# A generalized theory for full microtremor horizontal-to-vertical [H/V (z, f)] spectral ratio interpretation in offshore and onshore environments

## TL;DR

This paper extends the microtremor H/V spectral ratio interpretation to offshore environments, incorporating water layers into the model, and demonstrates its application through analysis of layered earth models.

## Contribution

It introduces a new algorithm for modeling microtremor H/V spectral ratios in marine environments, accounting for water layers, which was previously limited to onshore settings.

## Key findings

- Water layers cause up to 8% variation in fundamental frequency.
- H/V peak amplitude can vary by up to 50% due to water presence.
- The method effectively models seismic responses in offshore sedimentary environments.

## Abstract

Advances in the field of seismic interferometry have provided a basic theoretical interpretation to the full spectrum of the microtremor horizontal-to-vertical spectral ratio [H/V(f)]. The interpretation has been applied to ambient seismic noise data recorded both at the surface and at depth. The new algorithm, based on the diffuse wavefield assumption, has been used in inversion schemes to estimate seismic wave velocity profiles that are useful input information for engineering and exploration seismology both for earthquake hazard estimation and to characterize surficial sediments. However, until now, the developed algorithms are only suitable for on land environments with no offshore consideration. Here, the microtremor H/V(z, f) modeling is extended for applications to marine sedimentary environments for a 1D layered medium. The layer propagator matrix formulation is used for the computation of the required Green's functions. Therefore, in the presence of a water layer on top, the propagator matrix for the uppermost layer is defined to account for the properties of the water column. As an application example we analyze eight simple canonical layered earth models. Frequencies ranging from 0.2 to 50 Hz are considered as they cover a broad wavelength interval and aid in practice to investigate subsurface structures in the depth range from a few meters to a few hundreds of meters. Results show a marginal variation of 8 percent at most for the fundamental frequency when a water layer is present. The water layer leads to variations in H/V peak amplitude of up to 50 percent atop the solid layers.