S. Kostek
T. M. Habashy
C. Torres-Verdin
Schlumberger--Doll Res., Ridgefield, CT 06877-4108
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.