A correspondence principle for steady-state wave problems

A correspondence principle was developed for treating the steady state propagation of waves from sources moving along a plane surface or interface. This new principle allows one to obtain, in a unified manner, explicit solutions for any source velocity. To illustrate the correspondence principle in a particular case, the problem of a load moving at an arbitrary constant velocity along the surface of an elastic half-space is considered

New Approaches to Ultrasonic Flaw Classification Using Signal Processing, Modeling, and Artificial Intelligence Concepts

There are a number of modern approaches that can be used to characterize flaws in materials. For example, one method, which has been described recently by Wormley and Thompson [1], uses a model-based approach to obtain the “best fit” size and orientation parameters based on a simple equivalent shape such as ellipsoid. Before such sizing estimates can be activated, however, it is first necessary to determine if the unknown flaw being examined is a volumetric or crack-like flaw, since the sizing algorithm will be different for each case. This classification problem, although it is conceptually simpler than the more complete problem of flaw characterization, is, nevertheless, a difficult challenge because of the large number of parameters that can influence the resulting signals. A summary of our recent work on the flaw classification problem is given below. As will be shown, we have chosen to use a combination of signal processing, modeling and artificial intelligence tools to try to pare down the complexity of the ultrasonic responses and isolate those features that are dependent only on flaw-type

Ultrasonic Flaw Characterization in the Resonance Region by the Boundary Integral Equation Method

When the wavelength of the ultrasound being used to characterize a flaw is of the same order of magnitude as the flaw size, conventional low and high frequency scattering approximations fail. In this frequency range, called here the resonance region, numerical methods are necessary. Here we show that one such method, the Boundary Integral Equation (BIE) Method, is an effective tool for solving elastic wave scattering problems in the resonance region provided some important modifications are made in the method as used previously by other authors. To illustrate the BIE method, scattering from a cylindrical void in two-dimensions is considered. Comparisons are given with complimentary analytical and experimental results

Ultrasonic Scattering in Composites Using Spatial Fourier Transform Techniques

The heterogeneous nature of composite materials often makes their inspection using ultrasonics difficult unless the flaws are sufficiently large so that common B- or C- scans can be employed. Thus, flaw scattering models are essential in order to interpret the measured ultrasonic responses. However, even at low frequencies where the composite may be able to be replaced by an equivalent homogeneous, anisotropic material, conventional direct scattering methods such as the T-Matrix and Boundary Element techniques are not effective. This is because both methods rely on the superposition of exact solutions to the governing equations of elastodynamics and, except for very special anisotropics, such exact solutions are not available in closed form. One way around this difficulty is to pose the scattering problem in a spatial Fourier frequency domain where exact fundamental solutions for elastodynamics are available, even for general anisotropic materials (1). Employing these solutions in a conventional volume or surface integral equation for the scattering wavefields then yields a spatial frequency domain formulation to the direct scattering problem. Because the boundary conditions are given in the real spatial domain, it is necessary to iteratively satisfy these conditions via fast Fourier transforms (2). This approach is called the Spectral-Iteration Technique and has been applied successfully for a variety of electromagnetic scattering problems (3), (4). Here, we will obtain the equivalent elastic wave scattering formulations for cracks and volumetric flaws in a general anisotropic medium. Modifications of the standard Spectral-Iteration technique needed to ensure its convergence at low frequencies will also be discussed

Ultrasonic measurement models for surface wave and plate wave inspections

A complete ultrasonic measurement model for surface and plate wave inspections is obtained, where all the electrical, electromechanical, and acoustic∕elastic elements are explicitly described. Reciprocity principles are used to describe the acoustic∕elastic elements specifically in terms of an integral of the incident and scattered wave fields over the surface of the flaw. As with the case of bulk waves, if one assumes the incident surface waves or plate waves are locally planar at the flaw surface, the overall measurement model reduces to a very modular form where the far‐field scattering amplitude of the flaw appears explicitly

Ultrasonic Flaw Characterization in the Resonance Region by the Boundary Integral Equation Method

When the wavelength of the ultrasound being used to characterize a flaw is of the same order of magnitude as the flaw size, conventional low and high frequency scattering approximations fail. In this frequency range, called here the resonance region, numerical methods are necessary. Here we show that one such method, the Boundary Integral Equation (BIE) Method, is an effective tool for solving elastic wave scattering problems in the resonance region provided some important modifications are made in the method as used previously by other authors. To illustrate the BIE method, scattering from a cylindrical void in two-dimensions is considered. Comparisons are given with complimentary analytical and experimental results

Ultrasonic phased array system modeling-issues and solutions

In modeling ultrasonic phased array inspection systems one needs to characterize the electrical and electromechanical components of the system and the radiation properties of the individual array elements since both of these properties are important in being able to model the overall response of the array to any flaws present. Models for determining each of these elements will be obtained and issues unique to phased array systems will be discussed

Ultrasonic Flaw Classification Using a Quasi-Pulse-Echo Technique

In solving ultrasonic flaw characterization problems, flaw type information is often needed in order to pursue succeeding tasks such as flaw sizing. In a typical inspection, the interaction of the incident ultrasonic pulse with the flaw results in a series of signal trains. A variety of signal features are extracted from these flaw signals and then used as the basis for the classification process. This classification process is made difficult by the large number of possible scattered waves. For example, typical ultrasonic signals from a planar crack-like defect consist of reflected responses, surface traveling waves, edge diffracted waves and head wave components. For a volumetric void-like defect, the returned signal pattern similarly contains reflected waves of the same mode as well as mode-converted reflections and “creeping” waves. However, in pulse-echo testing a fundamental difference exists between a crack-like flaw and a volumetric flaw that can be used for classification purposes. This difference is reflected in the fact that a significant mode-converted diffracted wave component can exist for a crack-like defect (Fig. 1(a)) which does not exist in pulse-echo testing for a volumetric defect (Fig.1(b))

GRAIL Refinements to Lunar Seismic Structure

Joint interpretation of disparate geophysical datasets helps to reduce drawbacks that can result from analyzing them individually. The Apollo seismic network was situated on the lunar nearside surface in a roughly equilateral triangle having sides approximately 1000 km long, with stations 12/14 nearly colocated at one corner. Due to this limited geographical extent, nearsurface ray coverage from moonquakes is low, but increases with depth. In comparison, gravity surveys and their resulting gravity anomaly maps have traditionally offered optimal resolution at crustal depths. Gravimetric maps and seismic data sets are therefore well suited to joint inversion, since the complementary information reduces inherent model ambiguity. Previous joint inversions of the Apollo seismic data (seismic phase arrival times) and Clementine or Lunar Prospectorderived gravity data (mass and moment of inertia) attempted to recover the subsurface structure of the Moon by focusing on hypothetical lunar compositions that explore the density/velocity relationship. These efforts typically search for the best fitting thermodynamically calculated velocity/density model, allowing variables like core size, velocity, and/or composition to vary freely. Seismic velocity profiles previously derived from the Apollo seismic data through inversion of travel times vary both in the depth of the crust and mantle layers, and the seismic velocities and densities assigned to those layers. The lunar mass and moment of inertia likewise only constrain gross variations in the density profile beyond that of a uniform density sphere. As a result, composition and structure models previously obtained by jointly inverting these data retain the original uncertainties inherent in the input data sets. We will perform a joint inversion of Apollo seismic delay times and gravity data collected by the GRAIL lunar gravity mission, in order to recover seismic velocities and density as a function of latitude, longitude, and depth within the Moon. We will relate density to seismic velocity using a linear relationship that is allowed to be depthdependent. The corresponding coefficient (B) can reflect a variety of material properties that vary with depth, including temperature and composition. The inversion seeks to recover the set of density, velocity, and Bcoefficient perturbations that minimize (in a leastsquares sense) the difference between the observed and calculated data