Striated faults: visual appreciation of their constraint on possible paleostress tensors

Abstract

Two new types of geometric representation provide visual appreciation of the extent to which a possible common stress tensor is constrained by a set of striated faults (solving the ‘inverse problem’). The first type uses only orientation of fault plane and striation, and involves projections from a space, having dimensions of the six distinct elements of the stress tensor, in which faults are represented as poles on a hypersphere. Any girdle or clustering of poles permits identification of one or more normals, representing possible stress tensors. These tensors provide the dimensions of the second type of diagram in which directions represent both senses of shear and proportions in which component tensors are combined, so enabling identification of the total tensor which best matches the complete data. Examples illustrate uses for both homogeneous and heterogeneous sets of data, showing varying degrees of constraint on stress state. The discussion of mathematical issues includes the wider significance of tensor element space, regarding degrees of freedom, estimators of error and mismatch, and degeneracy.