Most chapters in this book deal with methods that enhance either the estimation of wavefront phase velocities (directions of arrival) or the covariance matrices from which those and other parameters are inferred. Occasionally the exact waveform from a single source or reflector is the desired result. This brings a few problems into play:
1) Multiple removal, where a reflection from a single boundary appears to have more than one arrival because it has been caught in a waveguide layer and transmits part of its energy to the surface with each cycle of reflection within that layer;
2) Secondary interference removal, where uncontrolled sources outside of the central seismic experiment cause wavefronts to be superimposed on the desired reflections;
3) Thin bed resolution, where features of distinct reflections from the top and bottom of the bed are to be individually analyzed but the waveforms are considerably overlapped in the profile; and
4) Separation of up- and down-going waves in vertical seismic profiling.
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Covariance Analysis for Seismic Signal Processing
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.