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Morawitz, WML, Cornuelle BD, Worcester PF.  1996.  A case study in three-dimensional inverse methods: Combining hydrographic, acoustic, and moored thermistor data in the Greenland sea. Journal of Atmospheric and Oceanic Technology. 13:659-679.   10.1175/1520-0426(1996)013<0659:acsitd>;2   AbstractWebsite

A variety of measurements, including acoustic travel times, moored thermistor time series, and hydrographic stations, were made in the Greenland Sea during 1988-89 to study the evolution of the temperature held throughout the year. This region is of intense oceanographic interest because it is one of the few areas in the world where open-ocean convection to great depths has been observed. This paper describes how the various data types were optimally combined using linear, weighted least squares inverse methods to provide significantly more information about the ocean than can be obtained from any single data type. The application of these methods requires construction of a reference state, a statistical model of ocean temperature variability relative to the reference state, and an analysis of the differing signal-to-noise ratios of each data type. A time-dependent reference state was constructed from all available hydrographic data, reflecting !he basic seasonal variability and keeping the perturbations sufficiently small so that linear inverse methods are applicable. Smoothed estimates of the vertical and horizontal covariances of the sound speed (temperature) variability were derived separately for summer and winter from all available hydrographic and moored thermistor data. The vertical covariances were normalized before bring decomposed into eigenvectors, so that eigenvectors were optimized to fit a fixed percentage of the variance at every depth. The 12 largest redimensionalized eigenvectors compose the vertical basis of the model. A spectral decomposition of a 40-km correlation scale Gaussian covariance is used as the horizontal basis. The uncertainty estimates provided by the inverse method illustrate the characteristics of each dataset in measuring large-scale features during a diversely sampled time period in the winter of 1989. The acoustic data alone resolve about 70% of the variance in the three-dimensional, 3-day average temperature field. The hydrographic data alone resolve approximately 65% of the variance during the selected period but are much less dense or absent over most of the year. The thermistor array alone resolves from 10% to 65% of the temperature variance, doing better near the surface where the most measurements were taken. The combination of the complete 1988-89 acoustic, hydrographic, and thermistor datasets give three-dimensional temperature and heat content estimates that resolve on average about 90% of the expected variance during this particularly densely sampled time period.

Duda, TF, Pawlowicz RA, Lynch JF, Cornuelle BD.  1995.  Simulated Tomographic Reconstruction of Ocean Features Using Drifting Acoustic Receivers and a Navigated Source. Journal of the Acoustical Society of America. 98:2270-2279.   10.1121/1.413341   AbstractWebsite

Numerically simulated acoustic transmission from a single source of known position (for example, suspended from a ship) to receivers of partially known position (for example, sonobuoys dropped from the air) are used for tomographic mapping of ocean sound speed. The maps are evaluated for accuracy and utility. Grids of 16 receivers are employed, with sizes of 150, 300, and 700 km square. Ordinary statistical measures are used to evaluate the pattern similarity and thus the mapping capability of the, system. For an array of 300 km square, quantitative error in the maps grows with receiver position uncertainty. The large and small arrays show lesser mapping capability than the mid-size array. Mapping errors increase with receiver position uncertainty for uncertainties less than 1000-m rms, but uncertainties exceeding that have less systematic effect on the maps. Maps of rms error of the field do not provide a complete view of the utility of the acoustic network. Features of maps are surprisingly reproducible for different navigation error levels, and give comparable information about mesoscale structures despite great variations in those levels. (C) 1995 Acoustical Society of America.

Worcester, PF, Cornuelle BD, Hildebrand JA, Hodgkiss WS, Duda TF, Boyd J, Howe BM, Mercer JA, Spindel RC.  1994.  A Comparison of Measured and Predicted Broad-Band Acoustic Arrival Patterns in Travel Time-Depth Coordinates at 1000-Km Range. Journal of the Acoustical Society of America. 95:3118-3128.   10.1121/1.409977   AbstractWebsite

Broadband acoustic signals were transmitted from a moored 250-Hz source to a 3-km-long vertical line array of hydrophones 1000 km distant in the eastern North Pacific Ocean during July 1989. The sound-speed field along the great circle path connecting the source and receiver was measured directly by nearly 300 expendable bathythermograph (XBT), conductivity-temperature-depth (CTD), and air-launched expendable bathythermograph (AXBT) casts while the transmissions were in progress. This experiment is unique in combining a vertical receiving array that extends over much of the water column, extensive concurrent environmental measurements, and broadband signals designed to measure acoustic travel times with 1-ms precision. The time-mean travel times of the early raylike arrivals, which are evident as wave fronts sweeping across the receiving array, and the time-mean of the times at which the acoustic reception ends (the final cutoffs) for hydrophones near the sound channel axis, are consistent with ray predictions based on the direct measurements of temperature and salinity, within measurement uncertainty. The comparisons show that subinertial oceanic variability with horizontal wavelengths shorter than 50 km, which is not resolved by the direct measurements, significantly (25 ms peak-to-peak) affects the time-mean ray travel times. The final cutoffs occur significantly later than predicted using ray theory for hydrophones more than 100-200 m off the sound channel axis. Nongeometric effects, such as diffraction at caustics, partially account for this observation.

Cornuelle, BD, Worcester PF, Hildebrand JA, Hodgkiss WS, Duda TF, Boyd J, Howe BM, Mercer JA, Spindel RC.  1993.  Ocean Acoustic Tomography at 1000-Km Range Using Wave-Fronts Measured with a Large-Aperture Vertical Array. Journal of Geophysical Research-Oceans. 98:16365-16377.   10.1029/93jc01246   AbstractWebsite

Broadband acoustic signals transmitted from a moored 250-Hz source to a 3-km-long vertical line array of hydrophones 1000 km distant in the north central Pacific Ocean were used to determine the amount of information available from tomographic techniques used in the vertical plane connecting a source-receiver pair. A range-independent, pure acoustic inverse to obtain the sound speed field using travel time data from the array is shown to be possible by iterating from climatological data without using any information from concurrent environmental measurements. Range-dependent inversions indicate resolution of components of oceanic variability with horizontal wavelengths shorter than 50 km, although the limited spatial resolution of concurrent direct measurements does not provide a strong cross-validation, since the typical cast spacing of 20-25 km gives a Nyquist wavelength of 40-50 km. The small travel time signals associated with high-wavenumber ocean variability place stringent but achievable requirements on travel time measurement precision. The forward problem for the high-wavenumber components of the model is found to be subject to relatively large linearization errors, however, unless the sound speed field at wavelengths greater than about 50 km is known from other measurements or from a two-dimensional tomographic array. The high-ocean-wavenumber resolution that is in principle available from tomographic measurements is therefore achievable only under restricted conditions.

Duda, TF, Flatte SM, Colosi JA, Cornuelle BD, Hildebrand JA, Hodgkiss WS, Worcester PF, Howe BM, Mercer JA, Spindel RC.  1992.  Measured Wave-Front Fluctuations in 1000-Km Pulse-Propagation in the Pacific-Ocean. Journal of the Acoustical Society of America. 92:939-955.   10.1121/1.403964   AbstractWebsite

A 1000-km acoustical transmission experiment has been carried out in the North Pacific, with Pulses broadcast between a moored broadband source (250-Hz center frequency) and a moored sparse vertical line of receivers. Two data records are reported: a period of 9 days at a pulse rate of one per hour, and a 21 -h period on the seventh day at six per hour. Many wave-front segments were observed at each hydrophone depth, and arrival times were tracked and studied as functions of time and depth. Arrivals within the final section of the pulse are not trackable in time or space at the chosen sampling rates, however. Broadband fluctuations, which are uncorrelated over 10-min sampling and 60-m vertical spacing, are observed with about 40 (ms)2 variance. The variance of all other fluctuations (denoted as low-frequency) is comparable or smaller than the broadband value; this low-frequency variance can be separated into two parts: a wave-front segment displacement (with vertical correlation length greater than 1 km) that varies substantially between rays with different ray identifiers, and a distortion (with vertical correlation length between 60 m and 1 km) of about 2 (ms)2 variance. The low-frequency variance may be explained as the effect of internal waves, including internal tides. The variance of the broadband fluctuations is reduced somewhat but not eliminated if only high-intensity peaks are selected; this selection does not affect the statistics of the low-frequency fluctuations.

Worcester, PF, Cornuelle BD, Spindel RC.  1991.  A Review of Ocean Acoustic Tomography - 1987-1990. Reviews of Geophysics. 29:557-570. AbstractWebsite

Research in ocean acoustic tomography during the last quadrennium has resulted in substantial progress in understanding the capabilities and limitations of the technique. Theoretical studies and numerical simulations have led to greater understanding of the oceanographic information available in a vertical slice from acoustic transmissions between a single pair of instruments, of the horizontal geometries required to map the ocean mesoscale field with specified precision, and of the properties of tomographic reconstructions of the two-dimensional vector field of current. Simultaneously, the instrumentation used in tomographic experiments has been significantly improved, increasing the precision of the measurements and making gyre and basin scale experiments feasible between moored instruments. Experimental efforts to test the accuracy with which the ocean temperature and current fields can be measured acoustically have now demonstrated that tomographic techniques provide measurements with oceanographically useful precision up to ranges of about 1000 km. Such demonstrations are difficult due to the incompatibility between point measurements and the spatial averages provided by tomographic techniques. The experiments have also yielded significant information on the character of acoustic propagation at long range in the ocean. Experimental precision is now adequate to distinguish between competing algorithms for sound speed as a function of temperature, salinity, and depth. Finally, and most importantly, emphasis has shifted to use of the technique for studying the ocean, rather than on understanding the capabilities and limitations of the technique. Two major experiments, the Greenland Sea Tomography Experiment and the Gulf Stream Extension Tomography Experiment, both conducted during 1988-89, were devoted to improving our understanding of ocean dynamics, although results are not yet available. There is increased emphasis on exploiting the integrating nature of acoustic transmissions to study gyre and global scale temperature variability, phenomena difficult to study in any other way.