Non-linear surface wave phase velocity inversion based on ray theory

The development of temporary and permanent broad-band seismic arrays reinforces the need for advanced interpretation techniques in surface-wave analysis. We present a new method based on 2-D paraxial ray theory of inverting teleseismic surface-wave phase information and constructing phase velocity maps on a regional scale. Measurements of local phase velocities and propagation directions of Rayleigh waves taken from full waveform synthetic seismograms are used to validate the ray theory for smooth structures on a regional scale. Curved wavefronts created by heterogeneous structure outside the study area are taken into account through joint inversion for the phase velocity field and the shape of the incoming wavefronts. In the forward ray tracing procedure, the curved wavefronts are introduced through the boundary conditions by equating the slowness vector of the ray at the edge of the study region with the known gradient of the arrival time of the wave. To make the inverse problem non-singular we constrain the parameters in the inversion primarily by applying a smoothness criteria on the velocity field and on the incoming wave-field. Inversions of synthetic data sets computed by direct ray tracing and by full waveform modelling show that for 100 km spacing between stations the minimum size of structure that we can image is approximately 150 km. Heterogeneities with a size approximately equal to the wavelength are reconstructed by the ray-based inversion even though velocity variations are underestimated due to the wave-field smoothing of the structures. A minimum signal-to-noise ratio of 3.5 is necessary in order to correctly retrieve the phase velocity field. Inversion of a subset of the SVEKALAPKO data for 60 s period demonstrates the applicability of the method on real data.