Probability of Occurrence and Displacement Regression of Distributed Surface Rupturing for Reverse Earthquakes

Probabilistic fault displacement hazard analysis provides a systematic approach to estimate the likelihood of occurrence and expected amount of surface displacement during an earthquake on-fault (principal fault rupturing) and off-fault (distributed rupturing). The methodology is based on four key parameters describing the probability of occurrence and the spatial distribution of the displacement both on and off-fault. In this work we concentrate on off-fault rupturing, and develop an original probability model for the occurrence of distributed ruptures and for the expected displacement distribution based on the compilation and reappraisal of surface ruptures from 15 historical crustal earthquakes of reverse kinematics, with magnitudes ranging from M-w 4.9 to 7.9. We introduce a new ranking scheme to distinguish principal faults (rank 1) from simple distributed ruptures (rank 2), primary distributed ruptures (rank 1.5), bending-moment (rank 21) and flexural-slip (rank 22) and triggered faulting (rank 3). We then used the rank 2 distributed ruptures with distances from the principal fault ranging from 5 to 1,500 m. To minimize bias due to the incomplete nature of the database, we propose a "slicing" approach as an alternative to the "gridding" approach. The parameters obtained from slicing are then is then combined with Monte Carlo simulations to model the dependence of the probability of occurrence and exceedance with the dimensions and position of the site of interest with respect to the principal fault, both along and across strike. We applied the probability model to a case-study in Finland to illustrate the applicability of the method given the limited extend of the available dataset. We finally suggest that probabilistic fault displacement hazard model will benefit by evaluating spatial distribution of distributed rupture in the light of spatial completeness of the input data, structural complexity and physics observables of the causative fault.