Divergence-based estimation of Rayleigh wave dispersion curves

We present a novel seismic acquisition and processing technique to efficiently evaluate the local dispersion curves of Rayleigh waves for subsequent inversion of shear velocities and near-surface characterization.

The proposed approach consists of computing the ratio between the (time derivated) horizontal spectra H(f)=(∂_tV_x(f)²+∂_tV_y(f)²)^1/2  and the pseudo-divergence spectra D(f), with D being the sum of the horizontal gradients of the horizontal components (i.e. D=∂_xV_x+∂_yV_y).

The processing method itself is comparable to the commonly used H/V approach, except that the H/D spectral ratio provides a direct estimate of the frequency-dependent phase velocities c_R(f)  instead of the site frequency amplification(s). This is demonstrated using synthetic data.

We describe how the D component can be obtained in practice, i.e. by finite-differencing closely spaced horizontal phones or potentially using Distributed-Acoustic-Sensing (DAS) and fibre-optic deployed at the surface. Some limitations about wavelength dependency and impact of Love waves are discussed, as well as potential mitigation measures.

A field test on several hours of ambient noise data collected in Germany with multi-component geophones results in realistic values of Rayleigh wave velocities ranging from ~770 m/s at 10 Hz to ~500 m/ at 30 Hz. Thanks to the local and omni-directional nature of the estimation, the minimal number of required channels and the applicability to ambient noise, we believe that the proposed H/D method can be an attractive alternative to expensive array-based techniques.