A Programmed Technique For Solving Dispersion Of Love Surface Waves Using Synthetic Seismograms

Abstract

We propose a programmed technique to analyze the dispersion data set of Love surface waves for the determination of two-dimensional (2-D) velocity structure (horizontally polarized shear-wave – )  of the subsurface. We assume synthetic data emulating the common-shot gather for which the weighted preconditioned linear radon transform (WPLRT), single-station (SS) method and two-station (TS) method are used in coordination. In the first step, the WPLRT provides a phase velocity dispersion curve, which is inverted to determine the one-dimensional (1-D) velocity structure representative of the average structure underneath the common-shot gather. Then the SS method provides tens of group velocity dispersion curves proportional to the number of geophones where each curve is inverted to establish the 1-D velocity structure descriptive of the average structure between the source and receiver. In the third step, the TS method yields hundreds of dispersion curves (both phase and group velocity) proportional to the number of inter-stations. Each set of phase and group velocity curve is jointly inverted to determine the 1-D velocity structure expressive of the average structure between two receivers. Each step in the proposed technique involves several phase and group velocity dispersion curves, which are difficult to hand pick. Instead, a programmed scheme, which saves us a lot of processing time, is developed to select the related dispersion curves. The area covered by the common-shot gather is discretized into a set of grid points. The path dependent dispersion curves obtained by the SS and TS methods are converted into individual dispersion curves at these grid points by solving properly defined linear systems through the travel times. The 1-D velocity-depth profiles obtained by the inversion of dispersion curves at the grid points are combined to build the 2-D cross section beneath the area under consideration.