Wavefield decomposition using ML‐probabilities in modelling single‐site 3‐component records

Abstract

This paper presents a new approach to the analysis of three‐component digital seismograms. Earlier approaches used techniques such as Principal Components to estimate particle‐motion using models of P and S waves. In this paper the Maximum‐Likelihood (ML) estimator is preferred because this allows the use of χ2‐probabilities to test whether energy of a specific wave type (P, S, Love or Rayleigh) is present. In addition, this analysis allows the joint estimation of azimuth of approach and in cases of P‐ and SV‐waves also apparent angle of incidence (and, hence, information on apparent velocity). For a single three‐component seismogram, the covariance matrix provides only six independent observations, thus restricting analysis to rather simple wave models. The technique works satisfactorily for P‐waves whereas shear and surface‐wave models sometimes prove cumbersome to handle due to correlation between radial and transverse components reflecting complex propagation characteristics in inhomogeneous media. This technique has been tested on synthetic data and in such cases works perfectly for all wave types. An important aspect of this work has been the visual display of the probability and velocity information as functions of time and azimuth. Displaying the data in this form provides information on the ray path in a manner similar to analysis performed by seismic arrays. Practical examples on a variety of siesmic data are given to illustrate the viability of the technique: the data cover a broad spectrum of frequencies and applications from broad‐band teleseismic data (1 Hz), regional seismic data (10‐40 Hz), seismic profiling data (125 Hz) and VSP (500 Hz) recordings. Copyright © 1988, Wiley Blackwell. All rights reserved