Source Waveform Research Articles

Acoustic Characterization of the NASA Langley 14- by 22-Foot Subsonic Tunnel using a Phased Array

A characterization test was conducted in the NASA Langley Research Center 14- by 22-Foot SubsonicTunnel to assess recent acoustic modifications in the facility. Test section reflectivity, backgroundnoise and shear layer effects were evaluated by taking measurements of known noise sources.Both conventional speakers and a high-pressure air source were employed as noise generationmechanisms. These were mounted to a pole or fairing at a consistent location in the test section.The source waveforms were used to represent the expected frequency content of scaled Urban AirMobility vehicles. Acoustic measurements were taken using two unique microphone arrays placed outside the core flow, one of which was a 54-element streamwise-traversing phased array. The other was an 11-element linear tower array. The applicability of phased array acoustic beamforming techniques to mitigate shear layer effects and reject background noise is presented. Additionally, beamforming results are compared to results from single-microphone processing techniques. Flow speeds investigated ranged from Mach 0.00 (static) to Mach 0.12. The tunnel has been partially acoustically treated but still exhibits flow noise, reducing the signal-to-noise ratio of the source under investigation. Conventional beamforming was able to capture high frequency content passing through the shear layer better than single microphone measurements. CLEAN deconvolution improves source mapping at low frequencies.

Comparing the compensatory reserve metric obtained from invasive arterial measurements and photoplethysmographic volume-clamp during simulated hemorrhage.

The compensatory reserve metric (CRM) is a novel tool to predict cardiovascular decompensation during hemorrhage. The CRM is traditionally computed using waveforms obtained from photoplethysmographic volume-clamp (PPGVC), yet invasive arterial pressures may be uniquely available. We aimed to examine the level of agreement of CRM values computed from invasive arterial-derived waveforms and values computed from PPGVC-derived waveforms. Sixty-nine participants underwent graded lower body negative pressure to simulate hemorrhage. Waveform measurements from a brachial arterial catheter and PPGVC finger-cuff were collected. A PPGVC brachial waveform was reconstructed from the PPGVC finger waveform. Thereafter, CRM values were computed using a deep one-dimensional convolutional neural network for each of the following source waveforms; (1) invasive arterial, (2) PPGVC brachial, and (3) PPGVC finger. Bland-Altman analyses were used to determine the level of agreement between invasive arterial CRM values and PPGVC CRM values, with results presented as the Mean Bias [95% Limits of Agreement]. The mean bias between invasive arterial- and PPGVC brachial CRM values at rest, an applied pressure of -45mmHg, and at tolerance was 6% [-17%, 29%], 1% [-28%, 30%], and 0% [-25%, 25%], respectively. Additionally, the mean bias between invasive arterial- and PPGVC finger CRM values at rest, applied pressure of -45mmHg, and tolerance was 2% [-22%, 26%], 8% [-19%, 35%], and 5% [-15%, 25%], respectively. There is generally good agreement between CRM values obtained from invasive arterial waveforms and values obtained from PPGVC waveforms. Invasive arterial waveforms may serve as an alternative for computation of the CRM.

Neuronal Modeling of Cross-Sensory Visual Evoked Magnetoencephalography Responses in the Auditory Cortex.

Previous studies have demonstrated that auditory cortex activity can be influenced by cross-sensory visual inputs. Intracortical laminar recordings in nonhuman primates have suggested a feedforward (FF) type profile for auditory evoked but feedback (FB) type for visual evoked activity in the auditory cortex. To test whether cross-sensory visual evoked activity in the auditory cortex is associated with FB inputs also in humans, we analyzed magnetoencephalography (MEG) responses from eight human subjects (six females) evoked by simple auditory or visual stimuli. In the estimated MEG source waveforms for auditory cortex regions of interest, auditory evoked response showed peaks at 37 and 90 ms and visual evoked response at 125 ms. The inputs to the auditory cortex were modeled through FF- and FB-type connections targeting different cortical layers using the Human Neocortical Neurosolver (HNN), which links cellular- and circuit-level mechanisms to MEG signals. HNN modeling suggested that the experimentally observed auditory response could be explained by an FF input followed by an FB input, whereas the cross-sensory visual response could be adequately explained by just an FB input. Thus, the combined MEG and HNN results support the hypothesis that cross-sensory visual input in the auditory cortex is of FB type. The results also illustrate how the dynamic patterns of the estimated MEG source activity can provide information about the characteristics of the input into a cortical area in terms of the hierarchical organization among areas.

Image analysis and resolution for detection-based synthetic-aperture passive source localization

This paper follows a detection-theoretic approach for using synthetic-aperture measurements, made at multiple moving passive receivers, in order to form an image showing the locations of stationary sources that are radiating unknown electromagnetic or acoustic waves. The paper starts with a physics-based model for the propagating fields, and, following the general approach of McWhorter et al (2023 arXiv:2302.06816, IEEE Open J. Signal Process. 4 437–51), derives a detection statistic that is used for the image formation. This detection statistic is a quadratic function of the data. Each point in the scene is tested as a possible hypothesized location for a source, and the detection statistic is plotted as a function of location. Because this image formation process is nonlinear, the standard linear methods for determining resolution cannot be applied. This paper shows how to analyze the detection image by first writing the noiseless image as a coherent sum of shifted complex ambiguity functions of the source waveform. The paper then develops a technique for calculating image resolution; resolution is found to depend on the sensor-source geometry and also on the properties (bandwidth and temporal duration) of the source waveform. Optimal filtering of the image is given, but a simple example suggests that optimal filtering may have little effect. Analysis is also given for the case in which multiple sources are present.

Acoustic source characterization for chemical explosions in air

Chemical explosions in the air generate large pressure disturbances. These pressure waves propagate as non-linear shock waves near the source and transition into acoustic waves in the far-field. Since low-frequency acoustic waves propagate long distances without significant loss of energy, acoustic signals induced by explosions are often used to determine explosion energies of the events in terms of an explosion yield. In order to estimate the explosion energy accurately, the relationship between acoustic energy and explosion yield must be understood. However, explosion yields are often measured by non-linear shock waves in the near-field, and it is not clear how much acoustic energy accounts for the explosion energy. In addition, acoustic signals typically have lower-frequency contents than shock waves in the near-field, and hence frequency-dependent explosion energy should be understood to accurately infer explosion yields based on acoustic observations. In this study, we investigate the relationship between acoustic energy and explosion yield based on ground-truth explosion data. A standard acoustic source waveform will be determined by acoustic observations, and frequency-dependent energy will be explored for yield estimation. We will demonstrate that this frequency-dependent acoustic source characterization can improve the accuracy and confidence of explosion yield estimation.

Simulation Analysis and Optimization Design of Electromagnetic Fields in Coaxial Processing Cavities Based on the Theory of Electrostatic Fields

The coaxial processing cavity is an important component of high-frequency electromagnetic water treatment devices. Due to its easy installation, wide applicability, and excellent scale removal effect, it has been widely used in various factories. To study the influence of excitation source waveform, processing cavity length, and anode-cathode radius ratio on the intensity and distribution of the electromagnetic field in the coaxial processing cavity under time-varying fields, this paper derives the numerical calculation formula for electromagnetic energy in the coaxial processing cavity based on the theory of electrostatic fields. The finite element method is used to visualize the intensity and distribution of the electromagnetic field in the coaxial processing cavity. By optimizing the structure of the coaxial processing cavity, the optimal range of the anode-cathode radius ratio is determined. The research results show that, under the conditions of electrostatic field theory, square waves have the maximum electromagnetic energy, the length of the processing cavity does not affect the distribution of the electromagnetic field, and the optimal anode-cathode radius ratio range is 0.375-0.5.

Motor unit tracking using blind source separation filters and waveform cross-correlations: reliability under physiological and pharmacological conditions.

Recent advancements in the analysis of high-density surface electromyography (HDsEMG) have enabled the identification, and tracking, of motor units (MUs) to study muscle activation. This study aimed to evaluate the reliability of MU tracking using two common methods: blind source separation filters and two-dimensional waveform cross-correlation. An experiment design was developed to assess physiological reliability, and reliability for a drug intervention known to reduce the firing rate of motoneurones (cyproheptadine). HDsEMG signals were recorded from tibialis anterior during isometric dorsiflexions to 10%, 30%, 50% and 70% of maximal voluntary contraction. MUs were matched within session (2 hr) using the filter method, and between sessions (7 days) via the waveform method. Both tracking methods demonstrated similar reliability during physiological conditions (e.g., MU discharge: filter ICC 10% of MVC = 0.76, to 70% of MVC = 0.86; waveform ICC: 10% of MVC = 0.78, to 70% of MVC = 0.91). Although reliability slightly reduced after the pharmacological intervention, there were no discernible differences in tracking performance (e.g., MU disc filter ICC: 10% of MVC = 0.73, to 70% of MVC = 0.75; DR waveform ICC: 10% of MVC = 0.84, to 70% of MVC = 0.85). The poorest reliability typically occurred at higher contraction intensities, which aligned with the greatest variability in MU characteristics. This study confirms that tracking method may not impact the interpretation of MU data, provided that an appropriate experiment design is employed. However, caution should be used when tracking MUs during higher intensity isometric contractions.

Investigation of self-supervised pre-trained models for classification of voice quality from speech and neck surface accelerometer signals

Prior studies in the automatic classification of voice quality have mainly studied the use of the acoustic speech signal as input. Recently, a few studies have been carried out by jointly using both speech and neck surface accelerometer (NSA) signals as inputs, and by extracting mel-frequency cepstral coefficients (MFCCs) and glottal source features. This study examines simultaneously-recorded speech and NSA signals in the classification of voice quality (breathy, modal, and pressed) using features derived from three self-supervised pre-trained models (wav2vec2-BASE, wav2vec2-LARGE, and HuBERT) and using a support vector machine (SVM) as well as convolutional neural networks (CNNs) as classifiers. Furthermore, the effectiveness of the pre-trained models is compared in feature extraction between glottal source waveforms and raw signal waveforms for both speech and NSA inputs. Using two signal processing methods (quasi-closed phase (QCP) glottal inverse filtering and zero frequency filtering (ZFF)), glottal source waveforms are estimated from both speech and NSA signals. The study has three main goals: (1) to study whether features derived from pre-trained models improve classification accuracy compared to conventional features (spectrogram, mel-spectrogram, MFCCs, i-vector, and x-vector), (2) to investigate which of the two modalities (speech vs. NSA) is more effective as input in the classification task with pre-trained model-based features, and (3) to evaluate whether the deep learning-based CNN classifier can enhance the classification accuracy in comparison to the SVM classifier. The results revealed that the use of the NSA input showed better classification performance compared to the speech signal. Between the features, the pre-trained model-based features showed better classification accuracies, both for speech and NSA inputs compared to the conventional features. The two classifiers performed equally well for all the pre-trained model-based features for both speech and NSA signals. It was also found that the HuBERT features performed better than the wav2vec2-BASE and wav2vec2-LARGE features for both speech and NSA inputs. In particular, when compared to the conventional features, the HuBERT features showed an absolute accuracy improvement of 3%–6% for speech and NSA signals in the classification of voice quality.

An information theoretic Bayesian uncertainty analysis of AEM systems over Menindee Lake, Australia

SUMMARY Long-range, active-source airborne electromagnetic (AEM) systems for near-surface conductivity imaging fall into two categories: helicopter (rotary-wing) borne or fixed-wing aircraft borne. A multitude of factors such as flying height, transmitter loop area and current, source waveforms, aerodynamic stability and data stacking times contribute to the geological resolvability of the subsurface. A comprehensive comparison of the relative merits of each system considering all such factors is difficult, but test flights over well-constrained subsurface geology with downhole induction logs are extremely useful for resolution studies. However, given the non-linear nature of the electromagnetic inverse problem, handling transmitter–receiver geometries in fixed-wing aircraft is especially challenging. As a consequence of this non-linearity, inspecting the closeness of downhole conductivities to deterministic inversion results is not sufficient for studying resolvability. A more comprehensive picture is provided by examining the variation in probability mass of the depth-wise Bayesian posterior conductivity distributions for each kind of AEM system within an information theoretic framework. For this purpose, probabilistic inversions of data must be carried out. Each acquiring system should fly over the same geology, survey noise levels must be measured and the same prior probabilities on conductivity must be used. With both synthetic models as well as real data from over the Menindee calibration range in New South Wales, Australia, we shed new light on the matter of AEM inverse model uncertainty. We do this using two information theoretic attributes derived from different Kullback–Leibler divergences—Bayesian information gain, and a strictly proper scoring rule, to assess posterior probabilities estimated by a novel Bayesian inversion scheme. The inversion marginalizes fixed-wing geometry attributes as generic nuisance parameters during Markov chain sampling. This is the first time-domain AEM study we know of, that compares nuisance marginalized subsurface posterior conductivities from a fixed-wing system, with rotary-wing derived posterior conductivities. We also compare field results with induction log data where available. Finally, we estimate the information gain in each case via a covariate shift adaptation technique that has not been used before in geophysical work. Our findings have useful implications in AEM system selection, as well as in the design of better deterministic AEM inversion algorithms.

Spatiotemporal Dynamics of Activation in Motor and Language Areas Suggest a Compensatory Role of the Motor Cortex in Second Language Processing.

The involvement of the motor cortex in language understanding has been intensively discussed in the framework of embodied cognition. Although some studies have provided evidence for the involvement of the motor cortex in different receptive language tasks, the role that it plays in language perception and understanding is still unclear. In the present study, we explored the degree of involvement of language and motor areas in a visually presented sentence comprehension task, modulated by language proficiency (L1: native language, L2: second language) and linguistic abstractness (literal, metaphorical, and abstract). Magnetoencephalography data were recorded from 26 late Chinese learners of English. A cluster-based permutation F test was performed on the amplitude of the source waveform for each motor and language region of interest (ROI). Results showed a significant effect of language proficiency in both language and motor ROIs, manifested as overall greater involvement of language ROIs (short insular gyri and planum polare of the superior temporal gyrus) in the L1 than the L2 during 300-500 ms, and overall greater involvement of motor ROI (central sulcus) in the L2 than the L1 during 600-800 ms. We interpreted the over-recruitment of the motor area in the L2 as a higher demand for cognitive resources to compensate for the inadequate engagement of the language network. In general, our results indicate a compensatory role of the motor cortex in L2 understanding.

ALMA 2022 experiment : Source paramater estimation comparison betweenLFM and MLS waveforms

For underwater source localization, accurate estimation of the time of flight (or travel time) is required and the observed waveform may include Doppler (waveform dilation). The source waveform, thus, needs to be sensitive to estimate both time of flight and Doppler. In this study, we compare two waveforms : Linear Frequency Modulated sweeps (LFMs) and Maximum Length Sequences (MLSs) with identical center frequency (6 kHz) and bandwidth (2 kHz). During an at-sea experiment conducted in March 2022 near in the Mediterranean Sea, near the coast of Toulon, a mobile source transmitted the two waveforms, recorded by a 192-hydrophone moored bilboard array. The source-array distance ranged from 2.5 to 8 km, and the source was towed at a constant speed (∼1.5 m/s) and depth (∼50m). The analysis of the gathered data shows that the MLS waveform outperforms the LFM waveform for estimating time of flight (uncertainty reduced by a factor 4) and radial velocity (uncertainty reduced by a factor 20). Preliminary results focus on single hydrophone processing, but possible applications to 2D array processing are discussed for localizing the source in range-dependent environments.

Aging alters across-hemisphere cortical dynamics during binaural temporal processing.

Differences in the timing and intensity of sounds arriving at the two ears provide fundamental binaural cues that help us localize and segregate sounds in the environment. Neural encoding of these cues is commonly represented asymmetrically in the cortex with stronger activation in the hemisphere contralateral to the perceived spatial location. Although advancing age is known to degrade the perception of binaural cues, less is known about how the neural representation of such cues is impacted by age. Here, we use electroencephalography (EEG) to investigate age-related changes in the hemispheric distribution of interaural time difference (ITD) encoding based on cortical auditory evoked potentials (CAEPs) and derived binaural interaction component (BIC) measures in ten younger and ten older normal-hearing adults. Sensor-level analyses of the CAEP and BIC showed age-related differences in global field power, where older listeners had significantly larger responses than younger for both binaural metrics. Source-level analyses showed hemispheric differences in auditory cortex activity for left and right lateralized stimuli in younger adults, consistent with a contralateral activation model for processing ITDs. Older adults, however, showed reduced hemispheric asymmetry across ITDs, despite having overall larger responses than younger adults. Further, when averaged across ITD condition to evaluate changes in cortical asymmetry over time, there was a significant shift in laterality corresponding to the peak components (P1, N1, P2) in the source waveform that also was affected by age. These novel results demonstrate across-hemisphere cortical dynamics during binaural temporal processing that are altered with advancing age.

Resolution of matched field processing for a single hydrophone in a rigid waveguide.

This paper studies resolution of matched field processing for locating, in range and depth, a broadband underwater acoustic source from data measured at a single hydrophone receiver. For the case of an ideal rigid shallow-water waveguide with a pressure-release top boundary and a rigid bottom boundary, the paper derives approximations for the main-lobe widths of the ambiguity surface. The two cases studied in this paper are (1) when coherent measurements of the pressure are available, with the transmitted source waveform precisely known, and (2) when only measurements of the received-signal pressure magnitude-squared are available, such as might occur when the transmitted signal is random and unknown. The analysis uses the normal-mode expansion for the pressure field to derive approximate expressions for the ambiguity-surface main-lobe widths, as a function of the number of modes and frequency band, for both range and depth. Numerical results are presented corroborating the analytical analysis. Finally, the paper argues that this ambiguity analysis can also give insights into Pekeris waveguides under appropriate conditions and shows numerical simulations of matched-field localization ambiguity surfaces for some realistic shallow-water Pekeris environments.

Adaptive filtering of microseismic data for monitoring a water-conducting fractured zone in a mine

Water-conducting fractured zones in a rock mass can cause problems in mining. Attempts have been made to monitor their development using microseismic signals. However, due to the lack of prior information, it is difficult to filter out mixed low-frequency interference with traditional denoising methods. In this work, the proposed adaptive filtering algorithm is applied after the wavelet packets are decomposed. It is based on a cross-correlation analysis. The algorithm takes a high-quality signal in the common source waveform as prior information and applies the corresponding correlation coefficients between subbands as a threshold. The algorithm was verified with simulations. The results show that low-frequency interference can be effectively suppressed by filtering. For single-frequency interference, the signal-to-noise ratio increased from − 10.18 to 13.97, and the root-mean-square error was 43.88. For multi-frequency interference, it increased from − 10.01 and − 2.63 to 13.50 and 7.99. The root-mean-square errors were 46.31 and 138.07. The narrower the main frequency band of the interference signal and the less the overlap of the main frequency band of the interference signal and the effective signal, the better the filtering effect. When the algorithm was applied to microseismic data collected in the field, the number of effective channels increased and the accuracy improved. The development of a water-conducting fractured zone in the field was consistent with the microseismic location obtained after interference was removed by the algorithm, which indicates that it is feasible to monitor a water-conducting fractured zone by analyzing microseismic waveforms with the adaptive filtering algorithm.

Acoustic scattering from dynamic rough ocean surfaces using finite-difference time-domain modeling techniques

Established models for underwater acoustic propagation and scattering typically assume the sea-surface to be either perfectly smooth or rough but static in time. When the sea-surface is rough and moving, received signals show anomalies such as additional transmission losses (due to scattering) and Doppler effects (due to surface motion). Understanding the mechanisms behind these anomalies leads to better sonar system designs without having to perform expensive at-sea experiments. The Finite-Difference Time-Domain (FDTD) method is ideal to predict these physical phenomena. This work presents a FDTD method implemented to model the impact of both sea-surface roughness and motion on underwater acoustic propagation. The FDTD method allows an arbitrary function to define the rough sea-surface and its time evolution. The surface characteristics are modeled using a Pierson-Moskowitz (PM) frequency spectrum. The PM surface model is simple to implement and fully defined by wind speed and direction. Time-domain results from FDTD simulations of static rough sea-surfaces are compared to an established Helmholtz integral equation (HIE) method to establish the validity of the approach. Broadband signals are used as the source waveform. Results demonstrate the anomalous transmission loss and Doppler in received signals. [Work supported by the Office of Naval Research.]

Modeling sonar performance using J-divergence

This presentation demonstrates the use of J-divergence as a performance measure for detection in a sonar system. The inherent inaccuracies between system-level performance and the cell-level (PD,PF) detector operating point used in traditional analysis open the door to using approximate performance measures such as J-divergence. The properties of J-divergence making it an appealing choice are covered: summing to accrue J-divergence across multiple independent measurements (e.g., from multiple source signals, waveforms, or arrays), a data-processing inequality dictating that processing cannot improve J-divergence, and an asymptotic relationship to the traditional (PD,PF) operating point. Simple forward models of J-divergence are presented for matched filters and energy detectors when applied to the standard signal models in Gaussian noise. A “design” J-divergence, which is chosen by the desired qualitative performance level, is used in simple equations to obtain the “design” SNR require to achieve it. This provides a direct replacement for the detection threshold (DT) term in the sonar equation that is easier to apply and evaluate. Example applications of J-divergence are presented illustrating its utility in the modeling and adaptation of current systems as well as the design and analysis of new ones.

Error bounds for extended source inversion applied to an acoustic transmission inverse problem

A simple inverse problem for the wave equation requires determination of both the wave velocity in a homogenous acoustic material and the transient waveform of an isotropic point radiator, given the time history of the wavefield at a remote point in space. The duration (support) of the source waveform and the source-to-receiver distance are assumed known. A least squares formulation of this problem exhibits the ‘cycle-skipping’ behavior observed in field scale problems of this type, with many local minima differing greatly from the global minimizer. An extended formulation, dropping the support constraint on the source waveform in favor of a weighted quadratic penalty, eliminates this misbehaviour. With proper choice of the weight operator, the velocity component at any local minimizer of this extended objective function differs from the global minimizer of the least-squares formulation by less than a linear combination of the source waveform support radius and data noise-to-signal ratio.

Insights into the dynamics of the Nirano Mud Volcano through seismic characterization of drumbeat signals and V/H analysis

Mud volcanoes are rapidly-evolving geological phenomena characterized by the surface expulsion of sediments and fluids from over-pressurized underlying reservoirs. We investigate the Nirano Mud Volcano, Northern Italy, with seismic methods to better understand the dynamic evolution of the system and shed light on its subsurface structure. Our study allowed to detect and characterize three different types of high-frequency drumbeat signals that are present in the most active part of the mud volcano plumbing system. With a back-projection method based on the cross-correlation envelope of signals recorded at different station pairs, we can determine the source location of the drumbeats. These coincide with the location of V/H (vertical-to-horizontal) amplitude peaks obtained from an ambient vibration profile and resistivity anomalies identified in a previous study. We observe that the drumbeats are P-wave dominated signals, with characteristics similar to those found in magmatic settings, i.e. LPs (long-period signals). We suggest that such tremors originate from the migration of mud and gas inside the mud volcanic conduits. The source location, waveform and frequency content of the drumbeats evolve over time. We found that drumbeat occurrence is directly linked with morphological changes at surface.

Ray-based blind deconvolution with maximum kurtosis phase correction.

Ray-based blind deconvolution (RBD) is a method that estimates the source waveform and channel impulse response (CIR) using the ray arrival in an underwater environment. The RBD estimates the phase of the source waveform by using beamforming. However, low sampling, array shape deformation, and other factors can cause phase errors in the beamforming results. In this paper, phase correction is applied to the beamforming estimated source phase to improve RBD performance. The impulsiveness of the CIR was used as additional information to correct the initially estimated source phase. Kurtosis was used to measure impulsiveness, and the phase correction that maximized the kurtosis of the CIRs was calculated through optimization. The proposed approach is called ray-based blind deconvolution with maximum kurtosis phase correction (RBD-MKPC) and is based on a single-input multiple-output system. The RBD-MKPC was tested with several CIRs and source waveform combinations in the shallow-water acoustic variability experiment 2015 using broadband high-frequency pulses (11-31 kHz) as the source and a sparse vertical 16-element line array as receivers. The results indicate that the RBD-MKPC improves the estimation performance. In addition, from an optimization point of view and compared with other initialization methods, the proposed method showed superior convergence speed and estimation performance.

Marine compressed air source array primary acoustic field characterization from at-sea measurements.

The primary acoustic field of a standard seismic survey source array is described based on a calibrated dataset collected in the Gulf of Mexico. Three vertical array moorings were deployed to measure the full dynamic range and bandwidth of the acoustic field emitted by the compressed air source array. The designated source vessel followed a specified set of survey lines to provide a dataset with broad coverage of ranges and departure angles from the array. Acoustic metrics relevant to criteria associated with potential impacts on marine life are calculated from the recorded data. Sound pressure levels from direct arrivals exhibit large variability for a fixed distance between source and receiver; this indicates that the distance cannot be reliably used as a single parameter to derive meaningful exposure levels for a moving source array. The far-field acoustic metrics' variations with distance along the true acoustic path for a narrow angular bin are accurately predicted using a simplified model of the surface-affected source waveform, which is a function of the direction. The presented acoustic metrics can be used for benchmarking existing source/propagation models for predicting acoustic fields of seismic source arrays and developing simplified data-supported models for environmental impact assessments.