The Statistical Eigenvector Analysis Technique (SEAT) for Image Log-Based Directional Measurements

Abstract

Directional measurements, or dip data, gathered from image logs (i.e. the dip/azimuth of planar features) are widely used in the oil and gas industry to interpret a variety of subsurface features relating to both structural and sedimentary geology. Gradual and/or abrupt variations in dip data over depth typically indicate major structural features (e.g. faults, folds, etc.) or sedimentological breaks (i.e. unconformity). The orientation and geometry of geologic structures can be precisely calculated using stereogram plots and the statistical eigenvector analysis technique. Although this method is widely utilized by field and academic geologists, it is not typically applied in the oil and gas industry to subsurface dip data. Poles to planes are plotted onto a stereographic projection over a given depth interval and are interactively analyzed using statistical distribution functions on the unit sphere. The maximum of the distribution function is achieved when a quadratic form is maximized. The quadratic form acquires its maximum in the eigenvector related to the largest eigenvalue of the corresponding 3×3 symmetry matrix. The pole associated to the eigenvector with the smallest eigenvalue is the axis of the best-fit great circle for a spread of poles. A series of interactively calculated axes over a given depth interval can accurately inform the geometry and orientation of a variety of subsurface features (e.g. upright and plunging folds, coaxial fault drag deformation, fault block rotation, etc.). The application of the statistical eigenvector analysis technique to subsurface dip data will improve the quality of subsurface structural and sedimentological interpretations.

AAPG Datapages/Search and Discovery Article #90259 ©2016 AAPG Annual Convention and Exhibition, Calgary, Alberta, Canada, June 19-22, 2016