The Reduced Detection Rate of Signals That Are Hidden by Earthquakes: Case Studies with Spotlight Detectors That Operate at Seismic Arrays

Signal detection methods that support explosion monitoring must often process noisy data streams that are contaminated by interference from natural processes (Ford and Walter, 2015; den Ouden et al., 2020). The signals from such processes can mask or diminish the amplitude of explosion signatures, such as seismic waveforms, and can thereby reduce the probability that processing algorithms will trigger against these signals (Carmichael and Hartse, 2016). In such scenarios, this interference elevates the risk that an explosion will go undetected at stations that are not deployed within the immediate vicinity of a source. Several researchers have proposed that certain data processing methods can overcome this risk and provide a confident detection, even during an earthquake (Kim et al., 2018). Array processing methods, for example, can separate some features of earthquakes and explosion waveforms through spatial and frequency filtering. In detail, such array processing methods screen the direction of arrival (back azimuth) of a waveform, its slowness, and the spectral energy sourced by an explosion from an earthquake in the frequency and wavenumber domain (using f‐k methods). Other proposals assert that sensor deployments that record signals from multiple standoff distances, or that record multiple modalities make effective masking unlikely. In the first case, a seismic station that is deployed near an explosion might critically record a signal that is temporally isolated from earthquake sourced signals recorded elsewhere. In the second case, multisensor deployments that include instruments to record infrasound signals, radionuclide particles, or electromagnetic emissions can often screen explosions that produce such signals from natural processes, which generally do not (Carmichael et al., 2020; Rodd et al., 2023). However, not all historical explosions produce the expected suite of multimodal signals immediately after a detonation (Ringbom et al., 2014). Seismic array processing does often provide the strongest immediate evidence of underground explosions in these cases (Gibbons and Ringdal, 2011; Ford and Walter, 2015; Schaff et al., 2018). This evidence often includes statistics from sensitive pattern matching methods called multichannel waveform correlation detectors, or correlators (National Academies of Sciences, Engineering, and Medicine, 2021). These correlators use historical records of ground motion measured by seismic sensors to build waveform templates (patterns to match) that they then scan against data streams that may contain waveforms with the same shape as the template (target waveforms) but that show different amplitudes and that are contaminated by noise ( Appendix A). The target and template waveforms match if the source mechanisms are similar and if they share a geographical location, such as an explosive test site (Vieceli and Dodge, 2022). These detectors behave differently when background seismicity contaminates the target waveforms and changes their shape (Harris, 1991; Carmichael and Hartse, 2016; Ganter et al., 2018; Sundermier et al., 2022). This contamination creates destructive waveform interference, degrades target‐to‐template waveform semblance, and reduces the ability of the correlator to perform its pattern matching operation (Carmichael, 2016). It remains unclear if contamination of explosion signals by earthquake signals degrades correlator performance enough to reduce the rate that explosions are confidently detected. It is also unclear if waveforms sourced by small explosions within local distances of seismic arrays remain confidently detectable during earthquakes if the origin time between such explosions and earthquakes are well separated (say, by many seconds). Without an explicit test against these scenarios, researchers may expect that array processing methods or correlators are sufficient to separate explosion and earthquake populations during detector processing.

We assess these expectations here. Our work suggests that even low‐magnitude (⁠$mb<2.3$⁠) seismicity that is common in earthquake swarms can contaminate explosion‐sourced waveforms enough that array‐based correlation detectors provide unreliable detection rates. We find even worse losses in detection rates between earthquake‐sourced template waveforms and target waveforms immersed in earthquake swarm seismicity. Our results therefore apply to seismic operations that monitor for both explosions and repeating natural seismicity.

Seismic network operators require a means to empirically test correlators against populations of target waveforms that are buried in noise and background seismicity that are large enough that they can quantify losses in monitoring capability. However, target waveforms with repeatable signal shape are rare. This means that populations of repeating target events (e.g., explosions at a test site) are generally too small for the statistics derived from correlators to confidently measure true positive detection rates. Although controlled source experiments (explosive chemical tests) at fixed testing locations can generate waveforms with repeatable shapes (e.g., Ford and Walter, 2015; Carmichael et al., 2020), they often remain too sparse in number to build performance curves in variable interference, such as background seismicity.

To quantify losses in correlator performance in the presence of contaminating background seismicity, we leverage an amplitude‐scaling and waveform‐injection technique (e.g., Schaff, 2008; Carmichael et al., 2020) that allows us to extend sparse records of waveforms to thousands of events that we can then process with our detectors. The first stage of this technique processes array data with a beamed power detector, called an F‐detector (Selby, 2008; Arrowsmith et al., 2009). This algorithm identifies waveforms sourced by seismicity located within a limited geographical region by first beamforming array data streams with prescribed P‐wave time shifts and then processing this array beam with a short‐term average to long‐term average (STA/LTA) detector. The second stage of this technique selects a template waveform within that geographical region that records a controlled explosion. We then build target waveforms by scaling the amplitude of this template and adding it back into the data at times that the F‐detector identifies waveforms sourced by background seismicity. This summation creates a compound data stream. We then process this compound data stream with a correlator to identify the target waveforms over a grid of amplitude scales and processing dates. To provide a comparison against baseline correlator performance, we repeat this process against data from the same recording period but instead inject templates at times that isolate them from known events. Our application of this method processes these compound data sets from short‐period sensors in the International Monitoring System (IMS) seismic array NVAR with a template that is sourced by an experimental chemical explosion conducted within the historical Nevada Test Site (NTS). We thereby operate our detector over two distinct month‐long time periods in January and June 2019 that include background seismicity. Our results provide quantitative measures of correlator performance in worst‐case versus best‐case signal environments.

We collect data from 11 short‐period vertical elements deployed within the NVAR array near Mina, Nevada, during two separate observational periods. One collection period includes a chemical explosion in June 2019 located near the legacy NTS that is within the current Nevada National Security Site (NNSS) (Fig. 1a; diamond markers). This event occurred during relative earthquake quiescence for that region. The other collection period (January 2019) includes an earthquake swarm centered in the same region that extends to eastern California. These periods thereby present distinct snapshots of background seismicity, one of which includes a target event.

The NVAR array aperture spans ∼12 km laterally and 500 m in elevation. The chemical explosion under study and the center of the January earthquake swarm each locate ∼250 km from the NVAR array center (Fig. 1b). Our first collection period (June 2019) captures the fourth Source Physics Experiment (SPE) shot (Snelson et al., 2013) in Dry Alluvium Geology, also known as DAG‐4 (Larotonda and Townsend, 2021). The explosive source for DAG‐4 was nitromethane, initiated by a small charge detonated on 22 June 2019 at 21:06:20 (UTC) at a depth of 52 m below the local ground surface at 37.1146, −116.0692. The DAG‐4 source had a TNT equivalent yield of 10.4 metric tons and an estimated body‐wave magnitude of $mb=1.96$⁠. This chemical yield roughly produces the same waveform amplitudes that are expected from a fully tamped nuclear explosion with a yield of 20 tons (Ford and Walter, 2013). We used the phase arrival times of the waveforms from this event (the “target”) at individual elements of the NVAR array to construct a multichannel power detector (an F‐detector; Selby, 2008) that focused its beam on the geographical region of the explosion. This geographical focus defines so‐called “spotlight” detectors (Kværna et al., 2021). To form such a beam, we first processed detrended individual channels with a three‐pole, minimum‐phase 2–4 Hz band‐pass filter and input these data into STA/LTA detectors that estimated waveform arrival times at each sensor; we found that a similar approach that estimated arrival times with intrachannel correlation produced a worse (lower semblance) beam. We therefore used the STA/LTA‐derived signal detection times to introduce channelwise P‐wave time shifts and form the digital energy beam for our F‐detector. This detector beamforms waveform energy according to these temporal shifts (Table 1) and then computes an array‐wide STA/LTA detection statistic (Fig. 2a,b). We processed data recorded from 1 January 2019 at 00:00:00 (UTC) to 31 January 2019 at 23:59:59 (UTC) and then from 1 June 2019 at 00:00:00 (UTC) to 1 July 2019 at 23:59:59 (UTC). A detector algorithm subroutine declared the presence of signals against a predetermined static threshold of 25 (units: counts/counts) (Fig. 2c). Although the nominal operation of our F‐detector uses adaptive thresholds that maintain a fixed false alarm rate against noise, we selected a static threshold to match operation of detectors that have “tuned” the NVAR beam to maximize the signal-to-noise ratio (SNR) of waveforms sourced at the NNSS (Dodge and Harris, 2016). We limited our analysis to the single octave, 2–4 Hz band. We also made no attempt to fuse detection results from multiple frequency bands or to screen regional and teleseismic arrivals with a frequency–wavenumber (f‐k) analyses (Rost and Thomas, 2002; their section 3.5) as performed elsewhere (Dodge and Harris, 2016). We found a larger record of seismicity than the 81 events reported in the cataloged generated by the U. S. Geological Survey (USGS) with a median value of ∼12 events per day. The background seismicity that we detected on the day of DAG‐4 includes only three events. We estimate an array‐averaged SNR value for waveforms sourced by the DAG‐4 shot that is lower (10 dB) than what we measured from average background seismicity (32 dB) over an SNR range of ∼60 dB. This indicates that the target source represents a seismic event that is smaller than that expected from ambient seismicity but that occurred on a day with low seismicity rates. This suggests that its waveforms are somewhat smaller in amplitude than typical earthquake waveforms sourced near the test site in June 2019 but that they originate from a time period that is advantageous for an explosion monitoring scenario.

Next, we processed records of seismicity sourced by the January 2019 earthquake swarm. The swarm’s activity spanned the first through the last day of January and included at least 200 events cataloged by the USGS located within 50 km of the second largest event (36.819°, −115.993°, 6 km depth), which had a source origin time of 23 January 2019 at 16:27:58 (UTC) and magnitude of $mb=2.1$⁠; this event was located 33.5 km from the DAG‐4 source and has a comparable magnitude. We selected these data and applied detector preprocessing operations that were identical to those that we applied against the June 2019 data. In detail, our algorithm computed detection statistics against the F‐detector array beam between 1 January 2019 00:00:00 (UTC) and 20190131 23:59:59 (UTC) and declared the presence of signals against the same static threshold. This process produced 1205 array-wide signal detections over January 2019, with a median detection rate of 38 events per day. The SNR of all detected events spanned ∼80 dB, with some SNR estimates <0 dB; we attribute this low score to the variance of our detector’s SNR estimator (Kubokawa et al., 1993; their equation 2.6) rather than to the detection of events far below the noise floor. The largest of these events also produced waveforms with an array‐beam estimated SNR value of ∼20 dB, as measured by our detector. The median waveform SNR from the remaining background seismicity is ∼10 dB. This matches the value of the DAG‐4 waveforms. The earthquake waveforms recorded during this period thereby create an environment that is less advantageous for an explosion monitoring scenario but that is not outside expectations for background seismicity near the NNSS.

Finally, we noted that our F‐detector output signal declares against waveforms sourced by events outside of the DAG-4 region, or swarm region. We therefore reviewed events that located 50 km or more from the DAG-4 source, which are cataloged by Rodd et al. (2023). We estimate that there is little event overlap (eight of 485 events) between our beamed solutions and those provided during a roughly 15‐day overlap in our time coverage and the events in their catalog. We concluded that seismicity exterior to our study region is not a significant fraction of the population that we declared with our F‐detector.

We now consider the performance of a correlator that processes background seismicity sourced near the DAG‐4 location during June 2019 and January 2019. We thereby constructed a detector template from 75 s (3000 sample) records of body waves sourced by the DAG‐4 explosion (Fig. 3a); this is the same event that defined the moveout across the array for our F‐detector beam. This template includes ∼1 s of pre-event noise per channel and substantial SNR thereafter. To prepare this template for our detector, we detrended each channel, Tukey tapered the ends to prevent spectral leakage, and band-pass filtered the results with a third-order Butterworth filter over 2–4 Hz. We confirmed that this template provided a near-unit correlation when we applied our correlator to an identically preprocessed data stream that contained the original template. To prepare our target data, we deliberately injected the 75 s template into identically preprocessed, noisy seismogram data that contained signals sourced by the other events that we already detected. Our algorithm selected injection locations to coincide with sample indices in which our F‐detector declared the presence of any signal (Fig. 4a) and maximized the interference between the template and target waveforms (Fig. 4b). This injection also maintained the relative moveout of waveforms across the 11 array elements (e.g., we preserved intra‐array phase delays). We selected >1700 injection times between the two months. These injection times were therefore not uniformly distributed over dates and more densely sampled periods of elevated background seismicity.

After contaminating these data, we then processed them with the correlator that operated with the original, preprocessed template. We used a declaration threshold consistent with a false alarm on noise probability of $10−10$ in each processing window (Fig. 5, red lines). Our algorithms then repeated the injection process by scaling the template waveforms with proportionality constants A over a logarithmically spaced, 136‐point grid (⁠$2.5×10−3<A<1$⁠) prior to injection. These waveforms mimicked signals triggered by explosions with yields that were smaller than or equal to that of DAG‐4. In detail, the kth scaling process premultiplied each channel of our 75 s template by the same factor $Ak$ prior to injecting it back into the target data (see  Appendix A). We spot checked several injection locations to ensure that our templates were sufficiently tapered so that the compound data stream was free of offsets between the injected waveforms and the original data stream. These injection times also coincided with waveforms that triggered our F‐detector during both 30-day collection periods. We then processed these compound data streams with our correlator as before and output a large volume of correlation detection statistics that sampled 136 distinct waveform amplitudes from the two full months of data, which included temporally variable noise and signal conditions (Fig. 5b). Because we processed target waveforms immersed in nontarget seismicity more often than expected by chance, the operation of our detector in this environment defines an empirical lower bound on its expected performance when processing data from a swarm or aftershock sequence (January 2019) and from a period of relative earthquake inactivity (June 2019). We relate both performance curves against yield (equations B3–B5) to measure the true positive rate (TPR) of our correlator against a source parameter (yield W) rather than against a signal parameter (A). This scaling cannot reflect yield dependent changes in corner frequency, nor effects that result from changes in depth of burial. Our experiment therefore reflects changes in the low‐frequency asymptote and negligible changes in corner frequency.

After we computed correlation detection statistics that we deliberately contaminated with nontarget background seismicity, we repeated our waveform injection process against seismograms dominated by noise. We thereby injected the same number of amplitude‐scaled templates back into the data per hour but used injection times that uniformly sampled the noise environment in time. If such an injection time was within half of the template’s temporal duration (33 s), we replaced it with a randomly selected injection time within that same hour of data that did not fall within 33 s of a prior STA/LTA‐derived detection time. We then processed each day of our target data with the same correlator template over the period that established our contaminated detections. We repeated our spot check for mismatches between the endpoints of the tapered templates and the detrended original data stream. In contrast to our prior operation that deliberately contaminated target waveforms, this process sampled time periods with absent or very sparse nontarget seismicity. We therefore expect that the correlation statistics output by processing amplitude‐scaled templates contaminated by only high background noise (and few or no waveforms) to be larger. The operation of the detector in this environment therefore defines a baseline for the TPR that is output by the detector. In words, it is an empirical upper bound on expected correlator performance.

We next tested if correlators that use earthquake‐sourced templates (rather than explosion‐sourced templates) could consistently miss repeating events sourced by natural seismicity, like those sourced by aftershock sequences and earthquake swarms. We therefore constructed a detector template from 75 s (3000 sample) records of body waves (Fig. 3b) sourced by the aforementioned $mb=2.0$ magnitude earthquake recorded on 23 January 2019 at 16:21:35 (UTC) (Fig. 1b, red star). We then processed the waveforms from this event with an STA/LTA detector to define channelwise detection times and P‐wave time shifts as an input to our beamed F‐detector. We then repeated our correlation experiment against the swarm data: we injected template waveforms back into our data at times to maximum waveform interference with seismicity and processed the sum of these seismograms with our correlator. We also recomputed a baseline for performance by injecting waveforms back into the data at times that were absent of detectable background seismicity; again, we required 33 s of known signal separation prior to injection. We then computed performance curves for both datasets and compared them against pseudo-yield, in which we converted our scaling amplitudes to relative magnitude rather than yield because the template source was tectonic ( Appendix B).

We compared the normalized detection counts for each correlator that processed target waveforms that we contaminated with noise alone and then noisy background seismicity. Our algorithm declared a detector trigger to be a true positive if its declaration time occurred within an uncertainty interval that surrounded the injection time of the template waveform into the target data. We set this interval to equal the duration of the short‐term window that our F‐detector used to identify the background seismicity. If our detector did not declare a trigger within this time interval, the algorithm assigned this event as a miss, or a false negative count.

To average our resultant performance curves over time, we assembled the true positive detection counts over our 136‐point amplitude grid. We then convert this amplitude grid to a yield grid (see  Appendix B) and separately summed our January and June time‐period count data into these bins. We first considered target waveforms injected into only recorded noise (or sparse seismicity). In this case, our binning produced empirical performance curves that quantify the best‐case, true positive detection rates for the multichannel correlator, when averaged over time. We next considered target waveforms that we deliberately injected into background seismicity, at times that we determined from the signal declaration times of our spotlight, F‐detector. This binning also produced empirical performance curves but that instead quantify the worse-case true positive detection rate for the multichannel correlator, when averaged over time.

A comparison between the upper and lower bound of our normalized detection counts demonstrates that our correlator that operates with an explosion‐sourced template has a significantly reduced capability to detect target waveforms that interfere with background seismicity. The results are similar for performance curve averages over the January 2019 dataset, averages over the June 2019 dataset, and averages over both months (Fig. 6, gray curves). For example, our model predicts that on average, a target waveform that is sourced by an explosion with a yield of 1.7 tons is detectable with a 0.97 detection probability when that waveform is contaminated by only noise (e.g., the baseline performance). The relative amplitude scale between the template and target waveforms is $7.15×10−2$ if we assume a two‐to‐one nuclear to chemical yield and the NNSS empirical models (see  Appendix B). Waveforms sourced by an explosion of that same size show a 0.37 probability of triggering our correlator when earthquake seismicity interferes with the same target waveforms (Fig. 6, black and gray curves) on average. This is far outside the range TPRs (⁠$$\begin{gathered} 0.8<PrD \\ <0.97 \end{gathered}$$⁠) that we consider acceptable for correlators that monitor test sites for low‐yield underground explosions. We subjectively consider detection rates that exceed 0.97 as certain for detecting small explosions (and numerically nonunique from one in certain processing calculations). The time‐averaged peak correlation detection statistics further show a significant drop relative to their baseline values over all yields (Fig. 6, blue curves). Our analysis suggests that interference from earthquakes that locate within even 10s of kilometers from a shallow explosion significantly reduces waveform detectability when targeted with detectors such as our correlator.

Our results also show that the correlator that operates with an earthquake‐sourced template has a diminished capability to detect target waveforms that are injected into background seismicity when compared over the same source parameter (yield rather than magnitude). Referring to the 1.7 ton yield reference value in Figure 6, we use the yield to body‐wave magnitude equivalents at the NNSS ( Appendix B) to estimate that a source with a magnitude of $mb=0.23$ produces waveforms with similar amplitudes to those sourced by a 1.7 ton explosion. Each average performance curve (over January, June, and both months) then shows that the correlator maintains a 0.92 detection rate against target waveforms that are contaminated by only natural noise. Target waveforms remain detectable with only a 0.16 probability when background seismicity contaminates these same target waveforms (Fig. 7, black and gray curves). The peak correlation detection statistics (labeled $r(x)$ in Fig. 5) also shows a moderate drop from their baseline values (Fig. 7, blue curves). This detection rate is markedly worse than that shown by the explosion sourced template.

Our results show that (1) background seismicity can mask waveforms sourced by small explosions from correlators if they operate with an explosion sourced template and that (2) seismicity from earthquake swarms can also hide repeating earthquakes from correlators if they operate with an earthquake‐sourced template. These results are remarkably consistent during both the January 2019 earthquake swarm and during the relative quiescence of June 2019, that is, the average performance curve for each month is almost indistinguishable from the average over both months (Figs. 6 and 7, gray versus black curves). We now consider if these results are significantly impacted by unknown locations of some background sources, by greater differences in source origin time, or by significant differences in apparent yield between the waveform sources. We also assess if our correlator really triggers on the injected waveforms immersed in the background seismicity as intended or on some other signal artifact of our injection process.

We first consider if the separation distance between the known location of the explosion source and the distributed background seismicity could significantly impact our results. Our analyses did not confirm that all the seismic waveforms that triggered our F‐detector were sourced by events located within several kilometers of the DAG-4 source. Most of these events are not listed in the USGS reports and are therefore uncataloged and unlocated. Regardless of whether these events did or did not locate near our target source, the moveout of their waveforms across the NVAR array elements created enough coherence in our F‐detector’s beam to trigger our algorithm’s event declaration subroutine. These signals then created enough destructive interference with the scaled copies of template waveforms that we injected back into the noisy data that our correlator showed diminished performance. Therefore, if sources of such background seismicity located off-site of the NNSS, our results (Fig. 6) indicate that waveforms from explosions can also be masked by nonlocal seismicity and still avoid correlator detection at multichannel seismic arrays such as NVAR.

We next quantify how the separation between the origin time of a repeating explosion and that of a nearby earthquake impact correlator declarations. More informally, we determine how closely spaced in time a small, repeating explosion and a nearby earthquake must be to “jam” a correlator. To perform this test, we selected an earthquake within the January 2019 swarm from the USGS catalog that occurred pm 23 January 2019 at 23:27:58.337 (UTC) and that located 34 km away from the DAG‐4 source, at (36.8187°, −115.9927°). We then processed 3600 s of 11 channel NVAR data records in the same manner as we processed the template. Next, we scaled the DAG‐4 template waveform to mimic a 1.7 ton explosion and injected it back into the data at 150 different synthetic origin times; we followed Rodd et al. (2023) and used the ak135 velocity model to predict these origin times. This scaling previously produced 0.97 detection rates against background noise (e.g., Fig. 6). We then processed these data with our correlator and compared its output against the relative time that separates the earthquake and synthetic origin times. This test showed that the correlator fails to trigger when the explosion origin time occurs between 80 s before and <20 s after the earthquake (Fig. 8). We interpret this to mean that 100 s is a sufficient event coincidence time to jam a correlator that targets such small nearby explosions.

We next assess if two waveforms sourced by explosions of significantly different yield (and different waveform amplitude) have sufficiently similar waveform shape to trigger a correlation detector despite their dissimilar corner frequencies. We first note precedents set by other workers that also use multichannel correlation detectors. Ford and Walter (2015) used a correlation detector at the NVAR array to detect signals from ∼1 t explosion with a template sourced by a ∼10 t explosion from the first phase of the SPE series (Snelson et al., 2013) that was emplaced 200 km away. The NNSS yield to amplitude scale ( Appendix B) predicts relative waveform amplitudes of $α=2.23×10−2$⁠. This is less than our relative amplitude scale of $α=7.15×10−2$ between the 1.7 ton and 10.4 ton shots. We next followed the approach of Ford and Walter (2015) and computed transfer functions between the DAG‐4 template signal and our injected target waveforms. We form these transfer functions from the spectral amplitude ratio of the event pairs using their known (scaled) yield and depth. Our model used these distinct yields and identical depths to predict the spectral amplitude from the Mueller and Murphy source model (Mueller and Murphy, 1971) and the DAG model for Yucca Flat (Ichinose et al., 2021, their table 2) (Fig. 9a). We then reviewed this ratio at one octave below (1–2 Hz) and one octave above (4–8 Hz) the processing band (2–4 Hz) that is relevant to the band used by our correlator to process data. This operation demonstrated that the spectral ratio was sufficiently flat over the frequency range that our linear correlator model (equation A1) likely applies (Fig. 9b), in general agreement with the SPE detection operation of Ford and Walter (2015).

Next, we considered if correlators can be defensible applied to earthquake sourced waveforms that span a similar range of magnitudes (or pseudo‐yields). In this case, we noted that prior work has already used template waveforms triggered by sources that exceed target waveform sources by 3.3 magnitude units to successful detect such events (Schaff and Waldhauser, 2010). From these comparisons, we concluded that it is reasonable to represent earthquake‐sourced target waveforms with our linear model (equation A1) and that our performance curves are defensible.

We finally assessed if waveforms with subunit SNR and immersed in background seismicity are truly detectable by our correlator or if our true positive counts only enumerated declarations on another unknown waveform injection artifact. For this assessment, we scaled waveforms sourced by the earthquake‐sourced template to have amplitudes equivalent to signals produced by events with a magnitude of $mb=0.4$ (or 2.2 ton yields), which produced visually absent signals at the array elements of NVAR but that our correlator declared as detections. We then manually reviewed the output from our correlator when it processed these waveforms that we injected into our data to mimic low‐magnitude repeating sources. Next, we summed large numbers of waveforms that our detector triggered against. We then aligned and summed these repeating signals. We found that as few as 12 such stacked waveforms matched the geometry of the original earthquake‐sourced template waveform (Fig. 10). This approach is supported by decades of seismic work that has delivered methods to stack (add) subunit SNR waveforms sourced by repeating sources, suppress incoherent noise, and resolves the signal geometry (Petersen, 2007; MacCarthy et al., 2008; Plenkers et al., 2013). Importantly, we found no evidence of coherent artifacts in the resulting sum that could arise from injection. We conclude that the waveforms that triggered our detector are amplitude scaled copies of the original, multichannel template (equation A1) rather than triggers against an artificial signal or background seismicity feature.

Finally, we concede that we did not supplement our injection schedule with other data that could identify the DAG‐4 source as an explosion. Data fusion methods (e.g., Carmichael et al., 2020) that combine infrasound, seismic, and electromagnetic signals from DAG‐4 (Rodd et al., 2023; Fig. 3) could almost certainly increase detection counts against the injected explosion‐sourced waveforms relative to our results that used one seismic array. Although such work is outside the scope of this current study, we are maturing our data fusion methods against multimodal sources such as the DAG‐4 explosion.

We conclude that earthquakes can effectively “jam” correlation detectors (correlators) that operate at single arrays and that monitor for small seismic events, such as underground explosions at local to near‐regional distances. In detail, we demonstrate that correlators that target repeating, low‐magnitude explosions located at test sites show significantly degraded performance if the waveforms output by these explosions temporally overlap with signals triggered by tectonically sourced seismicity. Specific results with an explosion‐sourced template show that a target waveform from a small explosion (1.7 tons) that is confidently detectable in nominal background noise (a 0.97 detection rate) is unlikely to be detected during earthquakes, on average (a 0.37 detection rate). Other results suggest that earthquakes located within 35 km of such a small explosion and that coincide within 100 s of its origin time can completely mask the explosion signals from a correlator. Although our example used a template sourced by a 10.4 ton chemical explosion, we interpret our data to qualitatively extend to larger sources. We assert that these collective results indicate that the classic scenario in which an earthquake “hides” an explosion is plausible under certain conditions: if the source is sufficiently small such that seismic signals are only detectable at a single array and if the containment of the source does not release other confirmatory signatures such as radionuclides. Without such confirmatory signatures, natural seismicity that is coincident in time with small explosions sourced at a test site can therefore create sufficient destructive waveform interference to effectively mask the explosion signals from a correlator.

We also showed that the same correlator algorithms that use earthquake‐sourced templates to detect natural seismicity output an even more degraded performance against correlators that use explosion‐sourced templates. That is, these detectors have lower TPRs against target waveforms for the same relative magnitude or yield. This latter result implies that a large fraction of natural events sourced by repeating seismicity might be missed by correlators if recurrence times are small.

The authors generated all scripts and figures with MATLAB, v.2024b, URL: https://www.mathworks.com/products/new_products/release2024a.html (last accessed September 2024, and Python3). The authors accessed all waveform data from EarthScope (formerly Incorporated Research Institutions for Seismology [IRIS]) using the MATLAB tool irisFetch.m. The signal detection tools that the authors used to assemble detections remain available to any reader from the corresponding author ([email protected]); the authors note they have been deprecated in preference to newer MATLAB written tools to leverage recently developed algorithms and mathematical methods. Information about the earthquakes queried are publicly available from the U.S. Geological Survey (USGS).

The authors acknowledge that there are no conflicts of interest recorded.

This article has been authored with number LA-UR‐22‐24224 by Triad National Security under Contract with the U.S. Department of Energy, Office of Defense Nuclear Nonproliferation Research and Development. This Low-Yield Nuclear Monitoring (LYNM) research was funded by the National Nuclear Security Administration, Defense Nuclear Nonproliferation Research and Development (NNSA DNN R&D). The authors acknowledge important interdisciplinary collaboration with scientists and engineers from Mission Test and Support Services (MSTS), Pacific Northwest National Laboratory (PNNL), and Sandia National Laboratories (SNL) to execute the DAG-4 shot. Los Alamos National Laboratory is supported by the U.S. Department of Energy National Nuclear Security Administration under Contract Number DE-AC52-06NA25396. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this article, or allow others to do so, for U.S. Government purposes. The authors thank Michael L. Begnaud, Ellen Syracuse, John Lazarz, and Rengin Gok for their feedback, as well as two anonymous reviewers that improved the article.

The theory of seismic multichannel correlation detectors that we use here was initially developed by Harris (1991), Weichecki‐Vergara et al. (2001), and Gibbons and Ringdal (2006) and then modified by others (Carmichael, 2016; Dodge and Harris, 2016; Gibbons, 2022; Sundermier et al., 2022). We use the notation and terminology of Weichecki‐Vergara et al. (2001) and Carmichael (2016) here.

Our correlation detector algorithm implements equation (A3) efficiently in the frequency domain and prenormalizes $x$ and $w$ in the time domain with a vectorized, sliding window operation. A subroutine computes equation (A4) in the time domain. It requires that multiple neighboring samples exceed a concurrent threshold to declare a signal and then defines the peak value of these samples as “the” detection statistic; it similarly uses the sample indices for this peak to store several parameter estimates (like A). This detector omits declarations for several samples after such a detection to mitigate multiple event declarations on the same waveform. Each hour‐long processing window computes a distinct value for η with equation (A5). This means that the declaration threshold can change 24 times a day when the detector algorithm processes a full day of data in hour‐long volumes. Carmichael and Hartse (2016) describe more algorithm details. Carmichael (2016) describes methods to use templates with large gaps between channels.