Eikonal surface wave tomography with smoothing splines—application to Southern California

SUMMARY The densification of both permanent and temporary seismic networks has raised new interest in surface wave eikonal tomography from which phase velocity maps can be obtained without resolving a tomographic inverse problem. However, eikonal tomography requires to reconstruct traveltime surfaces from a discrete number of measurements obtained at the station locations, which can be challenging. We present a new method to reconstruct these traveltime surfaces with smoothing splines discretized in a regular 2-D Cartesian grid. We impose Neumann boundary conditions so that the phase gradients on the edges of the grid are equal to the apparent slownesses of the average plane wave along the normal direction measured by beamforming. Using the eikonal equation, phase velocity maps are then derived from the norm of the gradient of the interpolated traveltime maps. The method is applied to Rayleigh waves recorded by the Southern California Seismic Network to derive phase velocity surfaces. Robust, stable and finely resolved phase velocity maps at 25 and 33 s period are obtained after averaging the phase velocity maps derived from the analysis of a selection of recent large (Mw ≥ 6.5) teleseismic events. The phase velocity map at 25 s mainly constrains the thickness of the Southern California crust, with results that are in excellent agreement with previous tomographic studies.