Timothy J. Ulrich

Determination of elastic moduli of rock samples using resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) is a method whereby the elastic tensor of a sample is extracted from a set of measured resonance frequencies. RUS has been used successfully to determine the elastic properties of single crystals and homogeneous samples. In this paper, we study the application of RUS to macroscopic samples of mesoscopically inhomogeneous materials, specifically rock. Particular attention is paid to five issues: the scale of mesoscopic inhomogeneity, imprecision in the figure of the sample, the effects of low Q, optimizing the data sets to extract the elastic tensor reliably, and sensitivity to anisotropy. Using modeling and empirical testing, we find that many of the difficulties associated with using RUS on mesoscopically inhomogeneous materials can be mitigated through the judicious choice of sample size and sample aspect ratio.

Time Reversal of Continuous-Wave, Steady-State Signals in Elastic Media

Experimental observations of spatial focusing of continuous-wave, steady-state elastic waves in a reverberant elastic cavity using time reversal are reported here. Spatially localized focusing is achieved when multiple channels are employed, while a single channel does not yield such focusing. The amplitude of the energy at the focal location increases as the square of the number of channels used, while the amplitude elsewhere in the medium increases proportionally with the number of channels used. The observation is important in the context of imaging in solid laboratory samples as well as problems involving continuous-wave signals in Earth.

Investigation of the robustness of time reversal acoustics in solid media through the reconstruction of temporally symmetric sources

We investigate some of the limitations of time reversal acoustics (TRA) in solid media with transducers attached to the surface. In particular, we consider the limitations due to the finite size of the transducers and elastic wave propagation. Using a theoretical approach, numerical simulations and validation from laboratory ultrasound experiments, we find that finite size transducers and the existence of longitudinal and shear waves play significant roles in perturbing the time reversal process. Despite these limitations, we show that TRA in solids is very robust, providing the means to reconstruct the main features of the source signal. The analysis of TRA retro-focusing properties in solid specimens is of foremost importance for the development of new non-destructive evaluation techniques.

Decoupling Nonclassical Nonlinear Behavior of Elastic Wave Types

In this Letter, the tensorial nature of the nonequilibrium dynamics in nonlinear mesoscopic elastic materials is evidenced via multimode resonance experiments. In these experiments the dynamic response, including the spatial variations of velocities and strains, is carefully monitored while the sample is vibrated in a purely longitudinal or a purely torsional mode. By analogy with the fact that such experiments can decouple the elements of the linear elastic tensor, we demonstrate that the parameters quantifying the nonequilibrium dynamics of the material differ substantially for a compressional wave and for a shear wave. This result could lead to further understanding of the nonlinear mechanical phenomena that arise in natural systems as well as to the design and engineering of nonlinear acoustic metamaterials.

Energy current imaging method for time reversal in elastic media

An energy current imaging method is presented for use in locating sources of wave energy during the back propagation stage of the time reversal process. During the back propagation phase of an ideal time reversal experiment, wave energy coalesces from all angles of incidence to recreate the source event; after the recreation, wave energy diverges in every direction. An energy current imaging method based on this convergence/divergence behavior has been developed. The energy current imaging method yields a smaller spatial distribution for source reconstruction than is possible with traditional energy imaging methods.

Symmetry-based imaging condition in time reversed acoustics

Introduced in this paper is a new method of determining and investigating focal positions of time reversed elastic wave fields. This method exploits the temporally symmetric nature of time reversed acoustics focused signals as they are akin to the autocorrelation function of the forward propagation received signals. Contrasting this symmetry with the degree of asymmetry at regions away from the focal location provides details about the original source that cannot be retrieved when using other standard imaging conditions.

Experimental implementation of reverse time migration for nondestructive evaluation applications

Reverse time migration (RTM) is a commonly employed imaging technique in seismic applications (e.g., to image reservoirs of oil). Its standard implementation cannot account for multiple scattering/reverberation. For this reason it has not yet found application in nondestructive evaluation (NDE). This paper applies RTM imaging to NDE applications in bounded samples, where reverberation is always present. This paper presents a fully experimental implementation of RTM, whereas in seismic applications, only part of the procedure is done experimentally. A modified RTM imaging condition is able to localize scatterers and locations of disbonding. Experiments are conducted on aluminum samples with controlled scatterers.

Time reversal reconstruction of finite sized sources in elastic media

The ability of the time reversal process to reconstruct sources of finite size relative to a wavelength is investigated. Specifically the quality of the spatial reconstruction of a finite sized source will be presented through the use of time reversal experiments conducted on an aluminum plate. The data presented in the paper show that time reversal can reconstruct a source equally well regarding less of its size, when the source is a half wavelength or less in size. The quality of spatial reconstruction when the source is larger than a half wavelength progressively decreases with the size of the source.

Comparison and visualization of focusing wave fields from various time reversal techniques in elastic media

This Letter presents a series of time reversal experiments conducted on the surface of a fused silica glass block. Four different time reversal techniques are compared using three different imaging conditions. The techniques include two classical time reversal experiments: one with a pulse waveform source and one with an impulse response generated from a chirp signal. The other two techniques utilize the deconvolution, or inverse filter, signal processing methods for obtaining the signals to back propagate using a pulse waveform and an impulse response from a chirp. The max-in-time, symmetry, and energy current imaging conditions are compared.

Three-dimensional time reversal communications in elastic media

This letter presents a series of vibrational communication experiments, using time reversal, conducted on a set of cast iron pipes. Time reversal has been used to provide robust, private, and clean communications in many underwater acoustic applications. Here the use of time reversal to communicate along sections of pipes and through a wall is demonstrated to overcome the complications of dispersion and multiple scattering. These demonstrations utilize a single source transducer and a single sensor, a triaxial accelerometer, enabling multiple channels of simultaneous communication streams to a single location.