Regional infrasonic observations from surface explosions – influence of atmospheric variations and realistic terrain

SUMMARY

A pair of 1-ton, conventional surface explosions were conducted at the Nevada National Security Site in the fall of 2020 producing seismoacoustic signatures observable hundreds of kilometres from the source location. Regional infrasonic observations include tropospheric ducting at large distances to the south, a wide stratospheric waveguide with signals observed more than 700 km to the east, and anomalous arrivals in the stratospheric shadow zone. Notable differences in propagation between the events are identified despite the explosions being conducted just two days apart due to a sharp temporal shift in the tropospheric winds as well as structural changes in the stratospheric winds. Propagation simulations of the two events have been completed using a combination of ray tracing and parabolic equation (PE) methods. Simulations have been conducted to quantify the impact of the temporal variations in the atmosphere as well as the influence of terrain on propagation. Temporal variations in reflection locations are found to produce notable changes in downrange propagation due to spatially varying terrain features. Finite frequency effects modelled by the PE are found to predict ensonification not included in corresponding 2D ray tracing simulations. Notable variations in predicted signal amplitude are found due to focusing by along-path and cross-path terrain gradients; though, the later of these is only modelled using fully 3D ray tracing analysis.

1 INTRODUCTION

Energetic events in the atmosphere produce a variety of signals that can be observed at local, regional and even global distances from the source for sufficiently high energy phenomena. Mechanical signals produced by such events (i.e. seismic and acoustic waves) are frequently utilized to locate and characterize sources for natural hazard, civil and scientific, as well as global security applications. The International Monitoring System (IMS) operated by the Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) utilizes seismic and infrasonic (sub-audible frequency acoustic) monitoring as its primary means of detecting below- and above-ground nuclear explosions (Christie & Campus 2010). In such analyses, accurate modelling of the propagation of seismic and acoustic waves through the Earth and atmosphere, respectively, is needed to locate and characterize the source. Computation of predictions for infrasonic signals is notably challenging due to the dynamic and sparsely sampled nature of the atmosphere and the resulting variability and uncertainty in infrasonic propagation.

In addition to the variable and uncertain nature of the atmosphere as a propagation medium for infrasonic signals, realistic modelling of acoustic wave propagation in the atmosphere is complicated by various effects, including finite-amplitude non-linear propagation in the rarefied middle- and upper atmosphere, as well as interaction with realistic terrain features, with scales that can be on the order of the infrasonic wavelength. The later of these has been a focus of propagation modelling development in ray tracing analysis (Jones 1986; Lamancusa & Daroux 1993; Blom 2020) as well as finite frequency modelling methods, including parabolic equation (PE) and finite difference time domain (McKenna et al. 2012; Parakkal et al. 2012; de Groot-Hedlin 2017; Kim et al. 2017; Waxler et al. 2022). In many applications, the numerical burden of including terrain interactions limits modelling to near-source and local distances; however, recent developments, including terrain interactions with 3D ray tracing, as well as an efficient Padé PE including terrain, make a more detailed analysis of regional propagation including such interactions numerically feasible (Blom 2020; Waxler et al. 2022).

Propagation modelling capabilities needed for infrasonic localization and characterization are often evaluated using unplanned events of convenience such as industrial and other accidents (Ceranna et al. 2009; Vergoz et al. 2019; Pilger et al. 2022) as well as by leveraging regularly occurring munition disposal and similar activities (Nippress et al. 2014; Park et al. 2014; Lalande & Waxler 2016; Blixt et al. 2019; Carmichael et al. 2022). In addition to such sources of opportunity, a number of planned, ground-truth experimental campaigns have been conducted in recent years producing high quality, multiphenomenology data sets with extensive, high precision source information. The Sayarim Infrasound Calibration Experiments were conducted in 2009 and 2011 and included three chemical explosions with Trinitrotoluene (TNT) equivalent yields of 7.4–96 tons, producing delectable signals more than 1000 km from the source (Bonner et al. 2013a; Fee et al. 2013). The Humming Roadrunner experiment conducted in the summer of 2012 consisted of six chemical explosions with yields ranging from 9 to 45 tons equivalent TNT that were captured on a dense local network of sensors as well as 14 regionally deployed infrasound stations (Kim & Rodgers 2017; Blom et al. 2018; Green et al. 2018; Blom & Waxler 2021). Other experimental campaigns in the Humming/Humble series have been leveraged in studying seismoacoustic signals from explosive sources in various emplacement conditions (Bonner et al. 2013b; Pasyanos & Kim 2019; Pyle & Walter 2022). Following Phase I of the Source Physics Experiment (SPE) (Snelson et al. 2013), the Forensics Surface Experiment (FSE) was conducted in the fall of 2016 and included four chemical explosions with yields between 90 kg and 1 ton equivalent TNT (Kim et al. 2017; Blom 2019, 2020). The FSE leveraged the instrumentation deployed for the SPE Phase I and provides a useful supplement to the series of below-ground explosions conducted as part of that campaign. These and similar controlled source experiments provide useful insights into infrasonic source and propagation physics and enable evaluation of capabilities for detection, localization, and characterization.

The discussion here is organized as follows. An overview of the recently conducted Large Surface Explosion Coupling Experiment (LSECE) is provided highlighting regional infrasonic observations from the two surface explosions. Several of the observations are discussed in detail and propagation modelling is applied to attempt to elucidate the characteristics of some of the observed infrasonic signals. General propagation effects to regional distances are considered using atmospheric data corresponding to the two event times via a combination of ray tracing and PE modelling methods with flat ground and realistic terrain to quantify the impact of terrain. Propagation towards several specific observing stations is considered to further investigate the combined influence of realistic terrain and atmospheric variability on infrasound propagation.

2 THE LSECE

Two conventional surface explosions were conducted in the fall of 2020 as part of the LSECE. The yield of each explosion was 992 kg TNT equivalent. The two explosions were conducted at 37.1149° N, −116.0691° E approximately 33 metres from surface ground zero of the SPE Phase II Dry Alluvium Geology explosion series at the Nevada National Security Site (NNSS; Snelson et al. 2013). The LSECE explosions were conducted on 2020 October 27 and 29, at 06:37 and 15:35 local PDT time (13:37 and 22:35 UTC, respectively) in an effort to quantify the influence of the dynamics of the atmospheric boundary layer on the propagation of blastwaves and infrasonic signals from surface explosions. The early morning event, named Artemis, aimed to capture propagation in the near-ground temperature inversion and wind fields associated with the nocturnal boundary layer, while the afternoon event, named Apollo, was conducted in the more turbulent atmospheric boundary layer produced by mid-day heating of the ground surface (Garratt 1992). Acoustic propagation in the nocturnal boundary layer has been previously studied for audible frequencies (Wilson et al. 2003; Waxler et al. 2006; Talmadge et al. 2008; Blom & Waxler 2012); however, propagation of blastwaves and infrasonic frequencies were not been included in such analyses.

2.1 Regional network

Regional infrasound observations of the LSECE explosions were made on a combination of temporary, experiment-related station deployments as well as permanent stations. In total, eight regional stations observed the LSECE explosions at distances between 140 and 735 km, covering azimuths from northeast to south as shown in Fig. 1. Stations in Pine Spring, Butcher Ranch and North Oquirrh Mountains, Utah (PSU, BRP and NOQ) are operated by the University of Utah (UU) as part of their seismoacoustic network while the I57US station in southern California is operated by the CTBTO as part of the IMS. Temporary stations in Elgin and Carp, Nevada (ELG and CRP) as well as St George, Utah (STG) were deployed by Los Alamos National Laboratory specifically to observe the LSECE and a temporary station in Red Hill, New Mexico (RHL) was deployed by Sandia National Laboratories (Dannemann Dugick & Bowman 2022). The sensor array geometries for all of these stations are summarized in Appendix  A.

Infrasonic propagation is strongly influenced by the speed and directionality of the winds at the tropopause (8–12 km altitude) as well as those near the stratopause (40–60 km altitude). The dominant tropospheric wind structure, frequently termed the jet stream, is typically oriented eastward with varying north- or southward deviations in the western US. Large-scale stratospheric wind structures associated with the circumpolar vortex are dominantly eastward in the northern hemisphere during the late fall and winter, producing an infrasonic waveguide for downwind propagation that is known to have a strong impact on infrasonic signals (Waxler et al. 2015). In cases where tropospheric winds are not strong enough to produce a waveguide, upward refraction of energy due to the negative temperature gradient in the lower atmosphere is expected to produce a shadow-zone extending from a few 10’s of km from the source out to the edge of the stratospheric arrival range at approximately 180–200 km. For the source location of the LSECE events, the ELG and CRP stations are within this expected shadow-zone region, while STG and PSU are within the expected direct stratospheric ensonification region. Previous observations of similarly sized surface explosions included tropospheric as well as direct stratospheric arrivals at distances on the order of 200 km (Blom 2019); however, it’s unclear from that analysis how much further downrange signals are observable (e.g. at NOQ, BRP and RHL).

Beamforming analysis has been applied to the various infrasound stations shown in Fig. 1 using a standard Bartlett beam, analysis windows 10 s in duration with 50 per cent overlap, and a frequency band from 0.5 to 5.0 Hz (Krim & Viberg 1996). Arrival signals were then identified manually by an analyst resulting in the detection information summarized in Table 1. Each of the events was detected on seven of the eigth regional infrasound stations shown in Fig. 1. No signal consistent with the Artemis event was detected at RHL, and there was no signal at I57US that would be consistent with Apollo. In the table, the detection time and various parameters are identified from the window with peak Fisher statistic (F-stat; Arrowsmith et al. 2008, 2009); though, such parameters are found to vary significantly within the detection window as noted in the subsequent discussions.

2.2 Tropospheric propagation to the south

The beamforming analysis results for I57US are shown in Fig. 2, where the lower panels show the trace velocity and back azimuth parameters of the optimal beam with darker colours denoting larger F-stat values and the upper panels show the optimal beam waveform. This best beam is computed via a delay-and-sum technique using the parameters maximizing the F-stat in each 10-s analysis window with tapering envelopes that sum to unity to smooth between the overlapping windows. The results for Artemis and Apollo are shown in blue and red, respectively, and the dashed line in the back azimuth panel shows the bearing to the LSECE source location. A signal from Artemis can be identified on I57US with a relatively fast celerity on the order of 345 m s⁻¹ and trace velocities close to the expected near-ground sound speed implying a shallow inclination angle for the arriving signal. These parameters are typical of a tropospheric arrival; though, the large stand-off distance of I57US (nearly 400 km south of the LSECE source location) makes such an observations relatively surprising. A later signal is identified with celerity 290–300 m s⁻¹ and rapidly rising trace velocity; though, the back azimuth of this signals is found to be inconsistent with the LSECE bearing. Similarly, a transient signal is observed within the Apollo analysis window with celerity on the order of 255 m s⁻¹ but also at a bearing inconsistent with the LSECE location so that no signal is identified from the Apollo event at I57US.

2.3 Stratospheric propagation to the east

Beamforming results for STG, RHL and the various UU stations are summarized in Figs 3–5, respectively. Detections at these eastward stations are found to have celerities ranging from 285 to 310 m s⁻¹ with additional arrivals at the PSU and BRP stations with celerities on the order of 260–270 m s⁻¹. Arrivals at PSU and STG exhibit a decreasing trace velocity with time expected for direct stratospheric arrivals with a steeply arriving “fast” stratospheric arrival followed by a shallower angled “slow” phase forming the familiar stratospheric pair (Waxler et al. 2015). This is particularly evident in the data from the STG station as shown in Fig. 3. The Apollo event arrivals exhibits a markedly steeper arrival phase with celerity on the order of 305–310 m s⁻¹ and trace velocity (also termed apparent velocity) above 400 m s⁻¹ followed by a shallower, high amplitude phase between 300 and 305 m s⁻¹ celerity and trace velocity on the order of 370 m s⁻¹. The Artemis arrival exhibits similar behavior with decreasing trace velocity later in the wavetrain; however, the amplitude is lower and the duration is notably longer than the Apollo event. The trace velocities for the Artemis arrival cover a larger range starting above 440 m s⁻¹ and extending down to 340 m s⁻¹. For a ground sound-speed on the order of 340 m s⁻¹, a trace velocity of 440 m s⁻¹ corresponds to an inclination angle of nearly 40° so that this initial arrival energy impinges on the array very steeply. The overall differences in these two results and the relatively high trace velocity of the Apollo slow stratospheric phase are possibly due in part to the difference in ambient atmospheric conditions at the times of Artemis (early morning) and Apollo (afternoon) resulting in a faster ambient acoustic speed for Apollo.

While the STG station is the nearest to observe a stratospheric arrival from the LSECE, the RHL station detected several phases that could be contributed to the Apollo event with celerities of 335, 305 and 295 m/s as shown in Fig. 4. The earliest arrival with celerity of 335 m s⁻¹ exhibits a back azimuth deviation of more than 15 degrees from the LSECE source bearing, and it’s unclear if this particular phase is from the Apollo event due to the overly fast celerity and the lack of similar tropospheric phases on other arrays to the east for Apollo; however, the later two arrivals at 305 and 295 m s⁻¹ celerity are consistent with stratospheric propagation and similar to the observation at STG and the various UU stations (see subsequent discussion). At more than 700 km from the LSECE source location, the stratospheric pair has undergone multiple ground reflections and become more dispersed due to propagation effects. These later phases exhibit back azimuths within 8° of the LSECE bearing more consistent with typical cross-wind induced biases and celerities consistent with the stratospheric phases observed on other regional stations to the east so that these two arrival phases can be more justifiably attributed to the Apollo event.

The three UU stations to the northeast are found to detect similar stratospheric arrivals with celerities on the order of 290–310 m s⁻¹ at all locations as shown in Fig. 5. Unfortunately, only two of the microbarographs at NOQ were recording data for the Artemis event so that beamforming analysis cannot be completed; however, comparison of the two over-pressure records (shown in light- and dark-blue in the top centre panel of the figure) shows coherent arrivals within this stratospheric celerity range consistent with observations from Apollo. At PSU, stratospheric arrivals similar to those at STG are identified; though, there is less difference in the signal durations at this location and the wavetrain separates into two more clearly resolved contributions in the Artemis analysis. Further downrange at NOQ and BRP, multiple distinct arrival phases are observed with celerities between 290 m s⁻¹ and 310 m s⁻¹ celerity. Back azimuth deviations at these locations are minimal with direction of arrival information highly consistent with the known source bearing. Also notable in the analysis for PSU and BRP are late arriving phases for Artemis with celerities of 260–270 m s⁻¹. At PSU, these are lower amplitude but highly coherent as evident by the darker red back azimuth and trace velocity values. A likely explanation for these delayed phases can be identified by analysis of the stations in the stratospheric shadow zone.

2.4 Observations in the stratospheric shadow zone

As mentioned above, upward refraction of acoustic energy in the lower atmosphere leads to a shadow zone that extends between the outer edge of the source region and near-edge of the stratospheric arrival zone when a tropospheric waveguide is not present. The stations in Carp and Elgin (CRP and ELG) are 140 km east of the LSECE source location and expected to be within this shadow zone; therefore, they are not expected to detect signals from the LSECE explosions. Despite this, signals from the LSECE events are very clearly detected on the two stations as shown in Fig. 6. At both stations, relatively high amplitude signals are identified with celerities of 270–285 m s⁻¹ and back azimuths oriented directly towards the LSECE source location. The Apollo event arrivals are slightly earlier and longer duration compared with those from Artemis; however, in all cases, the trace velocity increases later in the wavetrain consistent with previous observations of infrasonic arrivals produced by scattering and partial reflection from fine scale structure in the middle atmosphere (Kulichkov et al. 2010; Ostashev et al. 2012; Green et al. 2018; Blixt et al. 2019).

The later arriving phases from Artemis at PSU and BRP in the left and right columns of Fig. 5 have celerities similar to those observed at ELG and CRP and similarly exhibit increasing trace velocities later in the wavetrain. There is no late arriving phase for Apollo at BRP and the late arriving phase at PSU extends from 285 to 290 m s⁻¹ celerity while exhibiting a reversed trend with high trace velocity during the early portion of the wavetrain. It is likely that the late arriving energy from Artemis at PSU and BRP are multiground-reflection paths of partially reflected energy following similar propagation paths to those observed at CRP and ELG. The late arrival form Apollo at PSU may be due to a similar mechanism; though, it us unclear why the trace velocities decrease later in the wavetrain rather than increase so that this arrival might simply be a later arriving stratospheric phase. The lack of such late arriving phases at STG and NOQ imply that shadow zones exist for these partial reflection paths likely due to the limited altitudes at which scattering and partial reflection occurs.

3 PROPAGATION SIMULATIONS

The LSECE explosions were conducted 2 d apart and produced notably unique observations at a number of regional locations that can be explained by considering the temporal variations in the atmospheric state. Differences in the atmospheric structure at the time of each event result in unique propagation characteristics. Ground-to-Space (G2S) atmospheric specifications for the time period of the LSECE at the source location are displayed in Fig. 7 using a colour map to show the changes in the atmosphere from the morning of October, 27th (Artemis, blue) to the afternoon of the 29th (Apollo, red). The G2S specifications combine large amounts of empirical data in the lower- and middle atmosphere with climatology models for the upper atmosphere (Drob et al. 2003). These climatology models produce the 24-hr cyclic structure visible in the upper atmospheric temperature and wind structure in the figure. It is immediately evident from the tropospheric meridional winds shown in the right-hand panel of the figure that a strong jet stream wind towards the south was present during the Artemis event but dissipated by the the time of the Apollo explosion. This is in agreement with the I57US observations of a tropospheric arrival for Artemis, but no detection for Apollo. The middle atmosphere zonal winds were dominantly eastward as expected for late fall and winter in the northern hemisphere; though, some variability in the structure of the zonal winds in the middle atmosphere is evident. An inflection is present in the zonal winds at 40–45 km altitude for the Artemis event below the zonal wind maximum near 60 km altitude. This zonal wind inflection is no longer present at the time of the Apollo explosion.

The two LSECE explosions were conducted at different times of day with Artemis during the early morning and Apollo in the more turbulent afternoon atmosphere. These timings were intended to allow researchers to study the impact of the atmospheric boundary layer on propagation of the blastwave and infrasonic signal. This region of the atmosphere is limited to altitudes of 100’s of metres to a few kilometres depending on cloud cover, humidity and various other factors (Garratt 1992). Such atmospheric variations are known to have a significant impact on local distance propagation, and the impact of such conditions during the transition between blastwave and acoustic regimes is of interest. Though, regional infrasonic propagation extends into the middle- and upper atmosphere so that it is unclear how dependent such propagation paths are to this near-ground atmospheric structure or if any early morning and mid-afternoon atmospheric differences exist in the troposphere and stratosphere.

3.1 Regional propagation predictions

Regional propagation predictions have been computed using G2S atmospheric specifications corresponding to the times of the two LSECE events via a combination of ray tracing analysis as well as finite frequency analysis using a Padé PE (Blom 2020; Waxler et al. 2022). Ray tracing simulations utilized a range-dependent grid of atmospheric specifications with 2° resolution in latitude and longitude; though, the impacts of horizontal variations are found to be minimal for the propagation distances relevant to the LSECE. Because of this, the PE simulations were completed using an N × 2D approach assuming a stratified model neglecting any range-dependence in the atmosphere within the analysis domain. Propagation predictions were completed using both a flat-ground assumption and realistic terrain conditions defined by the ETOPO1 model (Amante & Eakins 2009; NOAA NGDC, 2009). Higher resolution topography models are available; however, the ETOPO1 model 1 arcminute resolution is sufficient for modelling infrasonic wavelengths and has been utilized in similar recent analyses (Blom 2020).

The ray tracing simulation results are shown in Fig. 8 where the Artemis and Apollo event times correspond to the upper and lower rows, respectively. The left and right columns show results for flat ground and realistic terrain, respectively. The points in the various panels denote the locations at which ray paths impinge on the ground surface and the color map shows the arrival celerity (horizontal group velocity) at that point along the ray paths. The various waveguides are straightforward to infer from the celerity values with overly fast celerities associated with tropospheric propagation (faster then 320 m s⁻¹, red), moderate celerity values with stratospheric ducting (280–310 m s⁻¹, yellow/green) and slower celerities likely due to refraction from the thermosphere (below 280 m s⁻¹, blue). It should be noted that while thermo-viscous losses can be computed along individual ray paths (Sutherland & Bass 2004), the results in the figure show the celerity along the various propagation paths and have not been filtered by such losses. The relatively small yields of the LSECE explosions are unlikely to produce sufficient energy to result in thermospheric arrivals so that any energy propagation along thermospheric paths is likely not detectable (Blom & Waxler 2021); therefore, only the tropospheric and stratospheric arrival predictions in these results are likely to compare well with observations.

The large number of ground reflections encountered for tropospheric propagation paths over realistic terrain leads to scattering of energy out of the waveguide. Because of this, a flat ground analysis is likely to overestimate the amount of energy contained in the waveguide as found in previous analysis (Blom 2020). The scattering of energy out of the waveguide is dependent on the terrain features as well as the strength of the waveguide. Stronger downward refraction is likely to contain a larger portion of the energy that scatters from the terrain gradients. This is evident for propagation slightly east of south in the upper-right panel of Fig. 8 where several narrow bands of highly efficient propagation are found. Several notable terrain features are located in the southeastern region of Nevada (visible in Fig. 1), including the Sheep Mountain Range southwest of CRP and Red Rock Canyon south-southeast of LSECE. Detailed analysis is needed to understand the impact of such individual terrain features on propagation as well as the cumulative influence that terrain has on propagation of infrasound through this southward tropospheric waveguide.

Propagation eastward in the stratospheric waveguide at the time of the Artemis event is found to exhibit multiple arrival bands due to the wind speed inflection at 40–45 km altitude identified in Fig. 7 for this event. The first band of arrivals is 10s of km east of CRP and ELG and the second covers the STG and PSU stations. The second of these has slightly faster celerity (yellow/orange compared with the green/yellow colours of the inner band of arrivals) due to the higher altitude zonal wind maximum being notably faster resulting in higher celerities despite the increased propagation path length. Such propagation effects are often termed “anomalous fast arrivals” due to the manner by which the increased ray path length is overcome by the faster propagation velocity resulting in signals with overly high celerities (Kulichkov et al. 2004; Evers & Haak 2007; Blom & Waxler 2012). These two distinct stratospheric arrival bands overlap further downrange with the two-reflection higher altitude paths overlapping with the three-reflection lower altitude paths in the vicinity of NOQ. At the time of Apollo, the inflection structure in the zonal winds is no longer present and a single, wider stratospheric ensonification band is predicted as shown in the lower panels of the figure that is similar to expected stratospheric propagation (Waxler et al. 2015). These temporal variations in stratospheric wind structure produce shifts in the spatial ensonification that can have a significant impact on downrange observations. For example, BRP is predicted to be between stratospheric arrival bands during Artemis but centred within such a band at the time of the Apollo event. This provides some explanation for the multiphase nature of the Artemis observations at BRP and the higher amplitude signal observed from Apollo.

The impact of including realistic terrain for the stratospheric waveguide is evident in the right column of the figure and most notable in the multireflection arrival bands in the eastern portion of the domain where localized regions of high ray density can be identified. Within each band of arrivals, interaction with the along-direction terrain gradients scatters energy out of the stratospheric waveguide and cross-direction gradients deflect energy out of the initial range-altitude plane (Blom 2020). The resulting regions of high ray density correspond to locations expected to observe higher amplitude infrasonic arrivals due to the concentration of energy there. Coupling this focusing and de-focusing due to terrain interactions with the general shifts in propagation due to temporal changes in the atmospheric structure results in highly variable propagation downrange. At increased distances, multiple ground reflections have occurred and temporal variations have shifted which terrain features are encountered so that regions of higher density arrivals are attributed to the combination of the two effects.

PE simulation results for the LSECE events are shown in Fig. 9 using the same column and row format as Fig. 8. The colour map in the figure shows transmission loss relative to 1 km from the source at a frequency of 2.0 Hz instead of the celerity values shown in Fig. 8. This frequency was chosen because, while analysis of the LSECE events covered the frequency band from 0.5 to 5 Hz, the dominant energy of the signal across the network of stations is found to be on the order of 1–2 Hz. The PE analysis utilized an N × 2D method that simulates propagation in a series of discrete range-altitude planes and merges the results. The individual simulations are evident in the far-field of the domain where radial lines of transmission loss can be seen emanating from the source location. Also, while the 3D ray tracing methods utilized a spherical coordinates geometry (Blom 2019), the PE implementation uses a Cartesian range-altitude geometry that does not include the full geometry of the propagation domain leading to some differences in predicted propagation effects.

Results are generally similar to the 3D ray tracing simulations; though, several notable finite-frequency effects are evident and limitations of the N × 2D method are found to have some impact on the predictions compared with fully 3D ray tracing. The stratospheric slow arrival ensonification has a sharp edge in the geometric limit that is known to be inaccurate but can be compensated for via finite frequency analysis (Waxler et al. 2015). This is evident in the multiheight stratospheric waveguide predicted for the Artemis event in the upper row of the figure where the increased spatial extent of the slow arrival phase leads to overlap between the two stratospheric arrival bands in the vicinity of the STG array. This prediction explains the multiple phases and large range of celerities observed on the STG station from Artemis. Fast and slow phases from multiple stratospheric refraction heights are possibly present in the observed wavetrain in the uppermost panel of Fig. 3.

The interaction of energy with realistic terrain in the PE simulation is limited to the along-direction gradients due to the N × 2D method that models propagation through a series of discrete, independent range-altitude planes. The scattering of energy out of the southward tropospheric waveguide is generally consistent with ray tracing predictions; though, the low scattering paths to the south are less evident in the PE simulation. This is potentially due to the lack of cross-direction effects for energy propagating between the Sheep Mountain Range and Red Rock Canyon mentioned above. Propagation downrange in the stratospheric waveguide predicts regions of higher amplitude similar to the high density ray arrival regions; though, the extent and locations of some such regions differ in some cases between the methods due to the combination of finite frequency effects in the PE simulation and 3D effects in the ray tracing (both due to cross winds and cross-direction terrain gradients). For example, the regions of increased ray density and lower attenuation in the vicinity of NOQ and BRP when including terrain in the simulations have some inconsistencies with a notable region without ray path arrivals to the west of BRP that the PE analysis predicts to have high amplitude signals. This is likely due to the cross-direction scattering included in the ray tracing but not in the PE as other portions of the stratospheric band in the region have higher density ray path arrivals that are in agreement with the PE predictions.

3.2 Station-specific propagation predictions

The general predictions discussed here provide qualitative explanations for a number of the LSECE regional infrasonic observations. The tropospheric arrival at I57US is expected given the strong southward winds near the tropopause in the G2S specification for Artemis and the lack of a detection for Apollo can be directly attributed to the change in the tropospheric winds between the two explosions. Similarly, the multiheight stratospheric waveguide during Artemis compared with the single zonal wind maximum in the G2S for Apollo provides some insight into the difference in stratospheric observations at STG between the two events. Lastly, the focusing de-focusing of energy due to a combination of temporal changes in the atmosphere and terrain interactions provides some insight into the observations observations in the far field.

Propagation simulation results for Artemis towards the I57US station are shown in Fig. 10 where the upper-left panel shows the adiabatic and effective sound speeds (dashed and solid lines, respectively). The effective sound speed is defined as the sum of the ambient sound speed and the winds along the direction of propagation, |$c_\text{eff} = c_0 + \hat{n}_\varphi \cdot \vec{v}_0$|⁠, and provides a useful means of simplifying the acoustic wave equation to make propagation modelling less numerically intensive (Godan 2002). In the upper- and middle-right panels, the colour map shows the PE prediction transmission loss, and the black curves denote the propagation paths computed using a 2D method with the effective sound speed approximation to ensure the PE and ray results coincide for comparison. The upper panel shows results using the flat ground assumption while the middle panels shows the impact of realistic terrain on propagation within this azimuthal plane. In the lower-right panel, the transmission loss along the ground surface is plotted for the flat ground (grey) and realistic terrain (black) simulations. The magenta triangles and vertical dashed line denote the location of the I57US station along this propagation azimuth.

The strong meridional winds in the troposphere produce a waveguide in the lowest 5 km of the atmosphere during the Artemis event but dissipate by the time of the Apollo event. Propagation predictions for the later event find no detectable signal expected for the 2nd LSECE explosion at I57US in agreement with the observations in Fig. 2. Predicted propagation effects at I57US for the Apollo event as shown in Fig. 11 using the same panel layout as Fig. 10 and the dissipation of the tropospheric meridional winds is found to have a notable impact on the propagation to the south with severe transmission loss extending below the lower limit of the plot. Ray paths are predicted with refraction altitudes in the thermosphere; however, as noted above, thermoviscous losses for the relatively high infrasonic frequency of 2 Hz are severe in the upper atmosphere and amplitudes are too low to produce nonlinear effects that would shift energy to lower frequencies (Blom & Waxler 2021).

Unlike tropospheric propagation to the east of the NNSS investigated previously (Blom 2020), the scattering of energy out of the low-altitude waveguide during Artemis is minimal within the first 400 km. This is likely due to a combination of a more robust waveguide (i.e. a larger ratio of the maximum sound speed at the upper limit of the waveguide to that near the ground surface) and smoother terrain with less severe gradients that produce smaller changes in reflection angles. The I57US station is located approximately 390 km south of the LSECE source location and minimal differences are predicted in the flat-ground and realistic terrain signal amplitude at 2 Hz. Although the overall transmission loss at this location is found to be minimally impacted by the terrain, other signal characteristics (e.g. signal duration, celerity and direction-of-arrival) are likely to be more notably impacted by the terrain interactions. The observed signal from Artemis at I57US in Fig. 2 shows a slight positive azimuth deviation during the later portion of the wavetrain with signal shifting east of the ground truth source location, and there are notable fluctuations in the trace velocity throughout the duration of the arrival. More detailed analysis of the propagation in the southward waveguide could be completed via a high-density 3D ray tracing simulation along with a broadband waveform prediction using the PE method; however, such analysis is beyond this initial investigation of regional infrasound from the LSECE.

Propagation predictions towards the STG station during the Artemis and Apollo events are shown in the upper and lower potions of Fig. 12, respectively, using the same panel layout as in Fig. 10. As noted in the previous section, the inflection structure in the zonal winds just above 40 km altitude during the Artemis event produces two sets of stratospheric returns. The region below the inflection produces a pair of stratospheric propagation paths, while a second set of ray paths are refracted from near the overall effective sound speed maximum above the inflection and just below 60 km. These distinct contributions are visible in the ray paths overlaying the PE transmission loss colour map with the higher altitude arrivals impinging on the ground surface near the STG station location approximately 220 km from the source and the lower altitude returns starting near a range of 160 km. Minimal differences in the direct stratospheric arrivals at 160 and 250 km are evident in the at-ground transmission loss results in the lower panel of the figure; however, further downrange it is evident that the initial interaction with the ground surface at the direct path reflections influences the arrival structure further downrange at the single-reflection stratospheric arrival (320 km and beyond).

Similar propagation effects are identified for the Apollo event at the STG station in the lower portion of the figure. Once again the onset of the directly ensonified stratospheric arrival zone is nearly unchanged; however, the outer portion of this region exhibits some terrain-induced variability with predicted decreased signal amplitude near 190 and 210 km. These variations become notably more pronounced downrange with a significant decrease in transmission loss in the 370–400 km range, followed by an enhancement of signal amplitude produced by the terrain interactions 410–430 km from the source. Beyond this, there is an enhanced shadow zone from 440 to 470 km before the 2-reflection stratospheric arrivals emerge at a range of approximately 470 km.

The focusing and de-focusing of energy due to terrain interactions becomes more severe with range due to multiple ground reflection. Combining this with the uncertainty in the atmosphere leads to highly variable regions of increased and decreased signal amplitude downrange. The resulting scatter in transmission loss downrange is likely much larger than that predicted using the same set of possible atmospheric states and assuming flat ground. Thus, improvements to yield estimation such as that by Blom et al. (2018) could be gained by using propagation statistics that include terrain to properly quantify confidence in results. Similarly, the interaction of geometric propagation paths with terrain results in an increase spread of travel time and back azimuth values, as discussed by Blom (2020), so that localization analysis would require similar models. Such statistical propagation models are beyond the scope of this discussion but are an ongoing area of research that is informed by the work presented here.

Propagation effects towards the RHL station are shown in Fig. 13 once again using the same panel layout as Fig. 10. At the time of the Artemis event, terrain interactions produce notable decreases in the expected signal amplitude in the outer edge of the stratospheric ensonification band that is relatively constant with range (transmission loss becomes more severe at distances of 280–350, 400–450, 600–700 and 800–850 km). Few regions exhibit focusing that produces amplitude exceeding the flat ground predictions; though, a number of locations are expected to have focusing that increases amplitude back to approximately the same value as the flat ground simulation results. In comparison, propagation during Apollo is expected to exhibit both focusing and de-focusing induced by the terrain as shown in the lower portion of the figure. Focusing of energy around 190 km becomes more severe when terrain is included and this focusing becomes enhanced downrange with multiple localized high amplitude regions expected within each stratospheric arrival band (e.g. around 390 and 410 km, 580 and 610 km).

For the specific G2S atmospheric information at the time of the Apollo event, a de-focusing of energy at the RHL location is expected, but 10–20 km beyond the station, location is a high amplitude focused region. There are known inaccuracies in G2S and similar atmospheric specifications so that uncertainty analysis is needed to accurately compare predicted propagation effects with observations. A full atmospheric updating analysis considering how perturbations to the zonal wind impact the predicted arrival at RHL would be needed to produce agreement between the observed and predicted propagation effects. Such perturbations would likely be within the expected 10–20 m s⁻¹ uncertainty for middle- and upper atmosphere winds (Drob et al. 2010); however, once again, such analysis is beyond this current discussion and will be included in ongoing research.

An additional contributing factor to the non-detection and detection of the Artemis and Apollo events at RHL, respectively, can be identified from the relatively slow propagation velocity for infrasonic waves and changes in the atmospheric state between the origin and detection times. While the origin time for the Artemis event is well before sunrise at 06:37 AM local MDT, it takes more than 40 min for the energy to propagate to the RHL station. The energy arrives there just before 07:20 AM local MDT, less than 15 min before sunrise (07:33 MDT on 2020 October 29 in Red Hill, NM), in a notably more energetic atmosphere than an hour earlier. Similarly, by the time the Apollo energy reached the RHL station, it was nearly 16:20 local time. The heat of the day had passed resulting in an atmosphere with decreasing levels of turbulence and lower wind noise. This difference in the ambient atmospheric state is evident in Fig. 4 where the mean background pressure fluctuations during the Artemis analysis window are notably higher than during the Apollo analysis window.

3.3 Predictions of partial reflection arrivals

Partial reflection of infrasonic signals from wind shear and similar fine-scale structure in the atmosphere has been observed and modelled in a number of previous studies (Kulichkov et al. 2010; Ostashev et al. 2012; Green et al. 2018; Blixt et al. 2019). The ray tracing methods utilized in this analysis do not include a partial reflection method; however, the upward and downward propagating energy from the reflection can be assumed to be nearly symmetric. Therefore, some insights can be gained from only the upward going modelling. The upward propagating ray paths towards the CRP station for Artemis and Apollo are shown in Fig. 14 from the source location out to the midpoint between source and receiver at approximately 70 km. The celerity along each ray path is shown in the colour map. The symmetry of the reflected propagation path leads to a doubling of both the propagation distance and propagation time along the ray path so that the celerity at the midpoint can be used as a reasonable estimate of the celerity at the end of the reflected path (there are likely small corrections due to cross wind deflection and similar effects).

The right-hand panel of the figure shows the celerity at the midpoint between the LSECE source location and the CRP and ELG stations using the G2S specifications for the two events. A notable shift to faster celerities is found for the Apollo event at both stations in agreement with the observations in Fig. 6. Comparison of the celerities of the observed signals at CRP and ELG in that figure leads to an estimate for the partial reflection altitude range of 30–45 km (denoted by the grey band of altitudes in the figure here). Interestingly, this analysis implies that although the arrivals at CRP and ELG differ in celerity and duration between Artemis and Apollo; it is likely that the altitudes from which energy is partially reflected is the same for the two events.

Partial reflecting propagation paths are also likely explanations for the late arriving energy observed at PSU and BRP during the Artemis event as mentioned in the discussion of Fig 5. Such propagation paths are challenging to model in detail. The altitudes at which partial reflection occurs can vary along each portion and a fixed altitude at which to compute a reflection oversimplifies the propagation. An idealized model using a constant sound speed is presented in Appendix  B and shows that, to a leading order, the propagation time (and therefore the celerity) depends only on the mean of the various altitudes at which partial reflection occurs. A more detailed analysis using more accurate ray paths is needed to fully elucidate these downrange arrivals due to partial reflection, and such an effort is planned for continued analysis of the LSECE and similar events where such signals have been observed.

4 CONCLUSIONS

Regional infrasonic observations from a pair of 1-ton surface explosions conducted during the LSECE have been investigated across a combination of permanent and temporary infrasound stations at standoff distances of 140–735 km. Notable differences in propagation effects were identified despite the explosions being conducted just 2 d apart. Analysis of available atmospheric specifications from the G2S tool show notable atmospheric variability during the experiment in agreement with these observations. Both events produced regional infrasound to large standoff distances with a tropospheric infrasonic signal observed from the earlier event nearly 400 km south and stratospheric arrivals observed from the earlier event to distances of nearly 550 km and to more than 700 km for the second event.

Observed signals downwind in the middle atmosphere waveguide to the east included arrivals with typical stratospheric celerities from 290–310 m s⁻¹. Further, slower phases with celerities covering 265–280 m s⁻¹ and trace velocities that increased later in the wavetrain were observed on several stations. Such trace velocity trends imply partial reflection from fine-scale structure in the middle atmosphere and similar slow phases were observed at locations within the expected stratospheric shadow zone approximately 140 km east of the source. Such observations imply that the 265–280 m s⁻¹ celerity arrivals further downrange were likely multiground-reflection arrivals partially reflected from the lower stratosphere. In addition to stratospheric and partial reflection observations to the east, a tropospheric waveguide was present during the first explosion, resulting in an observation from the event several hundred kilometres to the south with notably faster celerity on the order of 345 m s⁻¹.

Propagation simulations utilizing a combination of ray tracing and PE algorithms have been completed using the G2S atmospheric information for the two events. Predictions are qualitatively in agreement with observed signals. As in all infrasonic propagation analysis, atmospheric uncertainty requires detailed perturbations to produce accurate predictions for detection parameters (e.g. arrival time, duration, back azimuth, trace velocity); however, analysis of predicted ensonification and general propagation effects shows qualitative agreement with observations. Notably, the jet stream winds near the tropopause were predicted to produce a strong southward infrasonic waveguide for the first LSECE event but dissipated by the time of the second. This is found to be in agreement with observations as no signals were observed to the south for the second event. Further, a localized wind structure in the stratosphere produced an inflection in the effective sound speed near 40 km altitude that enhanced multipathing. This atmospheric structure was predicted to produce long duration signals during the earlier event but dissipated by the time of the second event resulting in shorter duration and higher amplitude signals that are more typical of stratospheric propagation.

In addition to the impact of temporal variations in the atmospheric structure, interactions with terrain are found to have a notable impact on propagation. Such interactions are particularly notable for paths that interact with the ground surface repeatedly (e.g. tropospheric propagation to the south, stratospheric propagation in the far-field following multiple ground reflections). Terrain in southeastern Nevada is predicted to produce channels of higher efficiency propagation through which energy can be focused; however, the geometry of these channels are found to differ in fully 3D ray tracing and N × 2D PE analysis due to the infinite frequency approximation of the first and limited range-azimuth plane geometry of the second. A 3D full waveform method is needed to produce a robust analysis of such propagation. Lastly, for propagation downrange in the stratospheric waveguide, focusing and de-focusing of energy due to interaction with terrain gradients is found to have a significant impact on detectability. More than 10 dB of difference in transmission loss predictions are found for flat ground versus realistic terrain simulations at some locations. Further, the interaction of atmospheric dynamics and uncertainty with this terrain induced focusing and de-focusing results in a significant amount of transmission loss uncertainty in the far-field. Regions of focused and de-focused infrasound may shift spatially or appear/disappear due to the changes in ensonification earlier along the propagation path. Such shifts are crucial to quantify when considering transmission loss statistics required for source characterization and yield estimation.

The multiphenomenological data set created during the LSECE is a useful resource for development and evaluation of source characterization and propagation models for a number of geophysical phenomenologies. The regional infrasonic observations summarized here provide useful data for evaluation of propagation modelling methods, including interaction with terrain, impacts of partial reflection and a number of other research topics needed to better understand regional infrasonic monitoring for a variety of applications. The analysis presented here provides a first-order analysis using newly developed propagation modelling capabilities, and additional analysis and evaluations leveraging this and similar planned, ground truth experimental campaign data sets is needed to continue to improve such capabilities.

ACKNOWLEDGEMENTS

We gratefully acknowledge the support of Dr. Richard Lewis and the Defense Threat Reduction Agency (DTRA) for funding the work presented here. The LSECE was conducted with support from DTRA, the National Nuclear Security Administration (NNSA), as well as Mission Support and Testing Services (MSTS) at the NNSS. This work was conducted by Los Alamos National Laboratory under award number 89233218CNA000001 with the U.S. government.

DATA AVAILABILITY

The regional infrasound data used in the analysis presented here as well as near-field overpressure and seismic data for these two explosions are available through Incorporated Research Institutions for Seismology (https://service.iris.edu/). Atmospheric specifications used in propagation simulations were obtained through the University of Mississippi National Center for Physical Acoustics (NCPA) G2S server (https://g2s.ncpa.olemiss.edu/). The array processing and ray tracing analysis conducted for this analysis utilized Los Alamos National Laboratory’s InfraPy and InfraGA software tools, respectively (both available at https://github.com/LANL-Seismoacoustics). The PE simulations utilized methods available in the NCPAprop software package (https://github.com/chetzer-ncpa/ncpaprop).

References

APPENDIX A: ARRAY GEOMETRIES

The various stations used in analysis of the LSECE events exhibited a range aperture and sensor counts as summarized in Fig. A1. As noted in Section 2.1, several of the NOQ station sensors exhibited poor data quality or missing data during the Apollo event so that analysis was limited to comparison of the two remaining channels.

APPENDIX B: CONSTANT SOUND SPEED ANALYSIS FOR PARTIAL-REFLECTION PATHS

At leading order, partially reflected propagation paths can be analysed by approximating the sound speed in the lower- and middle atmosphere as constant, |$c_0 \left( z \right) \approx \bar{c}_0$|⁠. For such an assumption, ray paths become straight lines and the propagation time along a path connecting a source and receiver separated by a horizontal distance r₀ for partial reflection at altitude z₀ can be written as,

The geometry of this propagation path is shown in Fig. A2. Solving this relation for the reflection altitude and replacing the travel time with celerity, |$\nu = \frac{r_0}{\tau }$|⁠, one finds,

Analysis of the available G2S specifications finds mean sound speed values for both Artemis and Apollo on the order of |$\bar{c}_0 = 302$| m s⁻¹ in the lower 40 km of the atmosphere. Combining this mean sound speed with the observed celerities in Fig. 6, one would estimate turning heights on the order of 25–35 km. This is an underestimate compared with the more robust analysis in Fig. 14 that identifies 30–45 km as likely altitudes for partial reflection; though, as a leading order estimate the result is not overly inaccurate.

Observations of the Artemis event at PSU and BRP include late arriving energy with increasing trace velocities later in the arrival phase consistent with partial reflection; however, the propagation distances from the LSECE source location to these two stations would require the propagation to partially reflect from structure in the atmosphere as well as from the ground surface. Some insight into such propagation can be gained using the leading order constant sound speed model. Consider the propagation geometry in Fig. A3 in which energy partially reflects at an altitude z₁, returns to the ground some distance r₁ from the source, reflects from the ground surface and partially reflects a second time at an altitude z₂ and finally returns to the ground surface at some distance r₀ = r₁ + r₂ where the receiver is located. The combined propagation time along the entire path can be written as,

In the limiting case of propagation over flat ground, the inclination angles of the upgoing legs of the two segment should be equal so that |$\frac{r_1}{z_1} = \frac{r_2}{z_2}$|⁠. Using this relation to replace z₂ and r₂ = r₀ − r₁ to replace r₂ in the above, one finds,

Defining the mean partial reflection altitude, |$\bar{z} = \frac{z_1 + z_2}{2}$|⁠, and further simplifying, one obtains,

For multiple ground reflections, generalization of this result leads to,

where n is the number of ground reflections occurring along the propagation path. Thus, at leading order, the propagation time for a partially reflected propagation path that undergoes multiple ground reflections to a receiver at r₀ is dependent only on the average altitude at which the various partial reflections occur. This preserves the trace velocity trend in that propagation paths with large mean reflection altitudes arriving later in the wavetrain and exhibiting steeper inclination angles that produce higher trace velocity values.