Distribution of Earthquakes on a Branching Fault System Using Integer Programming and Greedy‐Sequential Methods

• Published in: Geochemistry, geophysics, geosystems : G3 Vol. 21; no. 9
• Main Authors: Geist, Eric L., Parsons, Tom
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 01.09.2020; Wiley
• Subjects: Distribution; earthquake forecast; Earthquakes; Fault lines; Faults; Geological hazards; greedy‐sequential; Integer programming; Methods; Numerical experiments; Operations research; Seismic activity; Seismic hazard; slip rates; Uncertainty; San Francisco Bay
• ISSN: 1525-2027; 1525-2027
• DOI: 10.1029/2020GC008964

A new global optimization method is used to determine the distribution of earthquakes on a complex, connected fault system. The method, integer programming, has been advanced in the field of operations research but has not been widely applied to geophysical problems until recently. In this application, we determine the optimal distribution of earthquakes on mapped faults to minimize the global misfit in slip rates for multifault ruptures. Integer programming solves for a decision vector composed of every possible location that a sample of earthquakes can occur on every fault, subject to slip rate uncertainty constraints. Step over connections are straightforward to include, whereas branching fault connections are not. To include branching ruptures, we distinguish between individual multifault rupture paths, as opposed to formulating the integer programming problem based on individual faults as in previous studies. The new method is applied to the complex fault system in the San Francisco Bay Area as a case study. Results from the integer programming method are compared to those from a local optimization method, termed the greedy‐sequential method. Several experiments using these two methods indicate that shape of the on‐fault magnitude distributions and which branching faults are involved in multifault ruptures depend on how much emphasis is placed on fitting the target slip rate. In cases where the underlying data are not strong enough to warrant chasing the target slip rate, it is better to focus on the distribution of feasible results that better represents the uncertainty in the solutions imposed by the data. Plain Language Summary The possibility of earthquake ruptures involving multiple faults can significantly influence earthquake hazard estimates. For example, a large magnitude earthquake rupture can branch off a main fault onto a short fault that might not have been considered a significant hazard if the faults were assumed to be unconnected. We apply a method termed integer programming, originally developed from the disparate field of operations research, to determine the optimal spatial arrangement and distribution of large earthquakes on complex fault systems that include branching ruptures. The advantage of this method is that it finds the optimal solution for the entire study region, rather than finding locally optimal solutions. Solutions are constrained by the measured and inferred slip rates on faults from paleoseismic studies and geodetic data. The complex fault system in the San Francisco Bay Area is used as a test case for this new method, and results are compared to the greedy‐sequential method that has previously een developed for complex fault systems. Numerical experiments using both the integer programming and greedy‐sequential methods reveal differences on which branching faults are activated during multifault ruptures, depending on how strictly the model tries to fit a target slip rate with large uncertainty. Key Points An integer programming method is developed to determine the optimal distribution of earthquakes on a fault system with branching faults Results are compared to the greedy‐sequential method—a local optimization algorithm previously developed for complex fault systems Application of these methods to San Francisco Bay Area faults indicate which branching faults are involved in multifault ruptures