Causes of Excessive Volatility in Bellhop Transmission Loss

Transcription

1 Copy No. Defence Research and Development Canada Recherche et développement pour la défense Canada DEFENCE & DÉFENSE Causes of Excessive Volatility in Bellhop Transmission Loss Dr. Diana McCammon McCammon Acoustical Consulting Prepared by: McCammon Acoustical Consulting 475 Baseline Road RR#3, Waterville, NS B0P 1V0 DRDC Contract Scientific Advisor: Dr. Dale D. Ellis, ext 104 Contract number: W The scientific or technical validity of this Contract Report is entirely the responsibility of the contractor and the contents do not necessarily have the approval or endorsement of Defence R&D Canada. Defence R&D Canada Atlantic Contract Report DRDC Atlantic CR October 2011

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3 Causes of Excessive Volatility in Bellhop Transmission Loss Dr. Diana McCammon Prepared By: McCammon Acoustical Consulting 475 Baseline Road RR#3, Waterville, NS B0P 1V0 DRDC Contract Scientific Advisor: Dr. Dale D. Ellis, ext 104 Contract number: W The scientific or technical validity of this Contract Report is entirely the responsibility of the Contractor and the contents do not necessarily have the approval or endorsement of Defence R&D Canada. Defence R&D Canada Atlantic Contract Report DRDC Atlantic CR October 2011

4 Principal Author Original signed by Dr. Diana McCammon Dr. Diana McCammon Research Scientist Approved by Original signed by Dr. Dan Hutt Dr. Dan Hutt Head / Underwater Sensing Approved for release by Original signed by Dr. Calvin Hyatt Dr. Calvin Hyatt Chair / Document Review Panel Her Majesty the Queen as represented by the Minister of National Defence, 2011 Sa Majesté la Reine, représentée par le ministre de la Défense nationale, 2011

5 Abstract This study has examined the factors that control the ray amplitude as a function of range in the Bellhop Gaussian beam method of computing transmission loss (TL). These factors are the Gaussian weighting function and its standard deviation, the boundary losses and the beam width. For the single case tested here, it was determined that the beam width, a ray-traced quantity, was responsible for the large volatility of the transmission loss with range. And, more specifically, the amount of change in the sound speed (SP) gradient at the start of each SP layer was controlling the beam width. There were no simple remedies to the volatility of the beam width discovered in this study. For example, employing a larger number of sound speed points to reduce the gradient change between each layer did not change the result, but it did adversely impact the run time. Range and frequency averaging were tested, and for this test case, only range averaging was effective in reducing the TL volatility. Résumé La présente étude porte sur les facteurs qui contrôlent l amplitude du rayonnement en fonction de la distance dans la méthode des faisceaux gaussiens Bellhop pour le calcul des pertes de transmission (PT). Ces facteurs sont la fonction de pondération gaussienne et son écart-type, les pertes périphériques et la largeur du faisceau. Pour l unique cas mis à l essai dans le cadre de la présente étude, on a déterminé que la largeur du faisceau, une quantité de rayonnement tracé, était responsable de la grande volatilité des pertes de transmission en fonction de la distance. En particulier, le nombre de modifications dans le gradient de la vitesse du son (VS) au début de chaque couche VS contrôlait la largeur du faisceau. Pendant l étude, on n a découvert aucune solution simple à la volatilité de la largeur du faisceau. Par exemple, l emploi d un nombre accru de points de la vitesse du son pour réduire la variation du gradient entre chaque couche n a pas permis de modifier les résultats, mais a nui au temps d exécution. Le calcul de la moyenne des distances et des fréquences a été mis à l essai, et pour ce jeu d essais, seul le calcul de la moyenne des distances a permis de réduire la volatilité des PT. DRDC Atlantic CR i

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7 Executive summary Causes of Excessive Volatility in Bellhop Transmission Loss McCammon, D.F.; DRDC Atlantic CR ; Defence R&D Canada Atlantic; October Introduction or background Bellhop is ray-based model that uses Gaussian beams for calculating underwater sound transmission, developed by M. Porter and freely available over the internet from OALIB (Ocean acoustics Library). Over a period of years DRDC Atlantic has funded Dr. McCammon to adapt the model for the requirements of DRDC. One of the problems has been the rapid fluctuations in transmission loss as a function of range, which make it difficult to obtain good estimates of signal excess. This report is an attempt to understand the causes of this. Results This study has examined the factors that control the ray amplitude as a function of range in the Bellhop Gaussian beam method of computing transmission loss (TL). These factors are the Gaussian weighting function and its standard deviation, the boundary losses and the beam width. For the single case tested here, it was determined that the beam width, a ray-traced quantity, was responsible for the large volatility of the transmission loss with range. And, more specifically, the amount of change in the sound speed (SP) gradient at the start of each SP layer was controlling the beam width. There were no simple remedies to the volatility of the beam width discovered in this study. For example, employing a larger number of sound speed points to reduce the gradient change between each layer did not change the result, but it did adversely impact the run time. Range and frequency averaging were tested, and for this test case, only range averaging was effective in reducing the TL volatility. Insight into the causes of the TL volatility has been determined, and some mitigation procedures have been suggested. Significance BellhopDRDC is the propagation model used in the Environmental Modeling manager (EMM) and the System Test Bed (STB). Since these are used for signal excess calculations in the STB and Pleiades system, it is important to understand the problem and develop mitigation procedures. This volatility may be found in other Gaussian beam models; e.g., the NITES II system or CASS/GRAB which are used operationally. Future plans More effort is needed to better determine the causes of excessive volatility, and more general mitigation procedures. It would be worth determining if other ray-based models, or even full wave solutions, have this problem. DRDC Atlantic CR iii

8 Sommaire Causes of Excessive Volatility in Bellhop Transmission Loss McCammon, D.F.; DRDC Atlantic CR ; R & D pour la défense Canada Atlantique; Octobre Introduction ou contexte Bellhop est un modèle fondé sur les rayonnements qui utilise des faisceaux gaussiens pour calculer la transmission du son sous l eau. Ce modèle a été développé par M. Porter et est disponible sans frais sur Internet, à partir du site d OALIB (Ocean acoustics Library). Pendant quelques années, RDDC Atlantique a confié à M. McCammon le mandat d adapter le modèle en fonction des besoins de RDDC. L un des problèmes rencontrés a trait aux fluctuations rapides dans les pertes de transmissions en fonction de la distance, fluctuations qui rendent difficile l obtention de bonnes estimations de l excès de signaux. Le présent rapport tente de comprendre les causes de ce problème. Résultats La présente étude porte sur les facteurs qui contrôlent l amplitude du rayonnement en fonction de la distance dans la méthode des faisceaux gaussiens Bellhop pour le calcul des pertes de transmission (PT). Ces facteurs sont la fonction de pondération gaussienne et son écart-type, les pertes périphériques et la largeur du faisceau. Pour l unique cas mis à l essai dans le cadre de la présente étude, on a déterminé que la largeur du faisceau, une quantité de rayonnement tracé, était responsable de la grande volatilité des pertes de transmission en fonction de la distance. En particulier, le nombre de modifications dans le gradient de la vitesse du son (VS) au début de chaque couche VS contrôlait la largeur du faisceau. Pendant l étude, on n a découvert aucune solution simple à la volatilité de la largeur du faisceau. Par exemple, l emploi d un nombre accru de points de la vitesse du son pour réduire la variation du gradient entre chaque couche n a pas permis de modifier les résultats, mais a nui au temps d exécution. Le calcul de la moyenne des distances et des fréquences a été mis à l essai, et pour ce jeu d essais, seul le calcul de la moyenne des distances a permis de réduire la volatilité des PT. On a obtenu des indications sur les causes de la volatilité des PT et suggéré certaines procédures d atténuation. Portée Le Bellhop de RDDC est le modèle de propagation utilisé dans le gestionnaire de modélisation environnementale (GME) et le banc d essai de systèmes (STB). Comme ces deux systèmes sont utilisés pour calculer l excès de signaux dans le STB et le système PLEIADES, il importe de comprendre le problème et de développer des procédures d atténuation. On peut trouver cette volatilité dans d autres modèles de faisceaux gaussiens, comme le système NITES II ou le modèle CASS/GRAB qui sont utilisés de façon opérationnelle. iv DRDC Atlantic CR

9 Recherches futures D autres recherches sont nécessaires pour mieux déterminer les causes de la volatilité excessive, ainsi que des procédures d atténuation plus générales. Il serait judicieux de déterminer si d autres modèles fondés sur le rayonnement, ou même des solutions à ondes pleines, présentent ce problème. DRDC Atlantic CR v

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11 Table of contents Abstract... i Résumé... i Executive summary... iii Sommaire... iv Table of contents... vii List of figures... viii 1. Introduction Need for smooth transmission loss predictions Test case Bellhop mathematics Gaussian beams Terms affecting volatility Gaussian weight W Reflection loss R Beam width q Smoothing Range averaging Frequency averaging Summary References DRDC Atlantic CR vii

12 List of figures Figure 1. Three sound speed profiles used at 0, 10 and 40km down range Figure 2. Six bottom definitions. The black curve, #1, has LaHave Clay in the upper layer and shows the strongest resonances. The rest are sands and rock... 3 Figure 3. Surface loss curves for 10 kts wind at 1200 Hz. The curve chosen for these tests was Beckmann, labelled B... 4 Figure 4. Transmission loss from a 35 m source Figure 5. Transmission loss from a 70 m source Figure 6. Twenty selected transmission loss curves for receivers spanning the water column from each source depth Figure 7. Log of accumulated reflection losses from surface and bottom as a function of range. The plot shows 11 rays from ±5º about the horizontal Figure 8. Gaussian beam width, Log(q -1/2 ), versus range for11 rays from ±5º about the horizontal. Sound speed profiles (0,10 and 40km) were linearly interpolated with range Figure 9. Gaussian beam width, Log(q -1/2 ), versus range for11 rays from ±5º about the horizontal. Sound speed profiles at 10 and 40km were abruptly changed with no range interpolation Figure 10. Beam width amplitude factor log(q -1/2 ) versus range when using an isovelocity sound speed profile Figure 11. Upper black curves show the transmission loss using an isovelocity profile with all other environmental inputs the same as the lower curves Figure 12. Upper black curves use 90% of the tangential component of the gradient change along the sound speed profiles in the computation of the beam width q Figure 13. Upper black curves use 90% of the normal component of the gradient change along the sound speed profiles in the computation of the beam width q Figure 14. Range smoothing of transmission loss for a 35m source using a 2.5km window Figure 15. Range smoothing of transmission loss for a 70m source using a 2.5km window Figure 16. The lower curve shows a frequency-averaged TL over a 278 Hz bandwidth about 1200 Hz Figure 17. The lower curve shows a range-averaged TL in the same environment as the previous figure viii DRDC Atlantic CR

13 1. Introduction 1.1 Need for smooth transmission loss predictions The Bellhop propagation engine is a reasonably high-fidelity model providing acoustic field predictions that are very sensitive to small changes in the environment and consequently it produces a rather rough (jagged) propagation loss curve that is specific to a very specific scenario. Fleet prediction products like Figure-of-Merit (FOM) or signal excess (SE) rely on locating zero crossings in range of transmission loss combinations. If the TL is varying widely, these zero crossings are ambiguous, and therefore performance predictions are difficult to make. The sensitivity of Bellhop to the environmental inputs is also a problem because the input environment can only ever be a snapshot of the actual environment and therefore small changes in the environment can produce large changes in performance prediction. It is important for tactical applications to try to obtain a more general propagation expectation. The purpose of this report is to examine the mathematical reasons for the volatility of transmission loss predictions produced by Bellhop. Section 2 will discuss the mathematics of Bellhop and using a fairly complex test case, the terms that contribute to the jumpiness will be examined. Section 3 will discuss averaging techniques. 1.2 Test case To examine the behaviour of the transmission loss, a test case has been designed that includes three range dependent sound speed profiles with poorly sampled and sharply changing values (Figure 1), six range-dependent geoacoustic two-layer bottom definitions (Figure 2), the Beckmann surface loss curve for 10 kts (Figure 3), and a shallow bathymetry that features a sharp rise at 20km (visible on the TL and ray traces). Figure 4 -Figure 6 show transmission losses for a 35m and 70m source at 1200 Hz. There is no need to window the transmission losses at receivers that fall below the bathymetry hump because we are not concerned with the actual loss value but rather with its variability. For subsequent comparisons, the 35m source will be utilized as it projects most of its energy at steep angles into the bottom. Figure 6 shows most clearly the volatility of the transmission loss, with excursions that are up to 15 db in very short range spans. DRDC Atlantic CR

14 Figure 1. Three sound speed profiles used at 0, 10 and 40km down range. 2 DRDC Atlantic CR

15 Figure 2. Six bottom definitions. The black curve, #1, has LaHave Clay in the upper layer and shows the strongest resonances. The rest are sands and rock. DRDC Atlantic CR

16 Figure 3. Surface loss curves for 10 kts wind at 1200 Hz. The curve chosen for these tests was Beckmann, labelled B. Figure 4. Transmission loss from a 35 m source. 4 DRDC Atlantic CR

17 Figure 5. Transmission loss from a 70 m source. DRDC Atlantic CR

18 Figure 6. Twenty selected transmission loss curves for receivers spanning the water column from each source depth. 6 DRDC Atlantic CR

19 2. Bellhop mathematics 2.1 Gaussian beams The technique of Gaussian Beam tracing relies on defining a fuzzy spread of energy about a central ray that is traced through the environment [1]. That is, as the ray is traced, its location, [r 1,z 1 ] stepped to [r 2,z 2 ], is examined with respect to a receiver point [r r,z r ]. The normal distance from the ray to the receiver point is used to assign a Gaussian weighting to the ray amplitude that contributes to the field at the receiver. Let r = r r, z ] be the vector distance from the start of the ray step to the receiver. r r t [ r 1 r z1 = [ r2 r1, z2 z1] be the vector tangential to the ray step. r n = [ z1 z2, r2 r1 ] be the vector normal to the ray step. The distance n from the ray step to the receiver point along the ray normal is the dot product of the vector distances normalized by the ray step length. n = ( r r ) / r r n t The proportional distance along the ray step s is the dot product of the vector from ray to receiver and the tangential ray vector, normalized by the ray step length. This is used to linearly interpolate ray traced values of delay τ and beam width q. s = ( r r ) / r r t t Dr. Porter states in the code at the beginning of the ray trace step algorithm that the numerical integrator used to trace rays is a version of the polygon method (a.k.a. midpoint, leapfrog or Box method) and similar to the Heun (second-order Runge-Kutta method). However it is modified to allow for a dynamic step change while preserving the second order accuracy. The beam width q is a ray-traced quantity (and should not be confused with the Gaussian weighting width σ). It is defined by two ordinary differential equations for p(s) and q(s) that are integrated along the ray. Dr. Porter shows that the q can be related to the beam radius (half-width) and the p can be related to the beam curvature. These equations are derived by solving a parabolic equation in the neighbourhood of each ray [1]. They are evaluated at the same time that the standard ray position traces are performed. DRDC Atlantic CR

20 dq = c( s) p( s) ds dp cnn = q( s) 2 ds c ( s) (1) The term c nn contains the normal second derivative of the sound speed c(r,z). That is, it depends upon c rr, c zz, and c rz. The contribution to the acoustic field at the receiver is given by the ray amplitude A which is proportional to the inverse square root of the beam width q, the product of reflection losses from the boundaries R, the volume attenuation and cylindrical spreading term, and the Gaussian weighting term W. A = c cosθ / q R e αr r W W 2 2 exp[ n / 2σ ] = 2cσ q θ (2) The Gaussian standard deviation σ is usually found as a product of the beam width q and the angular step size Δθ divided by the sound speed. In Bellhop, σ is defined to have a minimum size of at least πλ, with a potential nearfield size of 0.2r 1 /λ. The logic is defined below. Note that the frequency dependence of the width of the Gaussian is either none, directly proportional or inversely proportional, depending on the position of the ray. σ = max[ ( q θ / c), min( 0.2r1 / λ, πλ) ] 2.2 Terms affecting volatility There are three terms in the acoustic pressure amplitude A (equation 2) that can potentially contribute to volatility of the transmission loss with range: W,R, and q Gaussian weight W Presently in Bellhop, the ray s contribution is added to the field at the receiver if the normal from the ray to the receiver point is less than 4σ. Experimentation with this quantity, using 8σ, 4σ, 2σ, and 1σ as the criterion for contribution distance from the receiver, has shown there are almost no noticeable differences in the TL, and certainly no smoothing of the field with the greater contribution distance. (Figures documenting this were unnecessary) Doubling or halving the size 8 DRDC Atlantic CR

21 of σ also did not improve the result in terms of stability. Therefore, it would seem that the term W is not directly contributing to the volatility of the TL result Reflection loss R The reflection losses from the surface and bottom are functions of frequency and angle. In the two-layer bottom reflectivity model, there are many sharp spikes of high loss corresponding to coherent interactions within the two layers of the sediment. For this reason, the reflectivity might be expected to add volatility to the transmission loss as small changes in grazing angle contribute large differences in reflection losses. Figure 7 shows a plot of the accumulated reflection losses for the 35m source rays from ±5º, in log space. The y axis has been shifted to enable comparisons with the beam width plots that follow. The losses are displaying a short-range variability of approximately 0.2 to 0.4 db as the range increases. In the region where the seamount intrudes into the sound field, beyond 20km, the losses increase with increasing ray angle, but the variability along each ray is very similar and it does not increase much. Figure 7. Log of accumulated reflection losses from surface and bottom as a function of range. The plot shows 11 rays from ±5º about the horizontal. DRDC Atlantic CR

22 2.2.3 Beam width q The factor q is called the Gaussian beam width. It is obtained by integrating the coupled p-q functions listed in equation 1 and is a function of the sound speed profile and its gradients. The 1/ 2 ray amplitude is proportional to q. The plot in Figure 8 shows the log(q -1/2 ) for the 35m source when using linear interpolation between the sound speed profiles. There is a great deal of volatility up to the onset of the seamount and beyond its other side. The amplitude excursions span 1 to 1 ½ decades in log space (10-15dB). In comparison to the excursions due to reflectivity shown in section 2.2.2, these are by far the larger. The linear interpolation in range between the sound speed profiles is not to blame, as Figure 9 shows the same beam width computed with no sound speed interpolation, and the excursions are just as large. Figure 8. Gaussian beam width, Log(q -1/2 ), versus range for11 rays from ±5º about the horizontal. Sound speed profiles (0,10 and 40km) were linearly interpolated with range. 10 DRDC Atlantic CR

23 Figure 9. Gaussian beam width, Log(q -1/2 ), versus range for11 rays from ±5º about the horizontal. Sound speed profiles at 10 and 40km were abruptly changed with no range interpolation. To be perfectly sure, an isovelocity profile was used in place of the three sound speed profiles, with all other environmental inputs as before, producing a smooth log q -1/2 curve (Figure 10) and a smooth transmission loss curve (Figure 11). DRDC Atlantic CR

24 Figure 10. Beam width amplitude factor log(q -1/2 ) versus range when using an isovelocity sound speed profile. 12 DRDC Atlantic CR

25 Figure 11. Upper black curves show the transmission loss using an isovelocity profile with all other environmental inputs the same as the lower curves. This seems to indicate that the traced beam width q is the progenitor of the volatility. It is interesting to note that while the p-q pair in equation 1 are derived with functional dependence on the sound speed and its derivatives, but in actual practice, Bellhop returns zeros for all second order derivatives in the term c nn. Therefore the only portion of the computation for p-q that can cause large swings in amplitude is the term that is computed whenever the ray trace crosses a sound speed layer. In Bellhop, this is referred to as a jump condition. When the ray crosses an interface, the difference in the sound speed gradients on either side of the interface is used to compute the gradient jump, and this is injected into the solution for p-q. Let i = ith sound speed layer with speed c i and gradient g i. Then the next layer will be i+1 with speed c i+1 and gradient g i+ 1. The difference in gradients, the gradient jump, is defined as g jump = gi +1 gi. The ray normal vector is computed in the (i+1) st layer from the ray tangent vector r t that was traced to that layer, r = r (2), r (1)]. n [ t t DRDC Atlantic CR

26 The components of the gradient jump in the normal and tangential directions to the ray are found by dot product, gn = g jump rn and gt = g jump rt. Then the additional term to the tracing of the p function is given in the code by r (1) (1) + r p p q g g t t i 1 = i+ 1 i+ 1 2 / + 1 (2) n t i rt rt (2) c To test whether this gradient jump is contributing to the volatility of the transmission loss, the jump condition was altered to use 90% of the actual gradient change for the tangential component gradient change shown in Figure 12 and 90% of the actual gradient change for the normal component of the gradient change shown in Figure 13. It is clear that these gradient changes are responsible for the large swings in q and in the transmission loss. Although the transmission loss does not have the correct amplitude, it is definitely smoother when computed with the smaller amount of gradient change. Figure 12. Upper black curves use 90% of the tangential component of the gradient change along the sound speed profiles in the computation of the beam width q. 14 DRDC Atlantic CR

27 Figure 13. Upper black curves use 90% of the normal component of the gradient change along the sound speed profiles in the computation of the beam width q. An experiment was then run in which the sound speed profiles in Figure 1 were more closely sampled with 1m spacing in depth over the water column. The reasoning was that shorter steps would decrease the size of the gradient change between layers. However, while the run time was greatly increased, this had no effect on smoothing the resulting TL. At present, there do not seem to be any quick solutions to the volatility of the beam width q. It would be worthwhile to examine other Gaussian beam algorithms to see if they integrate the p-q equations differently, possibly treating the jump condition differently. For example, in reference 2, some different starting values are discussed for the p-q integration. DRDC Atlantic CR

28 3. Smoothing 3.1 Range averaging If the requirement for a smooth transmission loss is to be met, averaging may be the short term solution. The best way to achieve this would undoubtedly be to run the propagation engine over a complete set of all possible environmental conditions, averaging the result. However this would be very time consuming, and in reality, a complete set of conditions could never be known. Another approach for obtaining a general propagation expectation would be to construct a statistical description of the environment and transfer that statistical variety through the propagation engine to obtain a statistical view of the propagation, which would presumably be a smooth curve with varying confidence bands. As this approach has not yet been investigated, the BellhopDRDC_Active program has resorted to a low-tech solution; applying a simple range average to the end product, the SE versus range. An example of the effect of weighted smoothing over a 9 point range window is shown in Figure 14 for a 35m source and in Figure 15 for a 70m source. Figure 14. Range smoothing of transmission loss for a 35m source using a 2.5km window. 16 DRDC Atlantic CR

29 Figure 15. Range smoothing of transmission loss for a 70m source using a 2.5km window. 3.2 Frequency averaging In a letter-to-the-editor, Harrison and Harrison [3] discuss the relationship between frequency and range averages. They note that for computations such as Lloyd s mirror and multipath, there is an equivalence between frequency and range averaging, that is, averaging in one variable is equivalent to averaging in the other. However, for dominant localized contributions such as a focus, caustic, shadow boundary or convergence zone, there is no equivalence. Because the bottom loss in the ray amplitude term is a function of frequency (causing displacement of the resonant peaks) and the Gaussian weighting function s standard deviation can be dependent on frequency, the act of frequency averaging the Bellhop transmission loss was tried. A third-octave band was defined about the center frequency of 1200 Hz. The frequency bandwidth was 278 Hz. Bellhop was exercised from 1069 Hz to 1347 Hz in steps of 1 Hz and the resulting transmission loss curves were averaged. To obtain the maximum interaction with the lossiest bottom, the entire range was defined to be propagated over clay/sand layers using curve #1 in Figure 2. The LaHave clay has speed 1453 m/s, density 1.41 and attenuation db/mkhz. The sand, 10m deeper, has speed 1557 m/s, density 1.73 and attenuation db/mkhz. DRDC Atlantic CR

30 The resulting loss curves shown in Figure 16 are found to be little affected by the frequency averaging. These curves appear different than those shown before because the bottom was highly lossy over the entire range so the presence of the seamount kills the acoustic field. In contrast, the next figure Figure 17 uses the same highly lossy bottom but is range averaged, and this does provide some smoothing, so clearly there is no equivalence between frequency and range averaging in this case. Figure 16. The lower curve shows a frequency-averaged TL over a 278 Hz bandwidth about 1200 Hz. 18 DRDC Atlantic CR

31 Figure 17. The lower curve shows a range-averaged TL in the same environment as the previous figure. DRDC Atlantic CR

32 4. Summary This study has examined the factors that control the ray amplitude as a function of range in the Bellhop Gaussian beam method of computing transmission loss. They are the Gaussian weighting function and its standard deviation, the boundary losses and the beam width. For the single case tested here, it was determined that the beam width, a ray-traced quantity, was responsible for the large volatility of the transmission loss with range. And, more specifically, the amount of change in the sound speed gradient at the start of each SSP layer was controlling the beam width. There were no simple remedies to the volatility of the beam width discovered in this study. For example, employing a larger number of sound speed points to reduce the gradient change between each layer did not change the result but it did adversely impact the run time. Range and frequency averaging were tested, and for this test case, only range averaging was effective in reducing the TL volatility. There are other Gaussian Beam techniques that might contain different approaches to obtaining the beam width. Dr. Porter s web version of Bellhop contains four different ray amplitude algorithms [4]. One of these, called Simple Gaussian Beams (SGB), employs the beam width factor in a different way. However they will all rely on the same ray tracing integration, and it might be assumed that they would all suffer from the volatility of the beam width. It would be worthwhile examining other ray tracing integration schemes and also finding out why Bellhop currently zeros all second-order derivatives of the sound speed profile. 20 DRDC Atlantic CR

33 References [1] Michael B. Porter and Homer P. Bucker Gaussian beam tracing for computing ocean acoustic fields, J. Acoust. Soc. Am. 82 (4), pp , (1987). [2] D. F. Gordon, Optimization of Gaussian Beam widths in Acoustic Propagation, Naval Ocean Systems Center, San Diego, California, Tech Doc 1678, (October 1989) [3] C. H. Harrison and J. A. Harrison, A simple relationship between frequency and range averages for broadband sonar, J. Acoust. Soc. Am. 97 (2), pp , (1995) [4] Paul A. Baxley, Homer 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) DRDC Atlantic CR

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35 Distribution list Document No.: DRDC Atlantic CR LIST PART 1: Internal Distribution by Centre: 3 DRDC Atlantic Library 1 Dale Ellis 1 Sean Pecknold 1 Jim Theriault 1 Dan Hutt 7 TOTAL LIST PART 1 LIST PART 2: External Distribution by DRDKIM 1 DRDKIM 1 Library and Archives Canada Attn: Military Archivist, Government Records Branch 1 Dr. Diana McCammon 475 Baseline Road RR#3, Waterville, NS B0P 1V0 Canada 3 TOTAL LIST PART 2 10 TOTAL COPIES REQUIRED DRDC Atlantic CR

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37 DOCUMENT CONTROL DATA (Security classification of title, body of abstract and indexing annotation must be entered when the overall document is classified) 1. ORIGINATOR (The name and address of the organization preparing the document. Organizations for whom the document was prepared, e.g. Centre sponsoring a contractor's report, or tasking agency, are entered in section 8.) McCammon Acoustical Consulting 475 Baseline Road RR#3, Waterville, NS B0P 1V0 2. SECURITY CLASSIFICATION (Overall security classification of the document including special warning terms if applicable.) UNCLASSIFIED (NON-CONTROLLED) DMC A REVIEW: GCEC JUNE TITLE (The complete document title as indicated on the title page. Its classification should be indicated by the appropriate abbreviation (S, C, R or U) in parentheses after the title.) Causes of Excessive Volatility in Bellhop Transmission Loss 4. AUTHORS (last name, followed by initials ranks, titles, etc. not to be used) McCammon, D. F. 5. DATE OF PUBLICATION (Month and year of publication of document.) October a. NO. OF PAGES (Total containing information, including Annexes, Appendices, etc.) 36 6b. NO. OF REFS (Total cited in document.) 4 7. DESCRIPTIVE NOTES (The category of the document, e.g. technical report, technical note or memorandum. If appropriate, enter the type of report, e.g. interim, progress, summary, annual or final. Give the inclusive dates when a specific reporting period is covered.) Contract Report 8. SPONSORING ACTIVITY (The name of the department project office or laboratory sponsoring the research and development include address.) DRDC Atlantic, 9 Grove St, Dartmouth, NS B2Y 3Z7 9a. PROJECT OR GRANT NO. (If appropriate, the applicable research and development project or grant number under which the document was written. Please specify whether project or grant.) 11ch 10a. ORIGINATOR'S DOCUMENT NUMBER (The official document number by which the document is identified by the originating activity. This number must be unique to this document.) 9b. CONTRACT NO. (If appropriate, the applicable number under which the document was written.) W b. OTHER DOCUMENT NO(s). (Any other numbers which may be assigned this document either by the originator or by the sponsor.) DRDC Atlantic CR DOCUMENT AVAILABILITY (Any limitations on further dissemination of the document, other than those imposed by security classification.) ( x) Unlimited distribution ( ) Defence departments and defence contractors; further distribution only as approved ( ) Defence departments and Canadian defence contractors; further distribution only as approved ( ) Government departments and agencies; further distribution only as approved ( ) Defence departments; further distribution only as approved ( ) Other (please specify): 12. DOCUMENT ANNOUNCEMENT (Any limitation to the bibliographic announcement of this document. This will normally correspond to the Document Availability (11). However, where further distribution (beyond the audience specified in (11) is possible, a wider announcement audience may be selected.))

38 13. ABSTRACT (A brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highly desirable that the abstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of the security classification of the information in the paragraph (unless the document itself is unclassified) represented as (S), (C), (R), or (U). It is not necessary to include here abstracts in both official languages unless the text is bilingual.) This study has examined the factors that control the ray amplitude as a function of range in the Bellhop Gaussian beam method of computing transmission loss (TL). These factors are the Gaussian weighting function and its standard deviation, the boundary losses and the beam width. For the single case tested here, it was determined that the beam width, a ray-traced quantity, was responsible for the large volatility of the transmission loss with range. And, more specifically, the amount of change in the sound speed (SP) gradient at the start of each SP layer was controlling the beam width. There were no simple remedies to the volatility of the beam width discovered in this study. For example, employing a larger number of sound speed points to reduce the gradient change between each layer did not change the result, but it did adversely impact the run time. Range and frequency averaging were tested, and for this test case, only range averaging was effective in reducing the TL volatility. 14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a 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 is not possible to select indexing terms which are Unclassified, the classification of each should be indicated as with the title.) Bellhop, Gaussian beams, transmission loss, variability, volatility, sound speed, underwater acoustics

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