Introduction

Dynamic earthquake triggering due to the passing seismic waves from large distant earthquakes has been welldocumented around the globe (e.g., Brodsky et al., 2000;Gomberg et al., 2004;Hill et al., 1993). In case studies, it is possible to visually inspect the triggered earthquakes to observe their sudden onset or their correlation with the passing surface waves (e.g., Hill et al., 1993;Velasco et al., 2008). Such temporal correlations are often used to establish a causal connection between the large event and the triggered earthquakes. This inferred connection can be further evaluated with statistical tests to examine the significance of the changes in seismicity rate (e.g., van der Elst & Brodsky, 2010). The temporal-correlation premise underlines almost all dynamic triggering studies (e.g., Brodsky & van der Elst, 2014;Hill & Prejean, 2015). However, Pankow and Kilb (2020) found that typical approaches for determining statistically significant seismicity rate changes are inadequate for reliably identifying temporal correlations, mainly due to poor accounting for the intrinsic variability of seismicity rate. Furthermore, it has not been systematically tested whether a temporal correlation is sufficient to establish causal connections.

Since triggered seismicity is not a direct measurement of the triggering process but rather its outcome, and because natural fault systems are complex and heterogeneous, any observed coincidence could be due to the intrinsic variability of local earthquake rates. Additionally, earthquake catalog completeness and regional seismic network configuration can have a strong impact in triggering identification. Therefore, it is critical to understand and account for the possibility of false negatives (failure to detect real dynamic triggering) and false positives (identifying dynamic triggering where there is none, e.g. mistaking unrelated earthquake rate changes for triggering) in dynamic triggering identifications. However, it is challenging to analyze false identifications in case studies due to their limited samples. Systematic studies covering a large number of candidate triggering earthquakes and a large seismically active area are better suited to evaluate false identifications. However, with large data sets, it is prohibitively time-consuming to visually inspect each instance of potential triggering. Systematic dynamic triggering studies primarily use statistical tests for triggering identifications and apply the same temporal-correlation premises to draw connections between the passing seismic waves and statistically significant seismicity rate anomalies.

Commonly used statistics to determine the statistical significance of apparent seismicity rate changes are the βstatistic (Matthews & Reasenberg, 1988):

and the Z-statistic (Habermann, 1983):

where for both equations, T a and T b are the test and reference time periods, N a and N b are the number of events in these time periods, and σ a and σ b are the standard deviations of N a and N b . The observed change in rate is considered significant at 95% confidence if the absolute value of the given statistic exceeds 1.96, assuming earthquake occurrence is random and independent. However, there are several difficulties when applying these statistics in practice: they assume independent events while earthquakes are known to cluster, earthquake rate variations make it difficult to define the reference rate (N b /T b ), standard deviations must be estimated in the context of the variable rate, and rates may be affected by catalog incompleteness. Fan et al. (2021) and DeSalvio and Fan (2023) implemented multiple improvements to the β-statistic and Zstatistic to account for these difficulties. Following Prejean and Hill (2018), the significance of each statistic is evaluated empirically by comparison with the distribution of statistics for random time periods of the same duration, drawn from the reference time period, rather than using a set threshold of 1.96. This accounts for intrinsic earthquake rate variability, as long as that variability is represented in the reference time period, as well as relaxing the assumption that earthquakes are independent. It also makes the tests less sensitive to the estimated standard deviations, because the denominators of Equations 1 and 2 become scaling factors common to the statistics of the real and random samples. DeSalvio and Fan (2023) also estimated standard deviations empirically through repeated sampling of the catalog. DeSalvio and Fan (2023) introduced the β m -and Z m -statistics, which are analogous to the β-and Z-statistics except applied to total moment instead of earthquake count, decreasing the sensitivity to catalog incompleteness at lower magnitudes. When a statistically significant seismicity rate (or moment release rate) change is identified in conjunction with passing seismic waves, a dynamic triggering case is inferred (DeSalvio & Fan, 2023). Applying these statistical tests to Southern California, DeSalvio and Fan (2023) reported that global M ≥ 6 earthquakes frequently trigger small earthquakes. Of the 1,388 global candidate triggering events they considered, 70% were associated with a significant increase in seismicity rate within the next day, somewhere in a set of 185 spatial bins spanning the Southern California fault system.

This statistical procedure provides a framework to test for false positives by looking for apparent triggering in catalogs without dynamically triggered events, or in time windows not associated with the occurrence of large global earthquakes. For example, DeSalvio and Fan (2023) introduced a check on the reliability of the β-, Z-, β m -, and Z m -statistics for dynamic triggering, by estimating the false positive rate through application of the statistical tests to synthetic catalogs that contain no true dynamic triggering. They generated synthetic earthquake catalogs using a Poisson model, an Epidemic-Type Aftershock Sequence (ETAS) model (Ogata, 1988), and by randomly shifting the observed catalog in time to break the temporal associations between the catalog and candidate triggering earthquakes. Because there is no true dynamic triggering in these synthetic catalogs, the rate of apparent triggering gives the false positive rate. There are two types of errors that can lead to false positives: erroneous statistical identification of a seismicity rate change, and mistaking the random temporal correlation of a candidate event with a true rate change for causation through dynamic triggering. While only the first type of error will occur for the Poisson catalogs, both types will be present in the ETAS, shifted, and real catalogs.

These tests lead to reported false positive rates of 0.31%-2.27% for Poisson and ETAS synthetic catalogs, and 2.26%-4.53% for shifted synthetic catalogs (DeSalvio & Fan, 2023). These are reasonably low false positive rates, consistent with the 95% confidence threshold used in many seismological studies. However, this rate of false positives, when applied to every combination of 1,388 candidate triggering events and 185 spatial bins, could result in thousands of false positives.

Here we use the statistical procedure proposed in DeSalvio and Fan (2023) to systematically evaluate the commonly adopted assumption in dynamic triggering studies that a temporal correlation with a statistically significant seismicity rate anomaly is sufficient to establish dynamic triggering. We generate synthetic catalogs to examine the false positive rate in dynamic triggering identification and compare it to the observed rate of apparent dynamic triggering in the real Southern California catalog. We then look for any differences in the spatial and temporal characteristics of apparent triggering in the real and synthetic catalogs. Our results show that the commonly used temporal-correlation premise can lead to many false positives in dynamic triggering identification when the fault system has frequent seismicity clusters that may have been caused by processes other than the passing seismic waves.

Data and Methods

We use the 10-year (2008-2017) Quake Template Matching (QTM) seismicity catalog (Ross et al., 2019a) and 185 spatial bins representing active faults in Southern California (e.g., Plesch et al., 2007) to analyze false positive rates in dynamic triggering due to the temporal-correlation assumption. We generate synthetic catalogs for Southern California that are different from those in DeSalvio and Fan (2023). Here, synthetic Poisson and ETAS earthquake catalogs are generated for each spatial bin, and each spatial bin is analyzed separately, as in the analysis of the real data in DeSalvio and Fan (2023). In contrast, DeSalvio and Fan (2023) used a single Poisson or ETAS catalog for all of Southern California, and analyzed the entire catalog together. Using identical analyses for the real and synthetic catalogs will lead to a more accurate assessment of the false positive rate. The smaller subcatalogs used here and for the real data are more prone to rate variability because a few temporal clusters can produce relatively large rate changes, whereas in the large entire catalog many clusters will stack to produce a more consistent rate, muting the true variability (Figure 1). Analysis of the synthetics as entire catalogs therefore may underestimate the potential for false positives in the real data.

We generate synthetic Poisson and ETAS earthquake catalogs in a manner consistent with the real Southern California data for 2008 to 2017, as used in DeSalvio and Fan (2023), and analyze the individual spatial bins independently. For each spatial bin, we compute R, the rate of earthquakes in the QTM catalog (Ross et al., 2019a) above the magnitude of completeness M c for that bin reported by DeSalvio and Fan (2023). For the Poisson catalog, we randomly select event times given this rate, and randomly select magnitudes from a Gutenberg-Richter distribution with b = 0.99. The ETAS (Ogata, 1988) simulations use the temporal decay parameters c = 0.0001 days and p = 1, productivity parameter k = 0.0027, and productivity scaling with magnitude a = b = 0.99, following DeSalvio and Fan (2023). The branching ratio, n, (e.g., Helmstetter & Sornette, 2003), the fraction of earthquakes that are aftershocks of a prior event, is computed from the other parameters, assuming M max = 6 and T = 10 years. The branching ratio varies from 0.36 to 0.69, depending on the M c of the bin. We randomly select independent event times for each bin given the independent event rate (1-n)*R. We iteratively simulate each generation of aftershocks using the inverse transform method of Felzer et al. (2002), which randomly selects the time until each aftershock from an inverse cumulative distribution function based on Omori's Law, and its magnitude from an inverse cumulative distribution function based on the Gutenberg-Richter distribution. To simulate the global candidate triggering events, we generate 1,500 global events occurring at random times uniformly spanning a 10 year period, and remove the first and last 0.5 years.

Additionally, we expand the shifted synthetic catalog tests from the 8 spatial bins analyzed by DeSalvio and Fan (2023) to include all 185 bins. We produce 6 versions of the shifted catalog, considering the relative time shift between the QTM and International Seismological Center (ISC) catalogs. For the first 4 shifted synthetic catalog tests, we randomly select a positive or negative time shift between 1 week and 1 year and add this time shift to the origin time of each global event of the ISC catalog before performing the seismicity rate anomaly analysis. For 3 of these tests, we wrap around synthetic candidate events that are shifted out of the study time period, to maintain the same number of global events. For the 5th catalog, we randomly select origin times for the global events, breaking any patterns in the occurrence times of global events. For the 6th catalog, we use different origin time shifts for each spatial bin.

For all synthetic catalogs, each spatial bin is analyzed for each global event, for 4 test time periods following the event (T a = 2-, 6-, 12-and 24-hr). We compute the β-, Z-, β m -, and Z m -statistics following DeSalvio and Fan (2023), with a reference time period of T b = 60 days for β-and β m -statistics and T b = 30 days for Z-and Z mstatistics. The false positive rate is taken as the fraction of trials with enough events for analysis (>3 events in the test time period, and ≥10 in the reference period) for which the given statistic is significant at 95% confidence. The 95% significance value ranges from ∼2.2 to ∼3.3 for both the real and synthetic catalogs, varying for each test because it's based on the distribution of values for randomly selected time periods.

Unlike the Poisson and ETAS catalogs, the shifted synthetic catalogs capture any correlation between adjacent spatial bins due to their overlap, as well as any spatial-temporal variations in earthquake rate due to processes other than earthquake-to-earthquake triggering. Using the shifted catalogs, we investigate the number of false positives as a function of spatial bin, global event, and test time period. We compare these spatial and temporal characteristics of the false positives to the characteristics of the apparent triggering in the real catalog.

In the synthetic Poissonian catalog, the seismicity is independent and uncorrelated; therefore, any identified seismicity rate anomaly is random rather than a true cluster, causing false identifications of dynamic triggering. In the synthetic ETAS catalog, there are temporal seismicity clusters from the simulated mainshock-aftershock sequences, some of which would be identified with 95% confidence as seismicity rate anomalies when the time windows of interest overlap with these clusters. In this sense, false identification in dynamic triggering can result from either misidentifying seismicity rate anomalies or misattributing temporal correlations.

For the shifted catalog tests, the local earthquake catalog (QTM) has intrinsic variability and contains seismicity clusters, including mainshock-aftershocks, swarms, and triggered sequences due to external forcings. Similar to the ETAS clusters, some of these clusters would be identified as seismicity rate anomalies at a 95% confidence level using the procedure proposed in DeSalvio and Fan (2023). If such a seismicity rate anomaly identification coincides with a selected test time window (i.e., 2-24 hr after a global earthquake), a dynamic triggering case is Journal of Geophysical Research: Solid Earth 10.1029/2025JB031566 inferred in the region. However, if the seismicity rate anomaly was not due to the passing waves but caused by intrinsic variability, this coincidence would lead to a false positive identification. In this case, the false positive results from the temporal-correlation premise mentioned above. As the seismicity rate anomaly may appear the same for intrinsically clustered and triggered seismicity, the likelihood of a false positive due to the temporalcorrelation premise depends on the intrinsic variability of local seismicity. In other words, for a region with frequent swarms or correlated seismicity, there is a higher chance of identifying seismicity rate anomalies for randomly selected time windows, and it would be more challenging to identify the true triggering versus false positives.

Results

False Positive Rate

Using our new synthetic catalogs and the same procedure proposed in DeSalvio and Fan (2023), we find false positive rates for dynamic triggering (Table 1) larger than those reported in DeSalvio and Fan (2023). For tests with the Poisson catalog, the overall false positive rate for all test time periods T a is ∼1.5%-2.5%. For tests with the ETAS catalog, which contains simulated earthquake clustering, the overall rate of seismicity-rate anomalies temporally correlated with global earthquakes is ∼5%-8%, which we consider representative of the false positive rate. The shifted catalogs, which contain all the true temporal clustering characteristics of the QTM catalog, as well as the correlation between adjacent spatial bins, has an overall rate of seismicity-rate anomalies temporally correlated with global earthquakes of ∼3.5%-8.5%, which we take as the false positive rate for the following discussion. Therefore, when realistic clustering is included, and the individual bins are considered individually, the overall false positive rate approximates a 5% rate, meeting the expectation for a test at 95% confidence.

For short test time periods, however, the false positive rate of the suite of tests can greatly exceed 5%. False positives for the β-and Z-statistics for T a = 2 hr range from ∼9% for the Poisson catalogs to ∼20% for the ETAS and shifted catalogs. Similarly, the β m -and Z m -statistics for T a = 2 hr exhibit false positives of around 12% for the ETAS catalog. Therefore, the false positive rate is large enough to explain all of the apparent triggering in the real Southern California catalog, without requiring any true dynamic triggering.

While the rate of apparent triggering in the shifted synthetic catalogs is similar to that of the real catalog, it is not the result of sampling the same earthquake clusters. For the earthquakes found to be apparently triggered in the shifted catalog tests, typically ∼25% were also identified as triggered in the real catalog. We repeat the false positive calculations for the shifted catalogs, this time removing all combinations of global candidate events and spatial bins in which apparent triggering was identified in the real and shifted catalogs in overlapping test time periods. The resulting false positive rates slightly decrease, with an overall false positive rate of ∼2.5%-6.5% (Table 2).

Spatial-Temporal Characteristics of Apparent Triggering

When only considering the seismicity occurrence, intrinsically clustered and triggered seismicity may yield similar seismicity rate anomalies. True dynamic triggering may be distinguishable from false positives through spatial-temporal characteristics other than the total observed rate of occurrence (e.g., Aiken et al., 2016Aiken et al., , 2018;;Pankow & Kilb, 2020). In this section, we compare the spatial-temporal characteristics of the apparent triggering in the real catalog with that of the six shifted synthetic catalogs (in which the global ISC catalog was shifted relative to the local QTM catalog). The shifted catalogs retain the spatial-temporal earthquake rate variability and clustering of the QTM catalog, and the correlated behavior of overlapping spatial bins, and so reflect any characteristics of false positives that result from those properties.

The spatial distribution of apparent triggering identified in the shifted catalog tests (Figure 2) closely resembles that of the real catalog shown in Figure 5 of DeSalvio and Fan (2023). Spatial bins along the San Jacinto, southern Elsinore, and southern San Andreas Faults, as well as the Coso geothermal field, exhibit the most triggering occurrences, up to ∼70 in the most active regions when the β-statistic is considered. In contrast, many bins in the western half of the study area exhibit <10 triggering occurrences. DeSalvio and Fan (2023) found that the number of triggering observations for a bin roughly correlates with the earthquake rate in that bin, which may explain the similar spatial patterns.

The number of bins apparently triggered per global event in the shifted catalogs (Figure 3) has similar characteristics to that of the real catalog shown in Figure 13 of DeSalvio and Fan (2023). For both the real and shifted catalogs, ∼70% of global events exhibit some apparent triggering when using the β-statistic (Figure 4a). Most of these global events are associated with apparent triggering in only a few (<10) bins. A few global events have more apparent triggers, up to ∼15. In the 10-years period analyzed, the only substantial difference is the ∼30 triggered bins following the 2010 M7.2 El Mayor-Cucapah, Mexico, earthquake in the real catalog. Widespread triggering in Southern California from the El Mayor-Cucapah earthquake has also been observed in earlier studies (e.g., Hauksson et al., 2011;Meng & Peng, 2014).

The distribution of the number of apparent triggering occurrences per global candidate triggering event is very similar between the real and shifted catalogs (Figures 4a and 4d), as is the distribution of the number of apparent triggering occurrences per bin (Figures 4b and 4e), and the number of apparent triggering occurrences for each of the test time period durations (Figures 4c and 4f). This is the case for both the β-statistic, which has the highest rate of false positives, and the Z m -statistic, which has the lowest rate. Therefore, aside from the nearby El Mayor-Cucapah, Mexico, earthquake, the reported triggering in the real Southern California catalog appears to lack any general spatial-temporal characteristics that would distinguish it from random false positives. Journal of Geophysical Research: Solid Earth

Discussion

False positive rates depend on both the statistical test used and on the characteristics of the catalog studied. For the QTM catalog and the bin configuration used here, we find that the modified Z-statistic has a somewhat lower false positive rate than the modified β-statistic. The moment-based β m -and Z m -statistics have substantially lower false positive rates than the corresponding β-and Z-statistics for short test time windows (T a = 2 hr, 6 hr). The false positive rates for the β m -and Z m -statistics are also lower for the shifted catalogs, which are the only synthetic catalogs that may be incomplete at low magnitudes, suggesting that considering moment rate rather than earthquake rate better accounts for possible incompleteness in real catalog data. Catalogs with fewer earthquakes during the test time windows generally have higher false positive rates, for example, the higher rate for shorter test time windows, and the higher rate when analyzing individual spatial bins compared to analyzing the entire catalog together. This is likely a consequence of allowing statistics to be computed for a relatively small sample size (N a > 3 and N b ≥ 10). Catalogs with more earthquake clustering also have a higher false positive rate, for example, the higher rates for the ETAS and shifted catalogs compared to the Poisson catalog. This can also be seen by performing additional ETAS simulations with varying productivity, where an increase in productivity and branching ratio (more clustering) leads to an increase in false positive rate (Table 3). Seismicity clustering has similarly been shown to increase false positives in the identification of other phenomena, such as proposed earthquake precursors (e.g., Hardebeck et al., 2008;Michael, 1997).

Our results imply that best practice is to estimate the false positive rate for each dynamic triggering study based on the characteristics of the catalog used and the study design. True detections could be inferred if the number of detections exceeds the expected number of false positives. For case studies, best practice would be to apply the same visual inspections consistently to an extended period beyond the selected triggering windows for falsepositive evaluations, as was done in Pankow and Kilb (2020).

For the catalog and study design of DeSalvio and Fan (2023), the false positive rate is about 3.5%-8.5%. This is not a very high false positive rate, and consistent with the 95% confidence usually used in seismological studies.

However, this false positive rate implies that 1 out of approximately every 20 tests will return a positive Journal of Geophysical Research: Solid Earth 10.1029/2025JB031566

identification in seismicity rate anomaly, likely representing a false positive in dynamic triggering. For each candidate triggering event, 185 spatial bins and 4 test time periods are considered. On average only ∼6.4% of these combinations have enough data for a statistical test, meaning that on average ∼47 tests are performed per candidate global event. If each test were independent (no spatial or temporal overlap), we could use the binomial distribution to determine that the probability of any global candidate earthquake randomly appearing to trigger at least once would be ∼91%. The observed apparent triggering by ∼70% of global events is therefore not surprisingly high. It is likely less than 91% because of the non-independence of the tests as well as spatially variable seismicity rates.

When tens of thousands of spatial-temporal windows are tested, even a low false positive rate can lead to thousands of false positives. The problem of large numbers of false positives will likely only worsen in the future, as it becomes possible to test larger numbers of spatial-temporal bins on increasingly larger earthquake catalogs.

Testing more combinations of candidate triggering events and target grid cells can increase the number of erroneous statistical identifications of a seismicity rate change, and increase the opportunity to mistake intrinsic rate changes for dynamically triggered changes. Additionally, new enhanced seismicity catalogs may reveal additional intrinsic rate complexity.

The statistically identified seismicity-rate anomalies can be further evaluated under additional empirical assumptions and requirements to reduce positive cases, thereby suppressing false positives. Given a lack of wellagreed physical models for dynamic triggering, these additional assumptions might be conditional on specific regions of interest or reflect a cautious preference. For example, Pankow and Kilb (2020) consider an earthquake rate increase to be significant only if it is in the highest 1% or 5% of earthquake rates in the full duration of the catalog for that location. This is analogous to expanding the resampling done by DeSalvio and Fan (2023) beyond the 30-to 60-day reference time period to the entire duration of the catalog at the given grid cell. This requirement implies an assumption that true dynamic triggering cases would cause extreme changes in seismicity rates over a large region. Consequently, this requirement will lead to fewer identifications, and may also yield a higher false negative rate. Even with these requirements, however, Pankow and Kilb (2020) found on inspection that few of the statistically significant rate increases were unambiguous cases of a clear step increase at the time of the global earthquake, and concluded that statistically significant rate changes alone are inadequate to demonstrate dynamic triggering. Pankow and Kilb (2020) find no dynamic triggering in the Anza region of the San Jacinto Fault in Southern California from 1985 to 2000 (while the magnitude of completeness of their catalog is relatively high) and very little during 2000-2017. Only four global earthquakes have triggering significant at 95% confidence and satisfy their holistic compatibility assessment (2001M7.0 Guam, 2005M7.2 Nicobar Islands, 2010M7.2 El Mayor-Cucapah, and 2013 M8.3 Sea of Okhotsk), in contrast with the ∼40 triggers for spatial bins in the Anza region reported in DeSalvio and Fan (2023).

Another approach to study triggered earthquakes is to stack observations to enhance any signals and reduce the random noise from false positives, albeit losing resolution in identifying individual triggering cases. Miyazawa et al. (2021) also studied the QTM catalog to investigate dynamic triggering in Southern California from 2008 to 2017. They stack results of triggering intensity to identify triggered local earthquakes in the region. This approach focuses on the populational behavior of the triggered earthquakes, such as a slower decaying rate for these earthquakes. Additionally, triggering behaviors can be compared with respect to the peak ground velocity (PGV), as a proxy for the peak strain change from the candidate global earthquakes. These ground motion measurements can serve as additional constraints. For example, only considering candidate earthquakes that have Using PGV as a proxy for strain does not account for variations in phase velocity or other focusing and defocusing of the strain wavefield. Where strainmeter data are available, the measured peak dynamic strain can be used directly (DeSalvio et al., 2025).

The false positive rates reported in this study suggests that the dynamic triggering reported by DeSalvio and Fan (2023) likely consists partially to almost entirely of false positives, which includes many cases reported in previous case studies (Aiken & Peng, 2014;Alfaro-Diaz et al., 2020;Li et al., 2019). Aside from the nearby El Mayor-Cucapah, Mexico, earthquake, the reported triggering in the real Southern California catalog appears to lack any general spatial-temporal characteristics that would distinguish it from random false positives. However, we also cannot exclude the reported cases in DeSalvio and Fan (2023) being true dynamic triggering without independent geophysical observations other than earthquake catalogs. We have not visually inspected each statistically identified case to establish whether or not a clear temporal correlation with the global earthquake is present during the passing seismic waves.

In examining the temporal-correlation premise that underlines almost all dynamic triggering studies, we have shown that a statistically temporal correlation of an apparent seismicity rate increase with a global candidate triggering event is not sufficient establish causal connection. False positives may occur either due to erroneous statistical identification of a seismicity rate change, or mistaking intrinsic seismicity rate complexity for dynamic triggering. However, the larger, more difficult problem how to establish causality in dynamic triggering studies remains.

Independent geophysical observations such as deformation anomalies could address the problem of erroneous identification of rate changes, by providing evidence that the rate changes reflect real anomalous behavior. However, this does not resolve the problem of whether the real seismicity and deformation changes are dynamically triggered, or are local phenomena that occurred coincidently following a teleseismic event.

To address the problem of coincidence, one could reduce the probability that the observations could occur by chance. e.g., a seismicity rate change over a large area (e.g., Hauksson et al., 2011) is less likely occur by chance. If there is a small probability (p) a seismicity anomaly randomly occurring at a single then there is a very small probability (p N ) that an anomaly would occur randomly at many (N) locations at the same time. Pankow and Kilb (2020) also advised that apparent triggering over a large area makes the case for dynamic triggering more convincing, and found that triggering with greater statistical significance often does trigger larger spatial areas. Similarly, because unrelated seismicity rate changes would have random amplitude with respect to the dynamic strains, a correlation of rate change with strain from the teleseismic event (e.g., van der Elst & Brodsky, 2010) would have a very small probability of happening by chance. However, emphasizing a coherent seismicity rate change over a large region could lead to a high false negative rate, as spatially localized true triggering cases would be disqualified by the evaluation. We note that any empirical, predefined selection procedure will impact the identification of seismicity rate anomalies, compromising the fidelity in different ways.

Here we considered false positives in seismicity catalogs where delayed dynamic triggering may occur up to 24 hr after a large global earthquake. Other dynamic triggering studies focus on detecting immediately triggered events within the surface wave train (e.g., Hill et al., 1993;Miyazawa & Mori, 2006;West et al., 2005). Such studies also rely on temporal correlation to establish dynamic triggering relationships, and also may experience false positives. Best practice would be to apply the same event detection techniques to a long time period to establish the reference seismicity rate and typical variability, and to estimate false positive rates using synthetic catalogs tailored to the specific experiment. We found for catalog-based studies that short test time intervals can have a higher rate of false positives due to the smaller number of events. Waveform-based studies usually have short test time periods, although this may be balanced by higher rates of detected small events. Waveform-based methods additionally have the advantage that they can relate the precise times of the detected events to the characteristics of the passing surface waves, albeit locations of these detected events are often unresolved. There is a very small probability that unrelated seismicity would occur, e.g., in synchronization with the peak extension of the Rayleigh waves as has been observed (e.g., Miyazawa & Mori, 2006;West et al., 2005).

Journal of Geophysical Research: Solid Earth 10.1029/2025JB031566

Conclusions

Dynamic earthquake triggering is commonly identified through the temporal correlation between increased seismicity rates and global earthquakes. Correlation does not imply causation, and false positives (dynamic triggering identified when none occurred, e.g. mistaking unrelated earthquake rate changes for triggering) may occur. We estimate the rate of false positives in Southern California, with global M ≥ 6 earthquakes as candidate triggers. We apply the same statistical tests as DeSalvio and Fan (2023) to synthetic earthquake catalogs with no true dynamic triggering. The rate of apparent triggering gives an estimate of the false positive rate. We find that the false positive rate varies for different statistical tests, and depends on characteristics of the catalog such as the rate of earthquakes and the extent of clustering. This suggests that best practice is to estimate the false positive rate for each study using synthetic catalogs with similar characteristics.

For the Southern California catalog, we find the false positive rate to be about 3.5%-8.5%, consistent with the 95% confidence often used in seismology. However, when large numbers of spatial-temporal windows are tested, many false positives are expected. This rate of false positives can the reported triggering in the real catalog (DeSalvio & Fan, 2023), including the observation that ∼70% of global M ≥ 6 earthquakes are associated with apparent triggering. The spatial-temporal distribution of triggering in the most realistic synthetic catalogs is indistinguishable from that of the real catalog, implying that all of the apparent triggering of the real catalog could be explained by false positives. The only exception is the nearby 2010 M7.2 El Mayor-Cucapah, Mexico, earthquake, which is known to have triggered earthquakes across much of Southern California (e.g., Hauksson et al., 2011). Therefore, the apparent dynamic triggering in Southern California might be largely false positives.

The problem of false positives requires careful evaluations when using statistical identification as larger earthquake catalogs make it possible to test larger numbers of spatial-temporal bins. When accurate physical insights are available, they can be imposed as additional constraints to further select the identified seismicity rate anomalies as triggering cases. To argue for causation will require going beyond individual temporal correlations between seismicity rate changes and candidate triggering events. To infer the triggering process, one can focus on the extreme cases, e.g., by studying correlations that exhibit larger patterns (e.g., seismicity rate changes over a large area, correlation between seismicity rate change and dynamic strain), which may have a low probability of occurring by chance.