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.

Seismic Discriminants of Stratigraphy Derived From Monte Carlo Simulation of Sedimentary Formations*

“…The statistical analysis of the structure of the seismic reflection to predict lithological changes has been attempted by Mathieu and Rice (1969) and Avasthi and Verma (1973).…”

“…The statistical analysis of the structure of the seismic reflection to predict lithological changes has been attempted by Mathieu and Rice (1969) and Avasthi and Verma (1973). Mathieu and Rice have attempted an analysis of a linear combination of more than one observed parameter of the seismic trace for the determination of variation in stratigraphic condition, for example, from dominantly sandy to shaly sections. The parameters they chose for discrimination were picked from seismic traces, and are: amplitude of a peak, time interval between peaks and qualitative changes in wave shape.…”

Introduction

“…Mathieu and Rice (1969);de Figueiredo (1982); Sinvhal and Khattri (1983); Sinvhal et al (1984); Kaman et al (1987); Chen and Fu (1987); statistical discriminant analysis has not yet been seriously considered for exploration problems. Mathieu and Rice (1969);de Figueiredo (1982); Sinvhal and Khattri (1983); Sinvhal et al (1984); Kaman et al (1987); Chen and Fu (1987); statistical discriminant analysis has not yet been seriously considered for exploration problems.…”

Principal Component Analysis Applied to 3D Seismic Data for Reservoir Property Estimation

“…The use of the reflection seismic-attribute data for the prediction of detailed reservoir properties began at least as early as 1969. 1 Use of seismic attributes for reservoir prediction has accelerated in recent years, especially with the advent of widely available high-quality 3D seismic data.…”