Wavelet modelling of broad-band receiver functions

We present a wavelet modelling approach to invert for S -wave velocities from broad-band receiver functions. Taking spline function as the basic wavelet, the broad-band receiver function is decomposed into five resolution scales by Mallat's pyramid algorithm. The linearized least-squares inversion procedure is applied to every resolution scale. The fifth-scale approximation of receiver function is first inverted to recover the slowly varying background velocity variations with respect to a reference model. This solution is then taken as the initial model for fitting the fourth-scale wavelet coefficients of receiver function to further tune the solution to resolve sharper variations. This procedure is iteratively carried out up to the first-scale wavelet coefficients of receiver function. In this manner, the model neighbourhood containing the global minimum is first searched from the coarsest-scale receiver function, and the search gradually focuses on the global minimum by introducing finer-scale information of receiver function. Noise-free synthetic receiver function tests show that wavelet modelling of receiver functions can guide a certain range of initial models to converge to the true velocity distribution. Tests on actual data indicate that wavelet modelling can provide results very similar to those inferred by joint inversion of receiver function and surface wave dispersion.