The Search of Diffusive Properties in Ambient Seismic Noise

ABSTRACT Ambient seismic noise (ASN) is becoming of interest for geophysical exploration and engineering seismology, because it is possible to exploit its potential for imaging. Theory asserts that the Green’s function can be retrieved from correlations within a diffuse field. Surface waves are the most conspicuous part of Green’s function in layered media. Thus, the velocities of surface waves can be obtained from ASN if the wavefield is diffuse. There is widespread interest in the conditions of emergence and properties of diffuse fields. In the applications, useful approximations of the Green’s function can be obtained from cross correlations of recorded motions of ASN. An elastic field is diffuse if the background illumination is azimuthally uniform and equipartitioned. It happens with the coda waves in earthquakes and has been verified in carefully planned experiments. For one of these data sets, the 1999 Chilpancingo (Mexico) experiment, there are some records of earthquake pre-events that undoubtedly are composed of ASN, so that the processing for coda can be tested on them. We decompose the ASN energies and study their equilibration. The scheme is inspired by the original experiment and uses the ASN recorded in an L-shaped array that allows the computation of spatial derivatives. It requires care in establishing the appropriate ranges for measuring parameters. In this search for robust indicators of diffusivity, we are led to establish that under certain circumstances, the S and P energy equilibration is a process that anticipates the diffusion regime (not necessarily isotropy), which justifies the use of horizontal-to-vertical spectral ratio in the context of diffuse-field theory.