Interpretation of seismic surface waves in regional networks: joint estimation of wavefield geometry and local phase velocity. Method and numerical tests

Teleseismic surface waves in general strongly deviate from plane waves as is evident from the analysis of surface-wave data recorded with dense networks. This causes conventional, ray-based tomographic techniques to break down if applied to network surface-wave data. We present a new inversion method based on the acoustic-wave equation and applicable to vertical-component surface-wave data which successfully deals with non-plane wavefield geometries.

The basic idea of the method is a joint estimation of the incoming wavefield and heterogeneous structure within the network region. Crucial to the success of the method is an adequate parametrization of the incoming wavefield which is realized using Hermite-Gaussian basis functions. Additionally, we apply a constraint on the wavefield parameters that expresses the idea that the samples of the wavefield taken at the station locations should be representative for the wavefield in the whole network region. In this way, wavefields that show stronger fluctuations in spectral amplitude than observed at the stations are rejected. To represent heterogeneous structure within the network region we use an expansion into 2-D Hermite-Gaussian functions.

Provided that the density of stations is sufficient, the proposed method retrieves heterogeneous structure in the network region very well. It is not sensitive to noise or non-uniform azimuthal coverage of earthquakes. Moreover, it yields smoothed versions of the true model if the roughness of the latter has been underestimated in the inversion. Conversely, if the true model is much smoother than anticipated, inspection of the trade-off between model smoothness and data misfit allows us to find the correct model.

The limiting factor for the inversion is the density of stations, which must allow for a reliable interpolation of the observed wavefield within the network. Therefore, in order to perform regional surface-wave studies it is essential to deploy seismic stations in the region of interest itself.