Iterative joint inversion for stress and fault orientations from focal mechanisms

Stress inversions from focal mechanisms require knowledge of which nodal plane is the fault. If such information is missing, and faults and auxiliary nodal planes are interchanged, the stress inversions can produce inaccurate results. It is shown that the linear inversion method developed by Michael is reasonably accurate when retrieving the principal stress directions even when the selection of fault planes in focal mechanisms is incorrect. However, the shape ratio is more sensitive to the proper choice of the fault and substituting the faults by auxiliary nodal planes introduces significant errors. This difficulty is removed by modifying Michael's method and inverting jointly for stress and for fault orientations. The fault orientations are determined by applying the fault instability constraint and the stress is calculated in iterations. As a by-product, overall friction on faults is determined. Numerical tests show that the new iterative stress inversion is fast and accurate and performs much better than the standard linear inversion. The method is exemplified on real data from central Crete and from the West-Bohemia swarm area of the Czech Republic. The joint iterative inversion identified correctly 36 of 38 faults in the central Crete data. In the West Bohemia data, the faults identified by the inversion were close to the principal fault planes delineated by foci clustering. The overall friction on faults was estimated to be 0.75 and 0.85 for the central Crete and West Bohemia data, respectively.