James H. Rose

Ultrasonic method to determine gas porosity in aluminum alloy castings: Theory and experiment

The characterization of porosity in solids using the frequency dependence of the ultrasonic attenuation is discussed both from the theoretical and experimental viewpoint. The major thrust of our work is the determination of the volume fraction and size of the voids for the case of dilute porosity (<6%) in structural materials. An aluminum alloy (A357) was chosen for study due to its economic importance in large‐scale casting and the particular suitability of aluminum for this type of study. Following recent papers the attenuation is described by an independent scatterer model for spherical voids. Numerical results are presented in a form suitable for use with a range of materials. A method for determining the volume fraction and pore size is given. Specific tabular results are given for stainless steel, IN‐100, Ti, Si3N4, as well as aluminum. Figures of merit which partially describe those situations in which the method is usable are also presented. In the experimental work a digitized spectrum analysis s...

Three-dimensional inverse scattering: plasma and variable velocity wave equations

Exact equations governing three‐dimensional time‐domain inverse scattering are derived for the plasma wave equation and the variable velocity classical wave equation. This derivation was announced for the plasma wave equation in a short note by the authors. That work was motivated by Newton’s three‐dimensional generalization of Marchenko’s equation. This paper gives the details of the new derivation and extends it to the classical wave equation. For the time domain derivation in this paper, the scattering region is assumed to have compact support and smoothly joins the surrounding three‐dimensional infinite medium. The derivation contains the following ingredients: (1) a representation of the solution at a point in terms of its values on a large sphere, (2) the far‐field form of the Green’s function, (3) causality, and (4) information carried in the wave front of the solution. The derivation of the classical wave inverse scattering equation requires that the velocity in the scattering region be less than ...

Physical basis of three-dimensional inverse scattering for the plasma wave equation

Exact inverse-scattering equations are derived for the time-domain plasma-wave equation. Care is taken to motivate each step of the derivation by elementary physical arguments. The inverse method in this formulation is shown to depend on (1) causality, (2) the far-field properties of the Green function, and (3) the representation theorem.

Three‐dimensional inverse scattering: High‐frequency analysis of Newton’s Marchenko equation

We obtain a high‐frequency asymptotic expansion of Newton’s Marchenko equation for three‐dimensional inverse scattering. We find that the inhomogeneous term contains the same high‐frequency information as does the Born approximation. We show that recovery of the potential via Newton’s Marchenko equation plus the ‘‘miracle’’ depends on low‐frequency information.