Coherent backscattering of elastic waves: Specific role of source, polarization, and near field (original) (raw)
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Coherent backscattering of acoustic waves in the near field
Recent studies have shown that interference plays an important role in various phenomena observed for waves propagating through random media. Among these phenomena, the so-called cone of coherent backscattering has received much attention in optics. In this paper, we study analytically and numerically the coherent back- scattering of acoustic waves in a seismological context. In particular, we focus on the near-field detection of scattered waves and the effect of transient sources. We show that interference results in an increase of the coda intensity as compared to the prediction of radiative transfer theory. After a transient regime, a spot of backscattering enhancement stabilizes in a sphere of radius half a wavelength centred at the source of seismic waves. Several effects such as absorption, boundary conditions and scattering anisotropy are investigated. Our study demonstrates the robustness of coherent backscattering and may offer a possible means of discriminating single versus multiple scattering in the observed coda.
COHERENT BACK-SCATTERING AND WEAK LOCALIZATION OF SEISMIC WAVES
I present a review of the weak localization effect in seismology. To understand this multiple scattering phenomenon, I begin with an intuitive approach illustrated by experiments performed in the laboratory. The importance of reciprocity and interference in scattering media is emphasized. I then consider the role of source mechanism, again starting with experimental evidence. Important theoretical results for elastic waves are summarized, that take into account the full vectorial character of elastic waves. Applications to the characterization of heterogeneous elastic media are discussed.
Coherent backscattering and far-field beamforming in acoustics
Coherent backscattering of waves by a random medium is spectacular evidence of interference effects despite disorder and multiple scattering. It manifests itself as a doubling of the wave intensity reflected exactly in the backward direction. This phenomenon has been observed experimentally in optics, acoustics, or seismology. While optical measurements are realized in far-field conditions with a plane wave illumination and a beamwidth much larger than the wavelength, ultrasonic experiments are carried out with wideband controllable arrays of ͑nearly͒ pointlike transducers that directly record the wave field, in amplitude and phase. Therefore it is possible to perform beamforming of the incoming and outgoing wave fields before computing the average backscattered intensity. In this paper, the advantages of plane wave beamforming applied to the study of the coherent backscattering effect are shown. Particularly, the angular resolution, the signal-to-noise ratio, as well as the estimation of the enhancement factor can be improved by beamforming. Experimental results are presented with ultrasonic pulses, in the 2.5-3.5 MHz range, propagating in random collections of scatterers. Since the coherent backscattering effect can be taken advantage of to measure diffusive parameters ͑transport mean free path, diffusion constant͒, plane-wave beamforming can be applied to the characterization of highly scattering media.
Enhanced Backscattering and Modal Echo of Reverberant Elastic Waves
Physical Review Letters, 2000
We report experimental evidence for coherent backscattering of waves in a three-dimensional elastic body. Ultrasonic spectral energy density consequent to a transient excitation is measured as a function of time and of distance from the source. In accord with the predictions of random matrix theory, an enhancement is found near the source by a weak localization factor of 2 at early times, but a factor of 3 at late times. The effect appears to be independent of absorption.
International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, 1993
Small-scale heterogeneity in the crust, which cannot be resolved deterministically by seismic surveys, nevertheless has significant effects on the wave propagation. In the random media concept, small-scale spatial fluctuations of the elastic parameters are described by only a few statistical measures, e.g. mean value, standard deviation and correlation distance. Knowing these quantities is sufficient for characterizing the effects of heterogeneity on travel-times and amplitudes of seismic waves in a statistical sense. A ray-theoretical relation can be established between the autocorrelation functions of the travel-time fluctuations and of the slowness fluctuations of the medium. This leads to a simple method to estimate the statistical parameters of a random medium from observed travel-times. Numerical computations of travel-times with a finite-difference method show that statistical heterogeneity introduces a velocity shift of the average velocity towards higher values. For amplitude studies of scattered waves, the Born approximation to the wave equation is used which neglects all multiple scattered waves. The scattered wavefleld from a point scatterer and the radiation pattern of the meansquare scattered amplitudes from a random distribution of scatterers are derived. Furthermore, the frequency-dependent attenuation of the transmitted wavefield can be obtained from the Born approximation. The theoretical Q-t agrees well with the results from numerical computations in I-D and 2-D media, even for strong heterogeneities. A still more complete description of the filtering effect of a random medium is achieved by the use of attenuation operators. Numerical modelling also is an important tool to investigate wave propagation in realistic heterogeneous structures. The reflection response from a lower crust containing a certain amount of random fluctuations shows that multiple scattering and interference effects significantly add to the complexity of the observed wavefield. Migration generally does not successfully reconstruct the true structure in such cases.
Passive retrieval of Rayleigh waves in disordered elastic media
When averaged over sources or disorder, cross correlation of diffuse fields yields the Green’s function between two passive sensors. This technique is applied to elastic ultrasonic waves in an open scattering slab mimicking seismic waves in the Earth’s crust. It appears that the Rayleigh wave reconstruction depends on the scattering properties of the elastic slab. Special attention is paid to the specific role of bulk to Rayleigh wave coupling, which may result in unexpected phenomena, such as a persistent time asymmetry in the diffuse regime.
Coherent backscattering of ultrasound without a source
EPL (Europhysics Letters), 2006
Coherent backscattering is due to constructive interferences of reciprocal paths and leads to an enhancement of the intensity of a multiply scattered field near its source. To observe this enhancement an array of receivers is conventionally placed close to the source. Our approach here is different. In a first experiment, we recover the coherent backscattering effect (CBE) within an array of sources and a distant receiver using time correlation of diffuse fields. The enhancement cone has an excellent spatial resolution. The dynamics of the enhancement factor is studied in a second experiment using correlation of thermal phonons at the same ultrasonic frequencies, without any active source.