Direct inversion of stress, strain or strain rate including vorticity: A linear method of homogenous fault–slip data inversion independent of adopted hypothesis

• A new (‘9d-space’) fault–slip data inversion method is presented.
• 9d-space inversion is applicable both to the dynamic and the kinematic hypotheses.
• The moment method can be expanded to a 9d parameter space to account for vorticity.
• 9d-space inversion is direct and linear, and can constrain up to seven degrees of freedom.

A direct linear fault–slip inversion method applicable to both the kinematic and the dynamic hypotheses is presented. If vorticity represents a parameter in the slip generating tensor, this results in an asymmetric tensor and increases the number of unknowns that must be determined by the inversion. By assuming that stress, strain or strain rate (depending on adopted hypothesis) are zero in the direction on the fault plane perpendicular to slip, it is shown that the moment method of fault–slip inversion can be expanded to a nine-dimensional parameter space to account for this asymmetry and calculate all seven parameters of the asymmetric slip generating tensor. While the symmetric part of the calculated tensor constrains the principal axes of stress, strain or strain rate in addition to their relative magnitude, the antisymmetric part of this tensor constrains the axis and magnitude of vorticity. The presented inversion method is robust because: (i) it is a direct linear calculation of the slip generating tensor; (ii) it is independent on the correct assessment of slip sense; (iii) it can evaluate the axis and magnitude of vorticity if present; and (iv) the same mathematical inversion method can be applied regardless whether the dynamic or kinematic hypotheses are adopted.