Gary E. J. Bold

Measurements of the frequency dependence of normal modes

An experiment using a vertical array to detect acoustic normal modes in shallow water is described. A high signal‐to‐noise ratio was achieved by the use of pseudorandom pulse sequences to modulate the projector. Wide bandwidth signals and a tunable acoustic source enabled the frequency dependence of normal modes to be measured and results are in good agreement with the theory. An improved method of extracting the signal present in a single mode is described and used to examine pulse shapes and frequency spectra of individual modes.

A top‐down philosophy for accurate numerical ray tracing

Several examples of the ease of application and accuracy of ray tracing resulting from the top‐down approach are given to demonstrate the results obtainable with today’s small computers. One example of a more traditional approach is given to demonstrate how easy it is to lose computational accuracy to mixing instead of isolating the steps in the solution. The current level of commonly available computing power means that it is important for the ordinary researcher to be aware of powerful integration subroutines. Their extraordinary accuracy makes the payoff worth the effort expended in understanding their use.

Signals for optimum bandlimited system interrogation with application to underwater acoustics

Consideration of the bandlimited system interrogation problem together with a reasonable definition of a measurement signal‐to‐noise ratio leads to a figure of merit for interrogation signals. Both time and frequency domain characteristics of the signal are important. Several candidate classes of interrogating signals are described and compared. Stepped frequency chirps are found to combine nearly ideal properties with ease of generation. An illustration of the use of stepped frequency chirps in an underwater acoustic experiment is given.

A comparison of measured and predicted broadband acoustic arrival patterns out to 10‐Mm range during the ATOC Acoustic Engineering Test

A low‐frequency acoustic source suspended from R/P FLIP approximately 340 nautical miles WSW of San Diego transmitted to receivers 90 to 10 000 km distant during the Acoustic Engineering Test of the Acoustic Thermometry of Ocean Climate (ATOC) Program. The source was sus‐pended for 7 days during November 1994 near the depth of the sound channel axis (about 650 m) in water over 4000 m deep, in order to avoid near‐source bottom interactions. The source transmitted a phase‐coded m‐sequence with a center frequency of 75 Hz and a digit length of 27 ms [Metzger et al., this meeting]. Measured receptions on five bottom‐mounted SOSUS receivers at ranges from 300–4000 km, on two vertical line array receivers at ranges of 90 and 3300 km, and on a sonobuoy modified to have the hydrophone on the sound channel axis at about 10 000‐km range, are compared with ray theoretic, adiabatic normal mode, and broadband parabolic equation predictions. [Work supported by the Strategic Environmental Research and Development Progra...

Minimum bandwidth interpolation of real discrete data

A DFT‐spectrum‐preserving transformation from one finite set of real numbers to a larger set of real numbers is developed. This transformation is completely in the time domain. Its convolution kernel, psinc(x;P), is analogous to the sinc(x) function familiar in Fourier transform work with continuous waveforms. The application to generation of periodic signals with specified bandlimited spectra is illustrated, as is interpolation using a mixture of time‐domain and radix‐2 fast Fourier transform (FFT) processing.

Long‐range arrival structure using timefront analysis

If the classical differential equations defining rays are rewritten in terms of travel time instead of ray path distance, it is straightforward to trace families of rays from a point with time as the independent variable. Points on rays having the same time coordinate define a timefront surface, thus designated to emphasize its high‐frequency nature. Timefronts are spherical at short ranges, slowly evolving into an accordian structure. The shape of the timefront changes relatively slower over time scales of seconds, enabling a physical picture of long distance arrival times to be seen by inspection. A simple algorithm for deducing accurate travel times of eigenrays to a given receiver steps the timefront iteratively until its branches cross the receiver coordinates. Several features characteristic of long distance arrival structure are demonstrated. Numerical results from typical profiles, some including surface ducts, are presented.

ATOC signal enhancement using adaptive filtering

A moored, autonomous recording system deployed off the east coast of New Zealand in early 1996 acquired signals from the Pioneer seamount ATOC source. Unfortunately, the data were corrupted by a very strong, aliased interfering signal electrically coupled from a malfunctioning power supply which drifted in frequency by over 400 Hz, and also by a mechanically coupled vibration at the rotation frequency of the hard disk used to store the data. Pulse compression of the biphase modulated psuedorandom sequence used to encode the transmission spreads the energy in these signals across the desired signal’s spectral passband, degrading the signal‐to‐noise ratio of the receptions. Since both unwanted components are unstable in frequency, classical digital filters are unable to eliminate them. However, an adaptive LMS filter has been used to track and virtually remove the interfering signals before pulse compression, resulting in signal‐to‐noise ratio gains of up to 6 dB.

New Zealand ATOC path stability test results

Signals were recorded at a site off the New Zealand coast during the 1994 ATOC Acoustic Engineering Test (AET) using a single hydrophone at the SOFAR axis suspended from a drifting sonobuoy. The receptions recorded were limited to a 2‐day period due to weather and logistic constraints, but those analyzed showed considerable variability in structure from transmission to transmission. This path is particularly interesting because of its length (10 Mm) and its transequatorial nature. A moored, autonomous system was deployed in early 1996 off the New Zealand coast to acquire data over several months to investigate signal variability further. The source was on the Pioneer Seamount, and the single hydrophone moored at the SOFAR axis channel depth. These data and their analysis will be presented and discussed.

Complex rays and waveforms near caustics

Ray theory can be carried into a shadow zone using rays of complex launch angle but the search for eigenrays is usually impractical. A new approach first finds the ‘‘measurement front,’’ i.e., the continuous curve of ray depth, as a function of arrival time at a fixed range. The measurement front folds back on itself when the rays touch a caustic. The measurement front can be continued beyond the caustic into the shadow zone using rays of complex launch angle. Points at a fixed depth on the measurement front represent ray arrivals at a hydrophone. Waveforms can be calculated directly from the ray arrivals. Airy functions are used for ray amplitudes near caustics.

ATOC—New Zealand receiver site survey and acoustic test

Possible New Zealand receiver sites for the ATOC experiment have been investigated. A suitable site requires a water depth of 2000 m at a distance of 30 nm or less from the coast and an unobstructed acoustic path to California. A detailed site surveyed and an acoustic trial were conducted in September 1992. In the acoustic trial a series of 1.8‐kg SUS charges was detonated off the California coast. Good signals were received in New Zealand at a distance of 10 360 km.