Robert P. Porter

A high-resolution pulse-Doppler underwater acoustic navigation system

A high-resolution underwater acoustic pulse-Doppler navigation system has been developed and tested at sea. The system provides continuous, highly accurate tracking of underwater and ocean-surface platforms in a fixed 50-km2navigation net. Three reference buoys, moored 20 m from the ocean bottom, provide the navigation net used by shipboard processing equipment. Each reference buoy contains an acoustic transponder, used to obtain the acoustic travel times from the transponder to the platform, and a continuous-tone beacon, used to obtain the Doppler shift due to platform motion. The system is capable of determining the position of a platform with respect to the reference net with an error of 2-3 m. The relative position of the platform on a fix-to-fix basis can be determined within several centimeters over short time intervals (\approx 10min).

Diffraction tomography and the stochastic inverse scattering problem

The Fourier diffraction theorem is the basis of diffraction tomography. The theorem states that the field scattered by a semitransparent object maps onto arcs in the Fourier space of the object. In this paper, the stochastic analog is derived to the theorem for a general anisotropic, statistically homogeneous random continuum. By acoustically probing the random medium from various angles, the second-order statistics of the medium can be recovered from the second-order statistics of the perturbed field. The robust nature of the result is confirmed by numerical experiments using finite arrays and autocorrelation estimation theory.

V Generalized Holography with Application to Inverse Scattering and Inverse Source Problems

Publisher Summary This chapter describes the generalized holography with application to inverse scattering and inverse source problems. Holographic imaging is a fundamental imaging method that relies on the general properties of diffracting wave fields to store information about 3D objects on two-dimensional recording surfaces. The chapter discusses the basic theory of generalized holography for scalar and electromagnetic waves. The holographic images produced by the films can closely approximate the images produced by the generalized holograms of arbitrary shape. The chapter reviews the solutions to the inverse source problem, focussing on the role played by radiating and nonradiating source contributions. The inverse scattering problem can also be solved with generalized holograms, which can produce a band-limited reconstruction of a weak scatterer. The duality between scanning the scatterer with plane waves from all directions or at all frequencies is shown. Solutions to the inverse scattering problem with wide-band plane waves and point sources are discussed.

Source localization using a reference wave to correct for oceanic variability

This paper describes a low‐frequency, long‐range acoustic propagation method for source localization. It is based on imaging techniques that remove the effects of adiabatic oceanic variability between an acoustic receiving array and an unknown source by combining measured data from the unknown source with measured data from a known reference source. At the heart of the concept is the realization that both sets of measured data are contaminated in the same way by the range‐integrated effects of the ocean, for the stretch of ocean that they share between their positions and the receiving array. These contaminants can be made to cancel, leaving the integrated, and much smaller, effects of the oceanic variability between the reference source and the unknown source.

CW beacon system for hydrophone motion determination

A system consisting of three bottom‐moored 12 000‐Hz CW beacons, each separated in frequency by 40 Hz, and separated in space by about 8 km, has been used to track the motion of ship‐suspended, ship‐mounted, sonobuoy‐deployed, and bottom‐moored hydrophones to an accuracy of 4 cm. The system uses Doppler tracking of the beacon signals to provide real‐time estimation of hydrophone velocity and displacement. Factors that might compromise system performance, such as surface, bottom or forward volume scattering, or multipath effects, were found to be negligible. Random phase fluctuations in beacon signals due to these phenomena are small compared with those due to hydrophone motion. Two tests of the system, near Eleuthera Island and near Bermuda, were made in September–October 1972. [This work was performed under U.S. Office of Naval Research Contract No. N00014‐72‐C‐0205.].

Long‐range sound fluctuations with drifting hydrophones

Phase fluctuations of underwater sound (406 Hz) transmitted between a fixed source and deep free‐drifting hydrophones have been obtained for transmission ranges of 200 km. Phase variations due to hydrophone drift are removed by a bottom‐moored, CW tracking system that corrects for motion‐induced phase variations of 0.06 rad or larger. Most of the energy traveled along refracted paths, eliminating much of the phase fluctuation due to bottom and surface scatter. Residual surface scatter effects are removed by narrow‐band filtering. Maximum observed phase fluctuations are 15 cycles over 3 h on the deepest hydrophones (1500 m). The mean‐square phase spectrum has a slope of −2 for frequencies between 0.4 and 40 cycles/h. The shallow hydrophone (300 m) data contain half the phase fluctuation of the deep hydrophones. Depth dependence of the fluctuations is attributed to internal gravity waves.

Scattered wave inversion for arbitrary receiver geometry

By combining images from backpropagated scattered waves from successive plane‐wave illuminated scatterers, we are able to reconstruct a low‐pass filtered version of the three‐dimensional scattering function of a weak scatterer. Imaging or, equivalently, backpropagation corrects for the spherically diverging scattered field permitting sparse sampling on the recording surface and making coherent wave inversion more practical. As in conventional tomography, true reconstruction requires a filtering operation on the scattered field recorded on a planar hologram or other recording medium. For holograms of arbitrary shape, a postfiltering operation is needed to produce a low‐pass replica of the object. This work draws heavily on the theory of generalized holography developed for holograms of arbitrary surface shape.

Dispersion of axial SOFAR propagation in the western Mediterranean

Dispersed high‐order modes have been observed at frequencies as high as 300 Hz and at ranges of 600 km for shots detonated and received on the axis of a SOFAR channel located in the western Mediterranean Sea. Spectrum analysis of shot records has revealed as many as five identifiable group‐velocity profiles that correlate with modes as high as 70. Accurate prediction of observed group‐velocity profiles is obtained by applying WKB mode theory to sound‐velocity data. In addition, dispersion of individual resolved multipath arrivals, for which low frequencies tend to arrive later, is observed and analyzed by a modified ray theory including diffraction effects.

Holography and the inverse source problem. III. Inhomogeneous attenuative media

The inverse source problem of the scalar wave equation for a monochromatic source is generalized to the case of an inhomogeneous attenuative medium. The attenuative medium can be a lossy deterministic medium or a lossless random medium in which the coherent field attenuates. Two generalized holographic imaging equations are obtained that are based on the use of two Green’s functions, G+* and G−. The kernel for the first equation with G+* is Hermitian and depends on the location and the shape of the recording surface, whereas the equation with G− has a non-Hermitian kernel that is independent of the recording surface. The solutions of the integral equations are investigated. The nonuniqueness of the solutions are also related to the nonradiating sources and to the minimum energy solution.

Acoustic‐internal wave interaction at long ranges in the ocean

Fluctuations in the amplitude and phase of low‐frequency sound propagated to long range in the ocean are predicted. Phase fluctuations are attributed to the passage of acoustic radiation through the internal gravity‐wave field; predictions are based on measured and modeled internal wave spectra. Ray theory is used to determine phase and amplitude variations as a function of time, space, and acoustic frequency. It is shown and experimentally verified that mean‐square phase fluctuations are depth dependent.