The basic property of passive imaging is that, given any two points, one of them can be taken as the source of the waves and the other as the recording station. This property can be derived from the statistical self-alignment of the rays along the vector joining the two points, and applies also to nondiffuse wavefields like seismic tremor. It provides a statistical basis for the use of the stationary phase integral, allowing passive interferometry under the mild constraint of mechanical homogeneity at a local scale. Combined with the tremor’s large spectral bandwidth, it allows one to recover the local Green’s function from spatial correlation. Furthermore, combining this property also with the azimuthal isotropy of either the wavefield or the array, and using the statistical mode as the estimator, provides a new technique to measure the local velocity dispersion in the subsoil. This technique exploits the potential of spatial autocorrelation (SPAC) and refraction microtremor (ReMi), allowing one (1) to use sparse small-aperture arrays with simple geometry, (2) to dispense with the fitting of Bessel functions, and (3) to measure, in a few minutes, the local (phase and group) wave velocity as a function of frequency of potentially all the wave-propagation modes — body and surface — and not just of the one prevailing at each frequency.

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