Further Notes on the New Empirical Earthquake Source-Scaling Laws

We articulate a few additional points, relevant to the empirical earthquake source-scaling laws (Thingbaijam et al., 2017). First, we report that adjustments, due to improved theoretical derivation of error-variance ratios, do not impact the general orthogonal regressions significantly. Hence, the earlier results are not affected. Second, we perform partial correlation analysis based on the residuals, to investigate influencing parameter(s) on the scaling relations. It is observed that rupture length L correlates poorly with rupture width W, if not influenced by magnitude MW. Therefore, overall relation between L and W is controlled by how they scale with MW independently. On the other hand, average slip correlates negatively with L and more strongly so with W, if influence of MW is eliminated. Third, we demonstrate that Monte Carlo approach would be appropriate while applying the scaling laws for predictions, to account for the associated data scatter. In case of uncertain independent variable, such approach allows capture the error propagations effectively. Lastly, we evaluate the effect of finite seismogenic depth, in estimation of maximum magnitude for near-vertical strike-slip faults.