Sonar Equation Research Articles

Numerical determination of parameter sensitivity of transmission loss in atmospheric sound propagation above a general ground surface

A transmission loss model, similar to the sonar equation, is used to study the transmission loss in atmospheric sound propagation over ground. The model takes into account contributing factors from spreading loss, absorption, wind, temperature gradient, and ground impedance. Numerical predictions obtained with the Crank-Nicolson Parabolic Equation implementation are used to quantify the effects of these factors. The transmission loss sensitivity to these parameters will be presented. These sensitivity findings will be compared to a set of field measurements. An acoustic source is placed in an open field and six horizontally aligned microphones are used to record the signal. Microphones were spaced at regular intervals up to approximately 400 m away from the source and 1 meter above the ground. Temperature, atmospheric pressure, and relative humidity measurements were made concurrent with the acoustic recordings.

IRAP: An integrated, real-time, autonomous passive acoustic monitoring system for beaked whale detection, localization, and tracking

The integration and demonstration of passive sonar hydrophone arrays into autonomous undersea platforms for acoustic marine mammal monitoring has witnessed significant advances in the last few years due to the availability and scalability of low-cost, low-power commercial technology for acoustic remote sensing. In this paper, we will review the at-sea performance of a nine-element Mills Cross high frequency hydrophone array (HFA) integrated into an autonomous undersea vehicle (AUV) for the detection, classification, localization, and tracking (DCLT) of beaked whales during a deployment conducted off leeward Kauai in February, 2016. Using passive sonar equation analysis, we will review the design rationale of the HFA, and quantify system performance using standard signal processing metrics such as measured array gain, tracking accuracy, and detection range on a calibrated high-frequency source transmitting replica beaked whale click trains at a de minimus source level. A candidate autonomous real-time passive sonar processing architecture that combines an adaptive beamformer/matched filter front-end with a false alarm mitigation back-end to balance detection sensitivity, classifier robustness, and processing throughput will also be presented. We conclude with a cost/power/persistence trade-off for some commercially available autonomous platforms. [This work was supported by NAVFAC Living Marine Resources Program.]

Harbor passive acoustic monitoring systems

The feasibility of detecting quiet moving targets (e.g., unmanned undersea vehicles) in harsh harbor environments by using passive acoustic bottom-mounted hydrophone arrays, combined with advanced signal processing detection systems tuned to the target’s radiated noise signature characteristics is presented. The harsh shallow water environment is in Narragansett Bay, Rhode Island where UUV operations have been conducted. The sonar equation study considers the use of high resolution, multi-channel hydrophone arrays, measured source levels of representative UUVs (they are quiet), measured noise levels in the harbor (can exhibit high levels), and corresponding array gain. The resulting detection ranges for quiet targets are presented along with estimated false alarm rates. It is shown that passive sonar systems can be a viable component or modality for an underwater harbor defense monitoring system.

Single-sensor, cue-counting population density estimation: Average probability of detection of broadband clicks.

Odontocete echolocation clicks have been used as a preferred cue for density estimation using single-sensor data sets, requiring estimation of detection probability as a function of range. Many such clicks can be very broadband in nature, with 10-dB bandwidths of 20-40 kHz or more. Detection distances are not readily obtained from single-sensor data. Here, the average detection probability is estimated in a Monte Carlo simulation using the passive sonar equation along with transmission loss calculations to estimate the signal-to-noise ratio (SNR) of tens of thousands of click realizations. Continuous-wave (CW) analysis, i.e., single-frequency analysis, is inherent to basic forms of the passive sonar equation. Using CW analysis with the click's center frequency while disregarding its bandwidth has been shown to introduce bias into detection probabilities and hence to density estimates. In this study, the effects of highly broadband clicks on density estimates are further examined. The usage of transmission loss as an appropriate measure for calculating click SNR is also discussed. The main contributions from this research are (1) an alternative approach to estimate the average probability of detection of broadband clicks, and (2) understanding the effects of multipath clicks on population density estimates.

Sonar equations for planetary exploration.

The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus.

Use of ADCPs for suspended sediment transport monitoring: An empirical approach

AbstractA horizontally mounted 300 kHz acoustic Doppler current profiler was deployed in Fraser River at Mission, British Columbia, to test its capability to detect size‐classified concentration of suspended sediment. Bottle samples in‐beam provide a direct calibration of the hADCP signals. We also deployed a 600 kHz vertically mounted ADCP from a boat in combination with bottle samples. Fraser River at Mission is 525 m wide with moderate suspended sediment concentration (up to 350 mg L−1 in our measurements, mostly silt), and a modest sand load only at high flows. We use an entirely empirical approach to calculate the sediment load using ADCPs to test the reliability of acoustic methods when assumptions embedded in the sonar equation about the relation between suspended sediment size and concentration, and acoustic signals are violated. vADCP calibration using matched individual bottle samples and acoustic backscatter departed from the expected theoretical relation. Calibration using depth‐averaged sediment concentration and acoustic backscatter more closely matched theoretical expectations, but varied through the season. hADCP calibrations conformed with theoretical expectations and did not exhibit seasonal variation. Silt and sand were successfully discriminated; however, silt dominates the correlations. We found no coherent relation between acoustic attenuation and silt concentration. In‐beam results are extended by correlation to estimate mean sediment concentration and total suspended flux in the entire channel: this auxiliary correlation cancels any calibration bias and permits monitoring of size‐classified suspended sediment in absence of detailed information of sediment grain‐size distribution.

Single-sensor density estimation of highly broadband marine mammal calls

Odontocete echolocation clicks have been used as a preferred cue for density estimation studies from single-sensor data sets. Such sounds are broadband in nature, with 10-dB bandwidths of 20 to 40 kHz or more. Estimating their detection probability is one of the main requirements of density estimation studies. For single-sensor data, detection probability is estimated using the sonar equation to simulate received signal-to-noise ratio of thousands of click realizations. A major problem with such an approach is that the passive sonar equation is a continuous-wave (CW) analysis tool (single-frequencies). Using CW analysis with a click’s center frequency while disregarding its bandwidth has been shown to introduce bias to detection probabilities and hence to population estimates. In this study, the methodology used to estimate detection probabilities is re-evaluated, and the bias in sonar equation density estimates is quantified by using a synthetic data set. A new approach based on the calculation of arrivals and subsequent convolution with a click source function is also presented. Application of the new approach to the synthetic data set showed accurate results. Further complexities of density estimation studies are illustrated with a data set containing highly broadband false killer whale (Pseudorca crassidens) clicks. [Work supported by ONR.]

Deep-water ocean acoustic propagation: Observations

There is a rich history of long-range, low-frequency, deep-water ocean acoustic propagation measurements extending back to the discovery of the deep sound channel by Ewing and Worzel in 1944. Experiments up to the 1970s focused on measuring parameters in the sonar equation, including transmission loss and ambient noise, motivated in part by the development of the U.S. Navy Sound Surveillance System (SOSUS). These measurements generally used wideband explosive sources or narrowband transducers. Beginning in the 1970s, low-frequency, broadband transducers and vertical receiving arrays that could operate autonomously and be moored for extended periods were developed in connection with the new field of ocean acoustic tomography. These developments allowed individual multipaths and modes to be resolved and long time series collected, so that the fluctuations in the received signals could be quantified. At about the same time, advances in characterizing ocean internal wave and mesoscale variability provided information on the causes of the acoustic fluctuations that could be used in theoretical calculations. The study of deep-water propagation and the development of ocean acoustic tomography have been intertwined ever since. The applications of deep-water propagation now extend beyond military uses to ocean acoustic remote sensing (active and passive), communication, and navigation.

A single equation for predicting required ocean and seismic acoustic fiber optic sensor response

In the past decade, requirements have evolved for systems of ocean bottom and seismic downhole acoustic sensors with high dynamic range, wider bandwidths, and which will operate reliably for a decade or more in high-pressure-high-temperature environments. As seismic and acoustic survey spatial resolution, operating depth, and range requirements have increased, higher sensor string counts have been required to provide the needed improvements in target definition. Fiber optic sensors and telemetry systems are being developed which allow HPHT operation, without vulnerable electrical telemetry in the “wet” end of the system, and which can reliably transmit high-sensor count string outputs which are 10's of km from the processor. This paper introduces a modified version of the SONAR equation which allows straight forward estimation of the required fiber optic acoustic sensor response, early in the system design stage, and allows the system engineer to define and optimize sensor response requirements and help minimize system performance risks.

Mapping probability of shipping sound exposure level.

Mapping vessel noise is emerging as one method of identifying areas where sound exposure due to shipping noise could have negative impacts on aquatic ecosystems. The probability distribution function (pdf) of sound exposure levels (SEL) is an important metric for identifying areas of concern. In this paper a probabilistic shipping SEL modeling method is described to obtain the pdf of SEL using the sonar equation and statistical relations linking the pdfs of ship traffic density, source levels, and transmission losses to their products and sums.

R. J. Urick—Introduction of the sonar equations

The Sonar Equations were developed during the Second World War to calculate the maximum ranges of sonar equipment. They were formally discussed in a series of reports published by the Office of Naval Research in the mid 1950’s entitled “A Summary of Acoustic Data” authored by R. J. Urick and A. W. Pryce. Later codified in Urick’s Book, Principles of Underwater Sound, they are the primary tool for design, development, and testing of undersea acoustic hardware. They also provide a useful means for estimating expected values of marine physical properties (e.g., ambient noise, transmission loss) or, conversely, a sanity check on data collected at sea. The presentation is focused on the history of the sonar equations, their early use and transition to modern form and employment.

Simulated Research on Passive Sonar Range Using Different Hydrographic Conditions

As an example using the passive sonar, it calculated the quality factor of passive sonar using the sonar equation. The sound field was calculated under different depth and range using multiform hydrographic conditions. The isoline of passive sonar quality factor was marked out on the sound field. The isoline also represented the passive sonar range. The simulation results showed that hydrographic conditions had important effect on passive sonar range. At the same hydrographic conditions, the permissible drawdown of passive sonar had important effect on passive sonar range. Thus, according to the hydrographic character, the passive sonar range could be improved by selecting suitable passive sonar permissible drawdown.

SONAR Equation perspective on TREX13 measurements

Modeling shallow water reverberation is a problem that can be approximated as two-way propagation (including multiple forward scatter) and a single backward scatter. This can be effectively expressed in terms of the SONAR equation: RL = SL-2 x TL + SS, where RL is reverberation level, SL is the source level, TL is the one way transmission loss, and SS is the integrated scattering strength. In order to understand the reverberation problem at the basic research level, both propagation and scattering physics need to be properly addressed. A major goal of TREX13 (Target and Reverberation EXperiment 2013) is to quantitatively investigate reverberation with sufficient environmental measurement to support full modeling of reverberation data. Along a particular reverberation track at the TREX13 site, TL and direct-path backscatter were separately measured. Environmental data were extensively collected along this track. This talk will bring together all the components of the SONAR equation measured separately at the TREX13 site to provide an assessment of the reverberation process along with environmental factors impacting each of the components.

Acoustical terminology in the Sonar Modelling Handbook

The UK Sonar Modelling Handbook (SMH) defines the passive and active Sonar Equations, and their individual terms and units, which are extensively used for sonar performance modelling. The new Underwater Acoustical Terminology ISO standard, which is currently being developed by the ISO working group TC43/SC3/WG2 to standardize terminology will have an impact on the SMH definitions. Work will be presented comparing the current SMH terminology with both the future ISO standard and other well-known definitions to highlight the similarities and differences between each of these.

Do changes in the size of mud flocs affect the acoustic backscatter values recorded by a Vector ADV?

A series of experiments were conducted to examine the effect of mud floc growth on the acoustic back-scatter signal recorded by a Nortek Vector acoustic Doppler velocimeter (ADV). Several studies have shown that calibration equations can be developed to link the backscatter strength with average suspended sediment concentration (SSC) when the sediment particle size distribution remains constant. However, when mud is present, the process of flocculation can alter the suspended particle size distribution. Past studies have shown that it is still unclear as to the degree of dependence of the calibration equation on changes in floc size. Part of the ambiguity lies in the fact that flocs can be porous and rather loosely packed and therefore will not scatter sound waves as a solid particle would. In addition, direct, detailed measurements of floc size have not accompanied experiments examining the dependence of ADV backscatter and suspended sediment concentration. In this set of experiments, direct measurement of the floc size distribution is made with time in a mixing chamber using a floc camera system. A Vector ADV and an OBS are also placed within the tank to measure acoustic backscatter and SSC as the flocs change size with time; concentration in the experiments ranges from 15 to 90mg/l. Results showed that the growth of mud flocs did influence the SNR recorded by the Vector ADV, and that the sensitivity of the SNR signal to changes in floc size was higher for flocs with diameters less than ≈80μm (it kr=1 at a diameter of 80μm). The response of SNR to changes in floc size and SSC was modeled with a modified sonar equation. If properly calibrated, the model was able to capture the functional behavior of SNR with changes in floc size and concentration. Values of the calibration coefficients showed that while changes in floc diameter up to about 80μm did alter the SNR, the change was less than what would be expected from a similar change in the size of solid scatterers.

Single-sensor, cue-counting density estimation of highly broadband marine mammal calls

Odontocete echolocation clicks have been used as a preferred cue for density estimation studies from single-sensor data sets, studies that require estimating detection probability as a function of range. Many such clicks can be very broadband in nature, with 10-dB bandwidths of 20 to 40 kHz or more. Because detection distances are not realizable from single-sensor data, the detection probability is estimated in a Monte Carlo simulation using the sonar equation along with transmission loss calculations to estimate the received signal-to-noise ratio of tens of thousands of click realizations. Continuous-wave (CW) analysis, that is, single-frequency analysis, is inherent to basic forms of the passive sonar equation. Considering transmission loss by using CW analysis with the click’s center frequency while disregarding its bandwidth has recently been shown to introduce bias to detection probabilities and hence to population estimates. In this study, false killer whale (Pseudorca crassidens) clicks recorded off the Kona coast of Hawai’i are used to quantify the bias in sonar equation density estimates caused by the center-frequency approach. A different approach to analyze data sets with highly broadband calls and to correctly model such signals is also presented and evaluated. [Work supported by ONR.]

Bill Carey and Bob Urick

Principles of Underwater Sound, written by Robert J. Urick, and last published in 1983, has been a staple on everyone's bookshelf. Bill Carey took on the job of updating that book, with the premise of not changing what was written, but simply updating each chapter with new information obtained over the succeeding three decades. One of the primary reasons the text was so popular is its ease in reading and grasping the import of the data and simplified ideas presented and their respective use(s) in the sonar equation. Work continues with Bill's firm imprint on the next edition, which is the focus of this discussion.

Utilizing an extended target for high frequency multi-beam sonar intensity calibration

There is an interest in expediting intensity calibration procedures for Multi-Beam Echo-Sounders (MBES) to be used for acoustic backscatter measurements. To this end, a target was constructed of irregularly oriented small chain links arranged in a “curtain” simulating an extended scattering surface, such as the seafloor. Tests with a 200-kHz, 7°, SIMRAD EK60 Split-Beam Echo-Sounder (SBES) were performed in a tank in order to investigate the targets angular- and range-dependent scattering strength. These tests suggest that the amplitude envelope of the scattered signal is Rayleigh distributed and that the backscatter strength depends linearly on the number of active scattering elements. Following these initial validation tests, a 200 kHz Reson SeaBat 7125-SV2 MBES was calibrated in the tank with the same extended target. During the calibration, the MBES was rotated so that every beam was incident on the target. This calibration test was performed once when the target was at normal and once at oblique (45°) incidence. The final output is a “catch all” beam-dependent calibration coefficient, C, determined from the sonar equation.

Issues in estimating the seafloor scattering cross section with synthetic aperture sonar

The high resolution capabilities of synthetic aperture sonar (SAS) make it an attractive technology for estimating the seafloor scattering cross section. However, differences between traditional systems used for backscattering measurements, whose apertures span a few wavelengths, and synthetic arrays, whose apertures can span thousands of wavelengths, can violate the assumptions used in typical cross section estimation techniques. The issues introduced by very long synthetic arrays are caused by the integration of acoustic energy over a range of azimuth and grazing angles in the local coordinates of the resolved area on the seafloor. The resulting pixel intensity is not directly proportional to the scattering cross section, and methods other than solving the sonar equation are required. This research explores the effect of naively using SAS data to estimate the cross section and presents alternative estimation techniques.

Acoustic Theory Application in Ultra Short Baseline System for Tracking AUV

The effective tracking area of ultra short baseline (USBL) systems strongly relates to the safety of autonomous underwater vehicles (AUVs). This problem has not been studied previously. A method for determining the effective tracking area using acoustic theory is proposed. Ray acoustic equations are used to draw rays, which ascertain the effective space. The sonar equation is established in order to discover the available range of the USBL system and the background noise level using sonar characteristics. The available range defines a hemisphere like enclosure. The overlap of the effective space with the hemisphere is the effective area for USBL systems tracking AUVs. Lake and sea trials show the proposed method's validity.