Outpost Method of Computing Leaking and Normal Modes for Elastic Multilayered Half-space

Abstract

Dispersion curves analysis of guided waves leaking modes provide P-wave velocity information in addition to the common techniques based on the Rayleigh modes dispersion curves inversion. Accounting for the leaking modes requires a fully automated and precise method for complex roots of dispersion equation computing. We have developed an extension of the so-called outpost method. That allows numerical computation of all the leaking and normal modes presented in the full wavefield in any elastic layered half-space. The method is based on the leaking modes property to come to the vicinity of complex plane real axis with increasing the frequency from zero to infinity. In principle, the approach consists of two steps. Firstly, we search for the moments of leaking modes crossing some line in the complex plane called outpost. We suggest a particular form of the outpost line. It crosses the branch cuts and is closed on the Riemann surface, accounting for all the possible leaking modes arising up in the wavefield. The second step is an individual continuation of every leaking mode as a curve parameterized by frequency starting from the outpost line. We give algorithms for leaking modes curves tracing through their peculiarities, which provides full method automation.