Chapter 15: Parameterization of Narrowband Rayleigh and Love Waves Arriving at a Triaxial Array
R. Lynn Kirlin, John Nabelek, Guibiao Lin, 1999. "Parameterization of Narrowband Rayleigh and Love Waves Arriving at a Triaxial Array", Covariance Analysis for Seismic Signal Processing, R. Lynn Kirlin, William J. Done
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It is desirable to separate and parameterize Rayleigh and Love wavefronts arriving at a three-component seismometer. We show that methods of modern array signal processing and parameter estimation will accomplish this task. An overall covariance matrix of vectors having elements representing the traces from each component of all seismometers yields the necessary information. We assume that the only vertical axis response is due to Rayleigh rv, and Love wave components Le and Ln appear only on east and north axes respectively.
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This reference is intended to give the geophysical signal analyst sufficient material to understand the usefulness of data covariance matrix analysis in the processing of geophysical signals. A background of basic linear algebra, statistics, and fundamental random signal analysis is assumed. This reference is unique in that the data vector covariance matrix is used throughout. Rather than dealing with only one seismic data processing problem and presenting several methods, we will concentrate on only one fundamental methodology—analysis of the sample covariance matrix—and we present many seismic data problems to which the methodology applies.