### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3aPA1. A new nonlinear approximation for elastic wave scattering.

**S. Kostek
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T. M. Habashy
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C. Torres-Verdin
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*Schlumberger--Doll Res., Ridgefield, CT 06877-4108
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A novel approximation to simulate elastic wave scattering in arbitrarily
heterogeneous media is introduced. The approximation, formulated in the
frequency domain, is derived from a volume integral equation governing the
displacement vector within the scatterer. It is shown that if the displacement
vector is assumed a locally smooth function of position within the scatterer
then it can be expressed as the projection of the background displacement onto
a scattering operator. This scattering operator is nonlinear with respect to
the spatial variations of density and Lame constants and can be computed via
simple explicit formulas. The scattering operator adjusts the background
displacement by way of amplitude, phase, and polarization corrections which are
needed to estimate the internal displacement due to an arbitrary source
excitation. It is also shown that the new approximation is substantially more
efficient than iterative Born techniques whose convergence is hardly guaranteed
for large contrasts in material properties. Validation tests are presented
which confirm that the new approximation remains accurate for large contrasts
of the elastic parameters and over a wide frequency range. Moreover, the new
approximation has nearly the computational efficiency of the first-order Born
approximation but is much more accurate. These two features make the scattering
formulation extremely attractive to approach multifrequency inversion problems
involving a multitude of scatterers.