P. A. Johnson

Imaging nonlinear scatterers applying the time reversal mirror

Nonlinear elastic wave spectroscopy (NEWS) has been shown to exhibit a high degree of sensitivity to both distributed and isolated nonlinear scatterers in solids. In the case of an isolated nonlinear scatterer such as a crack, by combining the elastic energy localization of the time reversal mirror with NEWS, it is shown here that one can isolate surfacial nonlinear scatterers in solids. The experiments presented here are conducted in a doped glass block applying two different fixed frequency time-reversed signals at each focal point and scanning over a localized nonlinear scatterer (a complex crack). The results show a distinct increase in nonlinear response, via intermodulation distortion, over the damaged area. The techniques described herein provide the means to discriminate between linear and nonlinear scatterers, and thus to ultimately image and characterize damaged regions.

Pump and probe waves in dynamic acousto-elasticity: Comprehensive description and comparison with nonlinear elastic theories

Standard nonlinear ultrasonic methods such as wave frequency mixing or resonance based measurements allow one to extract average, bulk variations of modulus and attenuation versus strain level. In contrast, dynamic acousto-elasticity (DAE) provides the elastic behavior over the entire dynamic cycle including hysteresis and memory effects, detailing the full nonlinear behavior under tension and compression. In this work, we address experimental difficulties and apply new processing methods, illustrating them with a Berea sandstone sample. A projection procedure is used to analyze the complex nonlinear signatures and extract the harmonic content. Amplitude dependences of the harmonic content are compared with existing models. We show that a combination of classical and hysteretic nonlinear models capture most of the observed phenomena. Some differences between existing models and experimental data are highlighted, however. A progressive decrease of the power-law amplitude dependence is found for harmonics l...

Stress induced conditioning and thermal relaxation in the simulation of quasi-static compression experiments

Local interaction simulation approach simulations of the ultrasonic wave propagation in multi-grained materials have succeeded in reproducing most of the recently observed nonclassical nonlinear effects, such as stress–strain hysteresis and discrete memory in quasi-static experiments and a downwards shift of the resonance frequency and the generation of odd harmonics at specific amplitude rates in dynamics experiments. By including a simple mechanism of thermally activated random transitions, we can predict the occurrence of experimentally observed effects, such as the conditioning and relaxation of the specimen. Experiments are also suggested for a quantitative assessment of the validity of the model.

In situ characterization of shallow elastic nonlinear parameters with Dynamic Acoustoelastic Testing

In situ measurement of the elastic nonlinear site response is advantageous to provide optimal information for prediction of strong ground motion at a site. We report the first implementation of a technique known as Dynamic Acoustoelastic Testing (DAET) in situ with the ultimate goal of developing a new approach for site characterization. DAET has shown promising results at the laboratory scale for the study of nonlinear elasticity of Earth materials, detailing the full nonlinear elastic properties of the studied sample. We demonstrate the feasibility of DAET in situ and compare it to other methods (nonlinear resonance spectroscopy, wave amplitude dependence of propagation velocity, and wave distortion). Nonlinear elastic properties are characterized by DAET with the advantage of providing a local assessment compared to other methods, here at a depth of 4 m to 5 m. A vertical dynamic strain amplitude of 5 ×10−5 produces a relative change in compressional wave modulus of 6%. We measure an effective parameter of quadratic elastic nonlinearity of order −103, the same order of magnitude measured at the laboratory scale in rocks and in packs of unconsolidated glass beads. Hysteresis is observed in the variation in soil elasticity as a function of the instantaneous dynamic strain that evolves as the dynamic strain amplitude is increased from 9 ×10−7 to 5 ×10−5.

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.

LISA simulations of time-reversed acoustic and elastic wave experiments

Several experiments in the last decade have demonstrated the enormous potential of time-reversed acoustic (TRA) and elastic (TRE) waves for applications in many fields, such as medicine, materials characterization and oceanography. In the present contribution, we demonstrate the applicability of the local interaction simulation approach (LISA) to simulate, by means of virtual experiments, both TRA and TRE and to reproduce the relevant features of both techniques.

Effect of boundary vibration on the frictional behavior of a dense sheared granular layer

We report results of 3D discrete element method simulations aiming at investigating the role of the boundary vibration in inducing frictional weakening in sheared granular layers. We study the role of different vibration amplitudes applied at various shear stress levels, for a granular layer in the stick-slip regime and in the steady-sliding regime. Results are reported in terms of friction drops and kinetic energy release associated with frictional weakening events. We find that a larger vibration amplitude induces larger frictional weakening events. The results show evidence of a threshold below which no induced frictional weakening takes place. Friction drop size is found to be dependent on the shear stress at the time of vibration. A significant increase in the ratio between the number of slipping contacts to the number of sticking contacts in the granular layer is observed for large vibration amplitudes. These vibration-induced contact rearrangements enhance particle mobilization and induce a friction drop and kinetic energy release. This observation provides some insight into the grain-scale mechanisms of frictional weakening by boundary vibration in a dense sheared granular layer. In addition to characterizing the basic physics of vibration-induced shear weakening, we are attempting to understand how a fault fails in the earth under seismic wave forcing. This is the well-known phenomenon of dynamic earthquake triggering. We believe that the granular physics are key to this understanding.

Robustness of computational time reversal imaging in media with elastic constant uncertainties

In order to image a source or a scatterer embedded in a three dimensional solid, acoustic/elastic wave data from an actual experiment are time reversed and backpropagated through a numerical model of the medium. The model makes use of estimates for the elastic constants of the laboratory solid. These estimates may not be very precise, for example, due to experimental uncertainties. Poor characterization of the medium leads to the degradation of the time reversal focus, therefore, to poor medium imaging. In this work, we report on the results of investigating the time reversal focus degradation as the estimates depart from the real values. Very small deviations from the medium’s actual elastic constants degrade the time reversal focus dramatically. However, decreasing the total duration of the signals used for time reversal can attenuate the degradation in some cases. We propose a new method to compensate for the deviations of the model medium’s elastic constants from the actual values. Finally, we explore...

Experimentally identifying masked sources applying time reversal with the selective source reduction method

This paper describes a time reversal (TR) method of spatially illuminating a source signal which has been masked by another source signal. This masking occurs as a result of inherent limitations in the traditional TR process. The selective source reduction (SSR) method employs a subtraction technique where one TR focus is selectively reduced to illuminate the masked focus. Experimental results and considerations are presented to demonstrate the SSR method for two elastic wave pulses emitted simultaneously from two spatially separated surficial sources and to examine the limitations of the method. A blind test was conducted to demonstrate that no a priori information about the source(s) is required. Spatial and/or temporal characteristics of multiple close-proximity sources can be resolved with the use of the illumination method. The measurements show that the SSR method’s limitations are chiefly due to imperfect temporal reconstruction of the source function in the time reversed focal signal, which conseq...

Probing the interior of a solid volume with time reversal and nonlinear elastic wave spectroscopy

A nonlinear scatterer is simulated in the body of a sample and demonstrates a technique to locate and define the elastic nature of the scatterer. Using the principle of time reversal, elastic wave energy is focused at the interface between blocks of optical grade glass and aluminum. Focusing of energy at the interface creates nonlinear wave scattering that can be detected on the sample perimeter with time-reversal mirror elements. The nonlinearly generated scattered signal is bandpass filtered about the nonlinearly generated components, time reversed and broadcast from the same mirror elements, and the signal is focused at the scattering location on the interface.