Modal and vectorial analysis for determination of stress axes associated with fault slip data : Qin Huang Math GeolV21, N5, July 1989, P543–558

Abstract

Based on Anderson's faulting theory, for a given set of fault slip data include the sense of slip on faults and fault planes, this paper provides two possible methods to reconstruct the principal stress axes using vectorial and modal analysis procedure. The vectorial analysis consists of computing eigenvectors of the orientation matrices defined by axes P{sub {theta}}, B, and T{sub {theta}} (P{sub {theta}}, B and T{sub {theta}} being geometrical axes parallel to axes {sigma}{sub 1}, {sigma}{sub 2}, {sigma}{sub 3} associated with a single striated fault) which are determined geometrically knowing the slip vector S, the normal to fault plane N, and the dihedral angle 2{theta}. A parameter R, related to the maximum eigenvalue of the orientation matrix and the size of data sample, is shown to be a good test value for the homogeneity of the data. A process of refinement of this parameter enables bad data (representing faults generated under different tectonic events) to be ignored in the final computation of the principal stress axes; results are thus significantly improved and the vectorial analysis procedure enables the orientation of stress to be numerically determined. On defining probability density regions around each P{sub {theta}}, B, and T{sub {theta}} axes thatmore » incorporate the variation of fault geometry, the modal analysis is carried out in two density functions established by a convolution process to locate modes which represent optimal locations of the principal stress axes in spherical space. Splitting of heterogeneous data samples into homogeneous subsets is achieved by a dynamical cluster procedure which enables the principal stress axes associated with each subset to be determined separately.« less