HVSR analysis of a layered saturated half-space using diffuse-field theory

SUMMARY The recently constructed diffuse field theory from isotropic energy equipartition has been well developed in elasticity for full-wave interpretation of horizontal-to-vertical ratio (HVSR), which links the signal autocorrelation with the imaginary part of Green's function. Here, the theory is extended to the saturated layered medium within the framework of Biot's theory to account for the offshore environment. The imaginary parts of Green's functions are obtained using direct stiffness method accompanied with Fourier–Hankel transform. In particular, the upgoing wave amplitudes are modified to tackle the overflow during wavenumber integral and allow for fast calculations. After validating the method from the perspectives of Green's function calculation, emphasis is laid on evaluating the inaccuracies of HVSR calculation induced by model misuses in the lack of prior geological and geotechnical information. The numerical results considering the effects of layer sequence, impedance ratio, porosity and drainage condition show that the predominant frequency of the one-phase medium is slightly less than the two-phase medium with the maximum shift no more than 0.1 Hz, while their amplitude differences can be prominent as impedance ratio and porosity increase, with the maximum difference up to 29 per cent. The shallowest soft layer has the dominant effects on HVSR amplitudes, whereas the buried low-velocity layer at depth over one-wavelength contributes little to the peak amplitude. Finally, the method is applied to a realistic case at Mirandola, Northorn Italy, which suffered extensive liquefaction-induced damages in 2012 Emilia earthquake. The well identified pattern of the experimental HVSR using the two-phase medium model illustrates the application potential of our method to further assist the subsurface geology retrieval.