Surface wave inversion for a p-wave velocity profile: Estimation of the squared slowness gradient

Surface waves can be used to obtain a near-surface shear wave profile. The inverse problem is usually solved for the locally 1-D problem of a set of homogeneous horizontal elastic layers. The output is a set of shear velocity values for each layer in the profile. P-wave velocity profile can be estimated if higher modes and P-guided waves are used in the inversion scheme. Here, we use an exact acoustic solution to invert for the P-velocity profile in an elastic model with a decreasing constant vertical gradient of the squared P-wave slowness, bounded by a free surface on the top and a homogeneous halfspace at the bottom. The exact acoustic solution can be expressed in Airy functions and leads to a dispersion equation. We can invert several modes of the dispersion equation for the single gradient parameter of the squared P-wave slowness from elastic data. As a first test case, we invert for the P-wave velocity profile of synthetic 2-D isotropic elastic data with a small Vs/Vp-ratio, using the first two dispersive P-wave modes. The method does not require any picking and should be able to provide an initial model for full waveform inversion when applied to real data