SCEC Award Number 15110 View PDF
Proposal Category Collaborative Proposal (Integration and Theory)
Proposal Title Bounding the Rate of Moment Deficit on Faults in Southern California
Investigator(s)
Name Organization
Paul Segall Stanford University Kaj Johnson Indiana University
Other Participants Jeremy Maurer, Stanford University
SCEC Priorities 1d SCEC Groups SDOT, Geodesy, EFP
Report Due Date 03/15/2016 Date Report Submitted 03/13/2016
Project Abstract
 The interseismic Moment Deficit Rate (MDR) is crucial input for earthquake hazard estimates that can be determined geodetically using various inverse methods. We present and evaluate a number of methods for estimating the MDR using fault-specific models. Testing with synthetic data demonstrates that one method we term Constrained Optimization Bounding (COB) gives satisfactory, albeit conservative, results in all cases. We apply this method to estimate the MDR in Southern California using a block model and Global Positioning System (GPS) station velocities from the SCEC Community Motion Map 4. Estimates of the MDR in the Southern California fault system range from (1.7 – 2.0) x 10^19 N-m/yr at the 95% confidence level. This is equivalent to 150-year earthquake moment magnitudes of 8.2 -8.3, resulting in nearly one magnitude 8 earthquake of unaccounted-for moment deficit accumulation since the 1857 Fort Tejon earthquake. We also estimate MDR for individual fault systems in southern California and show that the MDR on nearly all these sections is equivalent to at least a M 7 over 150 years. We conclude that there is surprisingly high rate of moment deficit accumulation in Southern California equivalent to two M8 events per 150 years. Unresolved questions include the amount of moment released seismically versus aseismically, as well as uncertainty resulting from choice of forward model to represent the complex faulting environment.
Intellectual Merit Several studies have estimated coseismic or interseismic moment by different methods. Johnson (1994) was the first to use constrained optimization to estimate the bounds on scalar moment during the 1992 Landers earthquake. Segall & Murray (2002) used Johnson’s approach as well as boot-strapping to estimate the interseismic moment deficit rate (MDR) at Parkfield prior to the 2004 earthquake, and showed that there is not a simple relationship between MDR and recurrence times for M6 events on this section of the San Andreas. Maurer & Johnson (2014) used both of these approaches to estimate the MDR on the creeping section of the San Andreas Fault (CSAF). Other studies that focus on slip deficit also cite a moment rate, but commonly only a single value that comes from the best-fitting slip model, and generally do not include uncertainties in the MDR, even if they do so for slip-rate.
We present and evaluate several methods for estimating the uncertainty in the MDR. We seek a method that is generally applicable and insensitive to features of the fault model such as grid size or regularization of the underdetermined inverse problem. Our work is motivated by several important scientific and hazard questions, including whether we can determine bounds on the MDR given the kinds of data available (GPS, InSAR, etc.), as well as inherent modeling uncertainties. We use synthetic tests to evaluate the performance of various methods for bounding the MDR for synthetic tests where the true model is known. We show that methods based on conventional Markov Chain Monte Carlo (MCMC) analysis fail to provide appropriate bounds on the MDR, the bootstrap provides optimistic coverage and fails catastrophically in some cases, while an approach we term Constrained Optimization Bounding (COB) provides conservative, reliable bounds as long as data and prediction errors are reasonably well known. We further consider variations in MDR estimated using different forward models as a measure of model based uncertainty.
Broader Impacts Training of graduate student.
Exemplary Figure Figure 1. Estimates of the MDR for Southern California from this study and others. The red and blue pdfs are Constrained Optimization Bounding estimates of the total MDR using a block model geom-etry discretized to 25 km depth. The red curve is based on an estimate of the full data covariance matrix, while the blue curve is based on a tridiagonal approximation to the data covariance. Solid curves are directly from the COB inversion; dashed lines are the same curves but offset to include moment deficit from off-fault deformation (Johnson, 2013). Lower horizontal axis gives the MDR in N-m/yr, and the upper horizontal axis is the equivalent 150-year earthquake magnitude assuming all of the moment deficit is released in a single event. Blue bars are from Kostrov summation esti-mates; solid line from Ward (1994) and Savage & Simpson (1997), dashed is Ward (1998). Green bars are from UCERF3: dashed is using the geologic slip rates and assuming a fixed locking depth, solid is a range of different kinematic models. Black square is from Meade & Hagar (2005). Red squares are from Johnson (2013): solid is a rigid elastic block model, open is a plate-block kinematic model, and crossed square is a viscoelastic cycle plate-block model. J. Maurer, K. M. Johnson, and P. Segall
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