General elastic wave scattering problems using an impedance operator approach - I. Mathematical development

General Theory of Elastic Wave Scattering

Shear-wave elastic impedance

impedance (AI) and a parameter related to shear-wave velocity from seismic data, our ability to discriminate between different lithologies and fluid phases will increase. Prestack inversion on individual CDP gathers and inverting directly for VP, VS, and density have been tested in several ways, but the estimated parameters are often poorly determined. A more robust approach is to apply poststa...

Electromagnetic Wave Scattering by Small Impedance Particles

Scattering of electromagnetic (EM) waves by one and many small (ka 1) impedance particles Dm of an arbitrary shape, embedded in a homogeneous medium, is studied. Analytic formula for the field, scattered by one particle, is derived. The scattered field is of the order O(a2−κ), where κ ∈ [0, 1) is a number. This field is much larger than in the Rayleigh-type scattering. An equation is derived fo...

An Application of Padé Approximants to Elastic Wave Scattering

Several Padé methods were used to try to accelerate the convergence of partial wave sums for scattering amplitudes. A specific test problem of longitudinal-to-longitudinal scattering from a spherical void was studied in detail. Results for this test case and the behavior of partial wave amplitudes for general cases are presented and discussed.

Elastic Wave Scattering from Griffith Cracks

To model elastic wave scattering from fatigue cracks in metals, studies were conducted of wave scattering from artificial cracks using ultrasonic spectroscopy. The cracks are of two dimensional planar strips oriented at various angles and embedded in diffusion bonded titanium alloy. The crack is assumed to behave as a Griffith crack and expressions (derived by Achenbach1) to describe diffracted...