Iterative direct inversion: An exact complementary solution for inverting fault-slip data to obtain palaeostresses

Abstract

The present study shows that reconstructing the reduced stress tensor (RST) from the measurable fault-slip data (FSD) and the immeasurable shear stress magnitudes (SSM) is a typical iteration problem. The result of direct inversion of FSD presented by Angelier [1990. Geophysical Journal International 103, 363–376] is considered as a starting point (zero step iteration) where all SSM are assigned constant value ( λ = 3 / 2 ). By iteration, the SSM and RST update each other until they converge to fixed values. Angelier [1990. Geophysical Journal International 103, 363–376] designed the function upsilon ( υ ) and the two estimators: relative upsilon (RUP) and (ANG) to express the divergence between the measured and calculated shear stresses. Plotting individual faults’ RUP at successive iteration steps shows that they tend to zero (simulated data) or to fixed values (real data) at a rate depending on the orientation and homogeneity of the data. FSD of related origin tend to aggregate in clusters. Plots of the estimators ANG versus RUP show that by iteration, labeled data points are disposed in clusters about a straight line. These two new plots form the basis of a technique for separating FSD into homogeneous clusters.