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Defence R&D Canada – Atlantic

DEFENCE DÉFENSE&

An Investigation of the Bellhop Acoustic

Prediction ModelCapabilities, Tests, Recommendations and User Guide

Dr. Diana F. McCammonMcCammon Acoustical Consulting

McCammon Acoustical Consulting475 Baseline RoadWaterville, NS B0P 1V0

Contract Number: W7707-042585/001/HAL

Contract Scientific Authority: Dr. Bill Roger (902) 426-3100 ext 292

Contract Report

DRDC Atlantic CR 2004-285

November 2005

Copy No.________

Defence Research andDevelopment Canada

Recherche et développementpour la défense Canada

This page intentionally left blank.

An Investigation of the Bellhop Acoustic Prediction Model Capabilities, Tests, Recommendations and User Guide

Dr. Diana F. McCammon McCammon Acoustical Consulting McCammon Acoustical Consulting Waterville, NS B0P 1V0

Contract number W7707-042585/001/HAL Contract Scientific Authority: Dr. Bill Roger (902) 426-3100 ext 292

Defence R&D Canada – Atlantic Contract Report DRDC Atlantic CR 2004-285

November 2005

DRDC Atlantic CR 2004-285 i

Abstract

This report documents some of the capabilities and limitations of the Bellhop-DRDC model and describes the alterations required to make the code compatible with DRDC’s Environment Modeling Manager for use in the frequency range 50 Hz to 1500 Hz. It presents examples of the output forms that are possible using a Scotia shelf example. The report documents the accuracy of the range dependence and frequency response of Bellhop-DRDC by tests with a parabolic equation. The lack of high-quality bottom treatment is probably the greatest limitation on accuracy in bottom-limited cases in the present configuration of Bellhop-DRDC. This report discusses possible options for improving the bottom loss methodology by seeking an alternative to the MGS province database and loss curves. Other additions that would also enhance the capabilities of Bellhop-DRDC include adding a beam pattern capability and computing a standard deviation output to quantitatively describe the sensitivity of the transmission loss to uncertainty in the inputs. A user guide is included in Appendix B.

Résumé

Le présent rapport décrit certaines des capacités et des limites du modèle Bellhop-RDDC, ainsi que les modifications requises pour rendre le code compatible avec le gestionnaire de modélisation de l'environnement (EMM) de RDDC pour une utilisation dans la plage de fréquences 50-1 500 Hz. Le rapport présente des exemples de formes de données de sortie possibles pour une zone de la plate-forme Scotian. Le rapport décrit aussi la précision de la dépendance à l’égard de la distance et de la réponse en fréquence du modèle Bellhop-RDDC en se basant sur des essais avec application d’une équation parabolique. L’absence d’une méthode de traitement du fond de haute qualité représente probablement la plus grande limite influant sur la précision pour les cas limités au fond, compte tenu de la configuration actuelle du modèle Bellhop-RDDC. Le présent rapport comprend une discussion sur les options qui, par la recherche de solutions de remplacement aux courbes de pertes et à la base de données des régions MGS, pourraient améliorer la méthode de traitement des pertes au fond. Parmi les autres modifications qui pourraient aussi améliorer le fonctionnement du modèle Bellhop-RDDC, on retrouve l’ajout du traitement de diagrammes de rayonnement et le calcul d’un écart-type pour décrire quantitativement l’incidence des pertes de transmission sur l’incertitude des entrées. Un guide de l’utilisateur est fourni à l’annexe B.

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DRDC Atlantic CR 2004-285 iii

Executive summary

Introduction

The current environmental prediction system for the Canadian Navy is the Allied Environmental Support System, or AESS. To add functionality, a client/server system called the Environment Modeling Manager (EMM) has been developed to provide a connection between an acoustic prediction engine and both client programs and sonar operators. AESS suffers from two problems that have forced the investigation of alternate solutions. First, it can be very difficult to extract many of the model results of specific interest to acoustic operators. Second, the software is classified, which requires all associated development to be performed within a special workspace that severely limits flexibility. Consequently a search is being conducted for an unrestricted acoustic prediction engine that could replace AESS within the EMM framework. One of the prime candidates is a freely available model called Bellhop.

This report documents some of the capabilities and limitations of the Bellhop-DRDC model and describes the alterations undertaken to make the code compatible with DRDC’s Environment Modeling Manager (EMM). It presents examples of the output forms that are possible, including classic ray tracing, transmission loss fields, and, tables indicating travel time, amplitude, phase, and arrival angle for the individual rays.

Results

The Bellhop model has been enhanced by adding: wind-driven surface losses, MGS bottom losses, low frequency terms in the Thorpe volume attenuation, and the capability for range-dependence in the sound speed profiles and the bottom loss provinces.

The output products of Bellhop-DRDC are ray traces, full field transmission loss matrices, and arrival tables including ray amplitude, phase, travel time, and arrival angle. Bellhop-DRDC will provide all the output products necessary to support both active and passive applications.

The accuracy of Bellhop-DRDC in handling range dependence and low frequency propagation is demonstrated in this report by comparison with a parabolic equation model in a decaying duct test case. Excellent agreement is obtained with the most common difference being 2 - 2.5 dB at all frequencies. The coherent comparisons showed good agreement in the placement of spikes and nulls and accuracy in the leakage of energy into the shadow zones as the duct decayed. This test lends credibility to the Bellhop-DRDC model for use in the low frequency band 50 Hz to 1500 Hz.

The lack of high-quality bottom treatment is probably the greatest limitation on accuracy in bottom-limited cases in the present configuration of Bellhop-DRDC. This

iv DRDC Atlantic CR 2004-285

report discusses possible options for improving the bottom loss methodology by seeking an alternative to the MGS province database and loss curves. The improved bottom treatment should be based on the physics of reflections from multiple layered sediments. Concurrent development of a relationship between sediment properties and water depth would be necessary to supply the inputs to the reflection model.

Significance

The replacement of the current prediction engine with Bellhop-DRDC will allow much greater control in accessing the full capabilities of the model, and provide a means to constantly improve the model as new algorithms are acquired. In particular, the model provides the necessary support for predictions of active transmissions. There will also be more control over tuning the EMM system to accommodate differing requirements from naval tactical decision aids.

Future follow-on work

The most important and most necessary task for future model upgrades is to replace the present bottom loss model (MGS provinces) with a higher fidelity bottom treatment. This is a critical need because of the extreme sensitivity of Bellhop-DRDC to the bottom loss and because of the inability of the MGS provinces and loss curves to adequately describe complex and rapidly changing littoral sediments. Using measured bottom characteristics rather than a single province number will provide significantly more accurate results, particularly in shallow waters. In addition, this will remove the requirement to run the system in a classified environment.

Other additions to Bellhop-DRDC could include a beam pattern capability and a standard deviation output to quantitatively describe the sensitivity of the transmission loss to uncertainty in the inputs. The ability to compute confidence bounds on transmission loss (from uncertainty in the inputs) would provide an important enhancement in tactical decision making.

McCammon, D. 2005. An Investigation of the Bellhop Acoustic Prediction Model. DRDC Atlantic CR 2004-285. DRDC Atlantic

DRDC Atlantic CR 2004-285 v

Sommaire Introduction

Le système actuel de prévision environnementale de la Marine canadienne est le système de soutien interallié dans le domaine de l'environnement (AESS). Dans le but d’ajouter des fonctionnalités, un système client-serveur, désigné « gestionnaire de modélisation de l'environnement » (EMM), a été développé afin de faire le lien entre un moteur de prévision acoustique, et, à la fois, les programmes clients et les opérateurs de sonar. Le système AESS présente deux problèmes qui ont poussé à l’analyse de solutions de remplacement. D’abord, il peut être très difficile d’extraire un grand nombre des résultats de modélisation présentant un intérêt particulier pour les opérateurs de systèmes acoustiques. Ensuite, le logiciel est considéré comme classifié et, donc, tous les travaux de développement qui y sont associés doivent être effectués dans un espace de travail spécial, ce qui limite sérieusement la souplesse du système. Par conséquent, on cherche actuellement un moteur de prévision acoustique sans restrictions, qui pourrait remplacer le système AESS dans le cadre d’application EMM. Un des principaux candidats envisagés est le modèle Bellhop, un modèle qui est largement disponible.

Le présent rapport décrit certaines des capacités et des limites du modèle Bellhop-RDDC, ainsi que les modifications entreprises pour rendre le code compatible avec le gestionnaire de modélisation de l'environnement (EMM) de RDDC. Le rapport présente des exemples de formes de données de sortie possibles, y compris des tracés de rayons classiques, des champs des pertes de transmission, ainsi que des tableaux indiquant le temps de propagation, l’amplitude, la phase et l’angle d’arrivée pour chacun des rayons.

Résultats

Le modèle Bellhop a été amélioré par l’ajout de pertes à la surface dues aux vents, de pertes au fond MGS et de termes de basse fréquence dans la réduction de volume (Thorpe) et par la prise en charge de la dépendance à l’égard de la distance dans les profils de vitesse du son et dans les régions caractérisées par des niveaux déterminés de pertes au fond.

Des tracés de rayon, des matrices de perte de transmission de champ complet et des tableaux de données d’arrivée, y compris de l’amplitude, de la phase, du temps de propagation et de l’angle d’arrivée du rayon, sont les produits de sortie du modèle Bellhop-RDDC. Ce dernier fournira tous les produits de sortie nécessaires aux applications actives et passives.

La précision du modèle Bellhop-RDDC dans le traitement de la dépendance à l’égard de la distance et dans le traitement de la propagation à basse fréquence est démontrée dans le présent rapport à l’aide d’une comparaison qui tient compte d’un modèle d’équation parabolique au cours d’un essai dans des conditions de dégradation du conduit. On a obtenu un excellent niveau de concordance, la différence la plus

vi DRDC Atlantic CR 2004-285

commune étant de 2 à 2,5 dB pour toutes les fréquences. Des comparaisons cohérentes ont démontré, d’abord, l’existence d’une bonne concordance en ce qui concerne la position des pointes et des zéros et, aussi, la précision dans les fuites d’énergie vers les zones d’ombre à mesure que le conduit se dégrade. Cet essai apporte une certaine crédibilité au modèle Bellhop-RDDC pour une utilisation dans la bande basse fréquence 50 - 1 500 Hz.

L’absence d’une méthode de traitement du fond de haute qualité représente probablement la plus grande limite influant sur la précision pour les cas limités au fond, compte tenu de la configuration actuelle du modèle Bellhop-RDDC. Le présent rapport comprend une discussion sur les options qui, par la recherche de solutions de remplacement aux courbes de pertes et à la base de données des régions MGS, pourraient améliorer la méthode de traitement des pertes au fond. La méthode améliorée de traitement devrait être basée sur la physique de la réflexion par des sédiments à couches multiples. Le développement simultané d’une relation entre les propriétés des sédiments et la profondeur serait nécessaire pour fournir les entrées du modèle de réflexion.

Portée

Le remplacement du moteur de prévision actuel par le modèle Bellhop-RDDC permettra un contrôle beaucoup plus grand de l’accessibilité à toutes les fonctions du modèle et offrira un moyen d’améliorer celui-ci de façon constante à mesure que de nouveaux algorithmes sont mis au point. Notons, en particulier, que le modèle fournit les capacités nécessaires pour les prévisions de transmission active. Un plus grand contrôle sur l’accord du système EMM sera également possible pour tenir compte des différentes exigences des aides à la décision navales tactiques.

Recherches futures

La plus importante tâche requise pour les futures mises à niveau du modèle est le remplacement du modèle actuel de traitement des pertes au fond (régions MGS) par une méthode de traitement de plus haute fidélité. Il s’agit d’un besoin essentiel en raison de l’extrême sensibilité aux pertes au fond du modèle Bellhop-RDDC et, aussi, parce que les courbes de perte et les régions MGS ne peuvent pas décrire adéquatement les sédiments complexes et changeants du littoral. L’utilisation de caractéristiques du fond mesurées plutôt que du seul numéro de région fournira des résultats nettement plus précis, particulièrement en eaux peu profondes. En outre, grâce à cette façon de faire, le système pourra être utilisé dans un environnement qui n’est pas classifié.

Parmi les autres modifications qui pourraient être apportées au modèle Bellhop-RDDC, on retrouve l’ajout du traitement de diagrammes de rayonnement et le calcul d’un écart-type pour décrire quantitativement l’incidence des pertes de transmission sur l’incertitude des entrées. La capacité de calculer des limites de fiabilité pour les pertes de transmission (à partir de l’incertitude des entrées) apporterait une amélioration importante en ce qui concerne la prise de décisions tactiques.

McCammon, D. 2005. An Investigation of the Bellhop Acoustic Prediction Model. DRDC Atlantic CR 2004-285. DRDC Atlantic

DRDC Atlantic CR 2004-285 vii

Table of contents

Abstract....................................................................................................................................... i

Résumé ....................................................................................................................................... i

Executive summary .................................................................................................................. iii

Sommaire....................................................................................................................................v

Table of contents ..................................................................................................................... vii

List of figures ........................................................................................................................... ix

List of tables ...............................................................................................................................x

Acknowledgements .................................................................................................................. xi

1. Introduction ...................................................................................................................1

2. Internet Versions of Bellhop .........................................................................................2

3. Bellhop-DRDC..............................................................................................................3 3.1 Internal calculations and algorithms.................................................................3

3.1.1 Ray trace techniques............................................................................3 3.1.2 Sound speed interpolation ...................................................................3 3.1.3 Top boundary condition ......................................................................3 3.1.4 Bottom boundary condition.................................................................4 3.1.5 Thorpe volume attenuation..................................................................7

3.2 Output Capabilities...........................................................................................7 3.2.1 Ray Trace ............................................................................................8 3.2.2 Transmission Loss...............................................................................8 3.2.3 Arrivals table .......................................................................................9

3.3 Limitations......................................................................................................12 3.3.1 Bottom loss........................................................................................12

3.3.1.1 High sensitivity to losses ...............................................12 3.3.1.2 Coarse bottom provincing..............................................12

viii DRDC Atlantic CR 2004-285

3.3.1.3 Eliminating provinces ....................................................14 3.3.1.4 Losses from sediment characteristics.............................15

3.3.2 Beam Patterns....................................................................................15 3.3.3 Variability..........................................................................................15

4. Comparisons between Bellhop-DRDC and PE ...........................................................17 4.1 1500 Hz ..........................................................................................................19 4.2 1000 Hz ..........................................................................................................21 4.3 800 Hz. ...........................................................................................................23 4.4 500 Hz ............................................................................................................25 4.5 300 Hz ............................................................................................................27 4.6 100 Hz. ...........................................................................................................29 4.7 50 Hz. .............................................................................................................31 4.8 Discussion of test case results ........................................................................33

5. Summary and Future Modeling Directions .................................................................34

6. References ...................................................................................................................36

Appendix A. Porter’s Recommendations.............................................................................37

Appendix B. Users Guide for Bellhop-DRDC ....................................................................38 B.1 Input Files:......................................................................................................38 B.2 Output Files: ...................................................................................................41

Bibliography .............................................................................................................................44

Distribution list .........................................................................................................................47

DRDC Atlantic CR 2004-285 ix

List of figures

Figure 1. Surface loss vs. grazing angle at three frequencies with wind speed as a parameter from 5 to 30 kts......................................................................................................... 5

Figure 2. MGS bottom loss vs. grazing angle at three frequencies with MSG Province number as a parameter from 1 to 9. .......................................................................... 6

Figure 3. Thorpe volume attenuation from 50 to 1500 Hz. ....................................................... 7

Figure 4. Sound speed profile and bathymetry for the Scotia shelf example. ........................... 7

Figure 5. Ray trace over a Scotia shelf area. ............................................................................. 8

Figure 6. Transmission loss field on the Scotia shelf at 1000 Hz.............................................. 9

Figure 7. Sample portion of arrival file for the Scotia shelf. ................................................... 10

Figure 8. Receiver arrival angle vs. range for a 37.5 m deep receiver over the Scotia shelf... 10

Figure 9. Travel time vs. range to 5 km for a 37.5 m deep receiver over the Scotia shelf. ..... 11

Figure 10. MGS Provinces for the North Atlantic circa 1980. ................................................ 13

Figure 11. Decaying bilinear duct test case. The sound speed profiles consist of 5 profiles with decreasing duct width, spaced 4 km apart in range. ............................................... 17

Figure 12. Bellhop ray trace of the subsurface decaying bilinear duct test case using 30 rays from –6 to 6 degrees. Rays escape the duct as it decreases. .................................. 18

Figure 13. Bilinear decaying duct transmission loss at 1500 Hz............................................. 19

Figure 14. 1500 Hz difference fields and histograms............................................................... 20

Figure 15. Bilinear decaying duct transmission losses at 1000 Hz. ........................................ 21

Figure 16. 1000 Hz difference fields and histograms............................................................... 22

Figure 17. Bilinear decaying duct transmission loss at 800 Hz............................................... 23

Figure 18. 800 Hz difference fields and histograms................................................................ 24




x DRDC Atlantic CR 2004-285




Figure 25. Bilinear decaying duct transmission loss at 50 Hz................................................. 31

Figure 26. 50 Hz Difference fields and histograms. ................................................................ 32

List of tables

Table 1. Bottom characteristics of the Scotia shelf on the bathymetry track of this example....................................................................................................................14

Table 2. Suggestions for bottom composition assignment based on water depth. ...................15

DRDC Atlantic CR 2004-285 xi

Acknowledgements

I gratefully acknowledge the help and advice received from the Bellhop creator, Dr. Michael Porter, whose generosity and promptness made this report a pleasure to compile.

xii DRDC Atlantic CR 2004-285


DRDC Atlantic CR 2004-285 1

1. Introduction The current environmental prediction system for the Canadian Navy is the Allied Environmental Support System, or AESS. To add functionality, a client/server system called the Environment Modeling Manager (EMM) has been developed to provide a connection between an acoustic prediction engine and both client programs and sonar operators. AESS suffers from two problems that have forced the investigation of alternate solutions. First, it can be very difficult to extract many of the model results of specific interest to acoustic operators. Second, the software is classified, which requires all associated development to be performed within a special workspace that severely limits flexibility. Consequently a search is being conducted for an unrestricted acoustic prediction engine that could replace AESS within the EMM framework. One of the prime candidates is a freely available model called Bellhop. In Section 2, this report documents the capabilities and limitations of the Internet versions of the Bellhop model and describes the alterations undertaken to make the code compatible with EMM. This specialized model has been named Bellhop-DRDC. Tests indicate that it provides reliable predictions down to a frequency of 50 Hz. Section 3 presents examples of the output forms that are possible, from classic ray tracing, to transmission loss fields with range and depth, to arrival tables of ray travel time, amplitude, phase, arrival angle, and number of boundary interactions. The example used to demonstrate these output products is a shallow-water sloping bathymetry on the Scotia shelf with a severely downward refracting sound speed profile. This example shows that Bellhop-DRDC can have an extreme sensitivity in its transmission loss to the choice of Marine Geophysical Survey (MGS) bottom province in a bottom-limited environment. In Section 4, this report shows visual and qualitative comparisons with a generic Parabolic Equation (PE) solution to demonstrate and validate both the range dependence of Bellhop and its behavior at low frequency. Section 5 provides a summary and discusses future modeling requirements in terms of modeling deficiencies that need to be addressed, along with other add-ons that would enhance the capabilities of the model.

2 DRDC Atlantic CR 2004-285

2. Internet Versions of Bellhop The Ocean Acoustics Library, OALIB is available via the World Wide Web at http://oalib.saic.com. It contains a large number of propagation models that are free to download. This library features Fortran models from the four major physical approaches to ocean propagation: ray theory, mode theory, wavenumber integration, and the parabolic equation. At the time of this writing, the ray theory model Bellhop resided in this library in two forms.

1. The first is a stand-alone model called Bell99.for and stored in BellhopRD.zip. It was developed in 1999 and features range dependence in bathymetry, sound speed profile and MGS bottom loss province number. It uses geometric ray theory and computes incoherent transmission loss only.

2. The second version is included in the Acoustic Toolbox in the file atWinPII_f95.zip

(6928 KB). This file contains the Fortran source code for the models Bellhop, Kraken, Scooter and Sparc, along with an associated Matlab GUI for running the toolbox. The version Bellhop.f90 dated 27 June 2002 by Michael J. Porter in this file is considerably more sophisticated than #1 because it offers a choice of 5 different ray trace algorithms, 4 different sound speed interpolation techniques, 8 different boundary conditions, and 6 different output products. However its range dependence is less complete, as it only accepts a range dependent bathymetry. It also has no codes for computing a conventional reflection coefficient from an MGS or Bottom Loss Upgrade (BLUG) bottom province or from the wind driven sea surface.

To provide the best model for EMM for use on Navy applications, the two Internet versions of Bellhop have been effectively combined. The second version, Bellhop.f90, was chosen as the basis and the code was modified to include full range dependence in bathymetry, bottom loss province and sound speed profile. MGS bottom loss curves and Naval Oceanographic Office (NOO) surface loss calculations were also added. In the rest of this report, this combination code will simply be referred to as ‘Bellhop-DRDC’.


3. Bellhop-DRDC

3.1 Internal calculations and algorithms

3.1.1 Ray trace techniques Bellhop.f90 contains 5 choices for ray trace techniques: Cartesian beams, Ray-centered beams, Simple Gaussian beams, Gaussian beams (GRAB style) and Geometric beams. Based on the recommendations from Dr. Porter listed in Appendix A, the propagation algorithm in Bellhop-DRDC has been defaulted to Grab-style Gaussian beams. Dr. Porters’ discussion of curvature doubling and beam shifts refers to options used for describing ray characteristics for research purposes. These options have been defaulted ‘off’.

3.1.2 Sound speed interpolation Bellhop.f90 offers 4 choices for sound speed interpolation: Cubic spline, C-linear, N2-linear or Analytic. In the Acoustic Toolbox bellhop help file, C-linear is the recommended technique. The N2-linear scheme mimics the profile structure used for normal mode programs with Airy function eigenfunctions. One would choose this option if they wanted to perform a detailed comparison between a ray trace model and a normal mode model. The Analytic choice permits the user to supply analytic formulas for computing speeds. The help file states “the Cubic spline yields a poor fit to certain kinds of curves, e.g. curves with sharp bends. Splines were previously recommended because the code did not have a careful treatment of discontinuities in the derivative of the SSP. The latest version does.” Based on these definitions, for EMM use, Bellhop-DRDC has been defaulted to the C-linear interpolation scheme.

3.1.3 Top boundary condition The bellhop.f90 code offers 8 boundary conditions: Twersky soft boss scatter model, Twersky hard boss scatter model, Twersky amplitude only soft boss, Twersky amplitude only hard boss, Acousto-elastic half-space, perfectly Rigid, a Vacuum, or a file containing reflection coefficients. The first five choices refer to ice models and require details of ice properties (density, compressional and shear speed, and compressional and shear attenuations) and geometries as inputs. While it is true that an ice reflection model would be useful for EMM purposes, these choices are highly research oriented and would not provide a simple loss vs. angle representation. Ice loss subroutines can be found in the literature and in other propagation models; in fact, an ice loss model is currently in the U.S. Navy standard surface loss model suite, and this would be the preferred model if an under-ice capability were desired. The Acoustic Toolbox Bellhop help file states that ‘for open ocean problems, the Vacuum option should be used’. However, the Vacuum boundary condition only provides a π phase shift at the surface, but does not include any surface losses. Therefore, in order to incorporate surface wind generated losses, the file option is defaulted; however, instead of reading


reflection coefficients from a file, the values are generated by a surface loss subroutine that has been added to Bellhop-DRDC. This loss algorithm is taken from the Naval Oceanographic Office (NOO) Surface Loss Code LFSOPN.FOR. Examples of these losses are shown Figure 1. The bellhop.f90 code also provides for reading in a top altimetry file, consisting of range/depth pairs for describing large ocean surface features such as the Gulf stream boundaries and eddies that are several feet above or below ‘sea-level’. As this is also a research tool that would not be particularly applicable to EMM operation, this option has been defaulted ‘off’.

3.1.4 Bottom boundary condition The bellhop.f90 code does not contain any bottom loss algorithms. There is provision for the entering of acousto-elastic halfspace parameters, but elastic losses are not actually computed. To provide a bottom loss capability, the U. S. Navy Standard high frequency bottom loss model HFBL.FOR has been added to Bellhop-DRDC. This is a model of the Marine Geophysical Survey (MGS) bottom loss province equations. It requires the frequency and MGS Province number (1-9) as inputs. Examples of these bottom losses are shown in Figure 2. Note that the losses above 1000 Hz are independent of frequency, depending only on angle and province number, while the losses below 100 Hz are independent of province number, depending only on angle. In between, an interpolation is used in frequency to obtain the loss curve. The MGS bottom loss algorithm has been criticized because it was created using a peak energy detector in a 2.2 msec time window. This means that any energy returning from rough sediments or sub-strata outside this window was not accounted for. This issue is referred to as a peak versus total energy problem, and in the 1980’s, Dr. Ed Jensen, NUWC, New London, CT was studying ways to convert from peak to total energy. I am not aware of his results.


Figure 1. Surface loss vs. grazing angle at three frequencies with wind speed as a parameter from 5 to 30 kts.

a) Loss at 1500 Hz. Note the loss cap at 11 dB for all wind speeds.

b) Loss at 500 Hz. The loss cap still affects the higher wind speeds.

c) Loss at 50 Hz. Losses are very small, only a little over 1 dB at 30 Kts wind speeds, so the loss cap does not apply.


Figure 2. MGS bottom loss vs. grazing angle at three frequencies with MSG Province number as a parameter from 1 to 9.

a) Loss at 1500 Hz. Loss is independent of frequency above 1000 Hz.

b) Loss at 500 Hz. Loss is interpolated in frequency between losses at 1000 Hz and 100 Hz.

c) Loss at 50 Hz. Loss is independent of MGS province number below 100 Hz.


3.1.5 Thorpe volume attenuation Bellhop.f90 contains an older version of the Thorpe volume attenuation equation that lacks low frequency terms. This has been updated in Bellhop-DRDC to the relation shown below where the last two terms have been added. A plot of this equation versus frequency from 50 Hz to 1500 Hz is shown in Figure 3.

mdbfxf

ff

f /003.01075.20.1

1.0.4100.40 24

2

2

2

2

+++

++

= −α

Figure 3. Thorpe volume attenuation from 50 to 1500 Hz.

3.2 Output Capabilities To demonstrate the capabilities of Bellhop-DRDC, a simple but realistic range dependent environment is taken from the Scotia shelf area. This consists of a sloping bathymetry and a severely downward refracting sound speed profile that is typical of the area, as shown in Figure 4. The source is placed at 38m. Figure 4. Sound speed profile and bathymetry for the Scotia shelf example.


3.2.1 Ray Trace Bellhop-DRDC can produce a classical ray trace file, showing the users choice of number of rays and angles to trace. Figure 5 shows an example of this type of output over the Scotia shelf area bathymetry by tracing rays from –8 degrees to 0 degrees. The severely downward refracting sound speed profile causes all the rays to repeatedly strike the bottom until about 15 km. This type of output does not show any ray amplitudes and is frequency independent. It is used primarily to identify ray paths and give a quick look at the potential propagation patterns and caustic positions.

Figure 5. Ray trace over a Scotia shelf area.

3.2.2 Transmission Loss The Bellhop-DRDC model can produce a file of coherent or incoherent transmission losses as a function of range and depth. The coherent losses are demonstrated for the Scotia Shelf in Figure 6 using different bottom losses. Transmission losses for specific receiver depths are used in both passive and active performance prediction computations. This example shows a very important feature of Bellhop-DRDC. Notice that the sound field extends below the bathymetry line. This region is not accurate because none of the bottom properties have been accounted for, and the attenuation in the bottom is at least an order of magnitude higher than in the water. However, this erroneous calculation does give an indication of how much sound energy would be available for bottom penetration. In practice, the region below the bathymetry should be blanked off for display purposes, and TL values should always be taken from the water column only.


Figure 6. Transmission loss field on the Scotia shelf at 1000 Hz.

3.2.3 Arrivals table Bellhop-DRDC can deliver a table of arrivals sorted by range and receiver depth. This table identifies the amplitude and phase of each arrival, along with its travel time, the source launch angle, the receiver arrival angle, and the number of surface and bottom bounces encountered along the way. An example of this type of output file is shown in Figure 7. The table consists of receiver depth (m), range (km), pressure amplitude, phase (degrees), travel time (sec), source angle (degrees), receiver angle (degrees), number of surface bounces and number of bottom bounces. The table can be used to construct graphs of arrival angle vs. range, as shown in Figure 8 as well as graphs of travel time vs. range as shown in Figure 9.

a) MGS bottom province #3 b) MGS bottom province #2

c) MGS bottom province #1 d) No bottom loss


Figure 7. Sample portion of arrival file for the Scotia shelf.

Figure 8. Receiver arrival angle vs. range for a 37.5 m deep receiver over the Scotia shelf.

BELLHOP- Scotia 1000Hz 38.0m source depth Rdepth Range Press amp Phase-deg Time Sangle Rangle Ntop Nbot 0.0 0.5 0.7258E-04 0.9000E+03 0.444 -40.55 -40.16 5 4 0.0 0.5 0.2479E-03 0.7200E+03 0.404 -33.53 -32.71 4 3 0.0 0.5 0.7041E-03 0.5400E+03 0.372 -25.30 -23.82 3 2 0.0 0.5 0.1471E-02 0.3600E+03 0.349 -16.26 -13.35 2 1 0.0 0.5 0.1520E-02 0.1800E+03 0.336 -9.92 -2.54 1 0 0.0 0.5 0.1440E-02 0.0000E+00 0.339 11.27 6.18 0 1

0.0 0.5 0.9981E-03 0.1800E+03 0.354 19.77 17.68 1 2

0.0 0.5 0.4299E-03 0.3600E+03 0.379 28.67 27.59 2 3 0.0 0.5 0.1411E-03 0.5400E+03 0.414 36.36 35.82 3 4 0.0 0.5 0.3985E-04 0.7200E+03 0.455 42.84 42.67 4 5 0.0 1.0 0.4868E-07 0.1800E+04 0.959 -44.87 -45.46 10 10 0.0 1.0 0.6259E-06 0.1800E+04 0.913 -42.03 -42.40 10 9


Figure 9. Travel time vs. range to 5 km for a 37.5 m deep receiver over the Scotia shelf.

The arrivals table can also be used to construct a time series. The coherent contribution of each arrival is found using the expression { }ϕωτ +−= iApressure exp , where A is the amplitude, ω is the radian frequency, τ is the time delay, and φ is the phase converted from degrees to radians. These pressures can be summed in the appropriate time bin and then convolved with the source pulse to produce a received time series for active performance prediction. Other active and passive displays that require arrival time or angle such as Lofargrams could potentially be constructed using the geometry and Doppler of the target and a set of arrival tables computed for several frequencies in the band.


3.3 Limitations

3.3.1 Bottom loss The lack of high-quality bottom losses algorithms and databases for use in Bellhop-DRDC is the major concern identified by this report.

3.3.1.1 High sensitivity to losses The example of the Scotia shelf area demonstrates the most serious deficiency in the Bellhop-DRDC model, namely, the lack of a robust bottom loss capability. The Scotia shelf area is dominated by bottom interactions both because of its relatively shallow bathymetry and because of the downward refracting sound speed profile. Consequently, the transmission losses shown in Figure 6 are extremely sensitive to the bottom characteristics. There is a mere 2 dB difference between each of the bottom losses for MGS 3, 2 and 1 at 1000 Hz, as shown in Figure 2-a; however, the transmission loss fields in Figure 6 show differences ranging from 10 dB to over 30 dB for each change in MGS number. Thus, the main problem with the use of MGS numbers for bottom descriptors is that a small change in MGS province number can produce very large changes in propagation in bottom-limited cases.

3.3.1.2 Coarse bottom provincing To compound this problem of sensitivity to MGS numbers, the existing database of MGS provinces by latitude and longitude is very coarsely sampled in the deep water, and is defaulted to MGS 2 worldwide in all shallow water areas. A chart of the North Atlantic section of this database that was operational in the 1980’s is shown in Figure 10. I am not aware of the current status of this province database, but I think it is not being maintained since the thrust of the databasing by The U.S. Naval Oceanographic Office in the 80’s and 90’s was to expand the Low Frequency Bottom Loss (LFBL) (BLUG) at the expense of the High Frequency Bottom Loss (HFBL) (MGS). In the Scotia area example, the geology for the area indicated that the bottom was a complex layering of several materials varying in composition and depth across the track as described in Table 1. The use of a single MGS province number to represent this complex layered structure will always give a poor representation at lower frequencies where significant energy is able to penetrate into the bottom and reflect from sub-surface layers. This was this very problem that the LFBL (BLUG) bottom loss provinces were supposed to address.


Figure 10. MGS Provinces for the North Atlantic circa 1980.


Table 1. Bottom characteristics of the Scotia shelf on the bathymetry track of this example.

Range km

Water depth m

Bottom Layer #

Thickness m

Velocity m/sec

Gradient sec-1

Density g/cm^3

Attenuation dB/(km Hz)

0 50 1 2

6 ∞

1780 5500 C 3300 S

2.0 2.6

0.009 0.100 C 0.500 S

17 83 1 2

10 ∞

1640 5500 C 3300 S

1.8 2.6

0.037 0.100 C 0.500 S

26 151 1 2 3

15 35 50 ∞

1510 1600 2400 5500 C 3300 S

1 1

1.6 1.6 2.0 2.6

0.054 0.054 0.050 0.100 C 0.500 S

28 153 1 2 3

2 20 75 ∞

1510 1600 2400 5500 C 3300 S

1 1

1.6 1.6 2.0 2.6

0.054 0.054 0.050 0.100 C 0.500 S

33 158 1 2 3

5 40 50 ∞

1490 1600 2400 5500 C 3300 S

1 1

1.5 1.5 2.0 2.6

0.050 0.050 0.050 0.100 C 0.500 S

43 168 1 2 3

15 55 50 ∞

1490 1600 2400 5500 C 3300 S

1 1

1.5 1.5 2.0 2.6

0.050 0.050 0.050 0.100 C 0.500 S

Unfortunately, there are currently no clear alternatives to MGS. The LFBLTAB algorithm, which is the U.S. Navy Standard bottom loss model for use below 5000 Hz, requires the LFBL (BLUG) database of values (11 different parameters) to produce its losses and DRDC does not yet have that database to support it. And even if and when DRDC acquires that database, there will still be limitations on its accuracy and capabilities, as many in the research community in the U.S. are very unhappy with the LFBL-LFBLTAB methodology.

3.3.1.3 Eliminating provinces As an alternative to databases of provinces that lead to stored parameters or curves, it has been suggested by Dr. John Osler that bottom characteristics could be determined directly based on the water depth. He suggests that we create a table of relationships between water depth and bottom composition such as those defined in


Table 2. He also notes that there are some areas with outcrop, usually glacial till and sometimes rock, that can often be identified by bathymetric gradients, which will need a slope to be defined. The use of this type of relationship might solve the problem of the lack of bottom province databases because, of course, now databases would no longer be required. One could obtain bottom compositions directly from the bathymetry. This intriguing idea has merit and should be investigated further.

Table 2. Suggestions for bottom composition assignment based on water depth.

Scotia Shelf water depth 10-15 n.mi. off shore

Bottom composition

<50 m sand, gravel, and shells 50-100 m sand

100-120 m sand and silt mixture 120-150 m silt

>150 m clay/mud

3.3.1.4 Losses from sediment characteristics Assuming we have knowledge of the sediment characteristics of speed, density, attenuation and layering structure, we now have the problem of computing losses. One solution would be to modify the Bellhop-DRDC code to actually trace rays within the sediment. (Remember that although the transmission loss curves are showing energy under the bathymetry line, it is not an accurate representation of the loss there because the sediment properties were not used to generate it.) If the sediment properties were included directly in the solution, the proper losses should be produced. The downside of this approach is that it would undoubtedly significantly increase the run time of the model. A second solution would be to use a full layered-media, elastic, reflection coefficient computation to produce a reflection coefficient at the water-sediment interface for input to Bellhop-DRDC in place of the MGS curve. There will still be issues of point source versus distributed sources in forming the reflectivity, particularly at low frequencies. However, this method would have the advantage of being relatively fast and relatively straightforward in implementation, and it is the method most often used in other high-fidelity models.

3.3.2 Beam Patterns The Bellhop-DRDC model does not contain any algorithms to compute beam patterns or to window the energy by beam weighting. Beam weighting should be applied to each ray as the field is combined, so a suggested improvement to the model would be to add a beam capability.

3.3.3 Variability Historically, calculations of transmission loss and reverberation from acoustic models have been incomplete. Since most of the quantities of interest from the sonar equation (probability


of detection, probability of false alarm, and so forth) are statistical estimates involving probabilities, the calculated transmission loss and reverberation should be treated as random quantities as well and should be accompanied by a confidence bounds or standard deviations. After all, the inputs to the Bellhop-DRDC model involve measurements of the environment or geometry therefore they are all subject to variability, short shelf life, operator error, instrument failure, etc. That is, there can be an element of randomness associated with each of the inputs of sound speed, bathymetry, source depth, range, etc. It makes sense to carry this randomness through the equation to determine its effect on the transmission loss. Mathematically, a statistical estimate of the transmission loss and reverberation is appropriate for the sonar equation. Operationally, it would be extremely useful to know the sensitivity of the predictions to these random perturbations in the inputs. In other words, the transmission loss predictions should be accompanied by confidence bounds to provide the best possible tactical decision aid. The Bellhop-DRDC model does not currently compute a standard deviation associated with its transmission loss, based on the known or suspected variability of its inputs. In fact, to my knowledge no other transmission loss models do either. However, the need is clear and the opportunity to be a step ahead of the others is exciting. I recommend we consider including randomness in the calculations to produce a transmission loss standard deviation.


4. Comparisons between Bellhop-DRDC and PE

A test case has been designed to examine both the range dependence and the frequency dependence of Bellhop-DRDC by comparing it with the Navy Standard Parabolic Equation, NSPE. This PE is a split-step Fourier solution currently designated the U.S. Navy standard passive propagation model for low frequency use.

The bilinear decaying duct test case consists of a subsurface duct that narrows from 100m in width to 20m in width in 5 steps spaced 4 km apart in range. A schematic drawing of these five profiles is shown in Figure 11, with each profile offset to represent the 4km range spacing. The minimum of the duct remains at the same depth (1050 m) for all five steps, as indicated by the horizontal line in the figure. The speed on either side of the ducts is a constant 1500 m/sec and the duct minimum speed is 1495 m/sec for all five steps. The source is placed in the centre of all of the ducts. The ducts are set deep in the water to eliminate any differences in surface and bottom treatment between the two models so that the focus of the test could be strictly on duct propagation issues.

Figure 11. Decaying bilinear duct test case. The sound speed profiles consist of 5 profiles with decreasing duct width, spaced 4 km apart in range.

A ray trace of the propagation in this test case is shown in Figure 12. There, rays can be seen escaping the duct as the duct narrows. The purpose of this artificial test case is


two fold. First, it will provide a test of the range dependence of Bellhop-DRDC because as the duct narrows, fewer rays should remain trapped by the duct. Second it will provide a test of the frequency dependence of Bellhop-DRDC because as the frequency falls, the duct becomes less able to support guided energy. This phenomenon, known as duct cut-off, describes the modal propagation of low frequencies. Traditional Ray Theoretic solutions were not able to predict duct cut-off because those solutions had no frequency dependence other than volume attenuation. The Bellhop model employs a more sophisticated solution, the Grab-style Gaussian Beam, that is said to have improved applicability to lower frequency problems.

Figure 12. Bellhop ray trace of the subsurface decaying bilinear duct test case using 30 rays from –6 to 6 degrees. Rays escape the duct as it decreases.

In each of the analyses that follow, colour field plots will be shown from Bellhop-DRDC and from the PE in the depth range from 860 m to 1240 m, in order to highlight the behaviour of the sound field in the ducts centred at 1050 m. The dB difference between Bellhop and PE will be computed and plotted in the same format to highlight the range variations. Finally the differences will be cast in a histogram to provide a more analytic representation. The Bellhop-DRDC model will be tested at 1500, 1000, 800, 500, 300, 100, and 50 Hz which will span the range of expected applicability of the model in EMM.


4.1 1500 Hz

Figure 13. Bilinear decaying duct transmission loss at 1500 Hz.

a) PE transmission loss

c) Bellhop-DRDC incoherent transmission loss b) Bellhop-DRDC coherent transmission loss


Figure 14. 1500 Hz difference fields and histograms.

At 1500 Hz, the most common difference between PE and Bellhop is about 2.5dB in either the coherent or incoherent cases. The patterns in the field plots are very similar and some of the larger errors are caused by dropouts or coherence peaks in the PE.

a) 1500 Hz Difference between PE and coherent Bellhop in dB.

b) Histogram of 1500 Hz coherent differences. Most common difference is 2.5 dB. Mean difference is 5.0 dB.

c) 1500 Hz Difference between PE and incoherent Bellhop in dB. Large errors are caused by PE dropouts and coherence peaks.

d) Histogram of 1500 Hz incoherent differences. Most common difference is 2.0 dB. Mean difference is 3.7 dB.


4.2 1000 Hz

Figure 15. Bilinear decaying duct transmission losses at 1000 Hz.

a) PE Transmission Loss

b) Bellhop-DRDC coherent transmission loss

c) Bellhop-DRDC incoherent transmission loss



a) 1000 Hz difference between PE and coherent Bellhop transmission loss in dB.


d) Histogram of 1000 Hz incoherent differences. Most common difference is 2-2.5 dB. Mean difference is 4.3 dB.

c) 1000 Hz difference between PE and incoherent Bellhop transmission loss in dB.


4.3 800 Hz.



b) Bellhop-DRDC coherent transmission loss c) Bellhop-DRDC incoherent transmission loss



a) 800 Hz difference field between coherent Bellhop-DRDC and PE.


c) 800 Hz difference field between incoherent Bellhop-DRDC and PE.



4.4 500 Hz






a) 500 Hz difference field between PE and coherent Bellhop transmission loss.



c) 500 Hz difference field between PE and incoherent Bellhop transmission loss.


4.5 300 Hz





4.6 100 Hz.








d) Histogram of 100 Hz incoherent differences. Most common difference is 3 dB. Mean difference is 3.9 dB.



4.7 50 Hz.





Figure 26. 50 Hz Difference fields and histograms.

a) 50 Hz difference field between coherent Bellhop-DRDC and PE.


c) 50 Hz difference field between incoherent Bellhop-DRDC and PE.

d) Histogram of 50 Hz incoherent differences. Most common difference is 1 dB. Mean difference is 3.4 dB.


4.8 Discussion of test case results To review, this test case was designed specifically to examine the range and frequency behaviour of Bellhop-DRDC as compared to a parabolic equation solution. The region of interest was set far from the boundaries to eliminate any boundary influence because the two models do not have the same bottom treatment. A bilinear decaying duct was set deep in the water column with the source in the centre of the duct. The test frequencies were chosen to span the expected range of usage of Bellhop-DRDC. Visual comparisons with the transmission loss field are presented at each frequency, and it seems clear that Bellhop-DRDC model is matching the PE very well in level, location of caustics, and strength of shadow zones. As the frequency falls, the duct becomes leaky and finally acoustically transparent, and Bellhop-DRDC shows this progression quite faithfully. A more analytical comparison is shown in the difference fields, where the absolute value of the difference in transmission loss dB values is plotted. In the coherent field comparisons, the major differences occur at the locations of the strongest coherence patterns (peaks and drop-outs) because, inevitably in conversion between English and Metric units, the two models outputs may be slightly displaced in range and depth. These differences are not meaningful at all. The histograms show that high-level differences are comparatively rare, and the most common differences are around 2.5 dB or less. Surprisingly, this difference remains constant over all frequencies tested, suggesting that it may be a simple bias in the computing methods. In the incoherent difference comparisons, the coherent patterns in PE that are not reproduced by the incoherent output of Bellhop-DRDC show up clearly as differences, however the amount of error this omission produces is small, of the order of 2.5 dB or less, suggesting that the incoherent output may be quite acceptable in EMM performance prediction analysis when a smoothed transmission loss representation is desired. To summarize, this test shows excellent agreement between the PE and Bellhop-DRDC in both range dependence and frequency dependence, with about a 2.5 dB difference biasing all results.


5. Summary and Future Modeling Directions This report has examined the capabilities of the unclassified Internet version of the acoustic model Bellhop. It has documented a specific version created for DRDC (called Bellhop-DRDC) to interface with the EMM and provide active and passive capability. Additions to this version include wind-driven surface losses, MGS bottom losses, low frequency terms in the Thorpe volume attenuation, and the capability for range-dependence in the sound speed profiles and the bottom loss provinces. The output products of Bellhop-DRDC are ray traces, full field transmission loss matrices, and arrival tables including ray amplitude, phase, travel time, and arrival angle. These outputs are demonstrated using a Scotia shelf example that features a sloping shallow-water bathymetry and a severely downward refracting profile. Propagation paths interact frequently with the bottom before reaching deeper water, and consequently, the computed transmission loss is extremely sensitive to the bottom loss derived from the MGS province. This sensitivity is aggravated by the coarseness of the latitude and longitude grid of provinces and by the limited choice of loss curves associated with these provinces. The lack of high-quality bottom treatment is probably the greatest limitation on accuracy in the present configuration of Bellhop-DRDC. This report discusses possible options for improving the bottom loss methodology. To address the coarse grid of provinces, one suggestion is to drop the database format altogether and associate sediment characteristics directly with the water depth. This idea has merit and should be investigated further. To translate these sediment characteristics into bottom loss, the model could either compute rays inside the sediment or employ a layered-media elastic reflection coefficient model. For validation of Bellhop-DRDC in range dependence and low frequency operation, a test case of an internal decaying duct was designed. Comparisons were made visually and analytically between the transmission losses from Bellhop-DRDC and a parabolic equation. The duct was kept well away from the boundaries in order to simplify the test. Excellent agreement was obtained between the two models, with Bellhop-DRDC having only about a 2.5 dB bias at all frequencies. The coherent comparisons showed good agreement in the placement of spikes and nulls and accuracy in the leakage of energy into the shadow zones as the duct decayed. This test lends credibility to the Bellhop-DRDC model for use in the low frequency band 50 Hz to 1500 Hz.

The Bellhop-DRDC model can provide all the desired outputs that form the basis for both passive and active operations, so I feel there is no need to consider adding another propagation model to the EMM. However, the most important and most necessary task for future model upgrade is to replace the present bottom loss model (MGS provinces) with a higher fidelity bottom treatment. Useful additions to the Bellhop-DRDC algorithm could also include a beam pattern capability and a standard deviation output. The standard deviation output would quantitatively describe the sensitivity of the transmission loss to uncertainty in the inputs. The ability to compute confidence bounds on transmission loss (from uncertainty in the inputs) would provide an important enhancement in tactical decision making.


To summarize:

1. An unclassified acoustic prediction engine, Bellhop-DRDC, has been created from the freeware version for use with the Environment Modeling Manager (EMM) to provide ray trace, transmission loss, travel time and arrival angle predictions. .Bellhop-DRDC will provide all the output products necessary to support both active and passive applications. Required inputs are SVP’s, bathymetry, geometry, and MGS bottom province.

3. The accuracy of Bellhop-DRDC in handling range dependence and low frequency propagation is demonstrated by comparison with a parabolic equation model. Excellent agreement is obtained with the most common difference being 2.5 dB at all frequencies.

4. The lack of a high-quality bottom loss treatment severely limits the potential accuracy of Bellhop-DRDC in bottom-limited cases. Study must be given to the creation of an alternative to the MGS province database. This is a most critical need because of the extreme sensitivity of propagation to the bottom loss and because of the inability of the MGS provinces and loss curves to adequately describe complex and rapidly changing littoral sediments.

5. Other additions to Bellhop-DRDC could include a beam pattern capability and a standard deviation output to quantitatively describe the sensitivity of the transmission loss to uncertainty in the inputs. The ability to compute confidence bounds on transmission loss (from uncertainty in the inputs) would provide an important enhancement in tactical decision making.


6. References

1. P.A. Baxley, Homer P. Bucker and Michael B. Porter, “Comparison of Beam Tracing Algorithms”, Proceedings of the Fifth European Conference on Underwater Acoustics, ECUA 2000, Edited by P. Chevret and M.E. Zakharia, Lyon, France, 2000

2. Michael B. Porter and Homer P. Bucker, “Gaussian Beam Tracing for Computing Ocean Acoustic Fields”, J. Acoust. Soc. Am., 82(4), pp1349-1359, 1987


Appendix A. Porter’s Recommendations

Bellhop.f90 contains 5 choices for ray trace techniques: Cartesian beams, Ray-centred beams, Simple Gaussian beams, Gaussian beams (GRAB style) and Geometric beams. I contacted the creator, Dr. Michael Porter, with questions about these techniques and he has emailed the following recommendations:

“I would look only at two ways of running it: Geometric beams or Grab-like Gaussian beams. The Cerveny beam option is really a research tool and it’s very hard to explain how to use it. When I do use it (which is rarely these days), I normally prefer the Cartesian beam option. Anyway, I would really recommend ignoring those options. If you don’t use the Cerveny option then you don’t need to worry about the curvature doubling. I would also not try to do anything with beam shifts. I worked on that several years ago and it’s fallen into disrepair. There are some sign changes I need to sort out for that to work properly again. If I recall, I only documented (bellhop.hlp) the options that I thought were safe for general use.”

“The two options I mentioned above are really very similar. Basically the first puts a hat-shaped (triangular) beam around each ray and the second puts a Gaussian. The key useful thing in what I’m calling Grab-like, was the idea of putting a limit (so many wavelengths) on how much those beams can focus, so that you don’t get singularities at caustics. Chic Weinberg did that in his implementation of Gaussian beams in CASS/GRAB and I liked it and put it back in mine. However, Chic did a bunch of other things that I didn’t try to implement. I’m not sure if those other things have significant value--- I did not see a difference in accuracy between GRAB and BELLHOP when I was involved in the validation tests for GRAB.”

“I usually recommend option 2 to people and it generally works extremely well. You’ll get a feel for that when you run the benchmark cases. Typically it does a much, much better job at producing a TL interference pattern relative to, for instance, a PE. However, I notice a bit of a bias in TL levels with it. I think I might be able to fix that range-dependent bias but have not have the time to look at it.”


Appendix B. Users Guide for Bellhop-DRDC This user’s guide refers to a version of Bellhop named Bellhop-DRDC created for use with the Environment Modeling Manager (EMM) at the Defence R&D Canada – Atlantic laboratory in December 2004.

B.1 Input Files: There are four input files: runinput.inp, speed.inp, bottomloss.inp and bathy.inp. The formats are free field, so the values on each row do not occupy specific column positions, but only need be separated by a space. runinput.inp: This file contains scenario and runtime choices.

Line # Notes 1. title Up to 70 characters enclosed in single quotes 2. frequency Hz 3. source depth Meters 4. number of receiver depths Integer number 5. top and bottom of receiver depth array Meters- note: needs slash at end value to denote

an array 6. number of ranges, longest range Integer number, Kilometers 7. wind speed Knots 8. ‘A’, ‘R’, ‘I’, ‘S’, or ‘C’ Desired output- in caps in single quotes

'A'=arrival structure 'R'=ray trace 'I'=incoherent TL 'S'=semicoherent TL 'C'=coherent TL

9. step size, number of rays, start angle, stop angle, kill-after-bounce number

Default value = -1 Step size in m, angles in degrees, negative angles first. These inputs are primarily for the ‘R’ ray trace output. For any other output, they should be defaulted or used with great care.

10 Range smoothing length Meters, Default = -1 (will set to no smoothing) Smoothing only affects the ‘C’ coherent TL

Figure B- 1. Sample runinput.inp file

'Scotia' ! TITLE 1000.0 ! FREQ (Hz) 38.0 !source depth 80 !# receiver depths 0.0 160. / !top and bottom of receiver depth array 90 45.0 !# ranges and longest range 10.0 !windspeed 'C' !run output product – needs caps -1 -1 -1 -1 -1 !step, #of rays, trace angles, Kill-after-bounce -1 !range averager length


speed.inp: This file contains sound speed profiles in depth and range.

Line # Notes 1. Number of range dependent profiles 2. Range, number of points in that specific profile range in km 3 to ? Depth, speed or temperature m, m/sec or ºC ?+1 Next range, number of points in that profile ?+2 to ?? Depth, speed or temperature Note: there should always be a point at the surface and the bottom

Figure B- 2. Sample speed.inp file.

2 !# of range dependent profiles 0 18 !range, number of SVP points 0 1510 !depth, speed 20 1510 25 1500 27 1497 30 1490 32 1488 35 1485 40 1483 50 1482 55 1482.5 60 1483 75 1488 85 1492 100 1493 125 1495 150 1496 200 1497 270 1497.5 20 7 !range, number of SVP points 0 1510 20 1510 30 1490 60 1485 80 1490 150 1495 270 1496


bottomloss.inp: This file contains the range dependent bottom loss provinces

Line # Notes 1. number of range dependent bottom provinces 2-? range, province number km, MGS province number

Figure B- 3. Sample bottomloss.inp file.

bathy.inp: This file contains the bathymetry.

Line # Notes 1. Number of bathymetry points 2-? Range, depth km, m Note: needs a point at zero range

Figure B- 4. Sample bathy.inp file.

4 ! number of range dependent bottom provinces 0 2 ! range (km) and province number 10 3 15 1 40 5

10 !number of bathymetry points 0 50 ! range (km), depth (m) 5 44 8 56 17 83 20 109 23 131 26 151 28 153 33 158 43 168


B.2 Output Files: There are four output files in Bellhop-DRDC. The computed data is written to .txt files, depending on the runtime choice made in the input file runinput.inp. Choice ‘A’ creates arrival.txt Choice ‘R’ creates rays.txt Choices ‘I’, ‘S’, or ‘C’ create TL.txt A Bellhop.log file is also created at every run that echoes some of the inputs and lists any error or warning messages generated in the running of Bellhop. arrival.txt: This file contains ray arrival structures. At the top, it lists the run title, frequency and source depth. Then it lists by column the receiver depth(m), range(km), acoustic pressure, phase(deg), delay time(sec), source angle(deg), receiver angle(deg), number of reflections from the surface, and the number of reflections from the bottom. A header with abbreviations of these outputs is given for the reader’s convenience. The Fortran output format for these numbers is (2f7.1, 2e12.4, f7.3, 2f7.2, 2i5).

Figure B- 5. Sample portion of arrival.txt.

rays.txt: This file contains the tracing of rays. At the top, it lists the run title, frequency and source depth, followed by the step size and the kill-after-bounce number. The number of rays being traced comes next. Then the launch angle (negative is upward) and the number of points in the trace at that angle. This is followed by range and depth paired coordinates which trace the evolution of that ray. The next launch angle follows the same formats. The Fortran output format for these numbers is free-field.

BELLHOP- Scotia 1000Hz 38.0m source depth Rdepth Range Press amp Phase-deg Time Sangle Rangle Ntop Nbot 0.0 0.5 0.7258E-04 0.9000E+03 0.444 -40.55 - 40.16 5 4 0.0 0.5 0.2479E-03 0.7200E+03 0.404 -33.53 -32.71 4 3 0.0 0.5 0.7041E-03 0.5400E+03 0.372 -25.30 -23.82 3 2 0.0 0.5 0.1471E-02 0.3600E+03 0.349 -16.26 -13.35 2 1 0.0 0.5 0.1520E-02 0.1800E+03 0.336 -9.92 -2.54 1 0 0.0 0.5 0.1440E-02 0.0000E+00 0.339 11.27 6.18 0 1 0.0 0.5 0.9981E-03 0.1800E+03 0.354 19.77 17.68 1 2 0.0 0.5 0.4299E-03 0.3600E+03 0.379 28.67 27.59 2 3 0.0 0.5 0.1411E-03 0.5400E+03 0.414 36.36 35.82 3 4 0.0 0.5 0.3985E-04 0.7200E+03 0.455 42.84 42.67 4 5 0.0 1.0 0.6259E-06 0.1800E+04 0.913 -42.03 -42.40 10 9


Note: Bellhop is constructed to take very small steps around a boundary reflection, and I notice that it often repeats a point there. In general, if the ray trajectories look jerky, lower the step size on line 9 in runinput.inp or add more interior points to the sound speed profile around any sharp changes in gradients and rerun the program. Figure B- 6. Sample portion of rays.txt which was generated using the default step size, tracing 8 rays from –8. to 0 degrees, using a kill-after-bounce 10.

BELLHOP- Scotia 1000.0Hz 38.0m source depth Step size = 13.5 m Kill Trace after 10 bottom bounces 8 -8.000000 3843 0.0000000E+00 38.00000 13.37199 36.14518 21.80882 35.00000 21.82477 34.99785 35.22577 33.35818 48.92846 32.00000 48.94449 31.99863 62.40194 30.92009 75.87022 29.98660 89.34779 29.19827 102.8331 28.55519 116.3245 28.05743 129.8205 27.70505 143.3195 27.49810 156.8200 27.43660


TL.txt: This file contains the transmission loss (either coherent, semi-coherent or incoherent, depending on the choice made in runinput.inp). At the top, it lists the run title, frequency and source depth. The next line contains the number of ranges and number of source depths. Following this are listed the range array in km, then the receiver depth array in m, then transmission loss in dB by range and receiver depth. The looping structure is: DO I = 1, NRD !receiver depth WRITE( 6,*) (-20.*log10(CABS(P( I, J ))+1.0e-10), J = 1, NR ) !range END DO Figure B- 7. Sample portion of TL.txt.

Bellhop.log: This file contains a log of the runtime statements generated in any run. Some inputs are echoed, and any warnings or errors are listed here as generated by the Bellhop code.

Figure B- 8. Sample Bellhop.log file.

BELLHOP- Scotia 1000Hz 38.0m source depth 90 80 1.0000000E-03 0.5056180 1.011236 1.516854 2.022472 2.528090 3.033708 3.539326 4.044944 4.550562 5.056180 5.561798 6.067416 6.573034 7.078651 7.584270 8.089888 8.595506 9.101124 9.606742 10.11236 10.61798 11.12360 11.62921 12.13483 12.64045 13.14607 13.65169 14.15730 14.66292 15.16854 15.67416 16.17978 16.68539 17.19101

BELLHOP- Scotia Frequency = 1000.000 Hz Coherent TL calculation - output in TL.txt Number of rays = 668 from -45.00000 to 45.00000 Using bottom-bathymetry file Step length 13.50000 m CPU Time = 6.56 seconds


Bibliography

Gaussian beam references from Michael Porter :

Deschamps, George A. and Mast, P. E., "Beam tracing and applications", from a symposium on quasi-optics, (1964). Tien, P. K., Gordon, J. P., and Whinnery, J. R., "Focusing of a light beam of Gaussian field distribution in continuous and periodic lens-like media", Proc. IEEE 53:129-136 (1965). Kogelnik, Herwig, "On the propagation of Gaussian beams of light through lens-like media including those with a loss or gain variation", Applied Optics 4(12):1562-1569 (1965). Keller, Joseph B. and Streifer, William, "Complex rays with an application to Gaussian beams", J. Optical Soc. Amer. 61:40-43 (1971). (important for establishing this link.) Deschamps, G. A., "Gaussian beam as a bundle of complex rays", Elec. Letters, 7(23):684-685 (1971). (important for establishing this link.) Ra, J. W., Bertoni, H. L., and Felsen, L. B.,"Reflection and transmission of beams at a dielectric interface", SIAM J. Appl. Math. 24(3):396-413 (1973). (analysis of this theoretical case important for correctly implementing same in beam tracing method.) Felsen, Leopold B., "Evanescent waves", J. Optical Soc. Amer., 66(8):751-760 (1976). Popov, M. M. and Psencik, Ivan, "Computation of ray amplitudes in inhomogeneous media with curved interfaces", Studia geophy. Et geod. 22:248-258 (1978). (An early paper on "dynamic ray tracing' which leads to differential equations governing amplitude along a ray. These equations are the same as those for the beam tracing method, but in this latter case we employ complex initial conditions.) Popov, M. M. "A method of calculating the geometric divergence in an inhomogeneous medium with interfaces", Doklady Akad. Nauk SSSR, 237:40-42 (1980). (One of the first papers on beam tracing.) Kachalov, A. P. and Popov, M. M.,"Application of the method of summation of Gaussian beams for calculation of high-frequency wave fields", Sov. Phys. Dokl., 26(6):604-606 (1981). (An early application of beam tracing) Babich, V. M. and Popov, M. M., "Propagation of concentrated sound beams in a three-dimensional inhomogeneous medium", Sov, Phys. Acoust., 27(6):459-462 (1982). (Not very readable.) Popov, M. M., "A new method of computation of wave fields using Gaussian beams", Wave Motion 4:85-97 (1982). (Perhaps the best presentation of 3-D formulation.)


Cerveny, V., Popov, M. M. and Psencik, I., "Computation of wave fields in inhomogeneous media- Gaussian beam approach", Geoph. J. R. astr. Soc., 70:109-128 (1982). (Probably the best introduction to the method. Addresses the practical issues of implementation.) Grikurov, V. E. and Popov, M. M., "Summation of Gaussian beams in a surface waveguide", Wave Motion 5:225-233 (1983). Cerveny, V., and Psencik, I., "Gaussian beams in two-dimensional elastic inhomogeneous media", 72:417-433 (1983). (Seems to be the first treatment of the elastic case.) Cerveny, V., "Synthetic body wave seismograms for laterally varying layered structures by the Gaussian beam method", Geophs. J. R. astr. Soc. 73:389-426 (1983). Nowack, R. and Aki, K., "The two-dimensional Gaussian beam synthetic method: testing and application", J. Geophysical Res. 89:7797-7819 (1984). (Several interesting examples which demonstrate the effect of varying the beam parameters.) Cerveny, V. and Psencik, I. "Gaussian beams in elastic 2-D laterally varying layered structures", Geophysical J. R. astr. Soc., 78:65-91 (1984). (Important for deriving reflection and transmission coefficients although Felsen's discussion suggests the results may not be exactly right since the beam shift is not evident.) Felsen, L. B., "Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams", Geoph. J. R. astr. Soc., 79:77-88 (1984). (Some valuable comments about the method, but no hard results.) Klimes, L., "Expansion of a high-frequency time-harmonic wavefield given on an initial surface into Gaussian beams", Geophys. J. R. astr. Soc., 79:105-118 (1984). (Cerveny's original treatment is not really right if the beam parameter is different for each beam. Klimes treats this case and obtains the correct formulas but shows that they don't change the result much.) Cerveny, V. and Klimes, L., "Synthetic body wave seismograms for three-dimensional laterally varying media", Geophys. J. R. astr. Soc., 79:119-133 (1984). (Interesting for comments about relation to Chapman-Maslow theory.) Muller, G. ,"Efficient calculation of Gaussian-beam seismograms for two-dimensional inhomogeneous media", Geophys. J. R. astr. Soc., 79:153-166 (1984). (Nice treatment of the 2-D problem triangulated into subdomains with constant sound speed gradient.) Madariaga, Raul, "Gaussian beam synthetic seismograms in a vertically varying medium", Geophys. J. R. astr. Soc. 79:589-612 (1984). (Makes an argument about how to choose the beam constant. Was able to obtain one solution of the p-q equations by inspection and therefore obtain an integral representation of the second solution. This is useful for obtaining analytical solutions to special problems like a constant gradient refractive index.) Pott, John and Harris, John G., "Scattering of an acoustic Gaussian beam from a fluid-solid interface", J. Acoust. Soc. Am., 76(6):1829-1838 (1984). (Not concerned with beam tracing


as a prop loss method but one of many theoretical papers on this subject which is important to understand in order to properly treat reflection/transmission.)


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An Investigation of the Bellhop Acoustic Prediction Model

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This report documents some of the capabilities and limitations of the Bellhop-DRDC model and describes the alterations required to make the code compatible with DRDC’s Environment Modeling Manager for use in the frequency range 50 Hz to 1500 Hz. It presents examples of the output forms that are possible using a Scotia shelf example. The report documents the accuracy of the range dependence and frequency response of Bellhop-DRDC by tests with a parabolic equation. The lack of high-quality bottom treatment is probably the greatest limitation on accuracy in bottom-limited cases in the present configuration of Bellhop-DRDC. This report discusses possible options for improving the bottom loss methodology by seeking an alternative to the MGS province database and loss curves. Other additions that would also enhance the capabilities of Bellhop-DRDC include adding a beam pattern capability and computing a standard deviation output to quantitatively describe the sensitivity of the transmission loss to uncertainty in the inputs. A user guide is included in Appendix B.

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document and could be helpful in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model designation, trade name, military project code name, geographic location may also be included. If possible keywords should be selected from a published thesaurus. e.g. Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus-identified. If it not possible to select indexing terms which are Unclassified, the classification of each should be indicated as with the title). Acoustic prediction Sonar Fortran programming Ocean acoustics

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