Seismic signals are sensed by geophones in land acquisition or by hydrophones in marine acquisition. Typically, the signals are excited in the earth with some sort of energy source such as an explosion, vibrator, or air or water gun. These signals travel through the subsurface structures and are reflected from boundaries having distinct physical properties. Eventually they produce multiple reflections observed at each recording phone. Often the geological structure is not simple, and although simple models have sufficed for many regions of exploration, the recorded reflections are interpreted well only if the geophysicist has much experience and is familiar with other sources of information.
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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.