Karen R. Felzer

A Common Origin for Aftershocks, Foreshocks, and Multiplets

We demonstrate that the statistics of earthquake data in the global Cen- troid Moment Tensor (CMT) and National Earthquake Information Center (NEIC) catalogs and local California Council of the National Seismic System (CNSS) catalog are consistent with the idea that a single physical triggering mechanism is responsible for the occurrence of aftershocks, foreshocks, and multiplets. Specifically, we test the hypothesis that tectonic earthquakes usually show clustering only as a result of an initial earthquake triggering subsequent ones and that the magnitude of each trig- gered earthquake is entirely independent of the magnitude of the triggering earth- quake. Therefore a certain percentage of the time, as determined by the Gutenberg- Richter magnitude-frequency relationship, an earthquake should by chance be larger than or comparable in size to the earthquake that triggered it. This hypothesis predicts that the number of times foreshocks or multiplets are observed should be a fixed fraction of the number of aftershock observations. We find that this is indeed the case in the global CMT and NEIC catalogs; the average ratios between foreshock, aftershock, and multiplet rates are consistent with what would be predicted by the Gutenberg-Richter relationship with b 1. We give special attention to the Solomon Islands, where it has been claimed that unique fault structures lead to unusually high numbers of multiplets. We use Monte Carlo trials to demonstrate that the Solomon Islands multiplets may be explained simply by a high regional aftershock rate and earthquake density. We also verify our foreshock results from the more complete recordings of small earthquakes available in the California catalog and find that foreshock rates for a wide range of foreshock and mainshock magnitudes can be projected from aftershock rates using the Gutenberg-Richter relationship with b 1 and the relationship that the number of earthquakes triggered varies with triggering earthquake magnitude M as c10M, where c is a productivity constant and is equal to 1. Finally, we test an alternative model that proposes that foreshocks do not trigger their mainshocks but are instead triggered by the mainshock nucleation phase. In this model, the nucleation phase varies with mainshock magnitude, so we would expect mainshock magnitude to be correlated with the magnitude, number, or spatial extent of the foreshocks. We find no evidence for any of these correlations.

The 1994 Java tsunami earthquake: Slip over a subducting seamount

On June 2, 1994, a large subduction thrust earthquake (Ms 7.2) produced a devastating tsunami on the island of Java. This earthquake had a number of unusual characteristics. It was the first recorded large thrust earthquake on the Java subduction zone. All of the aftershock mechanisms exhibit normal faulting; no mechanisms are similar to the main shock. Also, the large tsunami and the relatively low energy radiated by the main shock have led to suggestions that this earthquake might have involved slow, shallow rupture near the trench, similar to the 1992 Nicaragua earthquake. We first relocate the main shock and the aftershocks. We then invert long-period surface waves and broadband body waves to determine the depth and spatial distribution of the main shock slip. A dip of 12°, hypocenter depth of 16 km and moment of 3.5×l020 N m (Mw 7.6) give the best fit to the combined seismic data and are consistent with the plate interface geometry. The source spectrum obtained from both body and surface waves has a single corner frequency (between 10 and 20 mHz) implying a stress drop of ∼0.3 MPa. The main energy release was preceded by a small subevent lasting ∼12 s. The main slip occurred at ∼20 km depth, downdip and to the NW of the hypocenter. This area of slip is collocated with a prominent high in the bathymetry that has been identified as a subducting seamount. We interpret the Java earthquake as slip over this subducting seamount, which is a locked patch in an otherwise decoupled subduction zone. We find no evidence for slow, shallow rupture. No thrust aftershocks are expected if the entire locked zone slipped during the main shock, but extension of the subducting plate behind the seamount would promote normal faulting as observed. It seems probable that such a source model could also explain the size and timing of the observed tsunami.

Secondary Aftershocks and Their Importance for Aftershock Forecasting

The potential locations of aftershocks, which can be large and damaging, are often forecast by calculating where the mainshock increased stress. We find, however, that the mainshock-induced stress field is often rapidly altered by aftershock-induced stresses. We find that the percentage of aftershocks that are secondary aftershocks, or aftershocks triggered by previous aftershocks, increases with time after the mainshock. If we only consider aftershock sequences in which all aftershocks are smaller than the mainshock, the percentage of aftershocks that are secondary also increases with mainshock magnitude. Using the California earthquake catalog and Monte Carlo trials we estimate that on average more than 50% of aftershocks produced 8 or more days after M ≥5 mainshocks, and more than 50% of all aftershocks produced by M ≥7 mainshocks that have aftershock sequences lasting at least 15 days, are triggered by previous aftershocks. These results suggest that previous aftershock times and locations may be important predictors for new aftershocks. We find that for four large aftershock sequences in California, an updated forecast method using previous aftershock data (and neglecting mainshock-induced stress changes) can outperform forecasts made by calculating the static Coulomb stress change induced solely by the mainshock. Manuscript received 20 November 2002.

Long-Term Time-Dependent Probabilities for the Third Uniform California Earthquake Rupture Forecast (UCERF3)

The 2014 Working Group on California Earthquake Probabilities (WGCEP 2014) presents time-dependent earthquake probabilities for the third Uniform California Earthquake Rupture Forecast (UCERF3). Building on the UCERF3 time-in- dependent model published previously, renewal models are utilized to represent elastic- rebound-implied probabilities. A new methodology has been developed that solves applicability issues in the previous approach for unsegmented models. The new meth- odology also supports magnitude-dependent aperiodicity and accounts for the historic open interval on faults that lack a date-of-last-event constraint. Epistemic uncertainties are represented with a logic tree, producing 5760 different forecasts. Results for a variety of evaluation metrics are presented, including logic-tree sensitivity analyses and comparisons to the previous model (UCERF2). For 30 yr M ! 6:7 probabilities, the most significant changes from UCERF2 are a threefold increase on the Calaveras fault and a threefold decrease on the San Jacinto fault. Such changes are due mostly to differences in the time-independent models (e.g., fault-slip rates), with relaxation of segmentation and inclusion of multifault ruptures being particularly influential. In fact, some UCERF2 faults were simply too long to produce M 6.7 size events given the segmentation assumptions in that study. Probability model differences are also influential, with the implied gains (relative to a Poisson model) being generally higher in UCERF3. Accounting for the historic open interval is one reason. Another is an effective 27% increase in the total elastic-rebound-model weight. The exact factors influencing differences between UCERF2 and UCERF3, as well as the relative im- portance of logic-tree branches, vary throughout the region and depend on the evalu- ation metric of interest. For example, M ! 6:7 probabilities may not be a good proxy for other hazard or loss measures. This sensitivity, coupled with the approximate nature of the model and known limitations, means the applicability of UCERF3 should be evaluated on a case-by-case basis.

A Case Study of Two M ∼5 Mainshocks in Anza, California: Is the Footprint of an Aftershock Sequence Larger Than We Think?

It has been traditionally held that aftershocks occur within one to two fault lengths of the mainshock. Here we demonstrate that this perception has been shaped by the sensitivity of seismic networks. The 31 October 2001 Mw 5.0 and 12 June 2005 Mw 5.2 Anza mainshocks in southern California occurred in the middle of the densely instrumented ANZA seismic network and thus were unusually well recorded. For the June 2005 event, aftershocks as small as M 0.0 could be observed stretching for at least 50 km along the San Jacinto fault even though the mainshock fault was only ∼4:5 km long. It was hypothesized that an observed aseismic slipping patch produced a spatially extended aftershock-triggering source, presumably slowing the decay of aftershock density with distance and leading to a broader aftershock zone. We find, however, the decay of aftershock density with distance for both Anza se- quences to be similar to that observed elsewhere in California. This indicates there is no need for an additional triggering mechanism and suggests that given widespread dense instrumentation, aftershock sequences would routinely have footprints much larger than currently expected. Despite the large 2005 aftershock zone, we find that the probability that the 2005 Anza mainshock triggered the M 4.9 Yucaipa mainshock, which occurred 4.2 days later and 72 km away, to be only 14% 1%. This probability is a strong function of the time delay; had the earthquakes been separated by only an hour, the probability of triggering would have been 89%. Online Material: Movies exploring the spatial extent of aftershocks from the 2001 and 2005 Anza sequences.

A Synoptic View of the Third Uniform California Earthquake Rupture Forecast (UCERF3)

ABSTRACT Probabilistic forecasting of earthquake‐producing fault ruptures informs all major decisions aimed at reducing seismic risk and improving earthquake resilience. Earthquake forecasting models rely on two scales of hazard evolution: long‐term (decades to centuries) probabilities of fault rupture, constrained by stress renewal statistics, and short‐term (hours to years) probabilities of distributed seismicity, constrained by earthquake‐clustering statistics. Comprehensive datasets on both hazard scales have been integrated into the Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3). UCERF3 is the first model to provide self‐consistent rupture probabilities over forecasting intervals from less than an hour to more than a century, and it is the first capable of evaluating the short‐term hazards that result from multievent sequences of complex faulting. This article gives an overview of UCERF3, illustrates the short‐term probabilities with aftershock scenarios, and draws some valuable scientific conclusions from the modeling results. In particular, seismic, geologic, and geodetic data, when combined in the UCERF3 framework, reject two types of fault‐based models: long‐term forecasts constrained to have local Gutenberg–Richter scaling, and short‐term forecasts that lack stress relaxation by elastic rebound.

Reply to “Comment on ‘A model of earthquake triggering probabilities and application to dynamic deformations constrained by ground motion observations’ by Ross Stein”

[1] We thank Stein [2011] for pointing out the errors in the caption of Figure 1 of Gomberg and Felzer [2008], and we correct the caption appropriately herein. However, as we show below, the figure itself is not in error. We were also remiss in not providing a thorough description of how Figure 1 was created, and thus, do so in this reply. We also emphasize that the foundations of the study described by Gomberg and Felzer [2008] do not depend on its Figure 1, but instead Figure 1 simply strengthens them. The primary focus of Gomberg and Felzer [2008] was to glean some physical understanding about the processes that give rise to aftershocks, particularly the aftershock characteristics revealed in the study of Felzer and Brodsky [2006]. They showed that the aftershock density follows a continuous inverse power law decay over distances of many multiples of the rupture dimension and traditionally defined aftershock zone out to at least 50–100 km, separately for main shocks within bins M2–3, 3–4 and 5–6. Indeed, while Figure 1 of Gomberg and Felzer [2008] further corroborates the remarkable linearity of aftershock log‐density and its lack of dependence on main shock dimensions by combining results for multiple magnitudes, the premise of the paper derives from the original results of Felzer and Brodsky [2006], with or without this additional corroboration. [2] Stein’s [2011] message is that the M2–3 and M5–6 aftershock density measurements have not been correctly combined to show the continuity inferred by Gomberg and Felzer [2008]. Stein has four concerns: (1) he correctly notes errors in the caption of Figure 1, (2) he takes issue with the interpretation of the overlap between the two populations, (3) inclusion of only subsets of measurements from each population, and (4) the certainty of the correction for differences in populations due to the dependence of aftershock rate on measurement duration. We address these concerns sequentially. [3] First, Stein correctly notes that the statement “All aftershocks are M > 2 and occur in the first 5 min after their main shock” is in error, as it only applies to the M2–3 main shocks and the inequality should be M ≥ 2 (this inequality was similarly incorrectly reported by Felzer and Brodsky [2006]). In other words, we failed to note in the caption of Figure 1 that aftershocks are M ≥ 3 in the first 2 days for the M5–6 main shocks. However, these errors affect the caption only, and were accounted for in the creation of Figure 1. [4] Stein also correctly notes a second error in the caption of Figure 1 regarding the distance range of densities plotted for the M5–6 main shocks. We reported these were plotted only to distances of r < 3 km, when in fact as can be seen in Figure 1, they are plotted to 12 km and thus overlap with the M2–3 measurements from 3 to 12 km. However, we disagree that this overlap obscures the continuity between the two data sets and note that the overlap more robustly establishes continuity than had each data set been terminated at a “3 km boundary.” In addition, the overlap makes sense physically because the transition from near to far field occurs over a finite distance range, not at a sharp boundary. [5] Stein’s third concern pertains to the omission of measurements, that “outliers at distances greater than 10 km in Figure S5, and a change in slope of the data at 80–100 km in Figure S1, are excluded.”We remind Stein and the reader the latter is explained in the caption of Figure S1 of Felzer and Brodsky [2006], which states “At far distances there are more background earthquakes than aftershocks, and thus that the aftershock decay can no longer be observed. Since the main shock selection criteria only eliminated larger main shocks within 100 km (see Methods), there is contamination from aftershocks of larger mainshocks beyond 100 km, as well as contamination from other sources of background seismicity.” Careful inspection of Figure S5 reveals that in Figure 1 no points from the M5–6 data set were excluded within the 0–12 km distance range (chosen for reasons discussed above and in the caption) and the density range plotted. Stein states that the selection criteria applied to the M5–6 data set render “the M5–6 portion of theGomberg and Felzer [2008] Figure 1 irreproducible.” We note that this does not appear to be supported by the fact that Marsan and Lengline [2010] had no difficulty duplicating the results of Felzer and Brodsky [2006]. The critical point is being able to determine accurate locations for the main shock fault planes; Marsan and Lengline [2010] developed an automated algorithm for fault plane location and found that the aftershocks of a larger U.S. Geological Survey, Department of Earth and Space Sciences, University of Washington, Seattle, Washington, USA. U.S. Geological Survey, Pasadena, California, USA.