Determination of Mmax from Background Seismicity and Moment Conservation

Abstract

We describe a simple method to determine the probability distribution function of the magnitude M max and return period T R of the maximum plausible earthquake on crustal faults. The method requires the background seismicity rate (estimated from instrumental data) and the rate of interseismic moment buildup. The method assumes that the moment released by the seismic slip is in balance with the moment deficit accumulated in between earthquakes. It also assumes that the seismicity obeys the Gutenberg-Richter (GR) law up to M max . We took into account the aftershocks of large infrequent events that were not represented in the instrumental record, so that we could estimate the average seismicity rate over the entire fault history. We extrapolated the instrumental record, using the GR law to model the frequency of larger events and their aftershocks. This increased the frequencies of smaller events on average; when these smaller events were newly extrapolated, they predicted a higher frequency of larger events. We iterated this process until stability was reached, and then we assumed moment balance when we found the maximum magnitude; we have found this method to be appropriate in applications involving examples of fault with good historical catalogs. We then showed examples of applications to faults with no historical catalogs. We present results from nine cases. For the San Andreas fault system, we find

Assessment of seismic sources and capable faults through hierarchic tectonic criteria: implications for seismic hazard in the Levant

“…Previous analyses of maximum earthquake magnitude based on historical earthquakes or on background seismicity predicted magnitudes of ≤ 7.8M w for the largest segments (e.g. Stevens and Avouac, 2017;Klinger et al, 2015;Hamiel et al, 2018a).…”

A Geodesy‐ and Seismicity‐Based Local Earthquake Likelihood Model for Central Los Angeles

“…Some studies iteratively estimate M max in cumulative magnitude-frequency space (Stevens & Avouac, 2016, 2017; others estimate it using total fault areas and scaling relations (Field et al, 2014) or assume a value for the maximum earthquake's recurrence interval (Hsu et al, 2016). First, M max is unknown due to the short history of observation.…”

“…First, M max is unknown due to the short history of observation. Some studies iteratively estimate M max in cumulative magnitude-frequency space (Stevens & Avouac, 2016, 2017; others estimate it using total fault areas and scaling relations (Field et al, 2014) or assume a value for the maximum earthquake's recurrence interval (Hsu et al, 2016). Second, while some studies estimate b a priori from the catalog (Field et al, 2014;Stevens & Avouac, 2016, 2017, it is desirable to fully account for the covariances between b, M max , the moment deficit buildup rate, and other factors in estimating long-term earthquake rates.…”

“…Some studies iteratively estimate M max in cumulative magnitude-frequency space (Stevens & Avouac, 2016, 2017; others estimate it using total fault areas and scaling relations (Field et al, 2014) or assume a value for the maximum earthquake's recurrence interval (Hsu et al, 2016). Second, while some studies estimate b a priori from the catalog (Field et al, 2014;Stevens & Avouac, 2016, 2017, it is desirable to fully account for the covariances between b, M max , the moment deficit buildup rate, and other factors in estimating long-term earthquake rates. Third, it is uncertain whether to decluster the instrumental catalog first (Michel et al, 2018), which method to use if so, whether declustering should yield a smaller b-value (Felzer, 2007;Marsan & Lengline, 2008), and how this may affect the inferred long-term model.…”

“…The strain accumulation can also be expressed as a deficit of seismic moment, which can be assumed to be balanced over the long term by the moment released in earthquakes and aseismic slip (Avouac, 2015;Brune, 1968;Molnar, 1979). This approach has found use in several regional and global studies (e.g., Hsu et al, 2016;Michel et al, 2018;Rong et al, 2014;Shen et al, 2007;Stevens & Avouac, 2016, 2017.…”