Inversion of H/V ratio in layered systems

Abstract:

Both coda of earthquakes and microtremors are assumed to be diffuse fields resulting from multiple scattering. From the diffuse field theory, the average of the autocorrelation of displacement components at a given receiver measures the directional energy densities that are proportional to the imaginary parts of the Green’s function for source and receiver at the same point.

The directional energies have been recently related to the calculation of microtremor H/V spectral ratio (MHVSR). These ratios are widely used in the assessment of the dominant frequency of soil sites and their measurements are relatively simple as only one station is required. The H/V spectral ratios have also been interpreted as representing either directly the S wave amplification or the Rayleigh wave ellipticity.

Moreover, the H/V ratios can be also used for a finer characterization of the site assuming horizontally layered media without lateral heterogeneities. In that case and for an appropriate noise normalization the experimental spectral ratios H²/V² should correspond to their theoretical counterpart: the ratio 2 ImG₁₁ / ImG₃₃, where ImG₁₁ and ImG₃₃ are the imaginary parts of Green functions at the load point for horizontal and vertical components, respectively and for horizontally layered media. In order to guarantee a viable inversion, the imaginary part of the theoretical Green’s functions must be efficiently computed using both an integral in the complex k plane (in terms of homogeneous plane waves) and the pole contributions due to Rayleigh and Love normal modes, which result from the (application of the) Cauchy residue theorem.

 ACKNOWLEDGEMENTS. This research has been partially supported by DGAPA-UNAM under Project IN104712 and the AXA Research Fund.