IntroductionFor the past 20 years, the ASCE has been rating the condition of the nation’s critical infrastructure and assigned the “D+” rating in 2017; wherein, the overall infrastructure is in poor to fair condition, mostly below current design standards, and near the end of their respective design life (ASCE 2017). Infrastructure in the continental United States often exceeds the design life due to budgetary constraints and logistical hurdles. Keeping this infrastructure healthy is in the purview of multiple local and federal agencies, including the USACE, whose civil works projects are responsible for 707 dams, more than 23,300 km of levees, 220 waterway locks, and more than 900 shallow- and deep-draft channels and harbors. Most of the dams and levees are aging and in constant need of rehabilitation and repair; more than half of the USACE dams are beyond their 50-year service life (USACE 2018; Chamberlayne 2015). The ASCE estimates that $248 billion is needed to rehabilitate the nation’s bridges, dams, and levees (ASCE 2017). Ignoring the financial requirement, it is not logistically possible to rehabilitate all of these structures at the same time. How then to prioritize the infrastructure that needs inspection, particularly for structures with critical global issues? How do the infrastructure owners know that the status of the infrastructure has gone from bad to worse, with catastrophe imminent?Traditional monitoring of structures is discrete in both space and time: limited numbers of engineers spend limited time investigating the health of critical infrastructure. This snapshot approach is robust in engineering but impractical for covering large numbers of structures in wide areas, much less continually monitoring each to proactively intervene before critical failures. To address the issue of discrete monitoring, the USACE Engineer Research and Development Center (ERDC) has developed a technique to perform tens to hundreds of square kilometers of wide-area surveillance of infrastructure systems in both rural and built environments in a persistent fashion, essentially creating a structural baseline condition health map of a large area. This map is accomplished by utilizing arrays of geophysical instruments (infrasound arrays) to monitor structural health through “listening” for changes in the fundamental, vibrational modes of the structure of interest.Fundamental, vibrational modes of motion for large structures, such as bridges and dams, are in the subaudible acoustic frequency band (infrasound). These structures are coupled to the fluid atmosphere; thus, these structural vibrations perturb the atmosphere and generate acoustic waves in the infrasound acoustic spectrum. The infrasound frequency range is traditionally defined as less than 20 Hz, which is lower than the range of human hearing of 20 Hz to 20,000 Hz (Campus and Christie 2010). One advantage of energy in this frequency regime is that it can propagate tens to thousands of kilometers from the source to receiver with minimal attenuation (Bass et al. 2006). Traditionally, the infrasound community has utilized infrasound arrays to monitor large energy explosions, such as to support the Comprehensive Nuclear-Test-Ban Treaty (CTBTO) international monitoring mission. As early as the 1970s, the geophysical community reported that large human-made structures, such as bridges (Donn et al. 1974; Kobayashi 1999), could generate infrasound. However, little research was conducted on the diagnostic possibilities of infrasound recorded near these structures until 2006, when the ERDC demonstrated nonline-of-sight infrasound monitoring of the fundamental vibrational modes of structures and how these modes could be associated with the global condition of significant infrastructure (McKenna et al. 2009b). These modes are predominantly defined by the physical dimensions of the key structural component vibrating for a specific mode, with shifts in this vibrational frequency indicating a global structural health change (Chopra 2012; Salawu 1997).Modal analysis is a technique used to study the dynamic response of an object or structure to vibrational excitation. One common method of determining the modal characteristics of large structures is to measure the structure’s response to small ambient excitations and known loadings in a process known as dynamic testing (Duron et al. 2005). This form of analysis has been used to determine the modes at which the structure naturally resonates based on mass and stiffness. The natural frequency of a system depends on the stiffness and the mass associated with the structure. The degradation in structures produces a reduction of natural frequencies, increased energy dissipation, and changes in the mode shapes (Morassi and Tonon 2008; Ren et al. 2005; Kim et al. 2003; Clement et al. 1998; Salawu 1997; Doebling et al. 1996).The modal analysis of civil infrastructure utilizes two main techniques, that is, input-output analysis and output-only analysis. Input-output analysis methods induce vibrations in a structure using mechanical means (Morassi and Tonon 2008; Clemente et al. 1998; Conte et al. 2008; Cunha and Caetano 2006; Olson 2005; Pietrzko et al. 1996). Controlled excitation of very large structures can be a challenging prospect, but the dynamic properties of infrastructure are still of interest. For bridges, wind and traffic from daily operations typically provide the ambient excitations necessary for output-only analysis (Ren et al. 2005; Conte et al. 2008; Cunha et al. 2013; Brownjohn et al. 2010; Caicedo et al. 2001). Ambient vibrations in dams are related to standard daily operations and can include wind, wave action, traffic (particularly if the dam also serves as a roadway), and flow over spillways or through outlet pipes. These forcings are typically small and, as such, generate small random vibrations within the dam-reservoir-foundation system.The low amplitude infrastructure response accelerations, often on the order of μgs, have rendered them difficult to detect and properly analyze prior to improvements in sensors and computational processing power. Another historical drawback to the ambient vibration technique has been the lack of a measurable forcing with which to compute the frequency response function (FRF). However, recently developed analytical tools exist to provide very close approximations of FRFs using only response data (Caicedo et al. 2001). As a result, the ambient vibration technique of determining modal characteristics is becoming more common, particularly in large infrastructures, such as dams and bridges (Schwartz and Richardson 2001). Current engineering monitoring methods utilize on-structure or near structure instrumentation (Hunt 2009; Prendergast and Gavin 2014). The move to modal characterization utilizing ambient excitation provides challenges with instrumentation sensitivity and logistical issues of instruments colocated with structures during damaging events (Briaud et al. 2011).Although target structures of interest likely generate information in the frequency bands higher than infrasound (higher than 20 Hz), the higher-mode signatures are attenuated lower than the threshold of detection as the acoustic energy dissipates within a few kilometers of the structure, limiting the utility to observe higher frequency phenomena over the desired large region. The unique capacity of infrasound to propagate long distances and obviate the need to have direct contact with the structure makes it valuable. In fact, with an energetic enough structural source, infrasound can propagate tens to hundreds of kilometers, although the array processing needed to tease the modal signals from the background noise is complicated and currently time-intensive, as subsequently detailed. Combining the detection range expansion with the ability to detect the signals through ambient excitation alone shifts the structural monitoring paradigm from inspections at discrete points in time that might not capture the damage inflicted through seasonal cycles, such as scour, and on-structure instrumentation that can be damaged during severe weather events, allowing infrastructure owners to assess multiple structures during all weather conditions.Goal and ObjectiveThis paper details a collection of case studies blending modal analysis and persistent, remote geophysical infrasound monitoring of structures to create a continuous, noncontact infrastructure health assessment. The techniques detailed in this paper operate under the principle that fundamental modes of these structures can be determined through techniques based on geophysical array processing rather than traditional engineering analysis of on-structure instrumentation. For research validation purposes, conversion from infrasound geophysical data to structural analysis can be accomplished through numerical structural modal analysis coupled with signal processing techniques but is not required for pattern of life analysis of structures.This paper presents four major aspects of infrastructure health assessments: (1) establishment of methods to observe, detect, and analyze structural infrasound data; that is, a structural infrasound monitoring methodology; (2) application of structural infrasound monitoring for water control infrastructure systems; (3) application of structural infrasound monitoring for transportation infrastructure systems; and (4) pattern of life analysis of riverine infrastructure systems.MethodologyTo understand the basic infrasound detection methodologies, this section describes the purpose of these infrasound arrays, the principles of array design, the impacts of real-world environments on infrasound propagation, guidelines for array installation, and a summary of signal processing methods for targeting infrastructure.In the general sense, infrasound arrays are a suite of low-frequency microbarographs situated to meet one or more objectives, such as the detection of low-energy events or the localization of subaudible acoustic sources. Both of these objectives are critical to properly detecting, classifying, and locating structural sources, particularly in complex urbanscapes. The advantages inherent in using arrays include the separation of the signal from the local noise, the improvement of the signal-to-noise ratio for small events, and providing phase velocity and back azimuth estimates. Therefore, arrays are designed for the optimum detection of signals with sufficient reliability to enhance weak signals while simultaneously providing phase velocity and back azimuth information (Ringdal and Husebye 1982; Mykkeltveit et al. 1990).The physical sensors in these arrays are arranged over a specific footprint determined by the wavelength [Eq. (1)] of the signal of interest, and the coherence between the background noise and signals of interest (1) where f = dominant frequency (in terms of cycles per second); v = velocity of the arrival phase of interest (meters per second); and λ = wavelength of the arrival (for signals of interest in this study, tens to hundreds of meters).The higher the frequencies of interest, the smaller the physical dimensions of the array need to be to avoid spatial aliasing of narrowband signals. The typical infrasound sensing array utilized in the studies presented herein is a five-element array in a cross-pattern configuration of the desired size to properly sample the signals associated with the source signature of interest, where the infrasound sensors and associated wind filters are installed at ground level; the single meteorological sensor kit is at the central infrasound gauge, with supplemental weather balloon launches as necessary. The call-out in Fig. 4 indicates the central hub-site with fabric dome covering the infrasound sensor and associated meteorological sensor kit. The meteorological sensors include temperature, wind speed, and wind direction installed at 1-m and 2-m heights to estimate surface roughness and thermal impacts on the observed infrasound data. Detailed instrumentation specifications and installation instructions can be found in Simpson et al. (2019).In classical ray theory, for upwardly propagating infrasonic energy to return to receivers on the earth’s surface, the acoustic energy must reach a layer of sound velocity, Eq. (2), greater than the sound velocity at the source altitude. Short-lived, low-altitude temperature inversions can propagate low-power anthropogenic infrasonic energy over 100 km from the source (McKenna et al. 2008, 2012) because temperature inversions (temperatures at altitude are higher than at the ground) produce a vertical change in the effective sound speed, which provides the necessary propagation inflection point to return infrasound energy to the earth’s surface. These sound speed profiles are defined by effective sound speed, Ceff (m/s), computed vertically through the atmosphere (2) where Ct∼20.07(T)1/2; T = absolute temperature (Kelvin), and n·v = component of wind speed (meters per second) in the propagation direction.Radiosondes, or meteorological balloons, are often launched to capture these atmospheric conditions during case studies or proof-of-concept infrasound monitoring studies to assess the temporal and spatial variability of the atmospheric conditions that dictate the sound speed profile. The balloons/radiosondes record critical atmospheric data up to 26 to 34 km prior to bursting to define sound speed profiles. These profiles are utilized in infrasonic propagation modeling to refine the most favorable detection times in the infrasound recordings of a particular case study. In addition to temperature, seasonal prevailing wind direction affects infrasound propagation and, thus, influences array placement. Source signals propagating with the prevailing wind direction propagate farther than source signals propagating into the prevailing wind direction. The placement of arrays in the same locations for deployments over several seasons might produce different results because of the additive or destructive properties of the prevailing winds on infrasound propagation, which is one reason that more than one array per region is recommended. Regional deployments for permanent install experience a range of environmental conditions; however, the pattern-of-life sound maps for structures can be adjusted for seasonal sensitivity in the postprocessing of the data.In a uniform atmosphere and flat terrain (i.e., a clear, calm day on a flat football field), acoustic energy spherically propagates outward from the source and is detected by a receiver, that is, infrasound sensor. However, in real-world environments, topography and terrain conditions impact the propagation of acoustic energy. The topographical and terrain effects on infrasound propagation can be significant but can be minimized by careful array location selection (McKenna et al. 2012; Swearingen et al. 2013; Ketcham et al. 2013a). Tree cover can be either a help or a hindrance depending on the distance of the array from the source of interest (Swearingen et al. 2013; Ketcham et al. 2013a, b). The best areas in terms of terrain are those with scrubby grass or sparse trees with small amounts of underbrush. These scrubby areas act as another level of wind filter, in addition to the installed wind protection, without being so dense as to obstruct and distort the signals as they arrive (Walker and Hedlin 2010).Topography plays a similar role to vegetation and ground cover when choosing an array site because the infrasound and acoustics community well understand that large topographic features can impact how acoustic waves propagate, such as mountains creating acoustic shadow zones that blind sensors to signals originating on their opposite sides (Campus and Christie 2010; McKenna et al. 2012). In addition, individual array sites need minimal topographic relief to reduce interarray element elevation differences (Edward and Green 2012). Signal processing techniques presented here to detect and process structural infrasound signals make use of plane wave assumptions for which the signal moves across the array as a linear front. If the infrasound sensors are at significantly different elevations, these assumptions and the techniques used for signal processing are no longer valid. When possible, arrays should be located in such a way as to minimize both local and regional topographical effects. If this is not possible, additional processing techniques are required to account for the elevation differences between array elements (Edward and Green 2012).The distance from the source that arrays can be placed depends on the source signal strength (Campus and Christie 2010). Infrasound signals are capable of propagating thousands of kilometers if the source signal has low frequency and high energy, although structural signals for practical purposes are low frequency and low energy and have limited propagation distances (McKenna 2009a). The distance from source to receiver should be at least one full wavelength [Eq. (1)] but is recommended to be at least ten wavelengths away for plane-wave assumptions to be valid for signal processing. These frequencies can be estimated through a finite element model. Alternatively, assumptions can be made based on a literature review of bridge vibrational characteristics, as subsequently detailed, for which most large critical infrastructure emanates lower than 10 Hz for the fundamental modes (Whitlow 2019). Array deployments featured in this paper include one structural source validation array in close proximity to the structure, another within a few kilometers representative of nonline-of-sight, noncontact monitoring, and a third at a longer distance, generally surrounding the source/monitoring area of interest and ensuring plane-wave processing techniques are appropriate. Ideal localization of these arrays allows for the triangulation of sources using crossing backazimuths from each array pointed toward the source (Rost and Thomas 2002). For operational systems, regularly spaced arrays over a region are sufficient to create a baseline infrastructure sound map without having to have a “validation” array located at the structure itself.Processing can occur after the experiment, called postprocessing, or can occur simultaneously to the field collect, operating in near real-time. All of the data presented in the paper are postprocessed, although the ERDC is developing automated, near-real-time techniques to process structural signals at the array without experts-in-the-loop rather than requiring structural infrasound experts for analysis. The signals associated with a structural source are continuous-wave (CW) packets in the time domain with a spectral peak at the fundamental mode of the structure (Donn et al. 1974; McKenna et al. 2009a; McComas et al. 2016, 2018). The signal processing methods are designed to identify these features in the data and have been refined over years of study. Initial studies manually processed the data using Geotool version 2.1.3, a software package for the visualization and characterization of seismic and acoustic data available from the Comprehensive Nuclear-Test-Ban Treaty Organization (Coyne and Henson 1995). This analysis focused on reviewing time series data, generally filtered from 0.5 to 10 Hz with a three-pole Butterworth filter, from each array element in Geotool to identify these CW packet signals and characteristics (dominant frequency and back azimuth). For a detection to be declared, the signal packet must be observed on a minimum of three of the five array elements. Once a detection is declared, the dominant frequency of the packet is identified through a Fourier analysis that compares a window centered on signal packets and an equal size noise window immediately following or proceeding the signal window. Next, frequency-wavenumber (F-K) analysis is completed to determine the back azimuth, that is, the direction from which the signal originated (Rost and Thomas 2002). In subsequent studies, Infra Tool was added as a first pass processing to pinpoint times when acoustic signals are arriving from the back azimuth associated with the structure of interest (Hart 2004). Infra Tool is an automated F-detector nested inside of Matseis, a product of the Department of Energy National Laboratories that focuses on identifying correlated signals across array elements through an analysis of the F-statistic (Hart 2004; Blandford 1974). The Infra Tool detector was run on each array for each hour of the experiment to determine times of high correlation, defined as correlation greater than 70%, with a back azimuth in the direction of the structure of interest. These identified times were then processed manually in Geotool (as previously described) for individual CW packets. Specific processing for each noted event is detailed in the corresponding section and associated with appropriate figures.Water Control Infrastructure SystemsTo demonstrate the concept and potential use for monitoring water control structures, such as hydroelectric dams, a structural assessment was conducted at the Portugues Dam built near Ponce, Puerto Rico in 2013. Using the Portugues Dam provided a unique opportunity to study the dynamic properties of the dam under external dynamic loads changes, that is, dam empty, when filling, and during operation, due to the construction and operation of the dam by the USACE Jacksonville District, allowing the authors access the structure, plans, and surrounding areas. This access allowed for the highest resolution and detail for numerical model development for both the structure and infrasound propagation across the real terrain.The Portugues Dam is an arch-roller compacted concrete (RCC) dam, is 67-m tall, 375-m long, and has an ogee spillway 42.6-m long. The base and crest thicknesses are 33.8 m and 9.1 m, respectively, and more than 271,417 cubic meters of concrete were used in its construction. The dam’s natural frequencies were studied prior to the infrasound deployment using detailed finite-element (FE) models assembled in COMSOL Multiphysics software. This predeployment modeling effort was essential to determine the ideal placement of arrays by distance (ensuring the minimum wavelength distance criteria were met) and by orientation (how the dam radiates sound through the surrounding terrain and topography). The first goal was to confirm that the fundamental modes were in the infrasound passband, between 0.1 and 20 Hz, and suitable for infrasound monitoring techniques. A high-fidelity modal analysis utilizing the structural mechanics module of COMSOL Multiphysics software produced frequencies of 4.8 Hz (green), 6.7 Hz (blue), and 10.2 Hz (purple), indicating that the dam resonates in the infrasound passband. Figs. 1(a and b) provide examples of the modal motion of the dam (Diaz-Alvarez et al. 2015). A Fourier analysis of the sum of the vibrational outputs [Fig. 1(c)] estimates the response associated with the fundamental modes of vibration [Figs. 1(a and b)]. Fig. 1(c) represents the model output in power associated with each frequency. The colored bars represent the frequencies of interest that occur in the structural model and in the infrasound from the field data collected and are color-coded to enhance the visual associations.Once the first passband suitability criteria were met, active modal testing determined the dynamic structural behavior. To physically force the dam to acoustically radiate in without damaging the structural integrity, a cold gas thruster (CGT) was attached to the crest of the dam near the spillway to be used as a controlled excitation source (Duron et al. 2013). Using the CGT and accelerometers mounted on each monolith of the dam made it possible to measure its dynamic response. The dynamic assessment of the Portugues Dam consisted of testing at different sampling rates and times of day using different transducer arrangement locations at the center of each monolith. Prior to the CGT excitation, several ambient baseline datasets were collected at different sampling rates to check for aliasing. The sampling rates used for the ambient tests were 1, 20, and 50 kHz. The output accelerometers on monoliths all react to frequencies in the infrasound range between 2Hz and 20Hz. Estimations of the magnitude and phase of the frequency response function (FRF) were computed. The coherence between the input and the outputs were compared for validation purposes of the transducers.The modal shape, frequency, and damping were extracted and used to formulate a mathematical model to study the dam’s dynamic behavior. A seismic wave propagation analysis was developed as an input parameter for the pressure acoustic model based on the physical forcing of the CGT and measured by on-structure accelerometers. Fig. 2(a) indicates the propagation of the seismic wave caused by the CGT. The computational fluid dynamics (CFL) condition used for this model was CFL=0.1. From this, the maximum element size and the maximum time step, 7.1059 m and 3.33×10−4 s were calculated by using the P-wave velocity of 2,131.8  m/s for concrete, 50 Hz as the maximum frequency of the load, and N=6 (number of elements per local wavelength). The acceleration data from the surface of the dam was transformed to the frequency domain to generate the free-tetrahedral acoustic model; see Fig. 2(b). Vibrating the structure in COMSOL produced an estimate of the magnitudes of the energy emitted for the different frequencies of interest, further refining the likelihood of detection for potential infrasound signals.Three infrasound arrays were deployed at distances of 0.46-km upstream, 0.62-km downstream, and 6.0-km from the dam for multiple deployments beginning in 2013. Instrumentation for the three arrays consists of five Inter-Mountain Laboratory (IML Model ST, Sheridan, Wyoming) infrasound sensors, each with four porous hose wind filters, a 1-Hz triaxial seismometer, and two Reftek 130s digitizers (REF TEK Systems, Plano, Texas). The infrasound sensors are installed in a cross pattern with approximately a 60-m aperture. The data were collected on Reftek 130s six channel digitizers sampled at 1,000 Hz with unity gain. The arrays collected data for four days for each deployment to capture background noise for the area and to develop a frequency baseline behavior of the dam. Infrasound data were compared with resonant frequencies calculated from the dam’s modeled transient responses and measured on-structure accelerations. As an example, Fig. 3 indicates the infrasound signal gathered from a single sensor from the infrasound array at the downstream site before dam excitation using the CGT. To separate out the effects of the CGT impulse on the observed infrasound signals from the fundamental characteristics of the dam itself, a Fourier analysis for a 4.5-sec window must be done before the shot [Fig. 3(a), left box] and postshot [Fig. 3(a), right box]. This standard array processing practice samples the “background” noise from the event of interest. Although the impulsive CGT event is obvious in the time series and associated frequency analysis, the frequency peaks that exist both before and after the shot are of interest because they represent the passive, detectable modes of the structure. Detecting these modes is critical if these techniques are to be used in routine unforced operation to establish the baseline infrasonic behavior of the structure. Fig. 3(a) indicates the measured infrasound due to ambient excitation of the dam and the impulse from the CGT. In Fig. 3(a) (right box), the amplitude of the signal increased by approximately 1.82 mPa due to 9,072 kg of force applied at the crest of the dam to excite the lowest vibration mode of the structure. The peak in the infrasound sensor indicated the vibrations of the dam due to the CGT impulse at the green bar, correlating with the lowest structural model peak and one unlikely to be excited under routine operations. Fig. 3(b) corresponds to the Fig. 3(a) (left box) ambient structural signatures. Fig. 3(c) indicates the frequencies measured (4.8, 6, 10, and 18 Hz) by the infrasound sensors after the force excitation by the CGT, which confirm the predicted frequencies from the FE model and those measured from the transducer previously described, with matching frequency bands for the blue, purple, gold, and grey modes (frequencies 2–5 Fig. 1).A comparison of pre- and post-CGT data for the infrasound peaks at approximately 6, 10, and 18 Hz frequencies shows that the post CGT frequencies remained relatively constant with those before the excitation. Frequency changes outside these regions or significant shifts in the power and frequency of the infrasound signal, Fig. 3(c), are attributed to the acoustic emanations of the CGT and not the natural frequencies of the structure; the natural frequencies of the structure should dominate the acoustic emanations and, thus, the received signal peaks should remain relatively constant, as indicated in the comparison of Figs. 3(b and c). The frequencies of the relatively unchanged peaks agreed with the detailed FE model predictions and the on-structure accelerometers, confirming the detection of the structure’s natural vibrational modes via infrasound. Any changes thereafter to these identified infrasound peaks (frequency or relative power) would then signify a change in the structural integrity or loading condition of the dam.The infrasound data were analyzed to develop performance estimates to predict future dam behavior under different loading conditions, which have been validated under four conditions as of the time of publication. To date, the ERDC has reoccupied sites four times during the July–August period: 2013 (during construction), 2014 (during fill), 2015 (under normal operations), and 2019 (after Hurricane Maria). The repeated reoccupation of field sites provided a wide range of data to help understand how the dam’s natural frequencies change due to different loading conditions, such as the post-Hurricane Maria floods that devastated Puerto Rico in 2017. Thankfully for the people of Puerto Rico, data from this deployment confirmed no changes in the fundamental frequencies of the dam after the hurricane and, thus, no potentially catastrophic structural damage. After pandemic travel restrictions are lifted, the authors will assess damage from the earthquake swarm in the winter of 2019–2020.Transportation Infrastructure SystemsThe exploratory proof-of-concept effort for the application of these techniques for transportation structures occurred in 2006 and determined the structural capacity of a candidate railroad through-truss test bridge located in Ft. Leonard Wood, MO, which is owned and maintained by the US Army garrison of the same name (Diaz-Alvarez et al. 2009; McKenna et al. 2009a, b; Whitlow et al. 2012; Costley et al. 2016; Whitlow et al. 2013). The Ft. Wood 0.3 Bridge is a steel through truss with a 65° skew and is located at 37°54′56.7″ N, 91°56′50.7″ W near the junction of the Ft. Wood spur line and the main regional railroad line. Removed from noisy urban areas, the quiet source and site locations minimize the cultural noise contamination in the data and minimize other large structures as the source of the observed structural infrasound signals (McKenna et al. 2009c). The data collection and processing of the infrasound data occurred in the manner previously described, although the two remote arrays had an approximate 30-m aperture and consisted of four IMLs each, and the farther site had a Reftek 130 with two Chaparral microphones located at two of the IML gauge sites for calibration comparison. The data were collected on Reftek 125A single channel digitizers and Reftek 130 six channel digitizers and sampled at 1,000 Hz with a Nyquist frequency of 500 Hz, and 32-bit gain for the infrasound gauges. The noise reducing Apex hoses were only 2 feet and capped, which prevented the potential recording of infrasound frequencies lower than approximately 2 Hz. The first three modes of motion were 2, 6, and 13 Hz, and all three were detected at arrays placed 19 and 27 km away on quiet restricted sites, which corresponded with the acoustical model of the target bridge. A representational infrasound source based on the bridge geometry and material characteristics was developed in conjunction with assessing the effects of local topography on propagation in the same manner as the COMSOL models of the Portugues Dam, which coupled the structure to the surrounding fluid medium (air) through 30-m digital element model (DEM) topography. Additional research determined that the higher modes of the bridge were excited by traffic but not the lower infrasound modes that propagated at a distance (Costley et al. 2015). However, because the lower holistic modes did not require direct excitation for nonline-of-sight detection, these limitations were deemed not critical. Diaz-Alvarez et al. (2010) investigated the modal motions of the skew through-truss and refined the structural modeling techniques for that particular transportation infrastructure type. This experiment was conducted in well-controlled ideal signal-to-noise ratio conditions; however, questions remained about these techniques in less than optimal environments.Following the preliminary potential success of the Ft. Leonard Wood idealized case, two more studies were conducted on transportation infrastructure. To determine the feasibility of these techniques for commuter bridges that experience high traffic and routine use, the ERDC partnered with Caltrans to assess the Feather River Bridge (Br 18-0009), a scour-critical, twenty-four span, steel, two-girder bridge with the longest span of 49 m that carries Route 20 between Yuba City and Marysville, California (Fig. 4). This bridge was the subject of a pair of infrasound data collections with a network of three infrasound arrays deployed at distances of 2.6 to 24 km from Br 18-0009. The first experiment took place from February 26 through March 4, 2014, with a focus on the feasibility of infrasound data collection in an industrial environment with anthropogenic clutter from sawmills, airports, and other industrial activities. The second experiment took place on November 13–18, 2015, and was focused on capturing the fundamental modes of the bridge obtained with on-structure instrumentation to validate collected infrasound data. Infrasound sensor arrays were deployed with the same configuration and spacing as described in the Methodology section of this paper and are represented by the photograph of the infrasound array in the Fig. 4 callout. Each of these arrays consisted of a five-element IML Model ST infrasound array with 15.24-m (50-ft) porous hoses attached to the four inlet pipes as passive wind filters, two digitizers, and associated cables, connectors, batteries, and solar panels. Each of the IML infrasound sensors had a nominal signal frequency band of 2–30 Hz but were modified to collect signals lower than 2 Hz with a roll-off beginning at approximately 1 Hz. The digitizers utilized in the array were Reftek 130S-01 digitizers with an input preamplifier, digital antialias filters, and a high-precision external global positioning system (GPS) receiver/clock for time synchronization between digitizers. Gulf Coast Data Concepts multifunction extended life accelerometer data logger -×2 units (operated in high-gain mode) were used for the on-structure validation in the second experiment. These three-axis devices had a range of ±2  g and combined a battery-powered digitizer with a Class C microelectromechanical system (MEMS)-based accelerometer.A preliminary analysis of the collected infrasound data using Geotool and Infra Tool in conjunction with observed meteorological conditions yielded times of interest in the data from the first experiment from the array located at the Marysville City Cemetery, denoted as the FRC array (Fig. 4). The time series corresponding to these times was then manually processed by an analyst to identify CW packets associated with structural sources [Fig. 5(a)]. A Fourier analysis was performed to confirm coherent peaks in the expected frequency range, including multiple modes at 4 Hz and lower [Fig. 5(b)], verified with accelerometer data from structure mounted accelerometers during the second experiment [Fig. 5(c)]. The color bars in Figs. 5(b and c) highlight the frequencies associated with the bridge from both the remotely collected infrasound data [Fig. 5(b), middle] and the on-structure instrumentation [Fig. 5(c), bottom], verifying the fundamental modes collected with each method are the same for three peaks indicated in green, blue, and gold. Following this, F-K analysis was used to determine the back azimuth of the signal, yielding a back azimuth of 222° from the FRC array corresponding to one of the main spans of the Feather River Bridge. Long spans are capable of displacing more air as they resonate, generating the infrasonic waves potentially detectable at longer distance ranges. The combination of verified fundamental frequencies from remotely detected infrasonic data with on-structure instrumentation along with the results of the F-K analysis provide a back azimuth corresponding to the bridge of interest, Br 18-0009, validating the use of infrasound as a means of remote, noncontact bridge monitoring for commuter bridges in environments with a high noise floor (lower signal-to-noise ratios). McComas et al. (2020) include a more in-depth analysis of other industrial and anthropogenic sources associated with this study.Although transportation infrastructures exist in isolated, rural settings, most infrastructure is in and around cities. Traditionally, global infrasound monitoring for large geophysical events or nuclear test ban treaty monitoring focused array deployments in rural open spaces. Prior case studies for this team were conducted in rural areas or with minimal variation in buildings or other built environment structures. As described in the Methodology section, topography and terrain can have significant effects on the propagation of infrasound; therefore, it is imperative to investigate the applicability of these techniques in an urban environment with large buildings, urban canyons, sunken highways, or other structural sources of scales on the same dimension as the infrasound wavelengths produced by critical infrastructure, that is, the least optimal environment and likely the lowest signal-to-noise ratio.Development of nontraditional array design to overcome instrumentation deployment challenges in a dense urban environment coupled with high-fidelity urban terrain propagation models began in 2012. In partnership with Southern Methodist University (SMU), the ERDC deployed rooftop infrasound arrays in Dallas, TX, to determine the feasibility of monitoring infrasound signals in dense urban environments in which access to ground-level installation sites is prohibited. Two arrays were installed on rooftops of buildings on the SMU campus. A 38-m aperture five-element array was installed on the large open rooftop of Moody coliseum (Moody array), and a second five-element array spanned five rooftops with an aperture of 120 m (multirooftop array). Each array element was a Chaparral model 2.5 sensor with seven ∼8-m porous hoses connected to the sensor to provide wind noise reduction. These sensors were digitized with a Reftek RT 130-01 recorder sampled at 40 and 200 Hz. The analysis of the data from these arrays was focused on understanding whether any coherent signals could be identified in the chaotic urban environment from elevated, structure-coupled monitoring locations. The manual processing technique previously described in the Methodology section was used to manually comb through the six-month data set. This analysis identified repeating CW packets with dominant frequencies of 1.5–1.8, 4.3, or 5.1 Hz with back azimuths ranging from 147° to 166° and 132° to 143° for Moody and multirooftop arrays, respectively. An inspection of the range of back azimuths overlaid on aerial imagery highlighted the potential source as the Mockingbird Bridge over US Highway 75. This source is located 0.45 km from the Moody array and 0.7 km from multirooftop array.The hypothesized source, the Mockingbird Bridge, is an adjacent box beam bridge. This type of bridge construction creates a deck that acts as a monolithic structure (TXDOT 1993) and radiates infrasonic energy in the manner of a vibrating tube rather than a flexing deck, as in the Feather River Bridge case. The source was verified through on-structure measurements of the fundamental vibrational mode using Mark L-4 vertical seismometers placed on main structural members of the bridge east and west of the center support and outside the northwest and southeast corner edges. The seismometers were digitized with Reftek RT125A-01 recorders sampled at 200 Hz with a gain of 4. An analysis of spectrograms from the seismometers was used to identify the common vibrational modes of 1–2 Hz and 4–5Hz. These modes align with the observed dominant frequencies in the infrasound observations, thereby confirming the Mockingbird Bridge as the source. Additional confirmation was completed with a simplified bridge pressure acoustic model in the COMSOL Multiphysics 4.3a acoustic software package. This model predicted the first four modes and shape as vertical flexure 2.0 and 3.9 Hz and torsional at 4.3 and 5.2 Hz. These results align well with the on-structure measurements and infrasound observations. Full details of this study are published in McComas et al. (2016, 2018), with greater detail on the development of automated signal processing techniques tailored for noisy urban deployments. Further research is being conducted to understand how the ambient noise fields vary with the type of urban buildup and meteorological conditions, which will be used to develop detection thresholds for infrasound signals in urban scenarios. McComas et al. (2020) addressed some of the concerns of instrumenting the human-built environment, with detailed discussions of noise floor analysis and competing signature discrimination and an analysis of three urban/suburban areas: Dallas, TX (SMU deployment), Sutter County, CA (Feather River Bridge deployment), and San Diego, CA (not presented here).Aside from the physical monitoring concerns and challenges of the signal processing of urban data, moving from traditional rural monitoring environments created a gap in the understanding of how urban structural terrain affects the propagation of infrasonic energy. If the structures in the urban environment are large enough, they might create channels to enhance detections or act as a muffling cloak to prevent detections. The development of high-fidelity urban terrain modeling techniques utilizing an acoustic finite-difference time-domain code, PSTOP3D (Pace et al. 2015; Ketcham 2006), explored how urban terrain (buildings, bridges, and other human-made features) infrasound propagation. A real-world urban terrain model space was developed centered on the campus of SMU that realistically represented large-scale features of buildings and roadways in the space. The following discussion summarizes the model development and results, but Pace et al. (2015) and McComas et al. (2016, 2018) provided a complete methodology documentation and archived the data used to produce the models presented here. The model urban terrain was developed using spectroscopic aerial imagery and 1-m light detection and ranging (LIDAR) data; the terrain features included buildings, bridges, paved areas, and an atmosphere (temperature only) [Fig. 6(a)]. Simple model inputs for atmosphere and source were made to allow for a focused interpretation of the understanding of how large-scale urban terrain features impact propagation. The atmosphere input conditions were simple upward refracting static three layers with an adiabatic sound speed profile of 0–50 m at 344  m/s, 50–100 m at 337  m/s, and 100–256 m at 330  m/s. The model input source was a broadband Ricker pulse with a 10-Hz center frequency in the northeast corner of the model space [Fig. 6(b)], which does not correspond with a real structure but is representative of the types of structural signals modeled elsewhere in this paper. The model results yielded a ground-level peak pressure map over the model space. This map highlights regions of attenuation and amplification created by the urban terrain. One example of amplification extends from the northeast corner toward the southwest quadrant, which aligns with the sunken corridor of US Highway 75. This human-made feature creates a waveguide for acoustic energy that yields up to a 20-dB increase in acoustic energy over the surrounding region. An example of an attenuation region is the cluster of tall buildings in the southeast quadrant of the models that creates a shadow zone that reduces acoustic energy up to 10 dB. This is one representative model for a specific urban site; however, the techniques outlined here begin to characterize the impacts of different types of structural terrains on infrasound energy propagation that identify features that improve or hinder detection. Future research integrates these models with the ambient acoustic model research effort previously referenced to provide realistic boundaries on what is possible for monitoring multiple structures in urban environments.Riverine Infrastructure SystemsNavigating the Mississippi River near Vicksburg, MS, is known to be difficult for barge traffic in even the best of conditions due to the river’s sharp bend adjacent to the town (Fig. 7). Although the river ebbs and flows seasonally, the difficulty in piloting barges under the bridge rises significantly during times of flood. Ongoing studies by the ERDC are investigating infrasound as a way to correlate the low frequency acoustics generated by the river with the presence of hazardous conditions observed during the flood stage, that is, rough waters and high currents, which is thought to be a contributing factor in the frequent barge-bridge impacts for the two bridges connecting Louisiana to Mississippi. The I-20 Mississippi River Bridge runs east-west connecting Vicksburg, MS to Delta, LA. The bridge was opened to the public in 1973. It is a seven-span cantilever bridge that is 1,032.97-m long by 20.89-m wide and has two eastbound and two westbound lanes. Another older highway and railroad bridge, which had been part of US Highway 80, crosses the river approximately 91 m upstream from the I-20 Bridge. This bridge continues to be used by trains but is no longer used for vehicular traffic. The Highway 80 Bridge in Vicksburg, MS is the only rail freight crossing over the Mississippi River between Baton Rouge, LA and Memphis, TN. In January 2015 alone, five barge-bridge collisions occurred, which resulted in the closure of the river for barge transit and the Highway 80 Bridge for rail transit for multiple days, impacting transit of goods throughout the southeastern United States. Persistently monitoring impacts to the bridge is critical to ensuring the continued operation of critical commerce avenues.US Army Engineer Research and Development Center (ERDC) researchers installed a permanent infrasound array on the ERDC Waterways Experiment Station campus in Vicksburg, MS, called the Denied Area Monitoring and Exploitation of Structures (DAMES) Array. The 1.8-km aperture infrasound array was designed to be consistent with typical Comprehensive Nuclear-Test-Ban Treaty Infrasound monitoring stations within its International Monitoring System. Collocated with one of the large array elements is a nested 40-m aperture smaller infrasound array compatible with the deployed infrasound arrays in the case studies presented in this paper (Swearingen et al. 2013). The array consisted of IML model ST infrasound gauges, with a roll-off frequency of 1 Hz (nonstandard because most STs roll off at 2 Hz). Each of the infrasound gauges was equipped with four 15.24-m (50-ft) porous hoses to reduce wind noise. Data from the array is continually recorded on Reftek 130-A digitizers at 1,000 samples per second, archived onsite at the ERDC, and are available on request. The DAMES array has been operational since 2010, with archived data including signatures from the 2011 Mississippi River flood, the 2019 flood, all seasons in between, and an extensive catalog of structural signatures in Louisiana and Mississippi (Swearingen et al. 2013; Ketcham et al. 2013a, b). This array is located 4.3 km from the I-20 Bridge; see Fig. 7.Beginning with 2011 and going through January 2016, dates and times for analyzing the infrasound data collected by the DAMES Array were selected based on times of high flood and low river levels, as observed in Fig. 8. The infrasound data analyzed were collected at 0400 (CST) for one continuous hour for any persistent or dominant sources in the frequency range of 1 to 10 Hz, for the highest day of the year, lowest day of the year, and any reported barge strikes. During the five-year period, a total of nine confirmed barge strikes occurred, as validated from news reports and visual confirmation, and they are marked as red stars on Fig. 8, with five in one week in January 2016 alone. Two persistent sources were present throughout the infrasound data during high and low river levels based on data from the larger array, depicted as the cross in Fig. 7. One source was positively identified as the inflow of the Yazoo Diversion Canal into the main body of the Mississippi River by triangulation with portable arrays and associated narrow detection azimuth that does not vary with river level (315°, Fig. 7). The other source was investigated with the F-K analysis Infra Tool as described in the Methodology section. Although the frequency content remained the same, the back azimuth of the dominant source observed varies and correlates with the water level, although with similar power levels. During low river levels, the broadband source emanates from upstream of the bridge in between the inlet from the Yazoo Diversion Canal and the Highway 80 rail bridge. During times of high water, the source spreads out and moves downstream of the river. The breadth of the high and low flow detections is indicated by the colored bars in Fig. 7 (low water is yellow, high water is blue). Given the constant nature of the broadband source over the frequency range (1–10Hz), the low amplitude in terms of dB, and the proximity of the DAMES Array to the Mississippi River, which correlates to azimuth, it is estimated that the source observed in the infrasound data is the Mississippi River, similar to the surf infrasound recorded near coastlines (Garces et al. 2003). If these were sources from anthropogenic noise, the power level, frequency content, or location would vary according to human activity rather than pattern-of-river-life, as determined by comparing the times during high flood and low river levels. The pattern of dominant source detections could be the result of the changing river levels and the associated turbulent churn and where it is the strongest during each river condition. However, more research into the observed phenomenon is needed to validate using infrasound as a means to detect potentially hazardous conditions present on the river.One barge strike has been analyzed in detail to correlate specific infrasound signatures to damage events: on March 23, 2011, a freight barge impacted one of the piers of the I-20 Mississippi River Bridge, an unusual event because all eight other bridge-barge strikes in this dataset occurred on the upstream Highway 80 rail bridge. The strike was witnessed by the research team that was able to ground-truth the public reporting on the timing of the initial strike and subsequent distribution of barge containers into the shipping channel. At the time, the ERDC was also monitoring the bridge with on-structure instrumentation for another study. As such, it had detailed plans of the I-20 Bridge. Eigenfrequency and time-dependent finite-element (FE) models of the bridge and pier were developed to determine the bridge’s response to such an impact (Jordan et al. 2013). Modal analysis using the eigenfrequency model revealed resonances at 0.9 and 4.3 Hz. The mode shape corresponding to the 0.9 Hz resonance is depicted in Fig. 9(a). Modal analysis of the bridge pier indicated that the shape of its fundamental mode pier vibrated like a cantilever beam with a resonance of 4.3 Hz.The time-dependent model was used to determine the vibration response of the bridge for the period immediately after the impact. The barge impacted the pier supporting the span on its right side, as observed in Fig. 9(a). The force on the pier was represented as a smoothed step function with the amplitude determined from the estimated mass and speed of the barge. Spectra calculated from averaged displacements of points on the bridge deck as determined from the time-dependent model are plotted in Fig. 9(b). The peak at 0.9 Hz, indicated in the first graph of Fig. 9(b), is associated with the vertical vibration of the bridge deck. This mode is most likely to radiate sound because it displaces the most air as it vibrates. The peak at 4.3 Hz, indicated in the second graph of Fig. 9(b), is associated with the horizontal vibration of the bridge pier.FK processing from the nested 40-m array revealed that the source of the infrasound was the impacted pier. The spectrum of the signal recorded with one of the ERDC infrasound sensors is plotted in the bottom graph of Fig. 9(b). The peak in the infrasound frequency spectrum at 0.9 Hz is clearly evident, corresponding to the vertical vibration mode. The infrasound spectrum also contains peaks between 2 and 3 Hz, which might correspond to the small peak in the horizontal vibration spectrum. The small peak in the infrasound frequency spectrum at 4.3 Hz corresponds to the horizontal vibration mode of the pier. Both vertical and horizontal vibration modes and the infrasound frequency spectra contain a peak at 0.2 Hz, which was present in the FE time-dependent model but not the eigenfrequency modal analysis. This peak evidently corresponds to a lower vibration mode of the structure, which can be considered a fundamental property of that structure because it appears in both vibrational modes and the infrasound spectra, although it could be a function of the fluid–structure interaction of the river with the bridge itself.Implications of Structural Infrasound for Critical Infrastructure Inspection PrioritizationAs the science of structural infrasound transitions from theoretical to fielded, the ERDC envisions a future of critical asset management that couples these persistent, remote technologies with traditional engineering practices to ensure public safety in an era of diminishing funds for ever-aging infrastructure maintenance. The ERDC is working with state and federal Departments of Transportation to tailor techniques for owners and operators of critical infrastructure. For example, a network of infrasound arrays throughout the southeastern United States could be permanently emplaced to simultaneously monitor suites of structures to understand the near-real-time health and condition of infrastructure during natural disasters, such as Hurricane Katrina, or the potential of an earthquake in the New Madrid Zone. The ability to rapidly characterize structural conditions across a broad spectrum could significantly enhance postevent inspection/rescue prioritization and inform the movement of relief and rescue supplies into, and distressed populations out of, affected areas. Understanding the physics of the structural and atmospheric interactions that create a structural infrasonic source facilitates future near-real-time, remote assessments of dams or other critical water control structures under variable and potentially hostile meteorological conditions, such as wind loading from hurricanes or elevated water excitation from flood events.Another example of the potential uses of infrasound monitoring of structures is for scour monitoring of bridges. Initial research investigating the feasibility of infrasound for remote bridge monitoring indicated that scour—a global characteristic—could be more readily detected using infrasound (Taylor et al. 2012; Whitlow et al. 2012, 2013). In addition, the persistent nature of infrasound monitoring could be beneficial in capturing scour events as they occur. 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