Kinematically interpretable scalar measures of geodetic strain rate with implications for moment estimation: Application to the western United States

Corné Kreemer

In Preparation September 18, 2026, SCEC Contribution #15675

Scalar representations of geodetic strain rate tensors are widely used to characterize crustal deformation. The most important application of the strain rates is probably in the field of seismic hazard assessment, because the conversion of the scalar strain rate to expected seismic moment (rate) can be used to contextualize the observed seismic moment and also assess the observed and expected rate of earthquakes numbers. However, all existing scalar measures share a common deficiency: in mixed-mode deformation, individual eigenvalues conflate dilatational and shear contributions, preventing their decomposition into physically distinct components. We propose a shear strain rate () derived from the shear on zero-length-change directions, equaling twice the geometric mean of principal strain rate magnitudes and zero when both principal strains share a sign. A total strain rate — the explicit sum of absolute dilatation () and — always exceeds the Frobenius norm, with the ratio peaking analytically at . We also define a new style parameter equaling the fractional dilatational contribution: e.g., 0.5 for equal admixtures of extension and strike-slip, an interpretability existing definitions lack. .....

Key Words
Kinematics of crustal deformation, Space geodetic surveys, Seismotectonics, Theory

Citation
Kreemer, C. (2026). Kinematically interpretable scalar measures of geodetic strain rate with implications for moment estimation: Application to the western United States. Geophysical Journal International, (in preparation).