation. This includes a verification of the method against an analytic reference solution for wedge diffraction and a comparison with the pseudospectral method on Cartesian grids. The results demonstrate that high accuracies are obtained with few grid points and without extra computational costs as compared with Cartesian methods.