Modeling the Horizontal-to-Vertical Spectral Ratio and the Inversion of Subsoil Properties Using the Diffuse Field Theory

Session: Data Fusion and Uncertainty Quantification in Near-Surface Site Characterization
Type: Oral
Date: 4/30/2020
Time: 08:30 AM
Room: 110 + 140
Description: 

The microtremor horizontal-to-vertical spectral ratio (MHVSR), also called H/V is a popular measurement to assess the dominant period of soil sites. The MHVSR emerges from spectra of seismic ambient noise recordings at a single station and the processing is relatively simple. The information on dominant period is crucial for an appropriate site characterization and this contributes to mitigate seismic hazard. According to the diffuse field theory, both the coda of an earthquake and the noise emerge from multiple diffraction, which tends to equilibrate to generate a diffuse field. In that case, the ensemble average of the autocorrelation of motion components gives the directional energy densities (DEDs) which are proportional to the imaginary parts of the Green’s function when both source and receiver are at the same location and the directions of force and response coincide. Under the diffuse field theory, the MHVSR is then modeled as square root of 2×ImG₁₁/ImG₃₃, where ImG₁₁ and ImG₃₃ are the imaginary parts of Green’s functions at load point for horizontal (sub-index 1) and vertical (sub-index 3) components, respectively. This relationship has physical implications that emerge from the duality DED-force and allows understanding the behavior of the MHVSR. For a given model, the imaginary parts of the Green’s functions are integrals along the radial wavenumber. To solve these integrals, we have used either the popular discrete wavenumber method, the Cauchy’s residue theorem and the locked mode approximation as well. The last two approaches use the poles in the complex plane to account for normal modes of Rayleigh and Love waves. For the retrieval of the subsoil mechanical properties, we minimize the weighted differences between the observations and the calculated values using a joint inversion scheme for H/V and dispersion curves as well. We used simulated annealing but other optimization techniques can be used. An example for the mouth of Andarax River at Almería, Spain, is presented.

ACNOWLEDEMENT: I thank the support of DGAPA-UNAM under Project IN107720.

Presenting Author: Francisco J. Sánchez-Sesma

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