STATISTICS OF ELLIPSOIDAL DATA FROM RIDGE-TRANSFORM SYSTEMS

Our understanding of ridge-transform systems, shear zones, and faults is informed by various types of data. Among the richest data types to mine are ellipsoids, such as stress, strain, shape preferred orientation (SPO), and anisotropy of magnetic susceptibility (AMS). However, it is not obvious how one should perform statistical analysis on a given data set of ellipsoids. For example, if the ellipsoids represent a single population, then what is the mean of that population? Or how do the ellipsoids vary over space and by rock type? Geologic studies rarely address such questions statistically, even when the answers may affect their conclusions.

In this presentation we describe a coherent framework for statistics of ellipsoidal data. The theory is based on a natural vector space structure on the set of ellipsoids. Within this vector space, many techniques of multivariate statistics are safely and easily applied: principal component analysis, regression, spatial statistics, inference about the mean, etc. The results can be transferred back to more familiar forms, such as Hsu-Nadai and equal-area plots, for interpretation.

We demonstrate this methodology on AMS, SPO, and X-ray computed tomography data sets from fossil ridge-transform systems preserved in Cyprus and New Caledonia. In the latter setting, we use a non-steady, heterogeneous deformation model to predict the formation of spinel fabrics at the ridge and how they are affected by progressive deformation along the transform.