Elizabeth T. Küsel

Cetacean population density estimation from single fixed sensors using passive acoustics

Passive acoustic methods are increasingly being used to estimate animal population density. Most density estimation methods are based on estimates of the probability of detecting calls as functions of distance. Typically these are obtained using receivers capable of localizing calls or from studies of tagged animals. However, both approaches are expensive to implement. The approach described here uses a MonteCarlo model to estimate the probability of detecting calls from single sensors. The passive sonar equation is used to predict signal-to-noise ratios (SNRs) of received clicks, which are then combined with a detector characterization that predicts probability of detection as a function of SNR. Input distributions for source level, beam pattern, and whale depth are obtained from the literature. Acoustic propagation modeling is used to estimate transmission loss. Other inputs for density estimation are call rate, obtained from the literature, and false positive rate, obtained from manual analysis of a data sample. The method is applied to estimate density of Blainvilles beaked whales over a 6-day period around a single hydrophone located in the Tongue of the Ocean, Bahamas. Results are consistent with those from previous analyses, which use additional tag data.

Parabolic equation solution of seismo-acoustics problems involving variations in bathymetry and sediment thickness

Recent improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems. The variable rotated parabolic equation [J. Acoust. Soc. Am. 120, 3534-3538 (2006)] handles a sloping fluid-solid interface at the ocean bottom. The single-scattering solution [J. Acoust. Soc. Am. 121, 808-813 (2007)] handles range dependence within elastic sediment layers. When these methods are implemented together, the parabolic equation method can be applied to problems involving variations in bathymetry and the thickness of sediment layers. The accuracy of the approach is demonstrated by comparing with finite-element solutions. The approach is applied to a complex scenario in a realistic environment.

A single-scattering correction for large contrasts in elastic layers.

The single-scattering solution is implemented in a formulation that makes it possible to accurately handle solid-solid interfaces with the parabolic equation method. Problems involving large contrasts across sloping stratigraphy can be handled by subdividing a vertical interface into a series of two or more scattering problems. The approach can handle complex layering and is applicable to a large class of seismic problems. The solution of the scattering problem is based on an iteration formula, which has improved convergence in the new formulation, and the transverse operator of the parabolic wave equation, which is implemented efficiently in terms of banded matrices. Accurate solutions can often be obtained by using only one iteration.

Taming the Jez monster: Estimating fin whale spatial density using acoustic propagation modeling.

The spatial density of calling animals may be estimated acoustically using methods presented by Buckland et al. [Advanced Distance Sampling (Oxford University Press; Oxford, 2004)]; information on the call (or other cue) rate, the call detection probability as a function of range, and the probability of a false detection to obtain an estimate of spatial density. Here we use similar methods to estimate the density of calling fin whales (Balaenoptera physalus) from the level of received sound near 20 Hz—the so‐called “Jez monster.” Using published source levels and call rates of fin whales, a Monte Carlo method is developed that simulates a given spatial density of whales randomly situated around a hydrophone and uses acoustic propagation modeling (specifically, a parabolic equation model) to estimate the resulting level of received sound. Using this technique at several deep‐water sites in the North Atlantic, we derive a function that maps loudness to spatial density, and then use this function to estimate...

Effects of incident field refraction on scattered field from vertically extended cylindrical targets in range-dependent ocean waveguides

The effect of incident field refraction on the scattered field from vertically extended cylindrical targets is investigated. A theoretical model for the total scattered field from a cylindrical target in a range-dependent ocean waveguide is developed from Greens theorem. The locally scattered field on the target surface is estimated as a function of the incident field by applying the appropriate boundary conditions on continuity of acoustic pressure and normal velocity, making the model applicable to general penetrable cylinders. The model can account for depth dependence in medium sound speed and hence refraction in the incident field along the target depth. Numerical implementation is done for a passive acoustic reflector, a long cylindrical air-filled rubber hose, often deployed vertically in experiments to provide calibration and charting consistency for wide-area active sonar systems. Analysis with the model indicates that refraction in the incident field along the target depth must be taken into account to accurately estimate the scattered field level from vertically extended cylindrical targets. It is demonstrated that the standard Ingenito waveguide target scattering model, which assumes that the incident field is planar along the target extent, can lead to significant errors of 10 dB or more in estimating the scattered field level.

Estimating singing fin whale population density using frequency band energy

Fin whale (Balaenoptera physalus) song occurs in a narrow frequency band between approximately 15 and 25 Hz. During the breeding season, the sound from many distant fin whales in tropical and subtropical parts of the world may be seen as a “hump” in this band of the ocean acoustic spectrum. Since a higher density of singing whales leads to more energy in the band, the size of this hump—the total received acoustic energy in this frequency band—may be used to estimate the population density of singing fin whales in the vicinity of a sensor. To estimate density, a fixed density of singing whales is simulated; using acoustic propagation modeling, the energy they emit is propagated to the sensor, and the received level calculated. Since received energy in the fin whale band increases proportionally with the density of whales, the density of whales may then be estimated from the measured received energy. This method is applied to a case study of sound recorded on ocean-bottom recorders southwest of Portugal; is...

Energy‐conserving and single‐scattering parabolic equation solutions for elastic media

Parabolic equation techniques are efficient for solving nonseparable wave propagation problems. When the properties of the medium vary gradually in range, parabolic equation solutions are also very accurate for many problems. The key to achieving accuracy and efficiency simultaneously is to apply energy‐conservation or single‐scattering corrections to account properly for range dependence. This approach has proven to be very effective for acoustic media. Some progress has been made on the elastic case [J. Acoust. Soc. Am. 94, 975–982 (1993); 94, 1815–1825 (1993)], but this problem has not been fully resolved. In this paper we will discuss some recent progress in the formulation of the elastic parabolic equation [W. Jerzak, J. Acoust. Soc. Am. (submitted)], a single‐scattering approach for a vector wave problem [J. Acoust. Soc. Am. 104, 783–790 (1998)], and how they are being used to improve the accuracy of parabolic equation solutions for problems involving elastic sediments. [Work supported by ONR.]

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 clicks 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.

Scattering from extended targets in a range‐dependent fluctuating ocean waveguide from theory and experiments where the sonar equation is invalid.

Bi‐static, long‐range measurements of acoustic scattered returns from vertically extended, air‐filled cylindrical targets were made during three separate ONR‐sponsored field experiments in fluctuating continental shelf environments. We show that the sonar equation estimates of mean scattered intensity from these targets lead to large errors, differing by an order of magnitude from both our measurements and waveguide scattering theory. This is because the sonar equation approximation is not applicable to targets large compared to the acoustic wavelength in an ocean waveguide. We find that use of the Ingenito scattering model also leads to significant errors in estimating mean target scattered intensity in our field experiments because they were conducted in range‐dependent ocean environments with large variations in sound speed structure over the depth of the targets, scenarios that violate the basic assumptions of the Ingenito model. Here we describe scattering from extended cylindrical targets in a range...

Beaked whale density estimation from single hydrophones by means of propagation modeling.

Passive acoustic sonar systems offer many advantages to the study of marine mammals. For density estimation studies, it is important to evaluate the probability of detecting an animal as a function of its distance from the receiving sensor. In this work, acoustic propagation modeling is used to estimate the transmission loss as a function of depth and range between a source whale and a single‐hydrophone receiver. The computed transmission loss is compared to ambient noise levels and source level distributions to estimate the detection probability as a function of range. Results will be compared to beaked whale data recorded on bottom‐mounted sensors in the Atlantic Undersea Test and Evaluation Center (AUTEC) in the Bahamas, where the location of clicks is relative to one hydrophone. Source level and beam pattern extracted from digital acoustic tags (DTags) applied to a sample of animals at the same location will also be used in the detection model, and beaked whale spatial density will be estimated. The d...