Discriminant Function Analysis as Tool for Subsurface Geologist

Kevin Chesser

Sedimentary structures such as cross-bedding control porosity, permeability, and other petrophysical properties in sandstone reservoirs. Understanding the distribution of such structures in the subsurface not only aids in the prediction of reservoir properties but also provides information about depositional environments.

Discriminant function analysis (DFA) is a simple yet powerful method incorporating petrophysical data from wireline logs, core analyses, or other sources into groups that have been previously defined through direct observation of sedimentary structures in cores. Once data have been classified into meaningful groups, the geologist can predict the distribution of specific sedimentary structures or important reservoir properties in areas where cores are unavailable.

DFA is efficient. Given several variables, DFA will choose the best combination to discriminate among groups. The initial classification function can be computed from relatively few observations, and additional data may be included as necessary. Furthermore, DFA provides quantitative goodness-of-fit estimates for each observation. Such estimates can be used as mapping parameters or to assess risk in petroleum ventures.

Petrophysical data from the Skinner sandstone of Strauss field in southeastern Kansas tested the ability of DFA to discriminate between cross-bedded and ripple-bedded sandstones. Petroleum production in Strauss field is largely restricted to the more permeable cross-bedded sandstones. DFA based on permeability correctly placed 80% of samples into cross-bedded or ripple-bedded groups. Addition of formation factor to the discriminant function increased correct classifications to 83%--a small but statistically significant gain.

AAPG Search and Discovery Article #91038©1987 AAPG Annual Convention, Los Angeles, California, June 7-10, 1987.