We use a network of broadband microphones, including a 4-element array, to locate the sources of thunder occurring during an electrical storm in central New Mexico on July 24th, 2009. Combined slowness search and distance ranging are used to identify thunder regions in three dimensions (out to 12 km) and for two overlapping frequency bands (1–10 and 4–40 Hz). Distinct thunder pulses are locatable and used to predict time-of-arrival to neighboring stations and to identify correlated phases across the network. Spatial correlation is also found between the thunder source regions and regions of very high frequency (VHF) radiation as located by the New Mexico Lightning Mapping Array (LMA). Some of the misfit between the LMA and thunder locations is attributable to differences in excitation mechanisms of the respective radiation, which is related to current impulses in lightning channels (for thunder) and incremental ionization of the atmosphere (for VHF emissions).
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 The New Mexico Lightning Mapping Array (LMA) uses very high frequency (VHF) radio emissions to pinpoint ionization events associated with the formation of lightning channels [Rison et al., 1999]. Stepped leaders often form dendritic channel structures [Bazelyan and Raizer, 2000], which can be mapped with accuracies of tens of meters [Thomas et al., 2004]. In central New Mexico typical negative cloud-to-ground and intracloud lightning produce hundreds to thousands of locatable VHF emissions (referred to hereon as rf sources) occurring during a fraction of a second.
 Though stepped leader progression does not generate the most energetic thunder, it is responsible for forming an ionized channel that subsequently carries the predominant current events such as return strokes. Rapid channel heating results in the generation of shock waves along the channel that quickly decay to linear acoustic waves with intense energy in the audible band [Few, 1969; Holmes et al., 1971]. Simultaneously, it is predicted that the electrostatic relaxation within a charged source region will produce a volumetric contraction and a rarefactory lower frequency infrasound (below a few Hz) pulse [Dessler, 1973; Bohannon et al., 1977]. Precursory charge accumulation [Pasko, 2009], or positive streamer formation [Few, 1985] may also contribute to infrasonic pulses.
 Acoustic reconstruction of lightning channel geometry has been attempted using microphone arrays and ray tracing back to the acoustic source [e.g., Few, 1970; Few and Teer, 1974; Teer and Few, 1974; MacGorman et al., 1981; Arechiga et al., 2011]. Infrasound emissions have not been conclusively located in the same manner, but they have been correlated to electrostatic sources detected with electric field meters [Balachandran, 1983]. A study by Assink et al.  related infrasound sources recorded at regional distances (up to 50 km) with rf sources from electrical storm activity, where the infrasound signals are probably low-frequency remnants of long-distance propagating broadband thunder. Another study by Arechiga et al.  compared locations of rocket-triggered lightning sources (mapped with the New Mexico LMA) with broadband thunder sources occurring within a few km. This paper further explores techniques to jointly map and compare LMA and multiple thunder sources using array coherence mapping.
 In the summer of 2009 we recorded thunder using broadband microphones (AllSensors™ 1-inch MEMS transducers operated in absolute mode), which possess similar sensitivity, linear dynamic range to ±125 Pa, and flat responses in the band 0.01 to 500 Hz. Microphones deployed in this study consisted of a three-station ‘network’, where one station (referred to as GTM) was a four-element infrasound array with sensor nodes located at the center and vertices of an approximate 45-m equilateral triangle (Figure 1). Two other infrasound stations (KVH and LAN) were located within 1.5 km of GTM. At all stations broadband sound was recorded with GPS time-synced Reftek RT-130 data loggers acquiring at a resolution of 24 bits and a sample rate of 1000 Hz during six weeks from late July through the end of August.
 The experiment was conducted during central New Mexico's “monsoon” electrical storm activity. At least three separate storm systems (on July 24th, July 30th, and August 6th) traversed between the network stations providing a diversity of thunder signals that we recorded locally at ranges of a few hundred meters to more than ten kilometers (Figure 1). This study focuses on a one-hour period between 1 and 2 PM (19:00–20:00 UTC) on July 24th, during which 90 distinct lightning events were independently catalogued by the New Mexico LMA (Figure 2). Proximity of this lightning activity to the microphone network, time isolation of flashes, and generally low levels of ambient noise (owing to low winds), contributed to making this the best acoustic signal-to-noise dataset of all recorded thunderstorms.
 GTM was designated as the master array owing to its excellent signal-to-noise on all 4 array elements on July 24th. We use this array to locate thunder source regions through a combined slowness and distance ranging technique outlined below. We then compare thunder locations to LMA locations to assess the resolution capabilities for the linked processes and to elucidate the respective generation mechanisms of sound and VHF signals. Distinctive acoustic pulses are also located and used to predict corresponding pulse arrival times across the microphones network.
3. Methodology: Locating Thunder With a Single Array
 Following seismic array data processing techniques for presumed incident plane waves [e.g., Lacoss et al., 1969], we apply a 2-D slowness search (or velocity filtering) to identify coherent acoustic backazimuths and then calculate vertical incidence angles for band filtered acoustic signals. Horizontal slowness components (sx and sy) are equivalent to the inverse of horizontal apparent velocity in east-west and north-south directions and have units of s/m. Horizontal slowness searches, using multi-element seismic arrays, permit determination of plane wave propagation directions from one or more concurrent sources, both transient and tremor-like [e.g., see Almendros et al., 2002]. However, because seismic velocities are usually poorly constrained, there is inherent ambiguity in the vertical wave incidence angle of these sources.
 Acoustic waves in the atmosphere, on the other hand, have relatively unvarying speed (c0) that is predictable as a function of temperature (equal to 338 m/s at 10°C with ∼±0.6 m/s variation per ±°C). By assuming a temperature at the array, the vertical slowness (sz) can be uniquely determined from the two horizontal slowness components, i.e., sz = . Apparent source backazimuth and incidence are then calculated from the slowness unit vector ([c0sx, c0sy, c0sz]) and this, combined with distance ranging, can provide an absolute 3-D spatial location [e.g., Few, 1970].
 Slowness searches are performed in multiple frequency bands and over time to locate frequency band and distance-limited sources of thunder. In this study results are calculated for overlapping bands of 1–10 Hz and 4–40 Hz sound for respective moving time windows (Δt) of 2 s and 0.5 s with Δt/2 window overlap. Relatively broad spectral bands are analyzed to minimize array response aliasing that can be problematic for 4-element arrays. Window length is fixed as twice the period associated with the low corner frequency.
 Distance (r) ranging is calculated as the product of the presumed ambient sound speed (c0) and the elapsed time (t–t0) since lightning flash, allowing for a thunder source location, [xth, yth, zth], to be mapped as:
where [x0, y0, z0] are the coordinates of the acoustic array. Errors in the absolute locations of thunder sources are discussed in the auxiliary material.
 Elapsed time since flash is calculated directly from the thunder time series relative to the median occurrence times of the LMA rf sources for the event (see upward-pointed arrows in Figure 2). New Mexico LMA locations were all within the confines of the LMA network and were recorded continuously during the study interval. Event flash times and locations, accurate to a few tens of meters, were determined using 6 or more out of 9 active New Mexico LMA stations [Rison et al., 1999; Thomas et al., 2004].
 To avoid interference of overlapping thunder signals from multiple lightning flashes, we limit our analysis to time-isolated LMA events separated from previous and following events by at least 30 s. This reduces the July 24th dataset to 24 events (see Figure 2 shading) out of 90 total events identified in the LMA catalogue. We note that it is also possible to identify lightning event times (t0) directly from the electromagnetic noise picked up on microphone channels that are connected by 30-m cables to the central datalogger. This noise appears as a 100–600 ms sequence of distinctive high-amplitude spikes (Figure 3). In the absence of LMA data this noise provides convenient lightning occurrence timing. The duration of the electromagnetic noise is concurrent with the duration of the LMA flashes, but its intensity is not well correlated with the number of rf sources.
 For a given time window Δt centered at time t = t0 + r/c0 the coherence may be mapped as a function of source-receiver distance (r) and the horizontal slownesses. The energy of a beam-shifted stack of N array elements calculated in the time domain is proportional to:
for horizontal slowness values sx2 + sy2 < 1/c02. The variables Δxn, Δyn, and Δzn are the relative Cartesian coordinates of array element n with respect to the center of the array, j and Δt are the center sample and number of samples in the analyzed window, and pn is the band-filtered pressure waveform for channel n. A measure of uncorrelated energy (Eunc) can be obtained by calculating the average of equation (2) for all slowness values where sx2 + sy2 > 1/c02. Eunc corresponds to impossibly large slowness values traversing the array and is assumed to be equal to the stacked energy of uncorrelated noise. A normalized coherence is then defined as:
Coherence values, X, are converted to a Cartesian space by finding the maximum coherence in each (0.5 km)3 volume bin. These maximum values are then displayed in both plan and profile views (e.g., Figure 4). Coherence maps have advantages over the techniques for thunder localization presented by MacGorman et al. , Teer and Few , and Arechiga et al.  in that multiple coherent sources can be mapped for an individual distance range and peakedness of a slowness solution provides information about location uncertainty and/or frequency content of the source. Coherence maps calculated for synthetic pulses reveal that broader bull's-eyes are primarily an artifact of the frequency content of the source signal (see auxiliary material).
4. Results and Validation of Thunder Imaging
 General validation of the thunder imaging technique is evident through comparison with the distribution of rf sources located by the LMA (Figures 4 and S3). For the featured hour on July 24th most lightning events, and mapped thunder, occurred to the SE of the GTM array although lightning branches for some events extended to the NE (#9, 11, 14, 18, and 21–24), SW (#7, 10, and 16) and W (#1) of GTM. These branches were reliably detected by both LMA and acoustic sensing techniques. In general, thunder coherence maps are displayed as diffuse regions, especially for infrasonic (1–10 Hz) thunder, which encompass the clouds of rf sources located by the LMA. Coherence for higher frequency (4–40 Hz) sound is better for delineating fine-scale structure of thunder source regions. Coherence for even higher frequency sound (e.g., >10 Hz) is less good and tends to be poorly correlated with LMA rf sources.
 For select lightning events, correlation of multiple discrete infrasonic thunder pulses is evident across the network. As seen in Figure 4 (bottom) select thunder hypocenters, and error ellipses correspond to time-isolated, high-coherence pulses. In the absence of information about atmospheric structure the thunder location range, azimuth, and inclination errors (in meters) are respectively taken as Δr = ±160 m + 0.065 × r (for 0.5 s time windows), Δθ = ±0.05 × r, and Δϕ ≈ ± r × (i0 − sin−1(0.93 × sin i0) + 0.03 × cos i0), where i0 is incidence angle measured from the vertical (refer to Text S1 in the auxiliary material). The 3-D error ellipses associated with these thunder pulses are then used to estimate a range of sound propagation time-of-flight to stations KVH and LAN. Correlated pulses can be identified across the network including those occurring at ∼18 s (A), 23 s (B), 26 s (C), and 27.5 s (D) in the GTM trace of event #12 (Figure 4). For other lightning events the thunder pulses are often less well correlated across the network. This may occur due to complex interference arising from the different azimuthal and distance perspectives of the microphones.
 For a single point source at a given distance range, a ‘bull's-eye’ coherence map may be expected where the radius of the bull's-eye is related to the frequency content of the sound source. Broader coherence peaks should result from a lower frequency signal that might suggest a more diffuse, or extensive, source, such as would be attributed to electrostatic relaxation [e.g., Balachandran, 1979]. Higher frequency sources appear more peaked in the slowness solution and may reflect thermal shocking of an ionized channel, which is the source of audible thunder [e.g., Few, 1969]. In general, the 4–40 Hz coherence map appears to delineate finer-scale structure of thunder generating phenomena and more closely tracks channels identified by the LMA. Coherence maps may be calculated for synthetic thunder pulses (see Figure S1 in the auxiliary material) demonstrating how location resolution capabilities are worse for longer wavelength signals.
 Misfit between LMA and thunder locations is of particular interest. In some cases, thunder imaging identifies regions of sound production, which are not “seen” in the LMA record. One of many type examples can be seen as in event #1 (source C in the 1–10 Hz band). Other examples include thunder that is mapped as cloud-to-ground, such as those of events #3, 6, 10, 16, and 23, that are not obviously connected from cloud-to-ground in the LMA data. In other instances, notably in events #1, 5, 7, 17, 18, both LMA and thunder distributions clearly indicate cloud-to-ground lightning.
 Conversely, LMA mapping is able to detect some lightning channels, which are not well identified through thunder imaging. Events #16, 17, and 18 show kilometer-long “tendrils”, which are not identified in the acoustic mapping even though there is suggestion that their endpoints are associated with coherent thunder sources. Notwithstanding the possibility that acoustic detection is hampered by atmospheric propagation phenomena, inefficient sound radiation geometry, or obfuscating noise at the sensor array, it is probable that certain lightning channels do not ensonify the atmosphere due to relatively low current.
 Thunder imaging has the potential to elucidate processes in the atmosphere including both current conveyance and volume charging/discharging that are not easily seen with the LMA. Estimating the radiated acoustic energy in the infrasound and high frequency bands offers a means to potentially quantify or distinguish these two processes. For a homogeneous atmosphere with impedance ρc0 the energy contained in a band-limited acoustic thunder signal can be approximated by assuming spherical radiation of sound and integrating over the travel time (t-t0) since lightning flash (modified from Holmes et al. ):
The table in Figure 3 shows this integral calculated for broadband (0.5 Hz to 500 Hz) signal as well as for band-limited (1–10 Hz and 4–40 Hz) signal out to τ = 35 s. It is noteworthy that there is more than two orders of magnitude variability for the 24 featured events (ranging from 22 KJ total acoustic energy for event #6 to 2713 KJ for event #18). It is also significant that the spectral character of the thunder is widely variable, with some events (such as #1, 16, and 18) containing three times more energy in the 4–40 Hz band than in the 1–10 Hz band, whereas other events (such as #5–9) appear to radiate more energy at 1–10 Hz than at 4–40 Hz. The calculated acoustic energy in these three frequency bands does not appear correlated with the quantity of rf sources, as determined by the LMA. This last observation supports the conclusion that VHF and acoustic radiation represent inherently distinct processes; the LMA sees channel formation and fast current impulses, whereas the acoustic radiation reflects net charge transport.
 This work was supported by the U.S. National Science Foundation under grant AGS-0934472. We thank two anonymous reviewers for their input.
 The Editor thanks the two anonymous reviewers for their assistance in evaluating this paper.