Effect of Suspended Sediment on Acoustic Detection Using Reverberation

Similar documents
Effect of Suspended Sediment on Acoustic Detection Using Reverberation

Examples of Carter Corrected DBDB-V Applied to Acoustic Propagation Modeling

High-Frequency Scattering from the Sea Surface and Multiple Scattering from Bubbles

Characterizing The Surf Zone With Ambient Noise Measurements

Waves, Bubbles, Noise, and Underwater Communications

High Frequency Acoustical Propagation and Scattering in Coastal Waters

Waves, Bubbles, Noise and Underwater Communications

Marine Mammal Acoustic Tracking from Adapting HARP Technologies

Internal Waves and Mixing in the Aegean Sea

Acoustic Focusing in Shallow Water and Bubble Radiation Effects

Anthropogenic Noise and the Marine Environment

AN EXPERIMENTAL INVESTIGATION OF SPILLING BREAKERS

Kelly Legault, Ph.D., P.E. USACE SAJ

Determination of Nearshore Wave Conditions and Bathymetry from X-Band Radar Systems

( max)o Wind Waves 10 Short Swell (large wave steepness) 25 Long Swell (small wave steepness) 75

Air-Sea Interaction Spar Buoy Systems

Observations of Velocity Fields Under Moderately Forced Wind Waves

Determination Of Nearshore Wave Conditions And Bathymetry From X-Band Radar Systems

Waves, Turbulence and Boundary Layers

TITLE: Assessing the Hydrodynamic Performance of Fouling-Release Surfaces (ONR Research Contract # N WR )

Remote Monitoring of Dolphins and Whales in the High Naval Activity Areas in Hawaiian Waters

Rogue Wave Statistics and Dynamics Using Large-Scale Direct Simulations

Global Ocean Internal Wave Database

Measured broadband reverberation characteristics in Deep Ocean. [E.Mail: ]

Understanding the Dynamics of Shallow-Water Oceanographic Moorings

DEVELOPMENT OF PRIMARY FRAGMENTATION SEPARATION DISTANCES FOR CASED CYLINDRICAL MUNITIONS

DoD Coral Reef Protection and Management Program

NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS ENVIRONMENTAL VARIABILITY ON ACOUSTIC PREDICTION USING CASS/GRAB. Nick A.

Long-Term Autonomous Measurement of Ocean Dissipation with EPS-MAPPER

Navy Shipbuilding Industrial Base

BRRAKING WAVE FORCES ON WALLS

REPORT DOCUMENTATION PAGE

Internal Waves in Straits Experiment Progress Report

Using SolidWorks & CFD to Create The Next Generation Airlocks

Imaging the Lung Under Pressure

High Frequency Acoustical Propagation and Scattering in Coastal Waters

Behavioral Response of Dolphins to Signals Simulating Mid-Frequency Sonar

Surface Wave Processes on the Continental Shelf and Beach

Development of Low Volume Shape Memory Alloy Variable Ballast System for AUV Use

14/10/2013' Bathymetric Survey. egm502 seafloor mapping

Hyperspectral Optical Properties, Remote Sensing, and Underwater Visibility

Observations of Near-Bottom Currents with Low-Cost SeaHorse Tilt Current Meters

Internal Tides and Solitary Waves in the Northern South China Sea: A Nonhydrostatic Numerical Investigation

Broadband acoustic transmission measurements in surface ship wakes

z Interim Report for May 2004 to October 2005 Aircrew Performance and Protection Branch Wright-Patterson AFB, OH AFRL-HE-WP-TP

Uncertainty in Acoustic Mine Detection Due to Environmental Variability

Data Analysis: Plankton Distribution in Internal Waves in Massachusetts Bay

Hydro-Thermal Vent Mapping with Multiple AUV's AZORES-2001

ENVIRONMENTALLY ADAPTIVE SONAR

Rip Currents Onshore Submarine Canyons: NCEX Analysis

AFRL-RX-WP-TP

NONLINEAR INTERNAL WAVES IN THE SOUTH CHINA SEA

Seafloor Ripple Measurements at the Martha s Vineyard Coastal Observatory

STUDIES OF FINITE AMPLITUDE SHEAR WAVE INSTABILITIES. James T. Kirby. Center for Applied Coastal Research. University of Delaware.

CORRELATION BETWEEN SONAR ECHOES AND SEA BOTTOM TOPOGRAPHY

EFFECTS OF OCEAN THERMAL STUCTURE ON FISH FINDING WITH SONAR

from ocean to cloud PARAMETRIC SUB-BOTTOM PROFILER, A NEW APPROACH FOR AN OLD PROBLEM

Harbor Threat Detection, Classification, and Identification

FFI RAPPORT SENSITIVITY OF LYBINS TRANSMISSION LOSS DUE TO VARIATIONS IN SOUND SPEED. HJELMERVIK Karl Thomas FFI/RAPPORT-2006/01356

RIP CURRENTS. Award # N

High Ping Rate Profile Water Mode 12

The Great Coastal Gale of 2007 from Coastal Storms Program Buoy 46089

APPLICATION OF SOUND PROPAGATION (IN THE PERSIAN GULF AND OMAN SEA)

M2.50-cal. Multishot Capabilities at the US Army Research Laboratory

NAVOCEANO-NPS Thesis Program on Littoral Warfare Oceanography

Right Whale Diving and Foraging Behavior in the Southwestern Gulf of Maine

Distributed Integrated Ocean Prediction System (DIOPS) / SWAN Rapid Transition Program

Ocean Mixing. James N. Moum

Waves, Bubbles, Noise, and Underwater Communications

Surface Wave Processes on the Continental Shelf and Beach

Validation of the Distance Visibility Algorithm (DiVA) and the Impact of the Mesoscale Approximation to Mine Warfare Applications

Centre for Marine Science and Technology

Model-based Adaptive Acoustic Sensing and Communication in the Deep Ocean with MOOS-IvP

In ocean evaluation of low frequency active sonar systems

Transmission loss (TL) can be predicted, to a very rough degree, solely on the basis of a few factors. These factors are range, and frequency.

DUXBURY WAVE MODELING STUDY

PREDICTION OF ERODED VERSUS ACCRETED BEACHES

Quantifying Fish Backscattering using SONAR Instrument and Kirchhoff Ray Mode (KRM) Model

AFRL-RH-WP-TR

Calculation of the Internal Blast Pressures for Tunnel Magazine Tests

Impact Burial Prediction for Mine Breaching Using IMPACT35

Next Generation Modeling for Deep Water Wave Breaking and Langmuir Circulation

COMPUTATIONAL OCEAN ACOUSTIC TOOLBOX MANUAL. Computational Ocean Acoustics Toolbox (COAT) is a package written containing the following

Acoustic Seaglider for Beaked Whale Detection

Minimal influence of wind and tidal height on underwater noise in Haro Strait

Recommended operating guidelines (ROG) for sidescan Sidescan sonar ROG in wrapper.doc English Number of pages: 9 Summary:

SHOCK WAVE PROPAGATION THROUGH AERATED WATER

Three Dimensional Shallow Water Adaptive Hydraulics (ADH-SW3): Waterborne Vessels

At-Sea Measurements of Diver Target Strengths at 100 khz: Measurement Technique and First Results

Aircraft Fuel Cell Repair Equipment

The Evolution of Vertical Spatial Coherence with Range from Source

Chemical Plume Mapping with an Autonomous Underwater Vehicle

Nearshore Wave-Topography Interactions

Currents measurements in the coast of Montevideo, Uruguay

High-Resolution Measurement-Based Phase-Resolved Prediction of Ocean Wavefields

An experimental study of internal wave generation through evanescent regions

Plankton Distribution in Internal Waves in Massachusetts Bay

Implementation of Structures in the CMS: Part IV, Tide Gate

Radar Remote Sensing of Waves and Currents in the Nearshore Zone

LOADED MULTICELLULAR MAGAZINE. Laurent ALLA IN

Transcription:

TECHNICAL NOTE Effect of Suspended Sediment on Acoustic Detection Using Reverberation AUTHORS Peter C. Chu Michael Cornelius Naval Ocean Analysis and Prediction Laboratory Department of Oceanography Naval Postgraduate School Mel Wagstaff Naval Oceanographic Office Stennis Space Center ABSTRACT Sonar operates by ensonifying a broad swath of the seabed using a line array of acoustic projectors with acoustic backscattering from the ensonified sediment. The suspended sediment layer affects the sonar imagery through the volume scattering strength. Understanding the acoustic characteristics of the suspended sediment layer can aid the Navy in detecting sea mines with sonar imagery. In this study, the Navy s Comprehensive Acoustic Simulation System is used to investigate such an effect. A range of critical values of volume scattering strength for buried object detection is found through repeated model simulations. INTRODUCTION coustic detection of undersea objects is difficult due to the uncertain environment (Chu et al., 2002, 2004) and even more difficult when the objects are buried in the seabed. First, sediments generate high backscattering noise due to heterogeneous scatters within the sediments clouding the object. Second, the acoustic wave attenuation in sediments is much higher than in water. Acoustic shadows make the buried targets absent in the sonar images due to diffraction around the target, transmission through the target and relatively high acoustic noise due to backscattering from sediments surrounding the target. Classification of buried targets is also more difficult since there are no shadows, and the images do not contain much information about target shape since scattering from oblique target surfaces is not detectable. Acoustic images of buried targets primarily consist of echoes from the target surfaces that are normal to the incident acoustic ray path. Target surfaces with an oblique aspect to the incident ray path will backscatter much less energy at the lower operating frequencies of sub-bottom profilers since the acoustic wavelength is much longer than the surface roughness of most targets of interest. The suspended sediment layer occupies the lower water column. Presence of the suspended sediments creates a volume scattering layer which affects acoustic detection. Understanding the acoustic effects of the suspended sediment layer leads to the development of acoustic sensors with capability to scan the seafloor and to detect ordnance such as sea mines. 2. Comprehensive Acoustic Simulation System Sonar equations provide guidelines for system design (Urick, 1983). The governing equation for beam patterns with dominating volume reverberation is given by SL TL i TL r + TS - RL = SNR (1) where SL is the source level; TL i is the transmission loss of the incident wave; TL r is the transmission loss of the reflected echo; TS is target strength; RL is the reverberation level of sediments; SNR is the signal-to-noise ratio of the sonar data. The transmission losses of the incident and reflected waves, TL i and TL r, account for spherical loss (such as spherical spreading), acoustic attenuation, and boundary loss. Volume reverberation depends on the physical properties of the water column. With the presence of a suspended sediment layer, large quantities of sediment remain in the water column and significantly affect the acoustic transmission in the water. The denser the suspended sediment layer is, the harder it would be for sonar to penetrate through the water. Moreover, suspended bottom sediment layer increases the density of the lower water column and in turn changes the sound velocity profile and prevents acoustic energy from reaching a possible buried object. Reverberation can be used to represent the effects of a suspended sediment layer on acoustic detection. The differential form of the reverberation can be obtained from integration over the ensonified area (Keenan, 2000), d(rl) = SL + 10 log (SA) + SS TL t - TL f + BP t + BP r (2) where SA is the scattering area; SS is the scattering strength per unit area; TL t is the transmission loss to scatterer; TL f is the transmission loss from scatterer; BP t is the beam pattern to scatterer; and BP f is the beam pattern from scatterer. The most important design criterion for detecting mine-like objects is to maximize the SNR, the target echo to scattering noise ratio in decibels. Summer 2005 Volume 39, Number 2 105

Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 2005 2. REPORT TYPE 3. DATES COVERED 00-00-2005 to 00-00-2005 4. TITLE AND SUBTITLE Effect of Suspended Sediment on Acoustic Detection Using Reverberation 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Naval Ocean Analysis and Prediction Laboratory,Department of Oceanography,Naval Postgraduate School,Monterey,CA,94393 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13. SUPPLEMENTARY NOTES 14. ABSTRACT 11. SPONSOR/MONITOR S REPORT NUMBER(S) 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Same as Report (SAR) 18. NUMBER OF PAGES 5 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

The Comprehensive Acoustic Simulation System (CASS) is the Navy s standard model for acoustic and sonar analysis. It incorporates the Gaussian Ray Bundle (GRAB) eigenray modes to predict rangedependent acoustic propagation in the 150 Hz to 100 khz frequency band (Keenan et al., 1996; Keenan and Weinberg, 2001). CASS contains several equations for sound speed conversions. The current OAML approved Sound Speed Algorithm (Chen and Millero, 1977; Millero and Li, 1994) has been incorporated into CASS. The Chen-Millero- Li equations compute sound speed based on depth, temperature, and salinity. The Chen- Millero-Li, Wilson (1969), and Leroy (1969) equations are all very close in the salinity range 30 ppt to 40 ppt. For lower salinities the Chen-Millero-Li equation should be used. Near shore off the coast of Louisiana may have salinity variability especially near the Mississippi Delta. Thus, the Chen-Millero-Li equations are used in this study. CASS simulates the sonar performance reasonably well in the littoral zone with given environmental input data, such as bottom type, sound speed profile and wind speed and accurate tilt angle of the sound source (Chu et al., 2002, 2005). CASS successfully modeled torpedo acoustic performance in shallow water exercises off the coast of Southern California and Cape Cod. Recently, CASS was used to simulate mine warfare systems performance in the fleet (Keenan et al., 1996), and for AN/SQQ-32 mine hunting detection and classification sonar. CASS calculates the reverberation in nested do loops, seven deep. Reverberation is a function of time and the inner loop collected all the reverberation contributions over the user-requested sampling times. There are two loops on eigenray paths, one for the paths connecting the transmitter to the scattering cell and the other for the paths connecting the scattering cell to the receiver. Since the reverberation is calculated in the time domain and there may be contributions in the same time bin from different ranges, the next loop increments the range. CASS combines the five possible eigenray paths at each range step and decides if the ray paths contribute to the reverberation time bin (Keenan, 2000). Test rays are sorted into families of comparable numbers of turning points and boundary interactions. Ray properties are then power averaged for each ray family to produce a representative eigenray of that family. Target echo level and reverberation level are computed separately, and subtracted to get the signal-noise ratio in the absence of additive ambient noise noise level is typically power summed with the reverberation level for total interference. A detection threshold is applied to compute SE, and then the peak signal is used to determine SNR (Figure 1). 3. Environmental and Acoustic Parameters A nearshore location with silty clay bottom on the Louisiana shelf is selected. Horizontal extension of the area is 50 m 60 m. Total depth including water and sediment is around 100 m. A hydrographic survey was conducted in the area (Cornelius, 2004). The sound speed increases a little from 1520 m s -1 near the ocean surface to 35 m depth, and reduces drastically to 1510.5 m s -1 at 55 m depth. Below 55 m depth, the sound speed decreases slightly with depth and reaches 1510 m s -1 at 100 m. Suppose the sonar is towed at a depth of 30.4 m with a source level of 240 db. The water depth in the area varies from 77 to 95 m. The extent of the image is approximately 60 m in the y-direction and 50 m in the x-direction. The grain size index for a silty clay bottom is 8 from the Naval Oceanographic Office s standard. This parameter is related to specific geoacoustic parameters of bottom reflection (APL-UW, 1994). The bottom reflection effects are modeled using the Rayleigh model. The water column is assumed to be relatively clear above 77 m depth with a volume scattering strength of -95 db. The source of the water column scattering strength is extracted from a volume scattering strength database (CNMOC, 2004). A suspended sediment layer is present below 77 m depth characterized by a different scattering strength (-65 db). The source level is 240 db. The sonar frequency is 100 khz. The pulse length is 0.001 seconds. The time increment for modeling should not exceed one half of the pulse length to achieve proper resolution of each time step. Since the total distance traveled from the sonar to the end of the image is approximately 50 m, the total reverberation time is only 0.12 seconds. The maximum number of bottom and surface reflections is set at 30 to allow interference with reflected eigenrays. FIGURE 1 Steps taken to create a total reverberation image from CASS, compared to the side scan sonar image. 106 Marine Technology Society Journal

Test rays are sorted into families of comparable numbers of turning points and boundary interactions. Target echo level and reverberation level are typically computed separately, and then subtracted to get the signal-noise ratio. In the absence of additive ambient noise, the signal-noise ratio is typically power summed with the reverberation level to calculate total interference. A detection threshold is applied to compute SE, and then the peak signal is used to determine SNR (Figure 1). FIGURE 2 Bathymetry with mine-like object. 4. Mine-Like Object Let a hollow mine-like steel object (8 m 5 m 2 m) be placed near the center of the area with a height of 2 m. For the object, the grain size index is changed to -9 (clay) and the target strength is set as -35 db. The bathymetry is also changed to represent the existence of the object. The water depth is kept the same (87 m) in the vicinity of the object, and changed into 85 m over the object (Figure 2). CASS is integrated with the sonar parameters, sound speed profile (SSP), bottom type, bathymetry, and the scattering characteristics. The model output of the seafloor reverberation is used to represent the model generated sonar imagery (MGSI). An increase of the volume scattering strength in the lower water column reflects the presence of the suspended sediment layer. Clearly, the object is visible in the reverberation imagery. Since MGSI (Figure 3) is a replica of the sonar image, the effect of suspended sediment on acoustic detection may be studied using MGSI. FIGURE 3 Bottom reverberation with mine-like object inserted. Here, the horizontal-axis is cross track indices represented by time and the vertical-axis is along track indices represented by distance. 5. Effect of Suspended Sediment Suspended sediment increases the volume scattering strength. To simulate its effect, the volume scattering strength is increased by an increment of 5 db from the value of -65 db below 78 m depth while keeping the volume scattering strength constant (-95 db) above 78 m depth, and CASS is integrated with increasing the value of the volume scattering strength to investigate the effect of the suspended sediment on the object detection. Summer 2005 Volume 39, Number 2 107

The following procedure is used to determine the criterion of the volume scattering strength for the object absent from MGSI. If the simulated mine-like object is still visible in MGSI after increasing the volume scattering, the simulated suspended sediment layer is not strong enough to represent a layer that would prevent a minelike object from sonar detection. So the volume scattering strength is increased further. This procedure is performed until the minelike object is no longer visible. During the simulation, the water column is assumed to be relatively clear above 77 m depth, with an initial suspended sediment layer characterized by a slightly stronger scattering strength below 78 m. Sediment in the water column would increase the volume scattering and ultimately the volume reverberation. For MGSI with an object, a critical value of the volume scattering strength can be determined below 78 m depth to render the mine-like object undetectable. Volume attenuation and changes in the sound velocity profile will also have an effect, but they are not addressed in this work. As the volume scattering strength of the sediment layer (below 78 m depth) increases to a value of -30 db, the object becomes nearly undetectable. The CASS modeling continues with the increase of a smaller increment of 1 db. The mine-like object is completely obscured (Figure 4) by the suspended sediment layer at a value of -22 db (below 78 m depth), which is taken as the threshold. This threshold (-22 db) is large compared to existing observational data. For example, Kringel et al. (2003) measure the acoustic volume scattering strength in West Sound, Orcas Island, Washington, using the benthic acoustic monitoring system. It is a bottom-mounted, radially scanning sonar designed to record high-frequency scattering from the seafloor. The acoustic volume scattering strength is measured from 22 m of water column with 0.5 m vertical and 2 min temporal resolution. Their measurement shows that the volume backscattering strength varies between -75 db to -25 db. This indicates that the threshold (-22 db) is in the high end, which implies that high suspended sediment density is needed to completely block the mine-like object from acoustic detection. 6. Conclusions (1) CASS is used to investigate the effect of suspended sediment on detecting a minelike object in the silty clay bottom at the Louisiana shelf with water depth around 100 m. Hydrographic and meteorological surveys were conducted. The environmental data (wind and SSP) are taken as the input into CASS to simulate the sonar image with a mine-like object present through its reverberation characteristics. (2) A threshold of volume scattering strength (-22 db) for the mine-like object detection is found through repeated model simulations. When the volume scattering strength increases to the threshold, the mine-like object is acoustically undetectable. It is noted that this threshold is very large and valid only for this case and that the purpose of this study is to show the methodology rather than to provide an accurate threshold. (3) While CASS is useful, several shortfalls remain in this study. First, the process by which the environment and the object are modeled is cumbersome. Second, the appropriate volume scattering strength for the buried object should be given. A thorough study is suggested on the relationship between the suspended sediment layer density and type (e.g., sand, silt or clay), particle density in the layer, associated volume scattering strength and attenuation, and changes in the sound speed profile. Acknowledgments The Office of Naval Research, Naval Oceanographic Office, and the Naval Postgraduate School supported this study. FIGURE 4 Reverberation plot of bottom with mine object inserted. The horizontal axis is cross track indices represented by time and the vertical axis is along track indices represented by distance with mine object inserted and suspended sediment layer with -22 db volume scattering strength. 108 Marine Technology Society Journal

References APL-UW. 1994. High-Frequency Ocean Environmental Acoustics Models Handbook. APL-UW TR 9407, Applied Physics Laboratory, University of Washington, Seattle, 210 p. Chen, C. T. and Millero, F. J. 1977. Speed of Sound in Seawater at High Pressures. J Acoust Soc Am. 62(5):1129-1135. Chu, P.C., C.J. Cintron, S.D. Haeger, D. Schneider, R.E. Keenan and D.N. Fox. 2002. Yellow Sea acoustic uncertainty caused by hydrographic data errors. In: Impact of Littoral Environment Variability on Acoustic Prediction and Sonar Performance, eds. N.G. Pace and F. B. Jensen. pp. 563-570. Boston: Kluwar Academic Publishers. Chu, P.C., M.D. Perry, E.L. Gottshall, and D.S. Cwalina. 2004. Satellite data assimilation for improvement of Naval undersea capability. Mar Technol Soc J. 38(1):12-23. Chu, P.C. and N.A. Vares. 2005. Variability in shallow sea acoustic detection due to environmental uncertainty, U.S. Navy Journal of Undersea Acoustics, in press. Commander Naval Meteorology and Oceanography Command (CNMOC). 2004. Oceanography and Meteorology Master Library, Stennis Space Center, MS. Cornelius, M. 2004. Effects of a Suspended Sediment Layer on Acoustic Imagery. MS Thesis in Meteorology and Physical Oceanography, Naval Postgraduate School, Monterey, CA, 48 pp. Keenan, R. E., H. Weinberg, F.E. Aidala. 1996. Modeling Cape Cod site C and site D torpedo reverberation data with CASS. Naval Undersea Warfare Center Division, Newport, RI, NUWC-NPT Technical Report 10,590, 11 July 1996. Keenan, R. E. and H. Weinberg. 2001. Gaussian ray bundle (GRAB) model shallow water acoustic workshop implementation. J Comput Acoust. 9:133-148. Kringel, K., P.A. Jumars and D.V. Holiday. 2003. A shallow scattering layer: Highresolution acoustic analysis of nocturnal vertical migration from the seabed. Limnol Oceanogr. 48(3):1223-1234. Leroy, C.C. 1969. Development of Simple Equations for Accurate and More Realistic Calculation of the Sound Speed in Sea Water. J Acoust Soc Am. 46(1):216-226. Millero, F.J. and Li, X. 1994. Comments on On Equations for the Speed of Sound in Seawater. J Acoust Soc Am. 95(5):2757-2759. Naval Oceanographic Office Systems Integration Division. 1999a. Software Design Document for the Gaussian Ray Bundle (GRAB) Eigenray Propagation Model. OAML-SDD-74. Stennis Space Cneter, MS. Naval Oceanographic Office Systems Integration Division. 1999b. Software Requirements Specification for the Gaussian Ray Bundle (GRAB) Eigenray Propagation Model. OAML-SRS-74. Stennis Space Center, MS. Urick, R.J. 1983. Principles of Underwater Sound, McGraw-Hill, New York, 423 pp. Weinberg, H., and R. E. Keenan. 1996. Gaussian ray bundles for modeling highfrequency propagation loss under shallow water condition. J Acoust SocAm. 100(3):1421-1431. Wilson, W.D. 1960. Equation for the speed of sound in sea water. J Acoust Soc Am. 32:1357-1367. Keenan, R. E., 2000. An introduction to GRAB eigenrays and CASS reverberation and signal excess. Proceedings on IEEE/MTS Oceans 2000, 6 pages (in CD Rom). 11-14 September 2000, Providence Rhode Island. Summer 2005 Volume 39, Number 2 109