A quantitative analysis of acoustic field directionality from a seismic airgun array

Airgun arrays are used in seismic reflection surveys to generate high-amplitude, low-frequency (as low as 5 Hz) pulses that propagate down to and through the seafloor, resulting in multiple reflections back to the surface as the acoustic pulse encounters different seabed layers, which are measured by a towed hydrophone streamer. The short-range propagation characteristics of these impulses are highly dependent on water column properties, seabed properties, and airgun array design. These systems are designed to examine the solid earth kilometers below the seafloor, but the process of firing a seismic airgun array releases significant amounts of acoustic energy into the water column, only a small fraction of which is used to examine the seabed. The data collected in these surveys is intended for seabed imaging, but it can be extended to other uses, such as examining the acoustic field and source characteristics to compare with and incorporate into models. Accurate modeling of both the source characteristics and the acoustic propagation is important for designing arrays ideal for seismic imaging but also for evaluating the acoustic field and potential environmental impacts, such as those laid out by the National Marine Fisheries Service (NMFS, 2018). Specifically, regarding marine mammals, temporary threshold shift and permanent threshold shift values are defined for different frequency ranges based on the sensitivity of different marine mammals (which are specified as low as 7 Hz and as high as 160 kHz), such that a minimum range (mitigation range) from known marine mammal sightings should be defined by a model that incorporates local environment and source characteristics whenever possible. Accurately modeling the sound pressure level (SPL) or sound exposure level (SEL) at a given range depends on source characteristics beyond simply the source amplitude; the source spectrum and beam pattern (source directionality, or relative amplitude as a function of angle) are critical. Prior work has looked at modeling the propagation from airguns over short ranges (DeRuiter et al., 2006), using seismic streamer data to characterize the propagation (Abadi and Freneau, 2019a), and consideration of marine mammal protections (Hatton, 2008; Tolstoy et al., 2009; Abadi et al., 2015, 2017).

Understanding the characteristics of individual airguns is critical for designing airgun arrays. Much of the work of characterizing airguns began more than four decades ago through rigorous theoretical and experimental work. A key component of this work is the relationship between airgun design parameters such as chamber volume and pressure to signal characteristics such as bubble period, amplitude, and spectral content. A critical finding was that the acoustic pressure is proportional to the cube root of the chamber volume, which was experimentally verified (Johnston, 1980). Additional experimental analysis demonstrated relationships between other airgun design parameters, including bubble pulse width, chamber pressure, chamber volume, airgun depth, peak-to-bubble ratio, and signal amplitude (Vaage et al., 1983). Further work has considered more depth-dependent factors, including the impacts of ghost notches (caused by surface reflection interference) on the signal and airgun-to-airgun interactions (Ziolkowski, 1986; Haavik and Landrø, 2015).

Work on computation of interaction between airguns and airgun array signatures started several decades ago (Vaage et al., 1984; Vaage and Ursin, 1987; Laws et al., 1990), showing critical relationships between interactions and separation distance and the impacts on peak amplitude (low significance), secondary oscillation amplitudes (high significance), and bubble period (high significance) when two airguns are close. More recently, rigorous models of bubble oscillations from airguns (MacGillivray, 2000; Sertlek and Ainslie, 2015) have been incorporated into several airgun modeling tools, most of which generally agree on airgun signatures up to approximately 200 Hz and also agree with experimental measurements (Li et al., 2010) but displaying some intermodel divergence at higher frequencies (Ainslie et al., 2017). Both simple and complex models have been used to model airgun arrays, including their spectra and directionality (Ainslie et al., 2016; Duncan, 2017; Duncan and Gavilroy, 2019).

The factors mentioned previously all play a significant role in airgun array design, which generally aims to accomplish three goals: increase overall amplitude of the sound source, reduce the effect of bubble oscillations so that the signal is more impulsive, and focus the acoustic energy toward the seafloor. Some experimental benchmarking has been completed on airgun arrays, including direct measurements of airgun shots during seismic surveys (Ziolkowski and Johnston, 1997; Behura and Sneider, 2013; Abadi and Freneau, 2019b; Kyrvohuz and Campman, 2019; Prior et al., 2021). Most of this work has focused on the spectra at various locations relative to the array (different ranges and propagation angles), but fine measurements of beam patterns are lacking. Several studies have considered coarse measurements of broadband frequency patterns (Diebold et al., 2010), with only recent results showing more complete coverage of propagation angles using moored arrays, providing a very thorough analysis of airgun array signal and propagation characteristics (Sidorovskaia and Li, 2022). Still, none of these results provides broad frequency-dependent results or a means for beam pattern calculations using exclusively seismic survey data. Nor do they consider a frequency- and spatially dependent uncertainty in the airgun signal behavior despite past evidence of airgun variability (Dragoset et al. 1987).

The goal of this study is to use the data acquired by the seismic hydrophone streamers during a seismic survey to understand the beam pattern characteristics and variability. This is completed using opportunistic shots of a single 40 in³ airgun (typically referred to as the “mitigation gun”) and comparing them with full array shots that are spatially and temporally close to the single airgun shot. The driving assumption here is that the environment (both in the water column and seabed) has minimal lateral variation, such that these shots can be compared directly, and that if the beam pattern of the single airgun is known (typically assumed omnidirectional), then the array beam pattern can be determined from the experimental data. This analysis draws comparisons between simulated and experimentally determined beam patterns and considers a new method to incorporate into estimating beam pattern characteristics on existing and future seismic survey airgun arrays. Furthermore, uncertainty in the beam patterns is considered, as well as the potential influence of real-world variability on airgun array models. This analysis provides insight into the accuracy of airgun models for estimating directionality and the usefulness of such models in the presence of environmental variability and experimental uncertainty.

The analysis completed herein uses data from two seismic surveys, both of which used the same source array aboard the R/V Marcus G. Langseth. The MGL1212 experiment (Holbrook et al., 2012a, 2012b), a survey studying the Cascadia subduction zone off the coast of Washington state, provides data for the source array at 9 and 15 m source depths and was collected with a towed streamer with up to 8 km range (from source to receiver) and 636 receiver channels, towed at a depth matching the source array. The data used here were collected from lines 3, 5, 7, 9, 10, and T06 (“T” indicates a turn between two lines), as shown in Figure 1a. The second cruise, the MGL2104 experiment (Carbotte et al., 2021), also studying the Cascadia subduction zone but extending from southern Oregon to Vancouver Island in British Columbia, provided the data for the 12 m source depth. Data from lines PS03, PS05, PD02, PD15, and PS01D, as shown in Figure 1b, were used for this analysis. In this experiment, the hydrophone streamer extended up to approximately 15 km and 1200 channels. Both experiments used the same source array design, shown in Figure 2a. Here, four identical linear arrays are towed in parallel, with the ship towing in the negative x-direction, relative to the figure. Each rectangle represents an airgun, with the number inside corresponding to the chamber volume (in cubic inches), combining for a total array volume of 6600 in³. All airguns are fired at the same pressure (1950 ± 50 psi) and were intended to fire simultaneously. Throughout the experiment, different combinations of airguns may be used due to equipment failure, vessel turns, or other unexpected reasons. Occasionally, if a marine mammal is spotted in the vicinity of the experiment or there is a pause in data collection, a single 40 in³ airgun, typically referred to as the “mitigation gun,” is fired. The number of consecutive mitigation gun firings in the data varies from 2 to 36 and typically depends on the reason for its use. Any reference to a single airgun being fired in this manuscript is exclusively a 40 in³ airgun (mitigation gun). The receiver array also had the same design in both experiments, shown in Figure 2b, with the only difference being the length and thus number of channels. Although it is not considered further in this manuscript, it is worth noting that the outputs of each receiver channel consist of an average of the output of 14 hydrophones equally spaced 1.25 m apart, with four hydrophones overlapping between each consecutive group, potentially affecting the overall SEL and SPL levels and certain frequencies (Crone et al., 2014).

During the seismic surveys, shots are fired continuously every 37.5 m, or roughly every 16–18 s, and each shot is measured at a 500 Hz sampling rate. The bathymetry in the cruises varies from less than 100 m to more than 3 km, but only sections of roughly constant bathymetry and enough depth to isolate direct paths and bottom reflections are used here. For each shot, the bathymetry and receiver location are used to estimate an acoustic propagation angle from the airgun array, with the propagation angle defined as shown in Figure 3a. Rather than assume a constant sound speed profile as shown by the ray trace in the figure, a sound speed profile is incorporated into the propagation angle calculation based on an average of sound speed profiles from CTD casts taken during MGL1212 (Figure 3b), leading to a slightly more complex propagation path and small differences in propagation angles.

The data that used for the analysis in this manuscript are summarized in Table 1. The precise shot numbers, where to find them in the data sets, average bathymetry for the collections of shots, and approximate sea state are provided. Sea state is reported in meters and only recorded in the cruise documentation at the start and end of each line, so the value recorded closest (in time) to the shots indicated in the tables is taken. The gray cells indicate data that are not used for the forthcoming beam pattern analysis (but considered for evaluation of the single 40 in³ airgun properties), discussed further in the “Results” section. For the MGL2104 data, every shot is documented with the corresponding array volume, but MGL1212’s records are a series of notes in the observer’s log, from which single airgun firings had to be determined.

The presence of single-airgun firings provides a unique opportunity to evaluate the differences between the received signals when a single airgun is fired versus when the full array is fired, which leads to notably different results. In sections of the survey where environmental characteristics (e.g., bathymetry and sound speed profile) are expected or known to vary slowly, adjacent single airgun shots and full array shots can be compared directly. Figure 4 shows a sample of two adjacent shots from MGL1212, Tape 25. The first row clearly shows impulse responses corresponding to the direct path (source: hydrophone, dotted line in Figure 3a), first bottom reflections (source: seafloor–hydrophone, dashed line in Figure 3a), and second bottom reflections (source: seafloor–sea surface–seafloor–hydrophone), which are apparent in both measurements. The second row provides a magnified view of the first bottom reflections (the focus of the upcoming analysis) from the first row, showing similar structure between the two cases in terms of impulse response. Also apparent are some differences in the source signal itself, though the level of detail provided here is not enough for any robust conclusions. Here, the single airgun measurements are scaled by a factor of 10 relative to the array measurements. Arrows are provided to help indicate which features are the result of the direct path, first bottom reflection, and second bottom reflection.

The beam pattern analysis performed herein ultimately provides a beam pattern for the airgun array relative to that of a single airgun, which is assumed to be omnidirectional in free space, resulting in the absolute beam pattern. The effect of the ghost notches (created by interference with sea-surface reflections) impacts the beam pattern for both the single and full array cases, but direct comparison of the two beam patterns should suppress these effects because the ghost notch should affect both cases similarly. To justify the assumption that a single airgun is close to omnidirectional and that a nonnegligible beam pattern does in fact exist for the airgun array, the spectra of the direct path signal and the first bottom reflection at the same (closest) receiver are compared, shown in Figure 5. Levels are normalized based on their mean value, and then the maximum value between the two curves is set to 0 dB. The vertical dotted blue lines indicate frequencies at which maximum destructive interference is expected from the ghost signal. At these frequencies (and surrounding frequencies), larger disparities between the two paths are expected. The first column of Figure 5 shows the results for a single 40 in³ airgun at the three depths being considered, and the second column of Figure 5 shows the same results for the airgun arrays. All of the data specified in Table 1 are included in the averaged curves. Some of the shots used consisted of multiple 40 in³ airguns firing rather than a single airgun, which increased the amount of data used and thus the robustness of the estimates. Because airgun signatures are expected to be consistent between same-sized airguns and the out-of-plane separation between adjacent strings on the source yield path length differences of less than 0.2 m (the shortest wavelength available in these data, based on the sampling rate, is approximately 6 m), it is expected that multiple combined 40 in³ airguns are equally informative as single 40 in³ airguns. The inconsistent shot volume means that the source levels shown in Figure 5 are not reliably indicative of a single airgun. The expectation of this comparison is that a single airgun spectrum for the two propagation paths has a similar shape, with the key differences due to losses along the longer reflection path and the surface interaction that creates frequency notches in the reflected path. Assuming a −1 reflection coefficient at the ocean surface, it is expected that constructive interference will occur at $fconstructive=(n−1/2)ccosθ/2d$ and destructive interference at $fdestructive=nccosθ/2d$⁠, where $c$ is the speed of sound, $n$ is any positive integer, and $θ$ is the angle defined in Figure 3a. These frequencies are summarized for each depth in Table 2, assuming a sound speed of 1490 m/s, a 2 km water column depth, and vertical propagation (the frequencies will decrease for larger offsets as $θ$ decreases). Variations in sound speed, accuracy of source and receiver depth, and variations in departure and arrival angles from and to the source and streamer based on the sound speed profile have an impact on these frequencies; therefore, these variations are to be treated as a rough guide of where these minima should be seen at the closest receivers. The red curves in Figure 5 have been adjusted based on these expected interferences to improve the comparison. Both curves are normalized based on their peak value so that direct comparison is easier. (Absolute energy levels are not of interest for this figure.)

Considering the single airgun results in Figure 5, it is evident that the general shape of the two curves is mostly in agreement for each depth, with the largest deviations roughly where they are expected. These variations can most likely be explained by a combination of surface conditions and the effects of the downward-refracting nature of the sound speed profile. In addition to ghost notches, bubble notches dependent on the natural airgun spectrum are expected and present. The agreement between these curves strongly supports the omnidirectional assumption, with some small discrepancies, when extrapolating across the range of propagation angles. Given the other environmental conditions likely encountered (e.g., sound speed variations, sediment conditions, multiple bottom reflections, surface roughness), perfect agreement is not expected.

The airgun array results of Figure 5 ideally provide some indication of an array beam pattern. In general, each case shows notable disagreement above 40–50 Hz. Not only are the values quite different in these cases, but the general shapes of the curves do not resemble one another. Because the airgun arrays are designed to focus energy toward the seafloor, it is expected that the frequency response is different in the two directions. The differences in propagation paths are clearly much more significant for the array case, indicating not only that the omnidirectional assumption for the single airgun is reasonable but also that a notable beam pattern exists for the airgun array cases.

It is challenging to obtain a clean measurement of the signal from the reflected path measurements, but the direct path can be considered simply to highlight that the 40 in³ airgun and airgun array signals are in fact significantly different. Figure 6 shows an average of 40 in³ airgun measurements using 8, 9, and 34 shots and array measurements using 19, 20, and 34 shots (for the 9, 12, and 15 m depths, respectively). Shots with multiple 40 in³ airguns firing and shots with significantly different timing (due to changes in experimental parameters rather than experimental uncertainty) are excluded. The faint black curves indicate individual shots, included to show the level of variation from shot to shot. The 40 in³ airgun shows an expected signal for a single airgun, with multiple significant peaks (the nonsmooth behavior in the 9 m case is likely the result of inconsistent shot timing). The airgun array shots have both a significantly higher amplitude and a much larger peak-to-bubble ratio. Similar results are shown in the frequency domain in Figure 7 for both the individual 40 in³ airgun and full-airgun array for both the direct and first reflected paths. The main differences in the average spectra are due to the expected signal differences when comparing a single 40 in³ airgun to a full array. (An individual airgun contains expected frequency notches unrelated to the ghost signal.) Beyond this, the most obvious observation is higher variability in the reflected paths; this is not surprising because these paths interact with the seabed and propagate through the full depth of the water column. Higher shot-to-shot variability is also evident at higher frequencies, particularly above 50 Hz. The direct path shots provide more insight into the source variability, whereas the reflected paths are more indicative of the environmental variability. To quantify this behavior, the Pearson correlation coefficient is calculated for each shot’s power spectrum relative to that of each other shot, and these coefficients are averaged. (The beam patterns are calculated using magnitudes, not complex numbers, so the same is done for this calculation.) The correlation coefficients are summarized in Table 3. For the direct path cases, correlations are very high, indicating minimal shot-to-shot variability (which could be due to a combination of source and environmental variability). The full array has slightly higher correlation than the single airgun case, suggesting that the larger number of airguns perhaps improves the signal repeatability by suppressing shot-to-shot differences in individual airgun signals (due to variations in chamber pressure, location relative to other array elements, or shot timing). The coefficients drop by 7%–14% when considering the reflected paths, which is likely due almost entirely to environmental variability. This increase is expected due to longer path lengths (and thus more interaction with the propagating environment) and additional boundary interactions. Variability in sound speed profiles or other water column properties may be a factor, but the most significant contributors are lateral changes in bathymetry and seabed structure and composition as well as dynamic surface conditions. Another feasible contributor is inconsistencies in source and receiver locations relative to other elements as well as the sea surface. Despite these factors, the correlation values still suggest strong consistency between shots.

A final factor to consider in the experiments before the beam pattern analysis is the signal-to-noise ratio (S/N) present in the measurements. In general because of the high airgun amplitudes, S/N is typically not a significant issue when considering seismic survey data. However, when directly comparing the single airgun and airgun array data, measurements at the higher end of the bandwidth (where airgun energy is lower and more losses occur) and most distant receivers could result in nonnegligible S/Ns. In addition, at frequencies where nulls (local minima with significantly reduced energy) are expected due to the ghost notch effects, S/Ns may be significantly reduced. If the ambient noise is consistent, it would lead to the two types of shots looking more alike than they truly are (i.e., for very low S/N, one is essentially comparing two roughly equivalent ambient noise fields rather than the signals themselves). Figure 8 provides S/N plots for the data to be used herein, corresponding to each source/receiver depth, with the single 40 in³ airgun shots in the first column and array shots in the second column. These data are calculated by comparing 1 s of data prior to the first arrival (direct path) at each receiver to a 1 s window surrounding the arrival of the first bottom reflection. If 1 s of noise data was not available prior to the arrival of the direct path signal (typically the first 105 receivers), a 1 s window between the direct path and first bottom reflection was used. Rather than receiver number or range, the x-axis is given as propagation angle (per Figure 3) because this more closely resembles how the data are displayed throughout the remainder of the paper. For the full-airgun array, the S/N never appears to drop below 10 dB, and for most of the receivers and frequencies, it remains above 30 dB. In the case of the single airgun, all of the measurements remain above 0 dB S/N and much of the data above 20 dB, with notable low S/N regions corresponding to minima due to the ghost notches and some sections with higher frequencies and longer ranges (smaller angles). Still, the “low S/N” areas maintain values close to 10 dB or higher. The impacts of noise are expected to be minimal but not completely absent. In general, when low S/N exists in the single airgun case but not in the airgun array case, the beam pattern will still be fairly accurate if the omnidirectional single airgun assumption is valid. In locations where both S/Ns are low, the beam pattern comparison could be influenced by the comparison between two similar noise fields, which would lead to an artificially high beam value (i.e., close to 0 dB once normalized). Only the 15 m depth single airgun case contains regions with S/Ns close to zero, in regions where ghost notches are strongest and the airgun spectrum has nulls. The spectrum-based nulls should only impact the beam pattern relative to other frequency bins (discussed more in the next section), and the interference regions will largely cancel because they are present in both cases, though they are more significant for the single airgun case, likely leading to slightly broader beam patterns than in a noise-free case.

Two methods of airgun array simulation are used here to explore the array beam patterns. First, a simple simulation is used to estimate the beam pattern at each frequency by simulating an array of coherent omnidirectional point sources of different amplitudes. In these simulations, airguns follow the geometry laid out in Figure 2, are fired simultaneously with equivalent spectra, and scale in amplitude proportional to the cube root of airgun volume (Johnston, 1980). Second, simulations of airguns are completed using the AGORA airgun model (Sertlek and Ainslie, 2015), providing a more sophisticated calculation of airgun spectra and interactions. This serves to compare the importance of simple versus complex airgun models for beam pattern considerations and to compare simulation results with experimental data. When incorporating the ghost notches into the simulations, an identical array image is placed above the ocean surface, and a −1 reflection coefficient on the surface is assumed. The airgun interactions that exist in the experimental data and the AGORA simulations are of particular interest. AGORA includes airgun interactions by outputting “notional” signatures, the airgun signals expected when accounting for nearby airgun bubble effects, which can then be combined to generate an AGORA-based beam pattern. Table 4 summarizes the critical distances for each airgun (Vaage et al., 1984) and indicates which airguns (almost all for this array design) will have nonnegligible interactions with other airguns. Because the critical distances are almost all less than the airgun string separation distances, interactions are generally contained within adjacent airguns on a single string. Furthermore, the path length difference between equal-sized airguns in the array never exceeds 0.2 m, negligible relative to even the highest signal wavelength of about 6 m (at 250 Hz, the Nyquist frequency). Thus, the effects of subarray spacing can be almost entirely neglected. The simulations are not considering environmental or propagation characteristics aside from the surface interaction and thus do not account for attenuation, spreading losses, surface scattering, and so on.

The data used for the experimental beam pattern calculations are taken from sections of the experiments with slowly varying, near-constant bathymetry. This characteristic, paired with the close spatial and temporal proximity of each shot, is a key factor in the assumption that the impulse response between consecutive shots is varying slowly and that nearby shots can be compared directly. The slowly varying bathymetry assumption is addressed in Table 1 for each case. Because of the large depths, even the maximum depth differences between the single airgun and airgun array cases lead to less than a half-degree difference in departure or arrival angles at the closest source or receiver. (The beam patterns considered herein uses one degree of resolution.) The variations in depth are not expected to have significant impacts on characteristics such as attenuation or sound speed profile because the larger gradients in these properties tend to exist closer to the top of the water column or below the sea floor. In addition, because only spectral amplitude is considered and not signal phase, depth differences that are comparable to or larger than a signal wavelength do not have significant effects, assuming minimal losses in the water column. Across all of the experimental data used, the sea state remains at 4 m or below. (The sea state is only recorded at the start and end of each line, so it is not available at a higher resolution.) Sea state potentially affects the surface reflection coefficient, particularly because the highest reported wave height in the cruise logs (approximately 4 m) corresponds to roughly a half wavelength at the higher end of the bandwidth considered. The majority of the data are taken at sea states of 1 m or lower. The sea state influences the reflection coefficient, but by averaging over multiple shots, the characteristics of any single sea surface reflection do not significantly influence the final results.

To calculate the beam patterns, the full available bandwidth is used, though the bulk of the acoustic energy in the recorded data lies between 10 and 220 Hz. Prefiltering was completed at the point of data acquisition, with a Butterworth high-pass filter applied at 3 Hz (6 dB/octave) and a digital finite impulse linear phase high-cut filter at 206 Hz (276 dB/octave) (Crone et al., 2014). This filtering explains the unusual behaviors in the region greater than 220 Hz of the following figures. Receiver channels with inconsistent data (usually due to a physical issue with the receiver channel), which are identified here as receiver channels with a root-mean-square broadband acoustic pressure that differs by more than 25% from the average of the surrounding 20 channels, are excluded from the analysis. The first bottom reflection arrival time is estimated based on the recorded receiver ranges and bathymetry, and a 1 s window with this point at the center is used to calculate the spectra, isolating the first bottom reflections. Here, the variability in seabed composition is assumed to be negligible between adjacent shots. A departure angle (⁠$θ$ in Figure 3a) is calculated for each receiver, based on the range, bathymetry, and sound speed profile, rounded to the nearest integer degree. For receivers with the same departure angle, the spectral magnitudes are averaged. These angle-dependent spectra are then averaged across all shots, both for the single 40 in³ airgun and airgun array data. The averages of the airgun spectra are divided by the averages of the 40 in³ airgun spectra for each of the three source/receiver depths, which, if the impulse response functions are truly identical, would result in a unique beam pattern for each frequency bin (in this case, 1 Hz bins). Furthermore, if the impulse response function is assumed to include all of the information about the geometry and environment, then factors such as hydrophone group averaging, boundary interactions, and attenuation can be ignored because they would be expected to affect both types of signals equally and thus be removed in the final beam pattern analysis.

This result provides the source directionality at a given frequency, which is desired when considering propagation characteristics at a given frequency. By applying a frequency-dependent source spectrum, one can combine the spectral amplitudes with this beam pattern to obtain broadband propagation characteristics.

Finally, this technique produces a beam pattern in the direction of the towed streamer. However, because the array is not symmetric along this axis, it is expected that the beam pattern would show slightly different characteristics in the opposite direction and notably different characteristics in the perpendicular direction. The beam pattern analysis completed here is useful for modeling and evaluating experimental data in the towed streamer direction, but potential beam pattern differences should be considered for developing models for directions that are not along the towed streamer path. In the direction perpendicular to the direction of travel, one expects a simpler beam pattern because the adjacent arrays in that direction would consist of four to six equally sized airguns but more individual arrays. An improved understanding of the differences between experimental and simulated beam patterns resulting from this analysis can aid in accurate modeling for these propagation directions.

The two simulation techniques laid out in the “Methods” section are used here for all source depths and compared with experimental data, and cases with and without the ghost notches are considered. First, the result of an AGORA simulation for a single 40 in³ airgun is compared with the measurements of single airgun shots, shown in Figure 9. The simple simulations are left out because without any additional airguns or airgun interactions, the results are identical to the AGORA simulation because all frequencies are shown with equal weight. The dashed curves on the AGORA plots (Figure 9a–9c) indicate the expected null locations due to the surface interaction. The single airgun data shown here is reorganized to make the beam pattern analysis convenient, similar to the S/N plots in Figure 8, where the spectral magnitude at each channel is calculated and binned based on the propagation angle to that channel and averaged with others within the same bin, allowing the output to be expressed as a function of angle. The experimental output is not normalized at each individual frequency, so the spectrum of the airgun signal is evident, with notable peaks and notches below 100 Hz. In these plots, the notches due to the surface interactions are easily identified and agree well with the simulation. Furthermore, as expected, amplitudes significantly decrease as frequency increases and as angle decreases. (Larger angles correspond to larger propagation ranges.) Receiver issues at the 36° channels led to a gap in data, generating a null that is indicative of an equipment issue rather than any physics.

The outputs of the simple simulations, AGORA simulations, and experimental measurements for the full-airgun array are shown in Figure 10. The same expected nulls due to the ghost notches are clearly shown, but an additional set of nulls exist due to the array geometry. In simulation, these nulls are consistent and independent of array depth. Although differences can be seen between the simple simulations and AGORA simulations, they are not significant; the nulls are slightly less prominent, and some frequency-dependent ripples are present, but overall it appears as if the airgun interactions modeled in AGORA do not substantially impact the beam pattern. Looking at the experimental data, several straightforward conclusions are made. The nulls due to the ghost notches are again easily identifiable and agree well with the expected locations. The S/N is also higher across the frequency spectrum than in the single airgun case, as expected. The frequency content is more broadband, with frequency peaks and notches due to airgun design less prominent. Interestingly, the new notches introduced in simulations from the array geometry are not clear in these figures. (Some indications of the largest arc exist.) The amplitude generally decreases from the bottom left to upper right sections of the plots, indicative of a drop in energy, which may make the nulls harder to identify. This drop in the amplitude occurring in a region of the plot roughly corresponding to the first null shown in simulations may be indicative of some agreement. The experimental data in both Figures 9 and 10 potentially have effects of hydrophone streamer group averaging present in the results, reducing the overall levels by about 6 dB (Diebold et al., 2010; Crone et al., 2014), but this effect should be negated in the direct comparison between the single airgun and airgun array shots because it is equally present in both.

Figure 11 provides the beam patterns described in the previous section. Because the ratio of the airgun array and single airgun outputs is expected to negate the bulk of the environmental influences, the effects of the ghost notch should be significantly suppressed, so these are removed from the simulations in this figure. The simple simulations (Figure 11a–11c) indicate the same notches introduced in Figure 10 and suggest significant decreases in amplitude moving to the upper right of the plot. The AGORA simulations (Figure 11d–11f) are very similar, again with less prominent nulls due to airgun interaction effects and some frequency-dependent rippling but with overall differences that are minimal. Finally, the experimentally determined beam patterns are presented (Figure 11g–11i) for each depth. In these results, each frequency bin is normalized such that the maximum value is 0 dB; thus, the influence of the frequency-dependent amplitude factor has been removed. The prominence of the ghost notches are not completely absent, likely due to source variability in the array and dynamic environmental conditions (e.g., surface conditions and slowly changing seabed properties), but it has been significantly reduced. In general, the results agree with the simulations in that the amplitude is decreasing toward the upper right plot direction. The beams are very broad up to 50–75 Hz, with broad beam regions extending to higher frequencies in the 12 m case and even higher in the 15 m case. Frequencies above 220 Hz are not indicative of beam patterns; the filtering of the signals during data acquisition (mentioned previously) significantly reduces the amplitude of measurements taken in this range, making it negligible for this analysis. In the 15 m case, the beams appear narrower, and the range of low frequencies with nearly uniform beams decreases. As in the prior figure, the nulls indicated in simulation are not obvious. Although one can identify features potentially indicative of these nulls, the feature locations vary between the three cases, and thus the existence of the nulls cannot be stated with certainty. This may be due in part to a more rapid decrease in amplitude moving toward the upper right section of the plots.

The results thus far present both simulated and experimental estimates of the airgun array beam patterns. However, it is necessary to understand the variability in these results that are driven by experimental uncertainty, environmental conditions, or variations in airgun array behavior. Simulations provide an opportunity to examine how different characteristics of the airgun array impact the beam pattern. Airgun amplitudes can vary from shot to shot, and uncertainty exists in the relative airgun positions and firing times. Figure 12 considers fluctuations in these three variables by simulating 10,000 cases with each airgun in the array varying randomly based on a predicted uncertainty level. The first column is an average of 10,000 cases for each of three variables (airgun positions, airgun firing time, and airgun amplitude), and the second column shows the standard deviation of the beam pattern results divided by the mean in decibels (so that a result of 0 dB indicates that the standard deviation is equal to the mean of the beam pattern at that point). In the first row, airgun position is randomly adjusted from its nominal position with a standard deviation of 0.25 m in all three directions. The standard deviation results indicate that the airgun position makes very little difference to the resulting beam pattern, with the most significant differences occurring in the beam nulls, but even these are minimal. The second row randomly adjusts the shot timing with a standard deviation of 1 ms but a maximum of 2 ms (based on numbers reported in cruise documentation). Much more notable differences are visible as a result of variations in timing, with significant standard deviations in the results essentially everywhere outside of the bottom left corner of the plots (low-frequency signals focused toward the seafloor, where wavelengths are much larger than 1 ms times the speed of sound). The final row considers random amplitude variations of 25%, again showing mostly insignificant changes in the beam pattern but with nonnegligible effects in the nulls. These results demonstrate that more than all of the factors, shot timing is the most significant in impacting beam patterns, such that it should not be neglected when considering airgun models and the random variation among shots, especially for something such as marine mammal protection, where absolute acoustic energy is critical. The beam pattern nulls carry the most significant variation in results, suggesting that this region is the most sensitive to uncertainty. It also lends one possible explanation for why the nulls are not prominent in the experimental results of Figure 11: the variability in source array parameters will cumulatively impact these regions the most, reducing their prominence relative to the rest of the plot.

The experimental results in Figure 11 (final row) were produced using an average of many shots, and thus a standard deviation can be calculated from the experimental data. Considering the standard deviation at each point (i.e., each frequency and angle) shows which frequencies and propagation angles are associated with the lease certainty. This is calculated by considering the set of beam patterns generated from each available pair of airgun array and single airgun shots. Figure 13 shows this result for each of the three depths, expressed as the standard deviation divided by the mean (again, so that 0 dB indicates a standard deviation equal to the mean). Each result shows that minimal variation occurs at low frequencies, and in general, at shallower angles (longer ranges), the variation is smaller (some of this may be due to lower S/Ns). The highest level of variation occurs in the regions corresponding to the ghost notches. (Although this is not considered in Figure 12, it is consistent in that higher levels of uncertainty exist where nulls are expected.) These results suggest that overall, higher frequencies at propagation angles over approximately 50° have the most significant uncertainty levels. However, the overall standard deviations indicated in these plots are quite high, suggesting that despite the only moderate shot-to-shot variability observed in the prior section, the beam patterns are potentially much more sensitive.

Knowledge of an airgun array’s angle-dependent spectrum is critical in the design of an array and the process of accurately evaluating the propagation of these sounds in the marine environment and subsequently the comprehensive environmental impact of a seismic survey. The existing literature from the past 50 years contains significant work studying airgun spectra, but the beam patterns resulting from array designs are challenging to estimate due to many uncontrollable (or difficult to control) factors, such as environmental variability, design and implementation uncertainty, and nonlinear effects from airgun interactions. It is necessary to develop a quantitative understanding of these beam patterns, how the performance in the field compares with models, and how variable they can be.

The AGORA model is a free (for academic purposes) airgun array modeling package, chosen here for comparison with both simple airgun array beam pattern models and experimental data. Despite the complexity built into the AGORA model, the results of Figures 10 and 11 demonstrate that a model that treats each airgun as a simple source (i.e., omnidirectional at all frequencies) yields a similar beam pattern. AGORA provides valuable information with regards to individual airgun spectra, which are not obtained using the simple model considered herein and is an important feature for modeling airgun propagation. However, the modeled beam patterns are comparable to the simple model, despite the inclusion of airgun interaction, depth effects, and more in AGORA. This suggests that simple models are adequate to evaluate beam patterns for this array design, the influence of the factors mentioned previously needs more rigorous analysis and implementation, or the variability in the source array from shot to shot is simply too large for accurate comparison with field data.

Some discrepancies exist between the simulated and experimental results in Figure 11, though general trends that do agree are worthwhile pointing out. Typically, beam patterns up to approximately 50 Hz are broad, and much of the energy is being focused toward the sea floor, indicated by larger amplitudes toward higher angles. Moving from the bottom left portion of the plot to the upper right, the region where the amplitude begins to decrease substantially aligns reasonably well with the first null visible in simulation. However, beyond that shift to lower amplitude, the distinct nulls visible in the simulated cases are not easily identifiable in the experimental beam patterns. Frequencies above 220 Hz do not yield usable data due to filtering applied to the data upon collection. Prior work has found a lack of depth-dependence in source amplitude but direct relationships to bubble period and the primary–bubble amplitude ratio (Vaage et al., 1983). Furthermore, AGORA includes the airgun depth in its model of pressure from the airgun bubble (Sertlek and Ainslie, 2015). Despite this, simulated cases indicate almost no depth dependence. The experimental results suggest some depth-dependent trends (general narrowing of the beams across the spectrum); however, this cannot be stated conclusively due to uncertainty in the results (indicated in Figure 13) resulting from both source and environmental variability.

Of course, the field results presented here are contaminated by uncontrollable environmental factors and noise, as well as experimental uncertainty, but the high S/Ns of the seismic surveys and the averaging of many shots ideally control this to a reasonable degree. There are multiple possible explanations for the simulation-to-experiment discrepancy, several of which may be true. First, airgun models may need to account for stronger airgun interaction effects. The AGORA results indicate minor impact from airgun interaction, yet Table 4 suggests that nearly every airgun has nonnegligible interactions with at least one neighboring airgun. Second, the experimental results vary between the three depths (beyond expected surface interaction effects, which are expected to be significantly reduced here because they are present in both the single airgun and full array cases). It is unclear due to the data variability if this is due to a depth-dependence, unmeasured environmental variability, or another difference between cruises or cruise lines. Third, Figures 12 and 13 indicate some areas of nonnegligible variance in the beam patterns. This variance (which obviously does not exist in the simulated cases) can be due to environmental variability (changes to sound speed, bathymetry or geophysical dependence, surface conditions, and so on); noise; or inconsistencies in airgun geometry, shot amplitude, and shot timing. Both figures indicate that the nulls are most susceptible to variance and should represent the areas of greatest uncertainty. In particular, the uncertainty values in shot timing reported in the cruise reports show significant effects on the simulated results. This lends a potentially strong explanation to the nulls that appear to be missing in the experimental results. Another possibility not tested here is variable offsets of full airgun strings relative to one another along the towing direction (i.e., along the x-axis direction in Figure 2a), which is likely to be larger than variable distance between individual airguns and cause significant smearing of beam patterns. Finally, the level of variability present in the experimental data must generally be considered and should be included in modeling and prediction exercises; thus, an understanding of its manifestation is of use.

With the potential variance of airgun arrays being a significant contributor to the beam pattern results, not only is accurate modeling important, but array design and permitting should consider the variance in the beam patterns in addition to the mean. The results here show that in real-world implementation, the level of uncertainty present is nonnegligible, and prediction of the acoustics field and uncertainty is important. Absolute control of the airgun arrays will always have some degree of limitation, and the actual airgun array signals and behaviors are more important to understand than the expected or intended ones.

Knowledge of airgun array beam patterns is important for proper modeling of the acoustic field in seismic reflection surveys. The preceding results compare beam patterns estimated experimentally with the results generated from simulations. The effects of variation among different airgun array design variables are considered with simulations and field data to understand the variability expected in the results.

Several conclusions can be made from the results presented previously. First, the airgun array design is effective at concentrating acoustic energy toward the seafloor, particularly at frequencies above 50 Hz. This is one of the primary goals of the airgun array design and is valuable to confirm and quantify experimentally. Second, significant variance exists in the experimentally determined beam patterns, and simulations suggest that airgun array timing is likely the most significant contributor to shot-to-shot changes. Third, the general differences between simulations and field data discussed in the prior section suggest that enhancements to airgun array models would be advantageous. Finally, uncertainty in individual airgun array shots is nonnegligible and should be incorporated in analyses of airgun arrays.

This research was supported by the Office of Naval Research through grant no. N00014-21-1-2727. We thank the captains, crews, and technical and science parties for the R/V Marcus Langseth cruises MGL1212 and MGL2104. We also thank the developers of the AGORA Airgun Array Signature Model.

Data associated with this research are available and can be accessed via the following URL: https://www.marine-geo.org.

Biographies and photographs of authors are not available.