Dispersion analysis of multi-modal waves based on the Reassigned Cross-S-Transform

Abstract

The quantitative description of the propagation of the energy components in a signal is a fundamental task in signal processing. The correct identification of the components is important because they carry information about the medium in which they propagate. In this article, I introduce the Reassigned Cross-S-Transform to estimate dispersion curves from time-varying signals, a technique based on function maximization principles and time-frequency cross-correlation. The RCST provides a sharpened and direct estimate of the dispersion curve for multi-modal propagating waves. Furthermore, the RCST can be used with signals that are not synchronized with the same initial time. I present examples studying the degradation effects on the slowness curves due to mode mixture and reflected waves. I illustrate the application of the RCST technique to artificially generated Ricker wavelets, and to real recordings of seismic waves generated by an active source. Finally, using 2D numerical simulations of wave propagating through an elastic layered medium, I solve a mode identification problem by combining the RCST with a previously proposed technique to extract Rayleigh waves from signals.