Volume 50, Issue 1 e2022GL098737
Research Letter
Open Access

New Physical Implications From Revisiting Foreshock Activity in Southern California

Ester Manganiello

Corresponding Author

Ester Manganiello

Dipartimento di Scienze della Terra, dell’Ambiente e delle Risorse, Università degli Studi di Napoli Federico II, Naples, Italy

Correspondence to:

E. Manganiello,

[email protected]

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Marcus Herrmann

Marcus Herrmann

Dipartimento di Scienze della Terra, dell’Ambiente e delle Risorse, Università degli Studi di Napoli Federico II, Naples, Italy

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Warner Marzocchi

Warner Marzocchi

Dipartimento di Scienze della Terra, dell’Ambiente e delle Risorse, Università degli Studi di Napoli Federico II, Naples, Italy

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First published: 24 December 2022


Foreshock analysis promises new insights into the earthquake nucleation process and could potentially improve earthquake forecasting. Well-performing clustering models like the Epidemic-Type Aftershock Sequence (ETAS) model assume that foreshocks and general seismicity are generated by the same physical process, implying that foreshocks can be identified only in retrospect. However, several studies have recently found higher foreshock activity than predicted by ETAS. Here, we revisit the foreshock activity in southern California using different statistical methods and find anomalous foreshock sequences, that is, those unexplained by ETAS, mostly for mainshock magnitudes below 5.5. The spatial distribution of these anomalies reveals a preferential occurrence in zones of high heat flow, which are known to host swarm-like seismicity. Outside these zones, the foreshocks generally behave as expected by ETAS. These findings show that anomalous foreshock sequences in southern California do not indicate a pre-slip nucleation process, but swarm-like behavior driven by heat flow.

Key Points

  • We compare the foreshock activity in southern California with the expectation of the best-performing class of earthquake clustering models

  • Sequences with an anomalous excess of foreshocks are associated mostly with moderate mainshocks and preferentially with high heat flow

  • We neither find evidence against the cascade nucleation hypothesis nor in favor of the pre-slip nucleation hypothesis

Plain Language Summary

Many studies have observed that large earthquakes are preceded by smaller events, called foreshocks. If they have distinctive characteristics that make them recognizable in an ongoing sequence in real time, they can significantly improve the forecasting capability of large earthquakes. To investigate the nature of foreshocks, we compare actual seismicity with the expectation of the most skilled earthquake forecasting model, which assumes that foreshocks are not different from other earthquakes. We find that discrepancies between reality and expectation mostly affect foreshock sequences that anticipate moderate mainshocks with magnitudes below 5.5. We find that those anomalous foreshock sequences tend to occur more often where the heat flow is high. Those zones are already known for the occurrence of swarm-like sequences, which are prolonged episodes of seismicity without a dominant event. Outside these zones, the observed foreshock activity is explained well by the forecasting model. These findings indicate that anomalous foreshock sequences are not indicating impending large earthquakes but are influenced by the heat flow.

1 Introduction

It is well known that many large earthquakes are preceded by smaller events, for example, 1999 M7.6 Izmit, Turkey (Bouchon et al., 2011; Ellsworth & Bulut, 2018), 2009 M6.1 L'Aquila, Italy (Chiaraluce et al., 2011), 2011 M9.0 Tohoku, Japan (Kato et al., 2012), 2019 M7.1 Ridgecrest, USA (Meng & Fan, 2021), which are (a posteriori) called foreshocks. The role of foreshocks in earthquake predictability can be epitomized by two still debated conceptual hypotheses about earthquake nucleation: the “pre-slip model” versus the “cascade model” (Ellsworth & Beroza, 1995; Gomberg, 2018). According to the former, foreshocks are diagnostic precursors, because they are triggered by an aseismic slip that precedes large earthquakes; in the latter model, foreshocks are like any other earthquake, which trigger one another, with one of them eventually becoming exceedingly larger (the mainshock).

Notwithstanding the still active debate on these hypotheses, seismologists are not yet able to recognize foreshocks in real-time, tacitly implying that foreshocks are not different from the rest of seismicity, indirectly supporting the cascade model. This view is further supported by the fact that the current best-performing class of short-term earthquake forecasting models (e.g., Nanjo et al., 2012; Taroni et al., 2018)—the Epidemic-Type Aftershock Sequences (ETAS, Ogata, 1988) model—assumes that foreshocks, mainshocks, and aftershocks are undistinguishable and governed by the same process. ETAS describes a branching point process also known as Hawkes or self-exciting point process: every earthquake can trigger other earthquakes according to established empirical relations, with their magnitudes being independent from past seismicity. In essence, ETAS implicitly acknowledges the cascade model and its good forecasting performance makes ETAS an appropriate null hypothesis.

Instead, if foreshocks are dominated by other mechanisms than earthquake self-triggering, as the pre-slip model expects, foreshocks could be distinguished from general seismicity and potentially anticipate a larger earthquake. Several studies recently investigated foreshock sequences of southern California and found that they deviate from expectations of the classical ETAS model with spatially invariant triggering parameters. For example, Seif et al. (2019), Petrillo and Lippiello (2021), and Moutote et al. (2021) find, albeit at varying degrees, a higher foreshock activity in real seismicity than in synthetic catalogs simulated with ETAS. Hence, ETAS appears unable to completely reproduce observed seismicity, suggesting that foreshocks are distinct from general seismicity and governed by different mechanisms. These findings provide hope that identifying foreshocks as such could significantly improve earthquake predictability.

Here we reexamine foreshock activity in southern California; we investigate the existence and main characteristics of foreshock sequences that cannot be explained by ETAS, that is, anomalous foreshock sequences. In other words, we look for new insights on the evidence against the cascade model. To be comparable to previous analyses, we use ETAS with spatially invariant triggering parameters. We perform two statistical tests and consider the potential influence of subjective choices by using two different existing ETAS models and two different methods to identify mainshocks and their foreshocks. To fathom the main characteristics of possible anomalous foreshock sequences, we investigate different magnitude classes and analyze the spatial correlation with heat flow as a physical parameter.

2 Data and Methods

We use the relocated earthquake catalog for southern California catalog (Hauksson et al., 2012, see Data Availability Statement), selecting all earthquakes with urn:x-wiley:00948276:media:grl65307:grl65307-math-0001 from 1 January 1981 to 31 December 2019 except nuclear events (i.e., at the Nevada Test site), totaling 47,574 events.

Analyzing a catalog and distinguishing mainshocks, foreshocks, and aftershocks is unavoidably subjective because no absolute and precise procedure exists for this task (Molchan & Dmitrieva, 1992; Zaliapin et al., 2008). To reduce subjectivity, we analyze the catalog using two different techniques: the Nearest-Neighbor (NN) clustering analysis proposed by Baiesi and Paczuski (2004) and elaborated by Zaliapin et al. (2008), and the spatiotemporal windows (STW) method.

The NN method involves calculating distances in the space-time-magnitude domain between every event j and all previous events i. The event i with the shortest distance to j is called parent event, or NN; this distance is the NN distance ηj. By assigning a NN to each event j, all events become associated with another. To identify individual families (i.e., sequences) or single events, we use the same threshold urn:x-wiley:00948276:media:grl65307:grl65307-math-0002 as Zaliapin et al. (2008), which removes event associations with too large ηj. For each sequence, we refer to the event with the largest magnitude as the mainshock and all associated preceding events as its foreshocks. We only consider sequences with foreshocks and ignore those that have no foreshocks.

For the STW method, we initially consider all events with magnitude urn:x-wiley:00948276:media:grl65307:grl65307-math-0003 as possible mainshocks; to select foreshocks, we consider any preceding event within a spatiotemporal window of 10 km and 3 days from each mainshock (Agnew & Jones, 1991; Marzocchi & Zhuang, 2011; Seif et al., 2019). We exclude mainshocks that (a) do not contain any events within this window (i.e., sequences without foreshocks); (b) are preceded by a larger event within this window (Seif et al., 2019); and (c) are preceded by an event with urn:x-wiley:00948276:media:grl65307:grl65307-math-0004 within 100 km and 180 days (similar to Seif et al., 2019).

To simulate synthetic catalogs, we use two different parametrizations of the ETAS model that are already calibrated to southern California: (a) of K. Felzer (Felzer et al., 2002, see Data Availability Statement and Text S1 and Table S1 in Supporting Information S1), based on parameter values of Hardebeck et al. (2008), see Table S2 in Supporting Information S1 and (b) of S. Seif (Seif et al., 2017, see Text S1 and Table S3 in Supporting Information S1). In the Results section, we only show results based on the former ETAS model and refer to results of the second model in Supporting Information S1. We prefer using existing models for four reasons explained in Text S1in Supporting Information S1 (e.g., reduce degrees of freedom and confirm stability of our results). We verified the reliability of both ETAS models to produce realistic earthquake rates for different magnitude ranges using a Turing style test (Page & van der Elst, 2018), see Text S2 and Figures S1–S4 in Supporting Information S1.

Once the mainshocks and their foreshocks have been identified in both the real and 10,000 synthetic catalogs (1,000 for the second ETAS model), we compare their foreshock statistics using two tests named TEST1 and TEST2. Both are described in detail below; they both use ETAS as null hypothesis—which implies a cascade model as null hypothesis—but they examine different aspects of the problem. TEST1 involves the average number of observed foreshocks per sequence, whereas TEST2, which has been inspired by the work of Seif et al. (2019), involves the frequency of observing a certain number of foreshocks per sequence. We apply both tests to various mainshock magnitude classes urn:x-wiley:00948276:media:grl65307:grl65307-math-0005 and foreshock magnitude thresholds urn:x-wiley:00948276:media:grl65307:grl65307-math-0006; these choices are based on Seif et al. (2019), but we added the class urn:x-wiley:00948276:media:grl65307:grl65307-math-0007 to urn:x-wiley:00948276:media:grl65307:grl65307-math-0008. Although we report statistical test results, we do not formally account for applying the tests multiple times; the results are therefore meant to indicate possible patterns of (apparently) anomalous foreshock activity.

In TEST1, the null hypothesis under test urn:x-wiley:00948276:media:grl65307:grl65307-math-0009 is that the average number of foreshocks (among sequences with foreshocks) in the real catalog is not larger than the corresponding quantity in the synthetic catalogs. For each mainshock magnitude class urn:x-wiley:00948276:media:grl65307:grl65307-math-0010 and each foreshock magnitude threshold urn:x-wiley:00948276:media:grl65307:grl65307-math-0011, we count the number of mainshocks (with foreshocks), urn:x-wiley:00948276:media:grl65307:grl65307-math-0012, and the number of foreshocks urn:x-wiley:00948276:media:grl65307:grl65307-math-0013 in the real catalog; urn:x-wiley:00948276:media:grl65307:grl65307-math-0014 is normalized by urn:x-wiley:00948276:media:grl65307:grl65307-math-0015 to obtain urn:x-wiley:00948276:media:grl65307:grl65307-math-0016. We calculate the same quantity for each synthetic catalog and build its empirical cumulative distribution function (eCDF); if urn:x-wiley:00948276:media:grl65307:grl65307-math-0017 is above the 99th percentile of the eCDF, we reject urn:x-wiley:00948276:media:grl65307:grl65307-math-0018 at a significance level of 0.01.

In TEST2, the null hypothesis under test urn:x-wiley:00948276:media:grl65307:grl65307-math-0019 is that for each number of foreshocks, urn:x-wiley:00948276:media:grl65307:grl65307-math-0020, the frequency of observed cases is not larger than the frequency in synthetic catalogs. For each urn:x-wiley:00948276:media:grl65307:grl65307-math-0021 and each urn:x-wiley:00948276:media:grl65307:grl65307-math-0022, we count the number of mainshocks that have a certain urn:x-wiley:00948276:media:grl65307:grl65307-math-0023 and normalize it by urn:x-wiley:00948276:media:grl65307:grl65307-math-0024. In this way, we obtain the probability mass function (PMF) for the real catalog as a function of urn:x-wiley:00948276:media:grl65307:grl65307-math-0025. Then, we apply the same procedure to each synthetic catalog and obtain 10,000 synthetic PMFs (1,000 PMFs for the second ETAS model), for which we calculate the 99th percentile at each urn:x-wiley:00948276:media:grl65307:grl65307-math-0026. Finally, at each urn:x-wiley:00948276:media:grl65307:grl65307-math-0027, we reject urn:x-wiley:00948276:media:grl65307:grl65307-math-0028 at a significance level of 0.01 if the corresponding PMF value of the real catalog is larger than the 99th percentile (i.e., when the real catalog contains more foreshock sequences with this specific urn:x-wiley:00948276:media:grl65307:grl65307-math-0029 than expected by ETAS). In essence, TEST2 seeks anomalies at every urn:x-wiley:00948276:media:grl65307:grl65307-math-0030, whereas TEST1 could be seen as a cumulative version of TEST2.

Based on the results of the tests, we can label each foreshock sequence as “anomalous” or “normal” using an intuitive approach: for TEST1, if the null hypothesis is rejected for a certain class, all foreshock sequences with a urn:x-wiley:00948276:media:grl65307:grl65307-math-0031 larger than the 99th percentile of the eCDF in that class are labeled as “anomalous” (and “normal” otherwise); for TEST2, if the null hypothesis is rejected for a specific urn:x-wiley:00948276:media:grl65307:grl65307-math-0032, all sequences with this urn:x-wiley:00948276:media:grl65307:grl65307-math-0033 are labeled as “anomalous” (and “normal” otherwise). Effectively, a foreshock sequence in urn:x-wiley:00948276:media:grl65307:grl65307-math-0034 is labeled “anomalous” if it is “anomalous” in at least one class urn:x-wiley:00948276:media:grl65307:grl65307-math-0035 For TEST1, we argue that the approach is conservative due to comparing individual sequences with the average behavior of foreshock sequences; we therefore perform an alternative analysis (but not a test) without normalizing the number of foreshocks by urn:x-wiley:00948276:media:grl65307:grl65307-math-0036, see Text S3 and Figure S6 in Supporting Information S1.

To approach a physical interpretation of possible anomalous foreshock sequences in the real catalog, we analyze their spatial distribution. Specifically, taking inspiration from Zaliapin and Ben-Zion (2013), we interpolate heat flow measurements (see Data Availability Statement) with a radial smoothing approach (urn:x-wiley:00948276:media:grl65307:grl65307-math-0037) to acknowledge areas without data. We associate each foreshock sequence with the interpolated heat flow value at the mainshock location; if measurements within r are unavailable, we discard the sequence. Then we test if the distribution of associated heat flow values is significantly different for normal and anomalous foreshock sequences. We employ two statistical tests: the two-sample Kolmogorov-Smirnov test (null hypothesis: the two distributions have the same parent distribution) and the paired Wilcoxon test (null hypothesis: the two distributions have the same median). The Kolmogorov-Smirnov test is sensitive to any kind of difference between both distributions, whereas the Wilcoxon test is sensitive to one distribution having higher values than the other.

3 Results

3.1 Testing for Anomalous Foreshock Activity

Figure 1 shows the results of TEST1 for each class in urn:x-wiley:00948276:media:grl65307:grl65307-math-0038 and urn:x-wiley:00948276:media:grl65307:grl65307-math-0039 using the ETAS model of K. Felzer and NN to identify mainshocks and their foreshocks; the results using STW are reported in Figure S5 in Supporting Information S1. Each subplot compares the eCDF (based on synthetic catalogs) with the observed value from the real catalog. As shown in Figure 1 and Figure S5 in Supporting Information S1, TEST1 rejects urn:x-wiley:00948276:media:grl65307:grl65307-math-0040, that is, identifies anomalous foreshock sequences, exclusively for mainshock magnitudes urn:x-wiley:00948276:media:grl65307:grl65307-math-0041. Of a total of 152 foreshock sequences, we find 61 (40%) to be anomalous; with the STW method we find 143 foreshock sequences of which 34 (23%) are anomalous. Using instead the alternative analysis without normalizing by urn:x-wiley:00948276:media:grl65307:grl65307-math-0042 (Figure S6 in Supporting Information S1), we find 19 (13%) to be anomalous, which suggests that TEST1 overestimated the number of anomalies due to using averages, as anticipated in Text S4 in Supporting Information S1. Applying TEST1 to the second ETAS model, we find 47 anomalous foreshock sequences for both NN and STW methods (31% and 33%, respectively, see Figures S7 and S8 in Supporting InformationS1).

Details are in the caption following the image

Results of TEST1 for various classes of the mainshock magnitude urn:x-wiley:00948276:media:grl65307:grl65307-math-0043 (rows) and thresholds for the foreshock magnitude urn:x-wiley:00948276:media:grl65307:grl65307-math-0044 (columns). Each subplot displays the number of normalized foreshocks urn:x-wiley:00948276:media:grl65307:grl65307-math-0045 for the real catalog (vertical line; red if anomalous, black otherwise) and the empirical Cumulative Distribution Function (dashed curve) with its 99th percentile (dashed vertical line) for 10,000 synthetic catalogs. Each subplot also reports the number of anomalous foreshock sequences, urn:x-wiley:00948276:media:grl65307:grl65307-math-0046, the p-value for TEST1, and the number of mainshocks, urn:x-wiley:00948276:media:grl65307:grl65307-math-0047 . The results are based on K. Felzer's Epidemic-Type Aftershock Sequences (ETAS) model and the Nearest-Neighbor method; Figure S5 in Supporting Information S1shows results using the spatiotemporal windows method, and Figure S7 and S8 in Supporting Information S1 using the second ETAS model. Note that each subplot uses a different urn:x-wiley:00948276:media:grl65307:grl65307-math-0048-axis range to account for the varying data range.

Figure 2 shows the results of TEST2 for each class in urn:x-wiley:00948276:media:grl65307:grl65307-math-0049 and urn:x-wiley:00948276:media:grl65307:grl65307-math-0050 using the NN method; the results using the STW method are reported in Figure S9 in Supporting Information S1. Most PMF values of the real catalog are not anomalous because they are below the 99th percentile of synthetic PMF values. We find 22 of 152 (14%) foreshock sequences to be anomalous, most of which are again associated with urn:x-wiley:00948276:media:grl65307:grl65307-math-0051 < 5.5 (only three have larger urn:x-wiley:00948276:media:grl65307:grl65307-math-0052). Using the STW method we find 13 of 143 (9%) to be anomalous. Applying TEST2 to the second ETAS model, we identify 34 (22%) using NN method and 14 (10%, using STW method) to be anomalous (Figures S10 and S11 in Supporting Information S1, respectively).

Details are in the caption following the image

Results of TEST2 showing probability mass functions (PMFs) of the number of foreshocks urn:x-wiley:00948276:media:grl65307:grl65307-math-0053 for various classes of urn:x-wiley:00948276:media:grl65307:grl65307-math-0054 (rows) and urn:x-wiley:00948276:media:grl65307:grl65307-math-0055 (columns). The PMFs are shown for (a) the real catalog (triangles), (b) all synthetic catalogs (small gray dots as swarm distributions) with their 99th percentile (gray horizontal bars), and (c) when considering all synthetic catalogs as a single compound catalog (blue open circles, using the approach of Seif et al. (2019)). Triangles become red when they are located above the 99th percentile of (b). The results are based on K. Felzer's Epidemic-Type Aftershock Sequences (ETAS) model and the Nearest-Neighbor method; Figure S9 in Supporting Information S1 shows results using the spatiotemporal windows method, and Figures S10 and S11 in Supporting Information S1using the second ETAS model. Note that each subplot uses a different urn:x-wiley:00948276:media:grl65307:grl65307-math-0056-axis range.

For comparison, Figure 2 and Figures S9–S11 in Supporting Information S1 also report the results using the approach of Seif et al. (2019), which tests a similar yet different null hypothesis than TEST2. Specifically, they treat all synthetic catalogs as one single compound catalog. In this way, the PMF is normalized by a much larger number of mainshocks than contained in an individual synthetic catalog; for an increasing number of synthetic catalogs, the PMF decreases progressively (i.e., lowering the detectable minimum frequency) and moves further away from the real observation. In other words, our TEST2 honors that a finite earthquake catalog must have a lower detectable frequency of foreshocks in the PMF; this lower frequency depends on the number of mainshocks that have foreshocks, which in turn depends on the length of the earthquake catalog (the lowest frequency is one out of the number of mainshocks that have foreshocks). In addition, the approach of Seif et al. (2019) normalizes the PMF by the total number of mainshocks that have foreshocks (urn:x-wiley:00948276:media:grl65307:grl65307-math-0057, as we do in TEST2) or no foreshocks, which further reduces the PMF by another 0.5–1 order of magnitude depending on urn:x-wiley:00948276:media:grl65307:grl65307-math-0058.

We repeated TEST1 and TEST2 at a 0.05 significance level (i.e., 95th percentile), which was originally used by Seif et al. (2019), see Text S4 and Figures S12 and S13 in Supporting Information S1.

3.2 Correlating Foreshock Sequences With the Heat Flow

To investigate the physical cause of anomalous foreshock sequences, we inspect their correlation with the local heat flow. We choose this property because previous studies suggested a relation between heat flow and statistical properties of earthquake sequences (e.g., Chen & Shearer, 2016; Enescu et al., 2009; Ross et al., 2021; Zaliapin & Ben-Zion, 2013).

Figures 3a and 4a overlay the locations of normal and anomalous foreshock sequences identified by TEST1 and TEST2, respectively, on a heat flow map. Figures 3b and 4b show the corresponding eCDFs of the heat flow interpolated at the locations of normal and anomalous foreshock sequences. In both cases, anomalous foreshock sequences tend to occur more frequently at locations of higher heat flow than normal foreshock sequences. This trend is confirmed by the p-values of the two-sample Kolmogorov-Smirnov and paired Wilcoxon tests (see annotations in Figures 3b and 4b): Being below 0.05, they indicate that the two samples come from different parent distributions with different medians. Figures 3 and 4 are based on the NN method to identify mainshocks and their foreshocks; the results based on the STW method confirm our findings (see Figures S14 and S15 in Supporting Information S1), as do the results based on the second ETAS model (see Figures S16–S19 in Supporting Information S1) and on the 0.05 significance level (Figures S20 and S21 in Supporting Information S1). Moreover, TEST1-based results are stable even if we use the alternative analysis without normalizing by urn:x-wiley:00948276:media:grl65307:grl65307-math-0059 (see Figure S22 in Supporting Information S1). We verified the stability of our results using an independent modeling of foreshock sequences by Petrillo and Lippiello (2021): the authors provided us locations of their identified normal and anomalous foreshock sequences (see Data Availability Statement), letting us apply our analysis on a data set that is completely independent from our assumptions and modeling choices (see Figure S23 in Supporting Information S1). It confirms our findings of a preferential occurrence of foreshock anomalies in high heat flow zones. We summarize the p-values of all the different analyses in Table S4 in Supporting Information S1.

Details are in the caption following the image

Correlating foreshock sequences with the heat flow. (a) Locations of normal (empty circles) and anomalous foreshock sequences (filled circles) identified with TEST1 overlayed on a heat flow map. The circles sizes scales with urn:x-wiley:00948276:media:grl65307:grl65307-math-0060 (see legend). The interpolated heat flow map is based on sampled heat flow measurements (small gray dots, see Section 2); (b) empirical Cumulative Distribution Functions (eCDFs) of heat flow values at locations of normal (dashed curve) and anomalous foreshock sequences (solid curve); both eCDFs are compared using two statistical tests (see annotation with corresponding p-values). The results are based on K. Felzer's Epidemic-Type Aftershock Sequences (ETAS) model and the Nearest-Neighbor method; Figure S14 in Supporting Information results using the spatiotemporal windows method, and Figures S16 and S18 in Supporting Information S1 using the second ETAS model.

Details are in the caption following the image

Like Figure 3 but with foreshock sequences labeled as “anomalous” or “normal” using TEST2. Figure S9 in Supporting Information S1 shows results using the spatiotemporal windows method, and Figures S17 and S19 using the second Epidemic-Type Aftershock Sequences model.

Finally, we add a word of caution on the interpretation of the results, that is, the spatial coverage of heat flow data compared to the earthquake activity is rather incomplete in northern Mexico. For instance, several anomalous foreshock sequences occur in this area but cannot be included in the heat flow analysis due to the lack of data. In addition, the available heat flow measurements in northern Mexico are not consistent with the Geothermal map of North America (Blackwell & Richards, 2004), which indicates a generally high heat flow (>100 μW/m2) in this area along the San Andreas Fault.

4 Discussion and Conclusion

We have found that foreshocks have the same characteristics of general seismicity as expected by ETAS, except for some cases. Our finding is in general agreement with previous studies of foreshock activity, all of which found (with some important differences not discussed here) higher foreshock activity than expected (Chen & Shearer, 2016; Moutote et al., 2021; Petrillo & Lippiello, 2021; Seif et al., 2019). However, our results additionally show that foreshock anomalies are mostly associated with mainshock magnitudes below 5.5—independently from the two tests, the two ETAS models, the two procedures to identify mainshocks and their foreshocks, and an independent set of foreshock anomalies. Moreover, these anomalies are located preferentially (and statistically significant) in zones of high heat flow. The combination of these two findings suggests that sequences with anomalous foreshock activity behave more like seismic swarms. In fact, independent studies (e.g., Chen & Shearer, 2016; Enescu et al., 2009; Ross et al., 2021; Zaliapin & Ben-Zion, 2013) have shown that swarm-like seismicity is common in those areas where we have found anomalous foreshock sequences.

Our results do not allow us to further elucidate why foreshock anomalies correlate with high heat flow. The anomalies may be driven by specific physical mechanisms (e.g., actual seismic swarms mostly driven by fluids) or still relate to a cascade model that is not spatially uniform. The latter may be better described by an ETAS model with spatially varying triggering parameters. Indeed, Enescu et al. (2009) and Nandan et al. (2017) show that some parameters of a spatially varying ETAS model (which mostly depend on the more abundant aftershocks) correlate with the heat flow in southern California. Their more elaborated clustering model implies more active foreshock sequences where the heat flow is high, which agrees with our empirical findings using (less abundant) foreshocks.

Conversely, foreshock sequences located in zones of lower heat flow predominantly behave as expected, that is, in agreement with the null hypothesis given by the ETAS model (which mimics the cascade model). If we interpret the difference in foreshock activity as evidence of the pre-slip model, it must have a minor effect in zones of lower heat flow, but it may become more important in zones of high heat flow. In other words, our results are inconsistent with pre-slip as a general nucleation process; pre-slip may become only relevant under specific tectonic conditions, such as in high heat flow. Our results do not prove the cascade model as the truth, but neither do they bring any evidence against it nor in favor of the pre-slip model. Perhaps alternative hypotheses open up a middle ground: recent studies proposed that both processes can coexist and relate to each other (Cattania & Segall, 2021; McLaskey, 2019) or that nucleation follows a different process (Kato & Ben-Zion, 2021). But like the pre-slip model, these conjectures remain to be tested.

Our results also highlight the importance of analyzing earthquake sequences in zones of high heat flow in more detail, especially to understand the physical reasons of anomalous foreshock sequences: Are they related to seismic swarms with an implicit limitation to the mainshock magnitude? Or are they related to different clustering processes than those driving tectonic sequences? The difference is crucial, in particular regarding the forecasting of large earthquakes.

Our findings raise an urgent need to find (quasi-)real-time methods to discriminate swarm-like from ETAS-like sequences. Such a discrimination could lead to significant improvements in earthquake forecasting, because being able to identify a swarm-like sequence as such could markedly reduce the forecast probability for a large earthquake. A promising indicator could be the background rate component of ETAS, which has been found to increase during swarm-like seismicity (Hainzl & Ogata, 2005; Kumazawa et al., 2016; Llenos et al., 2009; Lombardi et al., 2006). Another possibility was raised by Zaliapin and Ben-Zion (2013) demonstrating that swarm-like sequences have a different topologic tree structure (i.e., an internal clustering hierarchy, which connects background and triggered earthquakes). Unfortunately, this approach can currently only be used retrospectively, limiting its applicability in earthquake forecasting. We envision other possible parameterizations of the topologic tree structure that may facilitate its use for earthquake forecasting.


We thank Luc Moutote and four anonymous reviewers for their feedback and suggestions, which significantly helped improve the article. We also thank G. Petrillo for providing us with independent data and S. Mancini for producing synthetic catalogs using S. Seif's ETAS model. This project has received funding from the European Union's Horizon 2020 research and innovation program under Grant Agreement 821115, Real-Time Earthquake Risk Reduction for a Resilient Europe (RISE).

    Data Availability Statement

    The southern California catalog of Hauksson et al. (2012) was obtained from https://scedc.caltech.edu/data/alt-2011-dd-hauksson-yang-shearer.html, version “1981–2019” (last accessed April 2021). Heat flow data were obtained from the following sources: National Geothermal Data System (http://geothermal.smu.edu/static/DownloadFilesButtonPage.htm, last accessed May 2021) using the data sets “Aggregated Well Data,” “Heat Flow Observation in Content Model Format,” “SMU Heat Flow Database of Equilibrium Log Data and Geothermal Wells,” and “SMU Heat Flow Database from BHT Data”; and RE Data Explorer (https://www.re-explorer.org/re-data-explorer/download/rede-data, last accessed May 2021) for northern Mexico. The ETAS simulator of Felzer was obtained from https://web.archive.org/web/20200712004939/https://pasadena.wr.usgs.gov/office/kfelzer/AftSimulator.html, last accessed February 2022). The alternative data set of anomalous foreshock sequences was provided by G. Petrillo (at https://doi.org/10.5281/zenodo.7251416). The methods to perform our foreshocks analyses are available as MATLAB code at https://doi.org/10.5281/zenodo.7438161 and https://gitlab.com/ester.manganiello/foreshock-analyses.