INVERTING FAULT SLIP RATES ON COMPLEX FAULT SYSTEMS TO OBTAIN THE OPTIMAL SPATIAL DISTRIBUTION OF EARTHQUAKES

A critical component of seismic hazard analysis is understanding the frequency and spatial distribution of earthquakes of different magnitudes on nearby faults. Knowing the long-term slip rate of faults from timed offset features, paleoseismic results, and geodetic studies, one can invert for the spatial distribution of earthquakes using combinatorial optimization. The problem can be stated simply: starting with a millennia-scale sample of earthquakes taken from a regional Gutenberg-Richter relation, what is the optimal spatial arrangement of earthquakes that minimizes the slip-rate misfit for all faults in a complex fault system? We have developed two different types of combinatorial optimization techniques to solve this problem: one termed the greedy sequential algorithm and the other termed integer programming (IP). The greedy sequential algorithm is a spatial gap-filling method in which earthquakes are sequentially placed in a locally optimal sense relative to the target slip rate of the faults. Starting with the largest earthquakes, constant slip rupture areas expand out from the hypocenters to match the target slip and can have an irregular shape. The IP method globally optimizes earthquake placement to minimize the misfit in slip rate on all faults taken together. The binary decision vector in the IP model is composed of every possible location that each earthquake in the G-R sample can occur. We have applied these techniques to complex fault systems in different tectonic environments, including the Nankai subduction zone and the San Andreas fault system. In general, the resulting on-fault magnitude distributions cannot be described as simply being either characteristic or Gutenberg-Richter. For example, faults may exhibit multiple “characteristic” magnitudes or a power-law distribution of magnitudes over a restricted range. Results from these methods are valuable for verifying the assumed magnitude-frequency distributions for faults in seismic hazard analysis.