Locating a weak change using diffuse waves: Theoretical approach and inversion procedure
Résumé
We describe a time-resolved monitoring technique for heterogeneous media. Our approach is based on the spatial variations of the cross-coherence of diffuse waves acquired at fixed positions but at different dates. The technique applies to all kind of waves, provided that waveforms can be acquired with a sampling frequency much larger than the wave frequency. To locate and characterize a weak change that occurred between successive acquisitions, we use a maximum likelihood approach combined with a diffusive propagation model. We characterize this technique, locating a weak change using diffuse waves, called LOCADIFF, with the aid of numerical simulations. In several illustrative examples, we show that the change can be located with a precision of a few wavelengths and that its effective scattering cross-section can be retrieved. We investigate how the accuracy and precision of the method depends on the number of source-receiver pairs, on the time window used to compute the cross-correlation and on the errors in the propagation model. Applications can be found in nondestructive testing, seismology, radar, and sonar location.
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