MULTIVARIATE ANALYSIS USED IN THE DETECTION OF STRATIGRAPHIC ANOMALIES FROM SEISMIC DATA

Abstract

In attempting to interpret stratigraphic changes from seismic data, we usually try to detect quantitative changes in one or two variables: amplitude of a peak, say, or time interval between peaks. At times, we may try to detect qualitative changes in wave shape. Differentiating stratigraphic conditions from a single variable, say time interval or amplitude, is often very difficult because the observed differences within the variable may be small and within the expected range of noise. However, a linear combination of a larger number of variables can, in some cases, uniquely describe a specific stratigraphic condition. Furthermore, linear coefficients can be computed which will optimize the discrimination between stratigraphic conditions. Stratigraphic conditions such as the variation from a sand to a shale can be described by seismic measurements, say amplitudes at discrete times. For example, [Formula: see text], [Formula: see text], ⋯, [Formula: see text] can represent the digitized amplitudes of a synthetic seismogram from one sand well; [Formula: see text], [Formula: see text], ⋯, [Formula: see text] would be amplitudes from another sand well; [Formula: see text], [Formula: see text], ⋯, [Formula: see text] would be amplitudes from a shale well; and so on. Discriminants [Formula: see text], [Formula: see text], ⋯, [Formula: see text] for sand and [Formula: see text], [Formula: see text], ⋯, [Formula: see text] for shale are computed such that the several seismograms of one group are brought close together while the two groups (sand, shale) are maximally separated. This technique, known as discriminatory analysis, is familiar to the statisticians. It is shown how the technique can be used effectively with seismic data, and an example is given in which it successfully delineated a known oil‐bearing sand body directly from seismic traces.