Full microtremor H/V(z, f) inversion for shallow subsurface characterization

The H/V spectral ratio has emerged as a single station method within the seismic ambient noise analysis field by its capability to quickly estimate the frequency of resonance at a site and through inversion the average profile information. Although it is easy to compute from experimental data, its counter theoretical part is not obvious when building a forward model which can help in reconstructing the derived H/V spectrum. This has led to the simplified assumption that the noise wavefield is mainly composed of Rayleigh waves and the derived H/V often used without further correction. Furthermore, only the right (and left) flank around the H/V peak frequency is considered in the inversion for the subsurface 1-D shear wave velocity profile. A new theoretical approach for the interpretation of the H/V spectral ratio has been presented by Sánchez-Sesma et al. In this paper, the fundamental idea behind their theory is presented as it applies to receivers at depth. A smooth H/V(z, f) spectral curve on a broad frequency range is obtained by considering a fine integration step which is in turn time consuming. We show that for practical purposes and in the context of inversion, this can be considerably optimized by using a coarse integration step combined with the smoothing of the corresponding directional energy density (DED) spectrum. Further analysis shows that the obtained H/V(z, f) spectrum computed by the mean of the imaginary part of Green's function method could also be recovered using the reflectivity method for a medium well illuminated by seismic sources. Inversion of synthetic H/V(z, f) spectral curve is performed for a single layer over a half space. The striking results allow to potentially use the new theory as a forward computation of the H/V(z, f) to fully invert the experimental H/V spectral ratio at the corresponding depth for the shear velocity profile (Vs) and additionally the compressional velocity profile (Vp) using receivers both at the surface and in depth. We use seismic ambient noise data in the frequency range of 0.2–50 Hz recorded at two selected sites in Germany where borehole information is also available. The obtained 1-D Vs and Vp profiles are correlated with geological log information. Results from shallow geophysical experiment are also used for comparison.