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

Abstract

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.

Geologic and geodetic constraints on the seismic hazard of Malawi’s active faults: The Malawi Seismogenic Source Database (MSSD)

“…2). In their compilation of dip-slip surface ruptures, Biasi and Wesnousky, (2017) noted only 10% of earthquakes exhibited branching 'Y' geometries in map view, and the paucity of branching earthquakes is consistent with numerical modelling (Bhat et al, 2007;Geist and Parsons, 2020). Therefore, where we identify fault branches, we consider these as distinct, partially overlapping fault seismogenic sources (Fig.…”

Earthquake Magnitude Distributions on Northern Caribbean Faults From Combinatorial Optimization Models

“…Harris et al, 2021). Incorporating step-over and branching connections into the integer-programming framework is described by Geist and Parsons (2020).…”

“…Dynamic rupture modeling can greatly aid in determining likely multi‐fault rupture scenarios given specific rock properties and 3D geometry (e.g., R. A. Harris et al., 2021). Incorporating step‐over and branching connections into the integer‐programming framework is described by Geist and Parsons (2020).…”

“…A long‐standing debate is whether on‐fault magnitude distributions accord with a Gutenberg‐Richter (G‐R) relation or with a characteristic model, where primarily one magnitude dominates the hazard (e.g., Hecker et al., 2013; Kagan et al., 2012). Recent system‐level rupture forecasts, however, reveal complexities of on‐fault magnitude‐frequency distributions (MFDs) that are not simply described by either of these end‐member characterizations (Geist & Parsons, 2019, 2020; Parsons et al., 2018). An open question addressed in this study is whether assumptions of segmentation and coupling on one fault in a complex fault system affect the MFDs on other faults.…”

Employing Remote Sensing, Data Communication Networks, AI, and Optimization Methodologies in Seismology

“…Newton's theorem [58]- [66] Secant theorem [67]- [71] Lagrange multiplier [72]- [78] Numerical Linear programming [79]- [85] Integer programming [57], [86]- [92] Quadratic programming [93]- [101] Non-linear programming [102]- [107] Stochastic programming [108]- [112] Dynamic programming [113]- [118] Combinatorial [77], [119]- [123] Advanced Genetic algorithm (GA) [124]- [130] Particle swarm [131]- [135] Karush-Kuhn-Tucker (KKT) [136]- [138] Simulated annealing [139]- [142] Ant colony [143]- [148] [3], [57], [154]- [162].…”