Simultaneous inversion of fundamental and higher mode Rayleigh wave using sensitivity models

Abstract

Rayleigh waves have been used increasingly as a noninvasive tool to invert S-wave velocity of near-surface materials. Rayleigh-wave phase velocity of a layered-earth model is a function of wave frequency content and four other earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers and determined by a characteristic equation in nonlinear, implicit form (dispersion equation). Accuracy of the partial derivatives is key in determining modifications to the earth model parameters and dramatically affects convergence of the inverse procedure. Analysis of the Jacobian matrix provides a measure of dispersion-curve sensitivity to earth properties. Like many other geophysical inverse problems, the inversion of Rayleigh wave dispersion curves is a typical nonlinear inversion problem. In this study Occam's algorithm was employed to invert the fundamental and higher mode Rayleigh wave data. The inversion strategy of this algorithm is to find the smoothest S-wave velocity profile subject to the constraint of a specified misfit between the observed and the calculated dispersion data. In this study we construct a 3-D sensitivity model of Rayleigh wave phase velocity respect to variation of shear wave velocity for different layers and different modes, The sensitivity model suggested that higher-mode Rayleigh-wave data have deeper investigation depths than do the fundamental mode data. By analyzing sensitivity model, the most sensitive data in terms of frequency and depth incorporated to construct the shear wave velocity profiles, in this study we use the data sensitivity as weighting parameter in inversion procedure. We developed an accurate and automatic inversion algorithm to generate shallow S-wave velocity profiles. we inverted different mode's data selectively in special frequency and depth ranges. With the achievement of a fast forward modeling method, this study focuses on the inversion of phase velocity dispersion curves of surface waves contained fundamental and higher mode simultaneously using sensitivity model. For the forward modeling, we used an efficient algorithm, based on Knopoff's method, we verify our modeling results with a synthetic model example. the computer program implemented in Matlab.