Inversion of fault data with low diversity for stress: Principles and applications

Although a minimum of four independent, single-phase fault data are required to solve for a unique reduced stress tensor, we prove in this paper that a smaller number of fault data are sufficient in some instances to solve for part of the reduced stress tensor. One of the principal stress directions is determinable from either two faults with a common null shear direction on the fault planes or three faults with a common intersection in a principal stress plane of the fault planes. This direction is combined with the fault data to determine the possible ranges of other principal stress directions. Determining whether the direction is for the maximum, intermediate or minimum principal stress depends upon constraints provided by slip tendency or more fault data. This approach can also be applied to a set of four or more fault data with low orientation diversity. This new method is finally applied to two different sets of fault data from along the active Chelungpu fault, western Taiwan. The stress orientations determined from the method lie in acceptable ranges for the maximum/minimum principal stresses using other existing and comparable methods, such as the right dihedra/trihedra methods. They differ moderately in the maximum/minimum principal stress directions when compared to the moment tensor method for fault kinematic analysis. The new method has advantages over the right dihedra/trihedra methods in the accuracy of stress estimate and the independence of stress estimate upon the small number of faults that are not parallel to the dominant fault set(s).