Impulse backscattering in granular beds: Introducing a toy model (original) (raw)
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Mechanical energy has been used in the detection of shallow buried objects in granular beds for more than half a century. Here we attempt to answer a fundamental question-at what depths would an object be detectable in an idealized, close-packed, granular bed made of monosized elastic spheres? Systematic particle dynamics based studies reveal the effects of varying the area across which the impulse is generated, object size, and restitution on locating the buried object.
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We consider the problem of imaging of objects buried under the ground using experimental backscattering time-dependent measurements generated by a single point source or one incident plane wave. In particular, we estimate dielectric constants of these objects using the globally convergent inverse algorithm of Beilina and Klibanov. Our algorithm is tested on experimental data collected using a microwave scattering facility at the University of North Carolina at Charlotte. There are two main challenges in working with this type of experimental data: (i) there is a huge misfit between these data and computationally simulated data, and (ii) the signals scattered from the targets may overlap with and be dominated by the reflection from the ground's surface. To overcome these two challenges, we propose new data preprocessing steps to make the experimental data look similar to the simulated data, as well as to remove the reflection from the ground's surface. Results of a total of 25 data sets of both nonblind and blind targets indicate good accuracy.
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Wave propagation in a granular bed is a complicated, highly nonlinear phenomenon. Yet studies of wave propagation provide important information on the characteristics of these materials. Fundamental nonlinearities of the bed include those in the particle contact model and the fact that there exists zero applied force when grains are out of contact. The experimental work of Liu and Nagel showed the strong dependence of wave propagation on the forming and breaking of particle chains. As a result of the nonlinearities, anomalous behavior such as solitary waves and sonic vacuum have been predicted by Nesterenko. In the present work we examine wave propagation in a granular bed subjected to vertical agitation. The agitation produces continual adjustment of force chains in the bed. Wave propagation speed and attenuation measurements were made for such a system for a range of frequencies considerably higher than that used for the agitation. Both laboratory experiments and simulations (using a two-dimensional, discrete soft-particle model) have been used. The present paper is a progress report on the simulations.
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The Journal of the Acoustical Society of America, 2006
Waveforms obtained by correlation of diffuse fields are now widely used to estimate times of flight and ballistic Green's functions. Theory, however, predicts that such passively obtained waveforms should equal the full Green function of a medium, and thereby convey information on the details of a structure and the presence of isolated scatterers. Here we investigate diffuse field correlations in a reverberant elastic body and demonstrate that their shear and Rayleigh waves allow us to image internal and surface features. Resolution in the resulting images is comparable to standard medical and seismic images.
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