No abstract

This work is concerned with the modeling of elastic wave scattering by solid or fluid-filled objects embedded in an inhomogeneous elastic background. The medium is probed by a monochromatic force and the scattered field is computed (forward problem) or observed (inverse problem) at some known receiver locations. Based on vector integral equations for elastic scattering, a general framework is developed, independent of both the problem geometry and the transmitter-receiver characteristics. This framework encompasses both forward and inverse modeling. In the forward model, a Born approximation for an inhomogeneous background is applied to obtain a closed form expression for the scattered field. In the inverse model, this approximation is also invoked to linearize for the multiparameter characteristic of the object. Finally, an iterative inversion scheme alternating forward and inverse modeling is proposed to improve the resolution and accuracy of the reconstruction algorithm.

This work is concerned with the influence of the finite-amplitude distortion of a driving diagnostic ultrasonic field on the collapse and rebound of a gas-filled spherical microbubble, present in the exposed compressible liquid. Such an analysis is especially important since one of the mechanisms for cavitation damage comes from the very large gas pressures generated at bubble collapse and in the subsequent pressure wave formed by bubble rebound. Gilmore's model [F.R. Gilmore, "The growth or collapse of a spherical bubble in a viscous compressible liquid," Hydrodynamics Lab. Rep. No. 26-4, California Institute of Technology, Pasadena, CA (1952)] for bubble dynamics is used to obtain the motion of the bubble interface when subjected to a pulsed diagnostic ultrasonic field of large amplitude. Knowledge of the bubble motion allows one to derive the pressure distribution around the bubble. Numerical results over a range of initial bubble sizes, acoustic pressures, and frequencies relevant to medical use show that the strength of the pressure spikes radiated by the rebounding bubble depends upon (i) the acoustic frequency (f), (ii) the initial bubble size (R0), and (iii) the magnitude of the pressure amplitude of the fundamental (PF) in a Fourier series description of the distorted pulse. As the pressure spikes propagate outward from the bubble wall, their strength is attenuated as the reciprocal of the distance from the center of collapse.

The scattering of elastic waves by multidimensional objects buried in a multilayered elastic background medium insonified by ultrasonic forces is studied. The framework developed is based on an integral equation formalism for elastic scattering, where a Born approximation for an inhomogeneous background medium is applied to obtain a closed-form expression for the scattered field. Both compressional and shear waves are allowed to propagate inside the layers, and take into account cross-polarization at the boundaries and multiple reflections within the layers to compute the scattered field. The procedure has been tested in cases where the Born approximation is severely put to test (100% contrast in shear modulus).

f Schlumberger-Doll Research, Ridgefield, C T 06877 A B S T R A C T The purpose of this work is to study, both analytically and numerically, the scattering from finite-size inclusions buried in a multilayered, elastic background structure, and to correlate this information to the geometrical and elastic properties of the inclusion. The framework developed is based on a vector integral equation formalism for elastic scattering, where a Born approximation for an inhomogeneous background medium is applied to obtain a closed-form expression for the scattered field. We allow both compressional and shear waves to propagate inside the layers, and take into account cross-polarization at the boundaries and multiple reflections within the layers. We have tested the procedure in cases where the Born approximation is severely put to test (100% contrast in shear modulus) and obtained good agreement with the results obtained independently through a finite-difference technique.