ABSTRACT
The detonation of a well‐recorded coupled explosion at the well‐characterized Nevada National Security Site, as part of Physics Experiment One, has provided us with an opportunity to compare and contrast methods and results of yield estimation and other event characterization methods. Yield estimates are made using several methods, including local/regional magnitudes, waveform envelopes, acoustic amplitudes, joint seismoacoustic yield, and moment tensors. We include in our analysis a discussion and comparison of applicability, calibrations, assumptions, and uncertainties involved in each. With the exception of magnitude‐based methods, all the techniques were more or less successful in recovering the known yield. It is, however, useful to be cognizant of requirements and calibrations, such as station coverage, emplacement conditions, propagation characterization, and uncertainties, to apply the methods to other areas with less complete information. We demonstrate that we can be successful at monitoring low‐yield explosions using a variety of methods assuming that the signal‐to‐noise ratio is adequate at recording stations, and that the material properties are taken into account. Depth estimates are also important, particularly if one allows the possibility of a surface explosion.
KEY POINTS
The detonation of a well‐recorded explosion has provided an opportunity to test yield estimation methods.
Estimates are made using magnitudes, envelopes, acoustic amplitudes, seismoacoustic, and moment tensors (MTs).
Most methods presented are successful in recovering the known yield, within the estimated uncertainties.
INTRODUCTION
Because we do not know the specific circumstances (e.g., size of explosion, emplacement conditions, sensor coverage, etc.) of future explosion monitoring challenges, we would like to develop a versatile tool kit for yield determination. As part of the Low Yield Nuclear Monitoring program, the National Nuclear Security Administration Office of Defense Nuclear Nonproliferation Research and Development has funded a multiphysics experiment, referred to as Physics Experiment One (PE1) (Myers et al., 2024). Although a series of experiments are planned, the first in a sequence of three emplacement conditions, shot A (referred to as PE1‐A), was a detonation of a fully coupled underground chemical explosion, with planned decoupled (PE1‐B) and partially coupled (PE1‐) explosions to follow. The explosion was prepared in P‐Tunnel in Aqueduct Mesa at the Nevada National Security Site (NNSS), and PE1‐A was conducted on 18 October 2023 at 15:15:00 UTC. It was well recorded by seismic and infrasound stations as well as electromagnetic sensors and air samplers. A large number of sensors were specifically deployed for the experiment (Myers et al., 2024), and additional sensors were operated by other networks in the region, including the U.S. National Seismic Network (network code: US), the Nevada Seismic Network (NN), and the southern Great Basin Network (SN) (Fig. 1). The explosive package of PE1‐A was composed of 13,580 kg (the equivalent of 16.3 tons of TNT yield) of comp B (composition B; a high explosive) in a chamber of 2.2 m radius, which was backfilled with dry sand. Aqueduct Mesa is composed of layered tuffs, and the explosion was conducted at a depth of 251 m from the top of the mesa [resulting in a scaled depth‐of‐burial or SDOB of ] at an elevation of 1683 m above sea level (Myers et al., 2024; Paeth and Dzenitis, 2024).
PE1‐A provided an opportunity to test, refine, and improve event characterization methods, including yield determination. In this study, we will be comparing and contrasting the following methods: traditional magnitude‐based yield estimation, waveform envelope yield, acoustic amplitude yield, joint seismoacoustic yield, and moment tensor (MT) analysis. While comparing methods, we will be discussing details of method applicability (e.g., How many stations? How close? Azimuthal distribution?), calibrations needed (of earth models, atmospheric conditions, stations, etc.), significant assumptions (e.g., about velocity model, explosion source model, etc.), and overall uncertainties.
MAGNITUDE‐BASED YIELD ESTIMATION
An established and widely applied technique for calculating yield is magnitude‐based estimation, with empirical relationships determined by regressing magnitudes (generally linearly) with ground‐truth (GT) yield estimates, with most traditional methods generally employing teleseismic magnitudes such as body‐wave magnitude (). In the process, these formulae attempt to simultaneously account for the material properties, attenuation characteristics, and the containment depth characteristics of the test site. One formula determined using underground nuclear explosions at the test site in Nevada is from Murphy (1981) who estimated , in which W is the yield in ktons of TNT equivalent. In an effort to examine smaller events not well‐recorded teleseismically, other formulae have been determined for regional magnitudes. An example of this is the study of Vergino and Mensing (1990) using based on regional Pn amplitudes. The formula for Rainier Mesa (the test site region that includes Aqueduct Mesa) is . It is worth noting that neither of these formulae takes into account changes to the relationship as a result of the corner frequency moving through the measurement frequency band. This was notably done in Bowers et al. (2001) for yield at the Soviet/Russian test site in Novaya Zemlya, with a formula , with b = 0.75 for W ≥ 1 and b = 1.0 for W < 1.
Several magnitude estimates were made for PE1‐A including a local magnitude () 1.71 ± 0.27 from the University of Nevada Reno Seismological Laboratory, from the Caltech Seismological Laboratory, and from the U.S. Geological Survey National Earthquake Information Center (NEIC). Magnitudes can vary due to different station sets, station corrections, and varying formulas accounting for attenuation, but an is consistent with all estimates within one standard deviation. Unsurprisingly, there was no reported teleseismic magnitude for this small event. Although and are not equivalent, they are generally comparable. In light of no specific local magnitude calibrations, we will apply the ‐based formula with to make a magnitude‐based yield estimate for PE1‐A. The NEIC magnitude was made using 12 components at 7 stations ranging from TPNV (located on NNSS) and S11A, out to a station at ∼250 km. From the NEIC , we therefore estimate a yield of 1.82 (1.37–2.41) tons using the Murphy formula and a yield of 4.23 (3.28–5.45) tons using the Vergino and Mensing formulas. Both of these estimates are significantly smaller than the GT yield. Several authors (e.g., Utsu, 2002) have attempted to regress various magnitude scales, but generally for larger events. For the western United States (WUS), Chung and Bernreuter (1981) found , which would result in even smaller magnitudes and yield estimates.
Magnitude–yield relationships have been calibrated using data from events buried according to established containment rules. Based on the Denny–Johnson scaling model (Denny and Johnson, 1991; Patton and Taylor, 2011), a depth correction is suggested for changes in the scaled depth (), in which h is the depth (in m). Making these corrections for this overburied explosion, we estimate a yield of 14.1 (10.6–18.8) and 26.2 (20.4–33.8) tons using the Murphy and Vergino formulas, respectively, providing estimates more consistent with the GT yield.
We will now discuss applicability of the method, calibrations needed, assumptions of the method, and major sources of uncertainty. We can reasonably expect to apply this formula any time a magnitude estimate can be made. Although in theory a single‐station estimate could be made, amplitude‐based magnitude estimates can vary wildly from station to station. As evidence of this variance, the NEIC has long used a trimmed mean approach to account for outliers (e.g., Yeck et al., 2024). In terms of calibrations, obviously an empirically based formula would either need to be constructed or adopted from another region. These can also vary significantly, particularly between stable cratonic and active tectonic regions, so care must be taken with this, and some validation is required. Most magnitude formulas also include station corrections, and these would be needed for optimal performance.
There are several notable assumptions. The first is that the emplacement conditions, such as material properties or depth‐of‐burial, do not vary significantly from the conditions of the calibrations. In the case of PE1‐A, the explosion is significantly overburied relative to common containment practices. The second major assumption is that the values of the magnitude used (e.g., ) do not vary significantly from the values of the calibration magnitude (e.g., ). Also note that this yield estimation method would only work for deeply buried explosions and would not be applicable, without modification, for a near‐surface explosion or likely for a decoupled one. Overall uncertainty comes from uncertainties in the magnitude estimate, the magnitude formula (as provided in Vergino and Mensing), plus additional perhaps hard‐to‐estimate components due to differences in material properties, depth, and yield size (from calibration events), and magnitude‐to‐magnitude conversion.
REGIONAL WAVEFORM ENVELOPES
A way of improving upon magnitude‐based methods is to model the observed waveforms more directly and over a broader frequency range. One such method is to model the envelopes of local and regional seismograms to estimate the yield and depth of explosions (Pasyanos et al., 2012). The method has been applied to a wide variety of explosions including North Korean underground nuclear explosions (Pasyanos and Myers, 2018), shallow and deep chemical explosions from experiments (Pasyanos and Kim, 2019), and the Beirut industrial explosion (Kim and Pasyanos, 2023). The technique uses a reduced‐order model, which seeks to characterize the essential source and propagation effects that affect the observed signals given incomplete knowledge of both of these terms in all but very rare conditions. An explosion source model provides a spectra, which is then propagated to local and regional recording stations. The spectral source depends on several factors including explosive yield, the emplacement depth, and material properties, which is captured in an explosion source model. The propagation that needs to be accounted for includes the geometrical spreading, the seismic attenuation, station site terms, and the coda decay rates. Yield and depths are then tested and compared to the observed waveform envelopes to minimize the misfit.
Yield analysis for PE1‐A is performed using U.S. National Seismic Network station TPNV (Topopah Spring, Nevada) at a distance of 31 km to the south‐southwest. Although not part of the PE1 deployment, this long‐running station is well calibrated for attenuation and site terms and has been previously used for the analysis of chemical explosions from other recent experiments at NNSS, including the buried Source Physics Experiment (SPE) and SPE Dry Alluvium Geology (DAG) explosions, and their associated surface explosions (Pasyanos and Kim, 2019). For the material properties, we use the model for tuff (P‐wave velocity = 3.5 km/s, S‐wave velocity = 2.021 km/s, and ) from Stevens and Day (1985). The in situ measurements made in the mesa vary considerably but are generally lower than the generic tuff values. As is common practice, waveform envelopes are generated using the log average of the two horizontal components (Mayeda and Walter, 1996), and the inversion is performed in four frequency bands (2–3, 3–4, 4–6, and 6–8 Hz) spanning from 2 to 8 Hz. The signal‐to‐noise ratio (SNR) across the frequency band is high, and the overall fits (Fig. 2a) are generally good, indicating that the coda shape parameters used seem appropriate for the region.
Figure 2b shows the root mean square misfit between the log velocity of the data and that of the model as a function of yield and depth. The misfit is transformed into a likelihood function (Fig. 2c) assuming Gaussian residuals and estimated model uncertainties. At subterranean depths, there is a trade‐off between yield and depth, with a larger yield required at depth to overcome the increasing overburden. At a standard SDOB of , which might be a reasonable assumption made in lieu of other information, we estimate a maximum‐likelihood yield of 8.5 tons with an uncertainty of 4.5–10 tons for solutions 50% as likely as the maximum. At the true depth‐of‐burial of 251 m, the yield estimate is 17 t (12.5–25 t). We also allow for the possibility that the event is a near‐surface or above‐surface explosion using the empirically determined surface coupling relations of Ford et al. (2014). As a result, the minimum misfit (and corresponding maximum likelihood) is a continual function rather than a point, due to the surface coupling used (Pasyanos and Ford, 2015). In this case, the estimated yields are higher for a near‐surface explosion because the seismic coupling is significantly reduced at these depths/heights. For explosions constrained to the surface, we find an estimated yield of 25 tons (16.5–35 t).
For comparison, this analysis was also performed at other nearby stations including TPW, an uncalibrated station 37 km to the south‐southwest, and S11A, a calibrated station 60 km to the northeast with poorer SNR. Single‐station estimates at these stations provided lower yields, but were only slightly smaller when combined with calibrated, high SNR TPNV analysis.
In terms of applicability, the waveform envelope method is, at its heart, an inherently local and regional method, so observing stations need to be closer than teleseismic distances. In general, it works as a single‐station method, although multiple recording stations can also be used. The signal needs to be large enough to record local or regional waves and their coda above the noise, so the distance of the recording station will obviously depend on the size of the explosion and the coupling characteristics (near surface, softer material, etc.). Because we are using the scattered wavefield, there is no azimuthal distribution requirement for the recording stations. Unlike the magnitude‐based yield estimates, this method can be applied to near‐surface events.
Empirical calibrations are generally needed to capture the propagation characteristics. Seismic attenuation is important, but high‐resolution attenuation tomography models are generally available for most continental regions, and are less important at shorter distances. Coda calibrations are definitely required but, once calibrated, are applicable over large regions, say, the WUS or the Middle East (e.g., Gök et al., 2016). Station site terms are also needed but can be calibrated using earthquakes as part of the amplitude tomography.
We made several assumptions related to the source. The first is the choice of the explosion source model. Although there are several well‐known explosion source models, such as Mueller–Murphy (Mueller and Murphy, 1971) and Denny–Johnson (Denny and Johnson, 1991), we chose to use the Walter–Ford model (Walter and Ford, 2018) because previous experience has shown that it more consistently predicts long‐period moment and corner frequency than the other models (Ford and Walter, 2013) and is generalizable for various material conditions, including high gas porosity. The other major assumption is the source material properties. Although we know that the geology of the working point is tuff, the specific characteristics of tuff can vary significantly, which could affect the estimated yield.
The major sources of uncertainties for this method are the material properties and propagation (attenuation, local site terms, and coda calibrations). At the local distances here, we are relatively insensitive to the attenuation parameter Q, but this is more important for far‐regional monitoring. Material properties at the shot point are critical because these directly affect the source spectra. Depending on the source emplacement, there could be additional source of uncertainty (e.g., seismic coupling for near‐surface or in‐water events, decoupling factor for cavity decoupled events, etc.).
ACOUSTIC YIELD
Joint seismoacoustic analysis has been demonstrated to significantly improve yield and depth determination and reduce uncertainties for near‐surface explosions, such as the Forensic Surface Events (Pasyanos and Kim, 2019), Large Surface Explosion Coupling Experiment (Kim and Pasyanos, 2023), and Beirut (Kim and Pasyanos, 2022). An outstanding question is whether or not we can find a similar improvement for PE1‐A, which is a significantly overburied explosion ().
We start by first estimating an acoustic yield. The observed acoustic signals of PE1‐A were complicated by several factors. First, we find significant interference between the acoustic signal and the seismic motions coupled into the microphones at short distances (Arrowsmith et al., 2010), which is a common occurrence for in‐close acoustic observations at the six arrays within 2 km (Fig. 3a). At longer distances (>4 km) where the acoustic and seismic signals do not overlap, we find two key features. The first is that beamforming array analysis for array PSEER indicates that the back azimuth of the acoustic signals corresponds to the PE1‐A explosion source (Fig. 3b). The local infrasound network consisted of four‐element, centered triangle arrays with a 35 m aperture. The beamforming analysis shows consistent back‐azimuth angle (338.2°) to the epicenter. The second is that the acoustic signals start arriving before the local sound speed (∼341 m/s) from the epicenter. The early part of the signals seems to have traveled faster than the sound speed in the air with a celerity of 550 m/s. This indicates that the signals could propagate as seismic waves at higher speeds near the source and were coupled into acoustic waves in the path to the observing station, PSEER. In consequence, the apparent sound speed shows a wide range of variation between 250 and 550 m/s depending on the seismo‐acoustic coupling location. These seismically driven acoustic waves were observed with overburied events (e.g., earthquakes, underground explosions), and surface topography and seismic surface waves can play an important role for their excitation (Assink et al., 2018; Che et al., 2022).
For near‐surface explosions, we normally employ an acoustic yield method based on the observed spectral amplitudes (Kim et al., 2021) and seismoacoustic energy partitioning near the epicenter (Ford et al., 2014, 2021). Given the complications of the acoustic radiation and the emplacement depth of PE1‐A, however, we needed to utilize a method that works on buried sources. Using SPE phase I data, Bowman (2019) used peak‐to‐peak amplitudes (P2PAs) to estimate the SDOB, with the simple concept that larger amplitudes indicate either a shallower depth or a higher yield. The regressed P2PA–SDOB relation is , in which is the P2PA in pascals, and , and SDOB is in units of and doubled for chemical explosions. The SDOB of PE1‐A is within the SDOB range for the SPE events (). For PE1‐A, the P2PAs were measured at the PSEER array including the PSEER, PER01, PER02, and PER03 elements after removing long‐period background noise by high‐pass filtering (>1 Hz) (Fig. 3c).
We found, however, that the observed P2PAs of PE1‐A are much larger than what would be expected from the SPE‐based model (Fig. 3d), which results in higher acoustic yield estimates (Fig. 3e). Whereas the equation would predict a P2PA of about 1 Pa at the SDOB of PE1‐A, we observed amplitudes ranging from 2 to 4 times that, which results in an estimated SDOB of about half of the true SDOB. This might indicate that the seismo‐acoustic energy partitioning of PE1‐A is significantly different from those of SPE. Larger acoustic amplitudes may indicate efficient acoustic coupling by local topography, which can focus seismic energy. The seismo‐acoustic coupling mechanism of PE1‐A also seems to be different from the SPE. Although the SPE signals were characterized by impulsive waveforms for a short period, PE1‐A signals show emergent envelopes with a long duration. This seismically driven acoustic waveform may not be fully explained by the spall‐driven acoustic coupling model in the SPE (Bowman, 2019; Ford et al., 2023).
Like the waveform envelope method, acoustic yield methods can be single‐station estimates. Acoustic observations are generally more sensitive to azimuthal distribution than corresponding seismic observations due to wind conditions affecting propagation paths and amplitudes. Previous studies indicate that infrasound amplitudes at local distances can drastically change with low‐altitude wind jets (Kim et al., 2018). However, these wind effects are cumulative as propagation distance increases and should be limited within ∼4 km from the source. As mentioned earlier, stations need to be close enough to have good SNR but not close enough so that there are interfering seismic signals. For PE1‐A, useful acoustic observations were available out to about 10 km distance. In this study, we only used the array PSEER at ∼4 km due to its reliable instrument responses and amplitudes.
For the normal acoustic yield method using spectral modeling, one major source of uncertainty, particularly at longer distances, is our incomplete knowledge of key features of the atmosphere (e.g., temperature, pressure, and wind speed as a function of height), which changes over short timescales. In previous studies, we used National Oceanic and Atmospheric Administration’s Rapid Refresh forecast model and profile (Rutledge et al., 2006) for numerical simulations, which provides a reasonable atmospheric specification. The effects of uncertainties in the atmospheric conditions on our yield estimate could be simulated by comparing the results using different forecast models, such as European Centre for Medium‐Range Weather Forecasts (European Centre for Medium‐Range Weather Forecasts [ECMWF], 2013).
Although source coupling curves for the direct acoustic signal has been extensively studied (e.g., Ford et al., 2014), there is more uncertainty for the indirectly generated acoustic signal (e.g., spall). For instance, Ford and Vorobiev (2023) found a transition between a gas‐generated acoustic pulse (the direct acoustic signals) and a spall‐induced pulse (the indirect acoustic signal) that occurs at around , but the details of this transition and the behavior at larger depths might vary significantly based on factors such as material properties and local topography. If these relationships were better understood then, in the future, we might employ the spectral yield method to explosions at a wider range of depths.
JOINT SEISMOACOUSTIC YIELD
We combine the seismic and acoustic results to estimate a joint seismoacoustic yield for PE1‐A, which provides data fusion on the phenomenological level rather than on the purely statistical level. For both the individual seismic and acoustic estimations of yield, a likelihood function is constructed from the misfit functions and uncertainty estimates, as specified in Pasyanos and Kim (2019). The combined results depend on the weighting used between the two components (Fig. 4).
In the absence of other information, we would likely weigh the seismic and acoustic components equally. In the case of PE1‐A, doing so rules out the possibility of a near‐surface explosion, which results in an estimated yield between 4.5 and 30 tons at any arbitrary depth, and a maximum likelihood of a 12 ton explosion at 125 m depth. Increasing the weight of the seismic component results in poorer depth sensitivity but smaller uncertainties at any particular depth. It is worth noting that, given the correct depth, all joint yield determinations include the GT yield but with increasing uncertainties as the acoustic weight is increased.
Applicability of a joint seismoacoustic yield is pretty much the subset of applicability of the two individual methods (regional waveform envelopes, acoustic yield), and is not further elaborated here.
MOMENT TENSOR ANALYSIS
MTs capture the force couples of seismic sources and are used to characterize the type of faulting (strike‐slip, normal, and reverse) of most seismic events like earthquakes. Enabled by advances in methodology (e.g., Minson and Dreger, 2008), codes, and velocity models, it has become increasingly common to move away from solutions constrained to be double couple (DC) or deviatoric‐only to provide unconstrained six‐component MT solutions. Full MT solutions allow non‐DC components, including isotropic components and compensated linear vector dipole, which are associated with volume change and volume‐compensated crack opening/closing, respectively.
Recent studies have found that full MT methods can reliably identify nonearthquake sources, such as explosions and collapses. Ford et al. (2020) developed an event screening method for explosions based on the MT hypersphere. The screening statistic is defined as the angle from the population (explosion or collapse) mean vector to a newly estimated unit MT . Pasyanos and Chiang (2022) applied the method to a much larger set of full MTs of explosions at the NNSS, and Pasyanos et al. (2023) extended the method to screen for a large set of collapses from around the world. Using this method, we are able to identify source type (between earthquakes, explosions, and collapses) with 97%–98% accuracy.
The long‐period data generally used to calculate MT solutions were mostly noisy for PE1‐A, but station TWP (Twin Peaks) located 3 km to the southeast was just above the noise and used in the inversion in the 0.3–0.65 Hz frequency band (Fig. 5a). On the fundamental lune, the solution plots in the upper hemisphere east of the positive crack mechanism (Fig. 5b). A moment magnitude of 2.00 is largely consistent with local magnitude estimates reported earlier.
MTs were performed using two different velocity models: the WUS of Ritsema and Lay (1995) and the DAG model of Ichinose et al. (2021). The models differ in their shallow structure (top 500 m), in which the DAG model has three low‐velocity sedimentary layers, but are otherwise identical. Of the two models, we would expect the WUS model to be more appropriate for Aqueduct Mesa than the DAG model, which was created to model the slower velocities due to the alluvium in Yucca Flat, where the DAG explosions took place. The additional model is provided to illustrate the effect of changes in the velocity model on yield estimates. The resulting MT solutions (in N·m, and described as ) obtained using the two models are and for the DAG and WUS models, respectively.
Using material values for tuff, we estimate a yield using various explosion source models (Table 1). Where the velocity model and/or the explosion model are suboptimal, the estimated yields are generally low, particularly if a more typical SDOB is assumed. The WUS velocity model and Ford et al. (2023) model, which was specifically derived from MTs, results in the closest yield estimate. Uncertainties of a factor of two are adopted from Pasyanos et al. (2023). We explored fusion of the MT‐derived yields with the joint seismo‐acoustic yields. We combined the likelihood function estimated from the WUS velocity and Ford et al. (2023) explosion model with the joint seismo‐acoustic likelihood, but this did not substantially change the results shown in Figure 4. This is likely due to the fact that the yield estimates using this explosion model are not depth sensitive.
Unlike the other methods presented, MT solutions are generally not single‐station solutions and can be improved significantly with stations at a variety of azimuths. Stations need to be close enough to observe the long‐period portion of the spectra, which will be a function of magnitude or yield. Because of these requirements, MT solutions will likely be applied to fewer events than many of the other seismic methods considered here.
One advantage of using longer period is that less model calibration is required than higher‐frequency methods. This is why a 1D model like the preliminary reference Earth model (Dzeiwonski and Anderson, 1981) can be used for large earthquakes globally, whereas regional specific velocity models are required for smaller events inverted using shorter periods (e.g., 15–50 s). As a result, the method is also relatively insensitive to attenuation variations. Quite important for generating the Green’s functions at these higher frequencies is having some information about the shallow earth structure, in particular, the absence or presence of sedimentary basins. This is one reason why we see such significant differences in the results using the WUS and DAG models.
One large source of uncertainty is the seismic moment (or isotropic moment ), which can vary significantly based on the velocity model and depth. Formal uncertainties from the inversion are generally severe underestimates because they do not account for all the sources of uncertainty. Uncertainties on the order of a factor of 2 are common, which would lead to similar uncertainties in the yield estimate (Pasyanos et al., 2023). Methods like BayesMT (Chiang et al., 2025) and MTUQ (Silwal and Tape, 2016; Thurin et al., 2022) are starting to address some of the issues associated with the effect of uncertainties in the velocity model on uncertainties in the MT. In addition, moment‐derived yield estimation depends on the explosion source model and the material properties. This is reflected in the significant (order of magnitude) variations we see from employing different source models in the yield estimate (Table 1).
CONCLUSIONS
We are developing a number of yield estimation methods that can work under a variety of emplacement conditions (e.g., buried or shallow, range of material properties, etc.) or sensor coverage (e.g., seismic or acoustic sensors, distance, azimuthal coverage, etc.). The purpose of this study is not to determine a single “best” method but to compare and contrast methods for a buried, tamped low‐yield chemical explosion having GT information, and well recorded by a variety of sensors.
On the whole, the methods described here work well for PE1‐A, which is summed up in Figure 6. Magnitude‐based yield estimation methods generally need empirically based calibrations from GT explosions (with known yields), which can be difficult for monitoring broad regions or a new test site. It also seems likely that, for smaller explosions, the observed magnitudes will likely be different from the magnitude type used in calibration. Magnitude‐based estimates are generally lower, but making a depth correction improves yield estimates considerably. Waveform envelopes can be used to estimate yields under a variety of emplacement conditions, but broad area attenuation and coda calibrations are required. The method is also subject to uncertainties in material properties and trade‐offs between yield and depth.
PE1‐A allowed us to test acoustic yield determinations for buried events with observed secondary acoustic signals (e.g., seismic signals radiated from topography), rather than the direct acoustic signal from epicentral ground motions. Our understanding of the generation of these secondary signals is incomplete, but progress in this area would improve our ability to apply acoustic analysis to more events, namely deeply buried explosive sources. Joint seismoacoustic yield determination is very effective for improving estimates and reducing uncertainties of near‐surface explosions, but only if the individual estimates of the constitutive technologies are reliable. This approach may also be extended to the study of deeply buried explosions.
Moment‐derived yields can be estimated if the seismic moment can be reliably determined using waveform modeling. Although this method has been shown to be effective for large explosions, for smaller sources, it can be challenging to get good SNR at frequencies generally lower than other methods, and to find applicable earth models. Coda spectral methods could be applied, but this technique does not isolate the isotropic moment as effectively as waveform modeling methods. This could lead to deviations in yield estimation in cases where there is significant nonisotropic moment. Coda methods to estimate source spectra (Mayeda and Walter, 1996) could also help resolve the source depth (Murphy et al., 2009), improving our yield estimates.
In all these methods, having good SNR is essential. Stating the obvious, you cannot make yield estimates for unobserved signals. In general, material properties continue to be the largest uncertainty in yield estimation. However, variation of these properties in hard‐rock sites often used for test sites are expected to be less variable than soft‐rock sites, in which local material properties can vary more significantly. Accurate depth estimates are also important to improving yield. We can revisit these methods for future proposed explosions within PE1, which include partially and fully decoupled explosions, and where the SNR will be reduced and methods must account for the reduced geophysical signals.
DATA AND RESOURCES
Analysis was performed with data from the following networks: US (U.S. National Seismic Network; Albuquerque Seismological Laboratory (ASL)/U.S. Geological Survey [USGS, 1990]), NN (Nevada Seismic Network; University of Nevada, Reno [1971]), and SN (southern Great Basin Network; University of Nevada, Reno [1992]), and are available at EarthScope (https://www.earthscope.org). Data from Physics Experiment One (PE1)‐A is anticipated to be released 2 yr after the end of the experiment. Figures 1, 2, 3e, 4, 5b, and 6 were created using the Generic Mapping Toolkit (GMT) (Wessel et al., 2019) (https://www.generic-mapping-tools.org). All websites were last accessed in December 2024.
DECLARATION OF COMPETING INTERESTS
The authors acknowledge that there are no conflicts of interest recorded.
ACKNOWLEDGMENTS
The authors thank deputy Editor Junghyun Park, Reviewer Brian Stump, and one anonymous reviewer for helpful reviews and comments on the article. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory (LLNL) under Contract DE‐AC52‐07NA27344 and is document LLNL‐JRNL‐2001744. 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 Los Alamos National Laboratory (LANL), LLNL, Nevada National Security Site (NNSS), Pacific Northwest National Laboratory (PNNL), and Sandia National Laboratories (SNL).