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In seismic modeling adaptive techniques are well known. Usually the adaption
of a quantity is in the direction of a physical dimension like
time or space. In general, adaption is guided by criteria to improve
numerical accuracy and stability or to increase the speed of the calculation.
In his Ph.D. thesis Cunha-Filho 1992
discussed the notion of treating
the propagating elastic wave field differently to the underlying medium.
His aim was to improve accuracy of reflected and transmitted amplitudes
across an interface. He derived his technique in combination with an averaging
scheme across the interface and made use of an unstaggered grid.
When examining the accuracy and stability of finite difference operators,
the staggered grid finite difference equation can be separated into
components that interpolate to the points where derivatives are evaluated.
For anisotropic media Igel et. al 1992
showed an error analysis of FD operators
and their spatial distribution.
Usual implementations have implicit interpolations of medium and wave field
properties built into the wave equation operator.
Splitting the wave equation operator and explicitly controlling
the interpolation
gives a well determined and more accurate wave propagation description.

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Stanford Exploration Project

11/17/1997