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Time difference of arrival (TDOA) methods for acoustically localizing multiple marine mammals have been applied to recorded data from the Navy's Pacific Missile Range Facility in order to localize and track humpback whales. Modifications to established methods were necessary in order to simultaneously track multiple animals on the range faster than real-time and in a fully automated way, while minimizing the number of incorrect localizations. The resulting algorithms were run with no human intervention at computational speeds faster than the data recording speed on over forty days of acoustic recordings from the range, spanning multiple years. Spatial localizations based on correlating sequences of units originating from within the range produce estimates having a standard deviation typically 10 m or less (due primarily to TDOA measurement errors), and a bias of 20 m or less (due primarily to sound speed mismatch). An automated method for associating units to individual whales is presented, enabling automated humpback song analyses to be performed. [ABSTRACT FROM AUTHOR]

Conventional detection of humpback vocalizations is often based on frequency summation of band-limited spectrograms under the assumption that energy (square of the Fourier amplitude) is the appropriate metric. Power-law detectors allow for a higher power of the Fourier amplitude, appropriate when the signal occupies a limited but unknown subset of these frequencies. Shipping noise is non-stationary and colored and problematic for many marine mammal detection algorithms. Modifications to the standard power-law form are introduced to minimize the effects of this noise. These same modifications also allow for a fixed detection threshold, applicable to broadly varying ocean acoustic environments. The detection algorithm is general enough to detect all types of humpback vocalizations. Tests presented in this paper show this algorithm matches human detection performance with an acceptably small probability of false alarms (PFA < 6%) for even the noisiest environments. The detector outperforms energy detection techniques, providing a probability of detection PD = 95% for PFA < 5% for three acoustic deployments, compared to PFA > 40% for two energy-based techniques. The generalized power-law detector also can be used for basic parameter estimation and can be adapted for other types of transient sounds. [ABSTRACT FROM AUTHOR]

Abstract: The geodynamo mechanism, responsible for sustaining Earth’s magnetic field, is believed to be strongly influenced by the solid inner core through its influence on the structure of convection within the tangent cylinder. In the rapidly rotating low-viscosity regime of the geodynamo equations relevant to the Earth’s core, the magnetic field must satisfy a continuum of conditions known as Taylor’s constraint. Magnetic fields that satisfy this constraint, termed Taylor states, have the property that their axial magnetic torque vanishes when averaged over any geostrophic contour, cylinders of fluid coaxial with the rotational axis. In recent theoretical developments, we proved that when adopting a truncated spherical harmonic expansion, the continuous constraint in space reduced to a finite spectral set of conditions. Furthermore, an expedient choice of regular radial basis presents an under-determined problem when constructing Taylor states in a full-sphere showing the ubiquity of such solutions. A spherical-shell geometry, with a conducting inner core, complicates the formulation of Taylor’s constraint due to the partitioning of the geostrophic contours into three distinct regions, ostensibly trebling the stringency of the constraint. This raises questions as to the admissible structures of such Taylor states, and their relation to those in a full-sphere. In this paper, we address these issues in two stages. First, we present a mathematical characterisation of the structure of Taylor’s constraint in a spherical-shell. We then enumerate the effective number of conditions that must be satisfied by any magnetic field that is everywhere inside the core, and show that, assuming an equal truncation in radial and solid angle representation, the number of conditions is approximately 5/3 times that for a full-sphere Taylor state. Second, we investigate the influence of the inner core on the structure of admissible Taylor states by constructing a low-degree family of optimally smooth observationally consistent examples in both a spherical-shell and a full-sphere. We show that the introduction of an inner core into a full-sphere increases the minimum magnetic field complexity, simply by virtue of the increased potency of Taylor’s constraint, a trait more pronounced in our quasi-axisymmetric models. We speculate that axisymmetric dynamo-generated exact Taylor states, particularly those generated in a spherical-shell, in general have small radial length scales that may be difficult to resolve. [Copyright &y& Elsevier]

Abstract: Considerations of a particular limit of the magnetohydrodynamic equations, appropriate for the generation of magnetic field in planetary interiors, lead to a set of constraints involving a certain class of homogeneous polynomials. This set is significantly degenerate owing to an identity satisfied by the polynomial coefficients, which involves linear combinations of simple Gauss hypergeometric functions. A generalised version of this new identity is proved by appealing to Wilf–Zeilberger theory. [Copyright &y& Elsevier]

Presents problems and solutions in industrial and applied mathematics. Combinatorial expression from oceanography; Polaron integrals; Volume of the intersection of a cube and a ball in N-space; Integrals from heat conduction.

Time difference of arrival methods for acoustically localizing multiple marine mammals have been applied to recorded data from the Navy's Pacific Missile Range Facility in order to localize and track calls attributed to Bryde's whales. Data were recorded during the months of August-October 2014, and 17 individual tracks were identified. Call characteristics were compared to other Bryde's whale vocalizations from the Pacific Ocean, and locations of the recorded signals were compared to published visual sightings of Bryde's whales in the Hawaiian archipelago. Track kinematic information, such as swim speeds, bearing information, track duration, and directivity, was recorded for the species. The intercall interval was also established for most of the tracks, providing cue rate information for this species that may be useful for future acoustic density estimate calculations. [ABSTRACT FROM AUTHOR]