New Scalar Measures of Geodetic Strain and Moment Rate from Kinematic Mode Decomposition: Application to the Southwestern United States

Scalar representations of geodetic strain rate tensors are widely used to characterize crustal deformation and, in seismic hazard assessment, to convert strain rate to expected seismic moment rate. Existing scalar definitions of shear strain rate, total strain rate and deformation style are not defined consistently and, because they depend on eigenvalues that carry both dilatation and shear, cannot be read as a partition of mixed-strain deformation. We propose definitions motivated by fault kinematics. The strike-slip strain rate (e_s), derived from the shear on zero-length-change orientations, is twice the geometric mean of the principal strain rate magnitudes and zero when both share a sign. The total strain rate (e_t) is the explicit sum of and the absolute dilatation (); except for uniaxial strain it exceeds the Frobenius norm (e_f), by up to a factor sqrt(3). The style parameter equals the fractional dilatational contribution in mixed-strain deformation and is extended to classify deformation in which both principal strain rates share a sign. We also propose a moment rate (M_split) that releases the strike-slip and dilatational contributions on separate strike-slip and dip-slip faults; for Andersonian dips it exceeds the minimum moment (M_min) by up to 37% for mixed-faulting settings. An application to southwestern U.S. geodetic strain rates shows that the 37% maximum difference is not a corner case: in the 53% of the area where each of the strike-slip and dilatational contributions is at least a quarter of the total strain rate, M_split exceeds M_min by 34%. The southwestern U.S. example demonstrates that these differences can be regionally significant, with moment-rate estimates differing by tens of percent in mixed-style deformation zones.