Frequency domain seismic forward modelling: A tool for waveform ...

Abstract
Modelling the propagation of seismic waves, and thereby predicting the response
at seismic receivers is crucial in order to interpret, or formally invert data
from seismic experiments. Commonly used seismic waveform modelling techniques
become impractical when one has to simulate datasets involving a large number of
sources.
The multiple source problem can be eciently solved by frequency domain
forward modelling.
Futhermore, viscous attenuation is easy to incorporate into
frequency-domain methods. Once the frequency domain equations are discretized,
the solution (at each given frequency) is implicit in the solution of an extremely
large matrix equation. The essential problem is to ensure the structural sparsity of
the matrix and to take full advantage of this. The sparsity of the matrix is best
handled by the nested-dissection method described by George and Liu (1981).
Ihave analysed and extended the visco-acoustic rotated nite dierence scheme
developed by Joetal.(1996). Ihave shown that these operators are optimal: if the
nested dissection method is used, nothing can be gained by higher order operators.
Several modelling and waveeld inversion examples using the scheme are desribed
that demonstrate the eciency of optimised frequency domain modelling scheme. A
waveeld inversion example proves that frequency domain modelling, when used as
an integral part of the inversion procedure, can generate an accurate, high quality
image quickly and eciently. A pre-processing technique for waveeld inversion is
developed and the eects of the pre-processing on the image and on the convergence
are analyzed. The need for an elastic scheme is identied.
To meet the need for an elastic sheme, I have further extended the rotated
operator method to the visco-elastic case. This extension leads to a high accuracy
sheme. The visco-elastic scheme is used to predict and identify the presence of shear
waves on a real data example.
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