SCEC Award Number 21017 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title A Bayesian Framework for the Joint Estimation of Corner Frequency and Rupture Directivity for Southern California Earthquakes
Investigator(s)
Name Organization
Daniel Trugman University of Texas at Austin
Other Participants
SCEC Priorities 1d, 2d, 3c SCEC Groups Seismology, FARM, CS
Report Due Date 03/15/2022 Date Report Submitted 03/04/2022
Project Abstract
 The spectra of earthquake waveforms can provide important insight into rupture processes, but the spectral analysis and interpretation is often challenging. In this project we developed a Bayesian framework that embraces the inherent data and modeling uncertainties of spectral analysis to infer key source properties. The method uses a spectral ratio approach to correct the observations spectra of for path and site attenuation effects. The objective then is to solve for joint posterior probability distributions of three source parameters -- seismic moment, corner frequency, and high-frequency falloff rate -- for each earthquake in a sequence, as well as a measure of rupture directivity for target events with good azimuthal station coverage. While computationally intensive, this technique provides a quantitative understanding of parameter tradeoffs and uncertainties and allows one to impose physical constraints through prior distributions on all source parameters, which guide the inversion when data is limited. We demonstrate the method by analyzing in detail the source properties of 14 different target events of magnitude M5 in southern California that span a wide range of tectonic regimes and fault systems. These prominent earthquakes are diverse in their source properties and directivity modes, with clear spatial patterns, depth-dependent trends, and a preference for unilateral rupture. These coherent spatial variations source properties suggest that regional differences in tectonic setting, hypocentral depth, or fault zone characteristics may drive variability in rupture processes. These observations have important implications for our understanding of earthquake physics and its relation to hazard.
Intellectual Merit This project develops the computational framework for advanced source spectral analyses on the cutting edge of observational seismology, integrating recent advances in probabilistic programming and inverse theory with high-resolution waveform measurements. Studies that built on this underlying framework are well-positioned to tackle several SCEC research objectives, specifically (1) how faults are loaded across temporal and spatial scales, (2) what is the role of off-fault deformation on dynamic rupture and radiated energy, (3) how does fault zone structure relate to seismic slip, and (4) how strong ground motions depend on complexities in dynamic earthquake systems. While the research performed as part of this project is a smaller scale pilot study, it already has uncovered important findings for our understanding of magnitude and depth-scaling trends, rupture directivity, and stress drop variability, and their relation to regional earthquake hazards. The promising initial results can be used as a springboard to foster multidisciplinary collaborations that examine each of these important issues in greater detail.
Broader Impacts This project supported both an early-career PI, in the first year of building his research group in a tenure-track faculty position, as well as postdoctoral fellow looking to expand her expertise in induced seismicity into the realm of source spectral analysis. Results from this project will be used in outreach efforts this summer to underrepresented high school students in Texas that showcase research at the interface between “big data” and modern geoscience. The codes developed as part of this project are publicly available on GitHub to foster future efforts to build on them further by interested researchers in the SCEC community. While this study is independent from the SCEC-supported Community Stress Drop Validation exercise, the PI has been an active participant in that effort, contributing expertise, datasets, and quality control checks. The method developed here could easily be applied to contribute more directly in the coming year. The research outcomes of this project also have important societal implications, as they provide new constraints on variability in rupture processes and their effects on strong ground motions at high frequencies. Future work could examine the relation between shaking hazard and rupture in greater detail.
Exemplary Figure Figure 3: Directivity observations. Top panel: azimuthal variations in source spectra for target event 37374687 (the 2016 Borrego Springs event). Each spectral ratio with EGF 15527617 is color-coded by the model-inferred modulation in corner frequency (%). The clear gradient from blue to red as one traverses the focal sphere indicates strong unilateral directivity. Bottom panel: relation between directivity and the spatial pattern of early aftershocks. For events like these three with clear unilateral directivity, there is a tendency for aftershocks to concentrate in the forward rupture direction.

Figure adapted from Trugman (2022), JGR-Solid Earth (in review).