Mathematics and Programming of the BellhopDRDC_active Program

Transcription

1 Copy No. Defence Research and Development Canada Recherche et développement pour la défense Canada DEFENCE & DÉFENSE Mathematics and Programming of the BellhopDRDC_active Program Diana McCammon McCammon Acoustical Consulting Prepared by: McCammon Acoustical Consulting 475 Baeline Road RR#3, Waterville, NS B0P 1V0 Contract number: W Scientific Authority: Dale D. Ellis, ext. 104 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 Mathematics and Programming of the BellhopDRDC_active Program Diana McCammon McCammon Acoustical Consulting Prepared By: McCammon Acoustical Consulting 475 Baseline Road RR#3, Waterville, NS B0P 1V0 Contract number: W DRDC Contract Scientific Advisor: Dr. Dale D. Ellis, (902) 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 Ron Kuwahara for Dr. Calvin Hyatt Head / 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 The program suite, BellhopDRDC_active_v5, is designed for computing active signal excess and reverberation time series at a single frequency. It consists of two separate programs which together produce a tactical parameter, the signal excess, for bistatic range-dependent scenarios with 3-D sensor beams. Range dependence in bathymetry, sound speed and bottom loss descriptions are handled for each bearing direction defined from the transmitter or sensor. A clutter capability has also been included. The propagation engine for this program is the web version of Bellhop, dated September The purpose of this report is two-fold. First, it documents the specific files from the web version of Bellhop that are used in BellhopDRDC_active_v5. Second, this report provides, in both mathematics and programming code, the details of the reverberation, target echo and signal excess calculations in BellhopDRDC_active_v5. Résumé La suite logicielle BellhopDRDC_active_v5 vise à calculer l excès de signaux actifs et les séries de temps de réverbération à une fréquence précise. Elle est composée de deux programmes distincts. Ensemble, ils calculent un paramètre tactique, l excès de signaux, destiné aux scénarios bistatiques en fonction de la distance utilisant des faisceaux de capteurs 3D. Elle calcule la portée acoustique (vitesse du son, perte au fond et bathymétrie) pour chaque radial à partir d un transmetteur ou d une sonde. Nous avons aussi ajouté le calcul du fouillis acoustique. Le moteur de ce programme est la version Web de Bellhop (version de septembre 2010). Le présent rapport a deux objectifs : d une part, répertorier les fichiers de la version Web de Bellhop utilisés dans BellhopDRDC_active_v5 et, d autre part, détailler, mathématiquement et en code informatique, les calculs de réverbération, d écho de cible et d excès de signaux faits par BellhopDRDC_active_v5. DRDC Atlantic CR i

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7 Executive summary Mathematics and Programming of the BellhopDRDC_active Program McCammon, D. F.; DRDC Atlantic CR ; Defence R&D Canada Atlantic; October Introduction or background Bellhop is a ray-based model for calculating underwater sound propagation loss, 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. The original model handled only one-way propagation and thus applicable to passive sonar; the current version calculates reverberation and target echo, so is suitable for active sonar applications. Results The program suite, BellhopDRDC_active_v5, is designed for computing active signal excess and reverberation time series at a single frequency. It consists of two separate programs which together produce a tactical parameter, the signal excess, for bistatic range-dependent scenarios with 3-D sensor beams. Range dependence in bathymetry, sound speed and bottom loss descriptions are handled for each bearing direction defined from the transmitter or sensor. A clutter capability has also been included. The propagation engine for this program is the web version of Bellhop, dated September The purpose of this report is two-fold. First, it documents the specific files from the web version of Bellhop that are used in BellhopDRDC_active_v5. Second, this report provides, in both mathematics and programming code, the details of the reverberation, target echo and signal excess calculations in BellhopDRDC_active_v5. Significance BellhopDRDC is the propagation model used in the DRDC Environmental Modeling Model (EMM), the acoustic propagation prediction module of the System Test Bed (STB) and Pleiades. This current version of BellhopDRDC extends its applicability to active sonar scenarios, in addition to passive sonar. Users guides for this and previous versions of the model are available, but this is the first documentation of the internal mathematics and programming. In addition to providing the capability for modeling active and passive sonar propagation, this provides a well understood acoustic model for testing and validation of other operational acoustic range prediction systems (ARPS). DRDC Atlantic CR iii

8 Future plans BellhopDRDC needs to be compared with results from other models on various reverberation and sonar test problems available in the underwater acoustics community. iv DRDC Atlantic CR

9 Sommaire Mathematics and Programming of the BellhopDRDC_active Program McCammon, D.F.; DRDC Atlantic CR ; R & D pour la défense Canada Atlantique; octobre Introduction ou contexte Modèle à tracé de rayons destiné au calcul des pertes acoustiques en milieu sous-marin, Bellhop a été développé par M. Porter; il est accessible en distribution libre à partir de la bibliothèque Internet OALIB (Ocean Acoustics Library). RDDC Atlantique finance depuis quelques années les recherches de Mme McCammon afin d adapter ce modèle à ses propres besoins. Le modèle originel ne calculait que la propagation unidirectionnelle, et n était donc applicable qu aux sonars passifs, mais la version actuelle calcule aussi la réverbération et l écho de cible; elle est donc approprie aux sonars actifs. Résultats La suite logicielle BellhopDRDC_active_v5 vise à calculer l excès de signaux actifs et les séries de temps de réverbération à une fréquence précise. Elle est composée de deux programmes distincts. Ensemble, ils calculent un paramètre tactique, l excès de signaux, destiné aux scénarios bistatiques en fonction de la distance utilisant des faisceaux de capteurs 3D. Elle calcule la portée acoustique (vitesse du son, perte au fond et bathymétrie) pour chaque radial à partir d un transmetteur ou d une sonde. Nous avons aussi ajouté le calcul du fouillis acoustique. Le moteur de ce programme est la version Web de Bellhop (version de septembre 2010). Le présent rapport a deux objectifs : d une part, répertorier les fichiers de la version Web de Bellhop utilisés dans BellhopDRDC_active_v5 et, d autre part, détailler, mathématiquement et en code informatique, les calculs de réverbération, d écho de cible et d excès de signaux faits par BellhopDRDC_active_v5. Importance Le module de prévisions de la propagation acoustique du Banc d essais de systèmes (STB) et du système Pleiades, c est-à-dire le Modèle de modélisation de l environnement (EMM) de RDDC, utilise le modèle de propagation BellhopDRDC. La version actuelle de BellhopDRDC amplifie ses fonctions, car elle prend maintenant en charge les sonars actifs en plus des sonars passifs. Les guides d utilisation de cette version et des versions précédentes du modèle restent disponibles; le présent rapport, cependant, est le premier à traiter des algorithmes internes et de leur mise en œuvre dans ce programme. En plus de modéliser la propagation acoustique des sonars actifs et passifs, ce logiciel présente un modèle acoustique éprouvé qui aide à mettre à l essai et valider d autres systèmes opérationnels de prédiction de la portée acoustique (ARPS). DRDC Atlantic CR v

10 Perspectives Il faudra comparer les résultats de BellhopDRDC et ceux d autres modèles appliqués à divers problèmes d essais de réverbération et de sonars utilisés par la communauté de l acoustique sousmarine. vi DRDC Atlantic CR

11 Table of contents Abstract... i Résumé... i Executive summary... iii Sommaire... v Table of contents... vii List of tables... ix 1. Introduction Overview of structure of BellhopDRDC_active_v BellhopDRDC_reverb_echo_v Program flow controlled by frontend_reverb_echo_v5.f Fortran files in BellhopDRDC_reverb_echo_v SE_v Program flow controlled by SE_v5.f Fortran files in SE_v Bellhop Propagation Engine Inputs Web version file usage Program Bellhop Subroutine TraceRay Subroutine Step Subroutine Reflect Subroutine Refco Subroutine InfluenceGeoGaussian Subroutine Quad Subroutine AddArr Function CRCI Subroutine Errout Reverberation Assembly Finding transmitter bearing and range to a scattering spot Reverb bearing mathematical description Reverb bearing programming description Reverberation Sums Reverb sum mathematical description Reverb sum programming description Reverb time bin assignment Reverb time bin mathematical description Reverb time bin programming description DRDC Atlantic CR vii

12 3.4 Clutter Positioning Clutter position mathematical description Clutter position programming description Target Echo Assembly Finding transmitter bearing and range to a target position Target Echo Sum Echo sum mathematical description Echo sum programming description Echo time bin assignment Echo time bin mathematical description Echo time bin programming description Signal Excess Application of Sensor Beampatterns Sensor beampattern in SE, mathematical description Sensor beampattern in SE, programming description Signal Excess Calculation SE mathematical description SE programming description Smoothing Smoothing mathematical description Smoothing programming description Summary and Future Work Summary Future Work Smoothing the SE Adding a narrowband capability Adding pulse waveform Adding target strength angle dependence References viii DRDC Atlantic CR

13 List of tables Table 1. September 2010 web version Bellhop usage DRDC Atlantic CR ix

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15 1. Introduction 1.1 Overview of structure of BellhopDRDC_active_v5 Bellhop is a computer program originally created by Dr. Michael Porter that computes single frequency acoustic fields in oceanic environments via ray tracing of Gaussian beams. This algorithm is the core propagation engine of the DRDC active model. The BellhopDRDC_active_v5 suite consists of two programs that were created for use with the Environment Modeling Manager (EMM) of the Canadian Navy at the Defence R&D Canada Atlantic (DRDC Atlantic) laboratory. The first program, called BellhopDRDC_reverb_echo_v5, computes the surface and bottom reverberation and the target echo for each bearing and depression/elevation (D/E) angle of each sensor. The matrices of reverberations are written to a file called Reverb_byAngles.txt. The matrix of target echo is written to a file called Signal_byAngles.txt. The second program, called SE_v5, reads these component files and applies the sensor beam pattern before summing over bearing and D/E to obtain the total reverberation and signal excess. Specific details of the inputs are found in reference [1] BellhopDRDC_reverb_echo_v5 This program reads the inputs, and for both transmitter and sensor locations, it calls the Bellhop propagation engine to compute the acoustic field and stores the results in SALT (Sound Angle, Level and Time) tables. It then compiles the reverberation and target echo by bearing and D/E angle and writes these matrices to files Program flow controlled by frontend_reverb_echo_v5.f90 Read general input in active.inp Read transmitter input file Compute number of rays and angle fan for ray trace and initialize arrays Loop over transmitter bearings * Transfer transmitter environment to Bellhop arrays for this bearing * Call Bellhop propagation engine to compute SALT table for transmitter for this bearing End transmitter bearing loop Loop over sensor number * Read sensor input file * Loop over this sensor s bearings ** Transfer sensor environment to Bellhop arrays for this bearing ** Call Bellhop propagation engine to compute SALT table for sensor for this bearing * End sensor bearing loop * Compute time series length from transmitter and sensor SALT table maximum delay * Translate clutter locations to this sensor s coordinates * Loop over this sensor s bearings ** Compute surface and bottom reverberation along this bearing for this sensor ** Compute target echo along this bearing for this sensor ** Write reverb and target echo to file for this bearing and sensor * End sensor bearing loop DRDC Atlantic CR

16 End sensor number loop Fortran files in BellhopDRDC_reverb_echo_v5 The BellhopDRDC_reverb_echo_v5 program consists of 17 Fortran source files and their subroutines: [1] Modbellhop_reverb_echo_v5.f90 module with internal data array declarations [2] Modinput_reverb_echo_v5.f90 module with range dependent input array declarations [3] Modrefco_reverb_echo_v5.f90 module with some reflection loss models CALCbotRC calls function for MGS NAVOCEANO bottom loss CALCtopRC choose surface loss algorithm Function BOTT_NEW MGS bottom loss Function SURF_NEW Beckmann-Spezzichino surface loss Subroutine LFSOPN Modified Eckart surface loss [4] Modreverb_v5.f90 module with reverberation arrays [5] Modsalt_v5.f90 module with SALT arrays [6] Modssp_reverb_echo_v5.f90 module with SSP arrays [7] frontend_reverb_echo_v5.f90 program to run this model and write output files [8] BellhopDRDC_reverb_echo_v5.f90 propagation engine Bellhop Bellhop_reverb_echo_v5 sets up traces and intensity calculations TraceRay traces each ray, adjusting for range dependent properties Distances computes ray vectors to boundaries Step takes one ray step Reducestep shortens the step length to land on specific points Reflect adds boundary loss - two layer geoacoustic reflection is embedded Refco linear interpolation of reflection coefficient table if used InfluenceGeoGaussian computes complex pressure from each ray, GRAB style Quad select method of SSP interpolation and return sound speed Linear bilinear interpolation of SSPs in 2D Function TMP_SSP convert temperature to sound speed using Leroy s equation AddArr stores arrival information in Bellhop internal arrays Function Thorpe computes Thorpe water column attenuation Function CRCI converts real wave speed and attenuation to a complex value ERROUT outputs error messages and warnings to Bellhop log file. [9] envstore_reverb_echo_v5.f90 transfers environmental inputs into Bellhop arrays Envstorex transfer transmitter environment for selected bearing Envstores transfer sensor environment for selected bearing [10] readinput_reverb_echo_v5.f90 reads from active.inp and sets defaults [11] readinput_sensor_v5.f90 reads input from each sensor file (named in active.inp) APLUWinputs assign inputs for scattering strength empirically [12] readinput_xmitter_v5.f90 reads input from the transmitter file (named in active.inp) [13] salt_v5.f90 for each bearing, calls Bellhop, then transfers arrival tables to SALT arrays [14] scatstrength_v5.f90 contains surface and bottom scattering strength algorithms OE - Ogden-Erskine surface scattering strength CH Chapman- Harris surface scattering strength EC Ellis-Crowe/Lambert bottom scattering strength 2 DRDC Atlantic CR

17 LB Lambert s rule for bottom scattering strength OM omnidirectional rule for bottom scattering strength JB APL-UW bistatic bottom scattering strength Function gam Gamma function for use in APL-UW bistatic model [15] targetecho_v5.f90 computes echo by time, range, depth and D/E angle for given bearing and sensor [16] reverb_v5.f90 computes surface and bottom reverberation by time and D/E angle for given bearing and sensor getbearing determine transmitter range and bearing from scattering spot getmu check for existence of clutter within the scattering spot [17] writeoutput_reverb_echo_v5.f90 writes all products to file WriteArrival output SALT tables Writerevb output non-zero surface and bottom reverberation by time and angle Writesignal output non-zero target echo values by depth, range, angle and time SE_v5 This program uses the output from the previous program to compute the total reverberation and signal excess for each sensor. The sensor number, source level, noise level, target strength and sensor beam pattern comprise the inputs. This program operates at a single frequency on only one sensor at a time. The input sensor number determines which sensor is being analyzed and the output files include the sensor file name for clarity Program flow controlled by SE_v5.f90 Read general input in SE.inp where the sensor number is selected Read Reverb_byAngles.txt file, choosing the data for the sensor number selected Read Signal_byAngles.txt file, choosing the data for the sensor number selected Loop over number of sensor beams *Write out beampattern slices if requested to file Beampatternslices.txt * Zero summing arrays * Loop over target bearing ** Loop over D/E angle *** Interpolate the sensor beam strength in bearing and D/E *** Loop over time **** Sum reverberation * beam strength over bearing and D/E **** Loop over target range ***** Loop over target depth ****** Sum echo * beam strength over D/E ***** End target depth loop **** End target range loop *** End time loop ** End D/E loop * End target bearing loop * Form total interference for this sensor beam number * If on beam#1, write total interference to file Reverb_{sensorfile name}.txt * Loop over target depth ** Loop over target bearing DRDC Atlantic CR

18 *** Loop over target range **** SIR = maximum of (target echo*sl*ts) / total interference **** save beam where maximum occurred *** End target range loop ** End target bearing loop * End target depth loop End sensor beam loop SE = 10*log(SIR) - DT Syslos Apply smoothing if requested Write signal excess to file SE_{sensorfile name}.txt Fortran files in SE_v5 The SE_v5 program consists of 7 Fortran source files and their subroutines: [1] ModSE_v5.f90 module with internal data array declarations [2] readinput_se_v5.f90 read the SE.inp file [3] read_reverb_v5.f90 read the Reverb_byAngles.txt file [4] read_echo_v5.f90 read the Signal_byAngles.txt file [5] SE_v5.f90 program to compute total reverberation and signal excess ERROUT outputs an error message [6] average.f90 smooth the SE by range averaging [7] TowedArrayBeam.f90 compute a horizontal line array beampattern 4 DRDC Atlantic CR

19 2. Bellhop Propagation Engine There are several publications that detail the mathematics of the Bellhop method of Gaussian beam tracing; see for example references [2] and [3]. The mathematics specific to the Bellhop method have not been altered in the BellhopDRDC algorithm therefore the Gaussian beam equations need not be repeated here. The version of the Bellhop propagation engine that is used in the DRDC active program is on the web site OALIB.hlsresearch.com from the Acoustics toolbox updated 1 September This section describes the differences between this web-offered model and the DRDC implementation. 2.1 Inputs The structures of the input files are completely different between the two models. Reference [1] details the input files for the BellhopDRDC_active_v5 program. The Subroutines readinput_reverb_echo_v5, readinput_sensor_v5, and readinput_xmitter_v5 perform the tasks of reading and storing the inputs in large arrays. Within the propagation engine, an effort has been made to preserve the array names so that the parts of the code that come from the web version of Bellhop will be easily recognizable and upgradeable. The Subroutines Envstorex and Envstores transfer data specific to the bearing and asset being tested into the arrays used by the Bellhop propagation engine. Two of the inputs to the web Bellhop provide the user choices of algorithms. These choices have been defaulted and any extraneous code relating to other choices has been removed in the DRDC version. The web version inputs Beamtype and Runtype are defaulted as listed below: Beamtype(1:3) = M (Cerveny beams), S (standard curvature), (empty= no beam shift) Runtype(1,2,4,5)= A (write arrivals), B (Grab), R (point source), R (rectangular grid of receivers) 2.2 Web version file usage Array storage in the web version is accomplished using dynamically allocated arrays defined in modules and accessed with USE statements. This same structure is used in BellhopDRDC, although the module names have been changed. Therefore, in all cases, the USE statements within the subroutines will be different. Table 1 lists the specific subroutines and files of the web version of Bellhop that are employed in BellhopDRDC. Table 1. September 2010 web version Bellhop usage. Subroutines used as written * Subroutine name Subroutine Distances Subroutine Reducestep Contained in web version file Bellhop.f90 Bellhop.f90 DRDC Atlantic CR

20 Code altered from the web version Other files supplying some specific coding Program Bellhop Subroutine TraceRay Subroutine Step Subroutine Reflect Subroutine Refco Subroutine InfluenceGeoGaussian Subroutine Quad Subroutine AddArr Function CRCI Subroutine Errout Subroutine READIN Subroutine ReadATI Subroutine ReadBTY Module bellmod * Apart from changes in the names of the modules in the USE statements Program Bellhop Bellhop.f90 Bellhop.f90 Bellhop.f90 Bellhop.f90 RefCoMod.f90 Bellhop.f90 Readin.f90 ArrMod.f90 Readin.f90 Errout.f90 Readin.f90 bdrymod.f90 bdrymod.f90 bellmod.f90 The purpose of this web version program is to direct the flow of a single calculation. In the DRDC implementation, this is transformed into the Program frontend_reverb_echo_v5 and Subroutine BellhopDRDC_reverb_echo_v5 so that acoustic fields can be computed repeatedly for a variety of bearings and sensors. There are extensive differences between these files as a result. The following list describes portions of code from various web files that are included in Subroutine BellhopDRDC_reverb_echo_v5 and Program frontend_reverb_echo_v5 which together have replaced Program Bellhop: 1. The USE modules are different. 2. The maximum number of steps along a ray is set to in the DRDC version in modbellhop_reverb_echo_v5 and in the web version in module bellmod. 3. The ray tracing limits (rbox and zbox) that were inputs to the web version are defaulted to rbox=1.001 Rmax and zbox=1.01 z(nssp). 4. The automatic step size definition is retained: deltas=0.1 z(nssp), 1/10 th of the water column depth at the first bathymetry point. This was computed in the web file readin.f In web file readin.f90, the web version defined the default number of rays as Nbeams = max(int(0.3*rmax*freq/1500.),300). However, in web Program Bellhop, an optimum number of rays for coherent summations is given as Nbeamsopt = 2 + int((alpha(nbeams)-alpha(1))/(sqrt(c/(6*freq*rmax))) ). The DRDC version uses the definition of Nbeamsopt, choosing the start and stop angles, alpha(nbeams)-alpha(1), as the input or defaulted start and stop angles in radians. The use of Nbeamsopt in place of Nbeams produces a much smaller number of rays, and hence a much faster calculation with only a small loss in accuracy. This assignment is made at the start of frontend_reverb_echo_v5.f The bathymetry structure array (Bot) including both linear and curvilinear options was constructed in Subroutine ReadBTY in the web file bdrymod.f90 and is now constructed in Subroutine BellhopDRDC_reverb_echo_v5. 7. The surface structure array (Top) was constructed Subroutine ReadATI in the web file bdrymod.f90. and is now constructed in Program frontend_reverb_echo_v5. 6 DRDC Atlantic CR

21 8. Multiple source (transmitter) depths are not permitted in the DRDC code. 9. Sound speed is computed from a direct call to Subroutine Quad, without going through the sound speed model selector web Subroutine SSP contained in the web file Readin.f The DRDC version includes a call to Subroutine CALCtopRC which computes a surface reflection coefficient table from input wind speed using a choice of models. The web version provided a table input for surface loss in Subroutine Readrc in the web file RefCoMod.f In the ray trace loop, the source beam pattern is not applied (to initialize Amp0). Instead, the beam pattern for transmitter is applied in the latter assembly stages of the reverberation and target echo, and the beam pattern for the sensor is applied in the program SE_v Some different arguments are passed to Subroutine TraceRay. 13. Function PickEpsilon in web file bellhop.f90 is not needed in the DRDC code. 14. Only one method of computing the pressure field is used (Subroutine InfluenceGeoGaussian) and some of its passed arguments are different. 15. Subroutine ScalePressure in web file bellhop.f90 is not needed in the DRDC code because these calculations (e -ar Subroutine InfluenceGeoGaussian Subroutine TraceRay The purpose of this subroutine is to trace a ray through the water column over range varying bathymetry. The DRDC code includes range dependent sound speed and bottom properties. The following list describes the differences between the DRDC version and the web version. 1. The passed arguments and the USE modules are different. 2. To obtain sound speed, Subroutine Quad is called directly, rather than going through the web version Subroutine SSP. 3. There are no altimetry arrays which simplifies the Top segment identification and Top normal assignments. 4. Code is inserted to allow range dependent sound speed and bottom loss descriptions. 5. The arguments passed to Subroutine Step are slightly different. 6. Stepping into new SSP segments or new bottom properties is handled in the same way as stepping into a new bathymetry segment in the web version. 7. The arguments passed to Subroutine Reflect are different. 8. The web version s ray stepping loop termination if the ray amplitude falls below has been retained. 9. The ray stepping loop is terminated if the number of bottom bounces exceeds an input to BellhopDRDC (KillAfterBounce) while no such limitation exists in the web version Subroutine Step The purpose of this subroutine is to take a single step along the ray path. The following list describes the differences between the DRDC version and the web version. 1. The Intel Visual Fortran Compiler Professional Edition 11.1 used by this developer was not able to pass the defined type array (raypt) as programmed in the web version, so the arguments passed to step and the module definitions in the USE statements are different. DRDC Atlantic CR

22 2. To obtain sound speed, Subroutine Quad is called directly, rather than going through the web version Subroutine SSP Subroutine Reflect The purpose of this subroutine is to reflect the ray from a boundary, either the surface or the bottom, applying the appropriate losses. The following list describes the differences between the DRDC version and the web version. 1. The passed arguments are different. In particular, the loss array for the surface loss and MGS or bottom loss table are passed. The USE modules are also different. 2. To obtain sound speed, Subroutine Quad is called directly, rather than going through the web version Subroutine SSP. 3. Bottom losses are obtained from a table, the HFBL (MGS) curve, or a two-fluid layer Rayleigh reflection coefficient which is computed within this subroutine. The web version only provides losses for a rigid boundary, a vacuum, an input table, or a sediment half-space. 4. The web version code that will terminate a ray if its reflection loss from the geoacoustic bottom loss calculation is less than 1.0e-5 has been retained Subroutine Refco The purpose of this subroutine is to interpolate tabulated values from reflection loss arrays at the angle of interest. The following list describes the differences between the DRDC version and the web version. 1. The passed arguments are different. 2. In the web version, if the requested angle is outside the angular definition of the table being interpolated, the loss and phase are set to zero and a warning is printed. In the DRDC version, the loss and phase are set to the value at the last tabulated angle and a warning is printed in the log file Subroutine InfluenceGeoGaussian The purpose of this subroutine is to compute a single ray s contribution to the complex pressure at the defined receiver depths and ranges using geometric Gaussian beams. The following list describes the differences between the DRDC version and the web version. 1. The passed arguments and USE modules are different. 2. Thorpe attenuation (alpha) is computed from Function Thorpe and the loss factor for volume attenuation and cylindrical spreading (factor = exp(- e amplitude. In the web version, these loss factors are applied in the Subroutines WriteArrivalASCII or WriteArrivalsBinary in the ArrMod.f90 file or in subroutine ScalePressure in web file bellhop.f In the DRDC version, code is included to shift the depth corresponding to the last receiver depth index to conform to the bathymetry as the ray steps out in range. This depth index is used to compute the field on the bottom for reverberation. The first depth 8 DRDC Atlantic CR

23 index is reserved for the surface field for surface reverberation. The target lies at depth indices [2, nrd-1]. 4. In the DRDC version, the incoherent intensity, (const*factor) 2 *W, is saved in the arrival tables, conforming to the definition of incoherent/semicoherent TL in the web version (case default) which uses the first power of the Gaussian spreading factor, W, times the square of the amplitude. The arrival table in the web version contains (const * W) which corresponds to the coherent pressure amplitude (case C) Subroutine Quad The purpose of this subroutine is to return the sound speed at a specified range and depth. The specific differences between DRDC s subroutine and the web version are: 1. The passed arguments and USE modules are different. 2. The first part of the web version reads the SSP data from an input file. In the DRDC version, these input reads are accomplished in the routines readinput_sensor_v5 and readinput_xmitter_v5. The Subroutines Envstores and Envstorex transfer the data for each bearing into the Bellhop storage arrays cmat, Czmat, zsspv and Rseg. 3. The search for the range-segment of the profile is preformed in the web version of Quad however in the DRDC version for efficiency, this search is preformed in Subroutine TraceRay after each range step. 4. The DRDC version offers a choice of range interpolation styles; None or Linear. If Linear, the Subroutine Linear is called in which the bilinear quadrilateral interpolation of the SSP data in 2D is preformed, following the coding of the web version of Quad. The Subroutine Linear also includes code specifically for finding the speed in the last range segment of the range dependent profiles, which is not done in the web version Subroutine AddArr The purpose of this subroutine is to add the relevant ray information (amplitude, phase, delay, source angle, receiver angle, number of top bounces and number of bottom bounces) from Subroutine InfluenceGeoGaussian to the Bellhop storage arrays for each receiver depth and range. The Subroutine Salt then transfers some of these data into SALT tables for the transmitter and each sensor as a function of bearing. The specific differences between the DRDC version and the web version are: 1. The passed arguments and the USE modules are different. In particular, in the web version, the arrival array is dimensioned as a defined type structure array. Previous versions of the web code used separate arrays for each quantity. For example in the September 2011 web version, the older array DelArr has now become Arr%delay and the older array PhaseArr has now become Arr%phase, etc. The older code array names have been retained in the DRDC version. 2. In the DRDC version, the amplitude stored is the incoherent ray intensity and includes the volume attenuation and cylindrical spreading. In the web version, it is the pressure coefficient multiplied by the Gaussian spreading function. This means that in the section of code where the arrival is found to be not a new ray, the web version is summing pressure coefficients (without phase) and the DRDC version is summing intensities. DRDC Atlantic CR

24 3. In the web version, the number of rays that can be stored, MaxNArr, is computed based on the number of receiver depths and the number of range points: MaxNArr = Max( /(Nrd*Nr), 10). In the DRDC version, MaxNArr is set as a parameter to 100 in Modbellhop_reverb_echo_v5.f90. In both versions, the strongest rays are saved by replacing the weakest arrival after the table is filled Function CRCI The purpose of this function is to convert real wave speed and attenuation in the sediment to a single complex wave speed. The differences between the DRDC version and the web version are: 1. The passed arguments differ slightly. In the DRDC version, the units of the sediment attenuation are input in the variable Atten_Unit in the input Active.inp and subsequently passed in a character variable AtUnit, while the variable is passed as AttenUnit in the web version. 2. In the DRDC version, only the units of db/(m-khz), db/wavelength, db/m or nepers/m are permitted. Code to compute the Thorpe volume attenuation in this subroutine has been omitted Subroutine Errout The purpose of this subroutine is to write to the Bellhop_active.log file the kind and severity of many of the errors that may be detected in the running of the program. This message can be either a warning or a fatal error, which stops the execution of the program. The difference between the web version and the DRDC version is an extra passed argument, the bearing, which can help identify specific locations of input errors in bearing dependent bathymetry, sound speed or bottom parameters. 10 DRDC Atlantic CR

25 3. Reverberation Assembly Both surface and bottom reverberation (without source level) are assembled as a function of time and depression/elevation (D/E) angle in Subroutine Reverb for each bearing from each sensor at a single frequency. The values used in this calculation come from SALT tables that are constructed for each sensor and transmitter by the Bellhop propagation engine. The SALT tables contain the intensity, launch angle, arrival angle, and travel time of each ray as a function of the ray number, range, target and boundary depth and bearing. The surface boundary is assigned the first depth array position, the target depths are assigned the next depth array positions and the bottom boundary is assigned the last depth array position. The value of the depth of the bottom boundary is changed to match the bathymetry as the ray range changes within the Bellhop propagation engine so that at each ray step, the correct depth conforming to the bottom is used. 3.1 Finding transmitter bearing and range to a scattering spot Reverb bearing mathematical description Reverberation is assembled about the sensor, using the range and bearing from the sensor to locate the scattering areas. The unknown quantities are the range and bearing [r x, x ] from the transmitter to the scattering spot. Let Subscripts s and x refer to the sensor and transmitter quantities respectively. Subscript b refers to the base location of the transmitter relative to the sensor. s = bearing angle of scattering spot from sensor. x = bearing angle of scattering spot from transmitter. b = bearing angle of transmitter from sensor. r s = range to scattering spot from sensor. r x = range to scattering spot from transmitter. r b = range to transmitter from sensor. Define two dimensional vectors between the sensor, scattering spot and transmitter. The number in brackets after the vector, (e.g. ) indicates the component of the vector. The negative bearing angles translate compass directions to [x,y] coordinate directions, with the x axis pointing North. V b r b cos( b ), sin( b ), V s r s cos( s ), sin( s ), V x V s V b r s cos( s ) r b cos( b ), r s sin( s ) r b sin( b ), r x (V x V x ), x tan 1 (V x [2]/V x [1]). (1) Converting back to compass bearings, = if <0, 360- otherwise. DRDC Atlantic CR

26 The derivative of the transmitter range with respect to the sensor range, dr x /dr s is used in time window calculations in Section 3.3. r x 2 V x 2 [1] V x 2 [2], 2r x dr x 2V x [1] dv x [1] dr s 2V x [2] dv x [2] dr s, dr x dr s V x[1]cos( s ) V x [2]sin( s ) r x. (2) Reverb bearing programming description In Subroutine Reverb, in the file reverb_v5.f90, each range step along a bearing from a sensor defines a scattering spot on a boundary. To compute the range and bearing to the transmitter from this spot, the following logic is used: Let rs be the horizontal range (m) from a sensor to the scattering spot, with index irs. rx be the horizontal range (m) from the transmitter to the scattering spot, with index irx. sbear = transmitter bearing from the sensor (deg from North) sbear is input in the sensor_info namelist as Xmitter_bearing_from_sensor, read in readinput_sensor_v5 and stored in Modbellhop_reverb-echo_v5. bearings = array of sensor bearings, with index iphis. The index is a passed argument. bearingx = array of transmitter bearings with index iphix. base = horizontal distance (m) between the sensor and the transmitter The DirectBlast_time (sec) is input in the sensor_info namelist, read in readinput_sensor_v5. It is converted to distance by multiplying by the speed of sound at the sensor depth, which is interpolated from the SSP. Base is stored in Modbellhop_reverb-echo_v5. The Subroutine getbearing located in file reverb_v5.f90 uses geometry to obtain the range and bearing [rx,xb] from the transmitter to the scattering point, given the location of the scattering point from the sensor, [rs,bearings]. In an [x,y] coordinate system with the x axis pointing north, the compass angles are negative. Vec1 = vector from the sensor to the transmitter, Vec1 = base*[cos(-sbear), sin(-sbear)] Vec2 = vector from the sensor to the scattering spot Vec2 = rs*[cos(-bearings), sin(-bearings)] Vec3 = vector from the transmitter to the scattering spot Vec3 = Vec2 Vec1 rx = magnitude of the vector from transmitter to the scattering spot rx Vec3) xb = angle (degrees) of the vector from transmitter to the scattering spot xb = arctan(vec3[2], Vec3[1]) translate [x,y] coordinate angles to compass bearings if xb<0 then use xb. If xb>0 then use 360-xb. drxdrr = derivative of rx with respect to rs, used in forming time window drxdrr= [vec3[1]*cos(-bearings) + vec3[2]*sin(-bearings)]/rx 12 DRDC Atlantic CR

27 These coordinates [rx,xb] are then located in the range and bearing arrays of the transmitter and their indices [irx,iphix] are obtained, rounded to the nearest entry. 3.2 Reverberation Sums Reverb sum mathematical description Let subscripts s and x refer to the sensor and transmitter quantities respectively. t = time extent of the reverberation from the beginning of the scattering spot to its end t is a function of range and bearing to the spot from the sensor and transmitter. = D/E or launch angle, (measured from the horizontal). = bearing angle (azimuthal angle). = arrival angle (grazing angle) at boundary. n = number of rays in SALT table, a function of range r and bearing. = surface or bottom reverberation at the sensor, not including the source level. While not stated, frequency is also a variable that will affect the intensity and scattering strength. (3) Where A = intensity of acoustic field. x ) = the transmitter beam pattern, assumed azimuthally symmetric. = scattering strength. Some models lack the bearing angle dependence. = area of the scattering spot from the sensor location. dr= r(i+1) r(i) = range increment chosen to be 1500 * dt, the time cell increment s s (i+1) - s (i)}/360º = bearing angle increment fraction. T = fraction of time occupied by the reverberation in. (See section 3.3) Reverb sum programming description The subroutine Reverb, in the file reverb_v5.f90, is passed the index of the sensor bearing, iphis, and the sound speeds at the sensor and transmitter depths, cs and cx respectively. The algorithm computes first the surface then the bottom reverberation using identical steps excepting that the index of depth in the SALT tables is 1 for surface and NRD for bottom reverberation and the scattering strength algorithms choices are different. The programming arrays names and logic for this reverberation calculation are given below. Let Nums = number of sensor rays arriving at the scattering spot at range index irs, bearing index iphis. DRDC Atlantic CR

28 Numx = number of transmitter rays arriving at the scattering spot at range index irx, bearing index iphix, located by the code described in Section amps = intensity of ray from sensor to scattering spot at range index irs, bearing index iphis. ampx = intensity of ray from transmitter to scattering spot at range index irx, bearing index iphix. ampbeam = transmitter beam pattern power interpolated to the launch angle of the transmitter ray, thetx SS or SB = scattering strength for surface or bottom at the boundary arrival angles alpas and alpax. The specific models are described in the file Scatstrength_v5.f90 da = area of scattering spot where rs = range from sensor to scattering spot, rs=r(irs) dr = range step based on pulse length distance dr = 1500 * t0/2 computed in frontend_reverb_echo_v5.f90 dphis = fractional width of bearing spacing for sensor dphis = (bearings(iphis+1) bearings(iphis))/360. The program loops over the range from the sensor (index ir), the rays from the sensor (index ies) and the rays from the transmitter (index iex). Then * S * da *Tratio S stands for the surface or bottom scattering strength, SS or SB. The double sums are over Nums and Numx. Tratio is defined in Section 3.3 below. It contains the ratio of the temporal length of the reverberation to the length of the time window. It stores the reverberation by time (itt) and D/E angle (iang) and writes the non-zero entries to file Reverb_byAngles.txt for the given bearing. The source level is applied in the SE calculation. 3.3 Reverb time bin assignment Reverb time bin mathematical description The reverberation coming from the scattering area must be placed the appropriate time bins in the time series. The area of scattering is the region encompassed by the width of a range step dr and the width of a bearing sector s. Let dt dr = 1500 dt = range cell width t s = arrival time of sensor-to-scattering area contribution. t x = arrival time of transmitter-to-scattering area contribution. x = extra travel time for transmitter to arrive at the center of the scattering spot. Because the range from the transmitter-to-scattering area is computed (see Section 3.1) it may not coincide with the ranges for which the SALT tables provide t x. Therefore a travel time addition for this range difference must be included. Let the nearest range for which SALT table entries apply be the range r(k). The actual range for the transmitter (Section 3.1) is r x, therefore the extra range traveled by the transmitter ray is r x -r(k). The horizontal speed of this ray is given by Snell s law as c/cos0º = c x x. Therefore the extra travel time for the transmitter ray is 14 DRDC Atlantic CR

29 x r x-r(k) x/c x (4) with c x being the speed of sound at the transmitter depth. The quantity ( ) is called the horizontal slowness in the GRAB documentation. Thus, the travel time to the midpoint of the scattering area is t t s + t x x (5) Now to find the travel time to the edges of the scattering area, (from the sensor s perspective), let t a = the travel time across the range cell dr in length. The change of time with respect to the sensor range is dt/dr s. t r x x/c x r s s/c s dt/dr s dr x/dr s x/c x s/c s t a dr dt/dr s The derivative dr x /dr s is computed in Section 3.1. Thus the travel time to the start t 1 and end t 2 of the scattering area (including the pulse length) is t 1 t s t x t x t a t 2 t s t x t x t a (7) The indices in the time series that span t 1 and t 2 are located and the reverberation (assumed constant across the entire scattering area) is saved in each of these time bins, multiplied by the fraction of time occupied by the reverberation in that bin. For example, for the ith time bin, with time extent dt, t i-1 t 1 (i-1) dt locates either the starting time of the time cell or the starting time of the reverberation, whichever is greater. And t i t 2 i dt locates either the ending time of the time cell or the ending time of the reverberation, whichever is smaller. Then the fraction of reverberation in the time cell will be T t i t i-1 dt (8) Reverb time bin programming description The time window for each segment of reverberation in Subroutine Reverb (each combination of sensor ray and transmitter ray within the double sum in Section 3.2.2) is computed loosely DRDC Atlantic CR

30 following the techniques of CASS and DMOS. The reverberation arrival is apportioned among the time cells by computing the beginning and end of each cell and storing the fraction of reverberation that lands in that cell. Let deltat = duration of time cell in time series = ½ pulse length, deltat = t0/2. This also determines the size of the range step, dr = 1500*deltat. tims = delay time for the sensor ray arriving at the scattering spot at range index irs, bearing index iphis. timx = delay time for the transmitter ray arriving at the scattering spot at range index irx, bearing index iphix. delrx = extra range the transmitted ray must travel beyond R(irx) to reach the scattering spot, delrx = rx R(irx). cvx = horizontal slowness, Snell s law constant, cvx = cos(thetx)/cx, with thetx being the transmitter ray launch angle and cx being the speed at the transmitter depth. When multiplied by delrx, this represents the additional travel time of the transmitter ray to reach the scattering spot. cvs = horizontal slowness from the sensor, cvs = cos(thets)/cs t1 = travel time to the leading edge of the time cell, t1 = tims + timx + delrx*cvx dr/2 * dtdr. t2 = travel time to the trailing edge of the time cell also including the pulse length t0 t2 = tims + timx + delrx*cvx + dr/2 * dtdr + t0. dtdr = derivative of the travel time with respect to the range from sensor to scatterer. dtdr = cvx * drxdrr + cvs. The derivative drxdrr is calculated in Subroutine getbearing. These times t1 and t2 are located in the time series with indices it1 and it2. Next, the positions of the start and end of the reverberation in each time cell are computed. For example, for time cell itt, tml = max(t1, deltat *(itt-1) ) is the larger of t1 or the beginning of the time cell. tmr = min(t2, deltat*itt) is the smaller of t2 or the end of the time cell. Then the fraction of reverberation that belongs in each time cell itt is the extent of the signal divided by the size of the time cell. Tratio = (tmr tml)/deltat. This fraction multiplies the reverberation contribution at time index itt, as written at the end of Section Clutter Positioning A clutter model designed by Ellis, Preston, Hines and Young [4] is a method of injecting high reverberation segments into the bottom topography. Clutter is defined in the input files as bottom areas that exhibit high scattering strength. The clutter position is specified with respect to the transmitter by compass bearing and range. In the program frontend_reverb_echo_v5, the clutter is translated to the sensor coordinate system for each sensor Clutter position mathematical description The mathematics for determining the location of the clutter in the sensor coordinate system are similar to those expressed by equation 1. Let Subscripts sc and xc refer to the sensor and transmitter-coordinate system clutter quantities respectively. Subscript b refers to the base location of the transmitter relative to the sensor. 16 DRDC Atlantic CR

31 sc = bearing angle of the clutter spot from sensor. xc = bearing angle of clutter spot from transmitter. b = bearing angle of transmitter from sensor. r sc = range to clutter spot from sensor. r xc = range to clutter spot from transmitter. r b = range to transmitter from sensor. Define two dimensional vectors between the sensor, clutter spot and transmitter. The number in brackets after the vector, (e.g. ) indicates the component of the vector. The negative bearing angles translate compass directions to [x,y] coordinate directions, with the x axis pointing North. Then V b r b cos( b ), sin( b ), V xc r xc cos( xc ), sin( xc ), V sc V xc V b r xc cos( xc ) r b cos( b ), r xc sin( xc ) r b sin( b ), r sc (V sc V sc ), sc tan 1 (V sc [2]/V sc [1]). (9) Converting back to compass bearings, = if <0, 360- otherwise. The position [r sc sc] defines the location of the clutter spot from the sensor coordinate system. As the bottom reverberation computations proceed, a logical comparison is made to determine if the clutter location falls within the current sensor range step r s ± dr/2 and bearing increment s ± s /2, and if true, the Mackenzie coefficient of the scattering strength is set to the user input value for the strength of the clutter and Lambert s Law is used to compute the scattering strength for equation Clutter position programming description The clutter is mapped onto the sensor coordinate system in the frontend_reverb_echo_v5 program. Let rc = range to clutter spot from transmitter (m) held in the array clutter. bc = compass bearing to clutter spot from transmitter held in the array clutter. Vec1 = vector from the transmitter to the sensor, Vec1 = base*[cos(-180 -sbear), sin(-180 -sbear)] (Note: The sbear is the bearing from the sensor to the transmitter and it must be reversed (180º) to obtain the bearing from the transmitter to the sensor. Base is the distance between transmitter and sensor. Vec2 = vector from the transmitter to the clutter spot Vec2 = rc*[cos(-bc), sin(-bc)] Vec3 = vector from the sensor to the clutter spot Vec3 = Vec2 Vec1 r = magnitude of the vector from sensor to the clutter spot, held in the array clutters DRDC Atlantic CR

32 r Vec3) Cc = angle (degrees) of the vector from transmitter to the scattering spot, held in the array clutters. Cc = arctan(vec3[2], Vec3[1]) translate [x,y] coordinate angles to compass bearings if Cc<0 then use Cc. If Cc>0 then use 360-Cc. In the bottom reverberation section of Subroutine Reverb, in the file reverb_v5.f90, which is executed for each sensor, the sensor range (R(irs)) and bearing (bearings(iphis)) are inputs to Subroutine getmu which determines if the clutter spot is within the range and bearing increments [dr,dphis] of the scattering spot at range (R(irs)) and bearing (bearings(iphis)). The clutter positions with respect to the sensor location, [r,cc] stored in the array clutters as described above, are used logically determine if the clutter is there. The range window of the sensor range step is R(irs) - dr/2 to R(irs) + dr/2. The bearing window of the sensor is phis dphis/2 to phis + dphis/2. If the clutter spot defined in clutters [r,cc], falls within this window, the scattering strength coefficient is set to the user input value. The clutter scattering strength is computed within the ray double loops using Lamberts Rule with the input clutter strength coefficient and the arrival angles of the rays at the clutter spot. This value is compared to the scattering strength otherwise computed using the user s selected model and the larger of them is applied to the reverberation term. Thus, if the clutter loudness is actually less than the modelled scatter, the modelled scatter will dominate. 18 DRDC Atlantic CR

33 4. Target Echo Assembly 4.1 Finding transmitter bearing and range to a target position The mathematics and programming used to locate the transmitter range and bearing to a target position that is specified by a range and bearing from the sensor is exactly the same as that described in Section 3.1, with the target position substituting for the scattering spot position. 4.2 Target Echo Sum Echo sum mathematical description Let subscripts s and x refer to the sensor and transmitter quantities respectively. t = time extent of the target echo. The time t is a function of range r s and bearing s to the target from the sensor and transmitter as well as the pulse length. = D/E or launch angle, (measured from the horizontal). = bearing angle (azimuthal angle). d = depth of target. r s = range to target from sensor. n = number of rays in SALT table, a function of range and bearing. = target echo at time t at the sensor (without source level or target strength). While not stated, frequency is also a variable that will affect the intensity. The arrival time and the range from sensor are related, of course, however the arrival time will include the time spread from different propagation paths and the pulse length, and so it will occupy some number of time bins. (10) Where A = intensity of acoustic field. x ) = the transmitter beam pattern, assumed azimuthally symmetric. T = fraction of time occupied by the echo in. (See section 4.3) Echo sum programming description The target reflected echo at each sensor bearing is computed in the Subroutine Targetecho in the file targetecho_v5.f90. The echo is computed for all sensor-transmitter combinations to the maximum range and at the depths that were specified by the user in the input file active.inp in the Target_info namelist. (See the Users Guide [1]). Target echo uses similar programming logic as reverberation, except that the scattering spot is replaced by a point target, there is no area factor, and no scattering strength. DRDC Atlantic CR

34 Let Nums = number of sensor rays arriving at the target at depth index id, range index irs, bearing index iphis. Numx = number of transmitter rays arriving at the target at depth index id, range index irx, bearing index iphix, located by the code described in Section 4.1. amps = intensity of ray from sensor to target at depth index id, range index irs, bearing index iphis. ampx = intensity of ray from transmitter to target at depth index id, range index irx, bearing index iphix. ampbeam = transmitter beam pattern power interpolated to the launch angle of the transmitter ray, thetx. The subroutine is passed the index of the sensor bearing, iphis. It begins by establishing a loop over the target depth, and for each depth a loop over the range to the target from the sensor. The bearing and range from the transmitter to the target position are found using the Subroutine getbearing, as described in Section 4.1. Next the subroutine loops over the number of sensor and transmitter rays existing for these bearings, ranges and depths. The sensor and transmitter intensities and the transmitter beam pattern are multiplied together. Note that presently the target strength is applied in the SE program, however if a more complex target strength defined as a function of angle, (D/E and/or bearing) were desired, it would be applied at this point. Then The double sums are over Nums and Numx. Tratio is defined in Section below. It contains the ratio of the temporal length of the target echo to the length of the time window. The Echo is stored by time, sensor range, target depth and D/E angle and the non-zero entries are written to file Signal_byAngles.txt for each sensor bearing. The source level is applied in the SE program. 4.3 Echo time bin assignment Echo time bin mathematical description Let = pulse length (sec). dt t s = arrival time of sensor-to-target contribution. t x = arrival time of transmitter-to-target contribution. x = extra travel time for transmitter to arrive at the target. Because the range from the transmitter-to-target is computed (see Section 4.1) it may not coincide with the ranges for which the SALT tables provide t x. Therefore a travel time addition for this range difference must be included. Let the nearest range for which SALT table entries apply be the range r(k). The actual range for the transmitter (Section 4.1) is r x, therefore the extra range traveled by the transmitter ray is r x -r(k). The horizontal speed of this ray is given by Snell s law as c/cos0º = c x x. Therefore the extra travel time for the transmitter is x r x-r(k) x/c x (11) 20 DRDC Atlantic CR

35 with c x being the speed of sound at the transmitter depth. The quantity ( ) is called the horizontal slowness in the GRAB documentation. Thus, the travel time to the target at the beginning of the pulse is t 1 and the time at the end of the pulse is t 2. t 1 t s t x t x t 2 t s t x t x (12) The indices in the time series that span t 1 and t 2 are located and the target echo is saved in each of these time bins, multiplied by the fraction of time occupied by the echo in that bin. For example, for the i-th time bin, with time extent dt, t i-1 t 1 (i-1) dt locates either the starting time of the time cell or the starting time of the echo, whichever is greater. And t i t 2 i dt locates either the ending time of the time cell or the ending time of the echo, whichever is smaller. Then the fraction of echo in the time cell will be T t i t i-1 dt (13) Echo time bin programming description In the Subroutine Targetecho in the file targetecho_v5.f90, the time in which the leading edge of the pulse arrives at the sensor, t1, is found by summing the travel times from transmitter-to-targetto-sensor with the adjustment of transmitter time to the actual range of the target. The time when the pulse passes the sensor, t2, is t1 plus a pulse length t0. These times are located by the time indices it1 and it2. The echo intensity for each time slot is multiplied by the fraction of the echo that occupies the time slot and summed into an Echo array as a function of time, sensor range to target, target depth and D/E angle. Let deltat = duration of time cell in time series = ½ pulse length, deltat = t0/2. tims = delay time for the sensor ray arriving at the target at range index irs, bearing index iphis. timx = delay time for the transmitter ray arriving at the target at range index irx, bearing index iphix. delrx = extra range the transmitted ray must travel beyond R(irx) to reach the target, delrx = rx R(irx). cvx = horizontal slowness, Snell s law constant, cvx = cos(thetx)/cx, with thetx being the transmitter ray launch angle and cx being the speed at the transmitter depth. When multiplied by delrx, this represents the additional travel time of the transmitter ray to reach the scattering spot. t1 = travel time to the leading edge of the time cell, t1 = tims + timx + delrx*cvx. t2 = travel time to the trailing edge of the time cell also including the pulse length t0 t2 = tims + timx + delrx*cvx + t0. DRDC Atlantic CR

36 These times are located in the time series with indices it1 and it2. Next, the positions of the start and end of the echo in each time cell are computed. For example, for time cell itt, tml = max(t1, deltat *(itt-1) ) is the larger of t1 or the beginning of the time cell. tmr = min(t2, deltat*itt) is the smaller of t2 or the end of the time cell. Then the fraction of echo that belongs in each time cell itt is the extent of the signal divided by the size of the time cell. Tratio = (tmr tml)/deltat. This fraction multiplies the echo contribution at time index itt, as written at the end of Section DRDC Atlantic CR

37 5. Signal Excess The signal excess in the Active suite of programs is computed in the program SE_active located in the file SE_v5.f90. In this program, the component files of reverberation and target echo computed in BellhopDRDC_reverb_echo_v5 are read for the designated sensor. The sensor beam pattern is applied and the components are summed. The reverberation and the target echo are multiplied by the source level of the transmitter. The target echo is also multiplied by the target strength. The signal excess is computed using the technique given in the Generic Sonar Model (GSM) [5] and the model CASS/Grab [6], except that in these codes, the SE is computed using pressure ratios because spectral differences and Doppler shifts associated with narrowband signals are included. In the BellhopDRDC_active model, SE is computed using power ratios without any weighting by spectral shaping and therefore is presently only accurate for a single frequency signal. 5.1 Application of Sensor Beampatterns Sensor beampattern in SE, mathematical description The following discussion describes the towed array beam patterns. Let = D/E or launch angle, (measured from the horizontal). = target bearing angle (azimuthal angle) measured from North. a = bearing angle relative to the array axis. j = the beam number of the sensor array. B j a ) = beam strength for the jth array beam, relative to the array axis. h = heading of the array axis, relative to North. j = steering angle of the jth beam of the array, relative to the array axis. n = number of elements in the array. W m = element weights. d = element spacing. c s = speed of sound at the sensor depth. (14) where. In this equation, a lower value is set to 0.001, to keep the beam loss under 30dB. The pattern is computed using angles relative to the array axis, then the heading is added to the azimuthal angle to rotate the pattern to be relative to North, = a + h. Other types of arrays will provide their beam patterns as an input into an array. These beampatterns are applied to the components of the reverberation and target echo. Let t = time. d t = depth of target. DRDC Atlantic CR

38 r = range to the target. n = number of target bearings defined for the sensor. n = number of D/E angles defined for the sensor. R S,B = surface or bottom reverberation provided in component fashion as functions of D/E, bearing angle and time, divided by the bearing sector angular width. E = target echo provided in component fashion as a function of time, range, depth, D/E, and bearing angle. The components of the reverberation and target echo intensities are combined, multiplied by the power beam pattern ( or B j a +h), depending on the type of array, its heading and beam number). (25) The target echo remains a function of bearing because the SE will be computed for each bearing from the sensor Sensor beampattern in SE, programming description The sensor beampattern is applied in the program SE_active, in the file SE_v5.f90. The reverberation and target echo have been written to the files Reverb_byAngles.txt and Signal_byAngles.txt as functions of D/E angle and bearing from the sensor (as well as time, target depth and range). The sensor beam pattern may be specified by an array of strength values as a function of D/E angle and bearing, or a towed array pattern can be computed in Subroutine TA in the file TowedArrayBeam.f90. For a given D/E angle and bearing, the closest indices of the beam pattern at these angles are found. (bearing index ibb, D/E index iaa) The beam pattern is then interpolated in db space within this region to the specific angle and bearing required. The beam strength is computed from the interpolated db value (beam) as beamstrength = 10 -beam(db)/10. The surface and bottom reverberations Breverb and Sreverb are divided by the angular extent of the bearing increment over which they were computed to produce values per 1 degree. They are then multiplied by the beamstrength and summed by 1 degree steps over bearing (index ib) and D/E angle (index ia) to produce a time series (index it) of beam weighted data, sumrb and sumrs. The target echo intensity is also multiplied by the beamstrength and summed over D/E angle yielding a time series (sig) as a function of bearing, target range and target depth. 24 DRDC Atlantic CR

39 5.2 Signal Excess Calculation SE mathematical description Let S L = the source level in energy units. T S = the target strength in energy units. = echo intensity time series for the jth sensor beam at the sensor range r s, bearing s and target depth d t from Section 5.1.1, without source level or target strength. Then the complete echo intensity E c (t) for the jth beam is: Let R S = surface reverberation intensity including the sensor beam pattern, Section R B = bottom reverberation intensity including the sensor beam pattern, Section N = ambient noise level in intensity assumed isotropic therefore not discriminated by the sensor beam pattern. Then the total interference intensity I(t) is: (16) And the signal-to-interference ratio, SIR, is the maximum over all time and over all sensor beams of the ratio E c (t)/i(t) (17) where t m = the specific time that maximizes the ratio. j = the specific beam that maximizes the ratio. (18) Let D t = detection threshold in db S loss = system loss in db Then the maximum active signal excess, SE, in db is: (19) DRDC Atlantic CR

40 5.2.2 SE programming description The SE computation takes place in the program SE_active located in file SE_v5.f90. The total interference (totalrevb) is composed of the sum of the bottom and surface reverberation time series, multiplied by the source level SLi and then added to the noise level NLi. totalrevb = (sumrs + sumrb)*sli + NLi The signal to interference ratio, SIR, is defined in this program as the time series of the ratio of target echo to total interference for a given depth, bearing and range to target, SIR = sig*sli *TSi / totalrevb At any range of the sensor to the target, there will likely be several values in adjacent time bins of the SIR time series, given the spread in arrival times of the rays as well as the pulse length. The definition of SE in this program uses the maximum over all time and over all array beams of the echo to the interference time series, SIR, adjusted by the detection threshold DT and the system loss, Syslos. SE = 10* log 10 (maximum(sir)) DT Syslos. The SIR may be averaged over 9 range bins if the smoothing option has been selected. 5.3 Smoothing Smoothing mathematical description Let n = number of points in the averaging window. j m = midpoint of the averaging window, j m = integer(n/2) +1. W j = weight for each term in the averaging window. W j j, n j 1, j j m j j m Then the average of an intensity array A v at range r i is (20) In this equation, the ratio of indices in the curley brackets is explained as follows: The array being smoothed over range contains signal excess and signal excess is inversely proportional to range. Recall, SIR = echo/reverberation. The echo contains a cylindrical propagation loss from transmitter to target multiplied by a cylindrical propagation loss from the target to the sensor. Hence, the echo is proportional to 1/r 2. The reverberation also contains a product of propagation losses (1/r 2 ) but it is multiplied by the area ensonified which provides a direct dependence on r, giving it a total range dependence of 1/r. The ratio SIR therefore has 1/r dependence. This means 26 DRDC Atlantic CR

41 there will be a range bias introduced in the averaging over r. To remove this bias, each term is multiplied by its range and the entire sum is renormalized by dividing by the range to the midpoint of the range window,. Since the range is found by multiplying the range index by the range step, this ratio is just the ratio of the indices. This technique can also be used to smooth the reverberation in time because since the reverberation is inversely dependent on time, the bias removal would be identical Smoothing programming description The smoothing algorithm is Subroutine Average in the file average.f90. The passed arguments include the range extent of the average, pt, the maximum range of the array, pmax, the array and its size, narr. Let ip = the number of points in the averaging window, ip=int(pt/(pmax/narr)). ipmid = midpoint of averaging window, ipmid = ip/2 +1. wgt = weighting function = simple progression from 1 to midpoint and back to 1 norm = sum of the weights for normalization array(narr) = array being smoothed, an argument to the subroutine temp(i) = temporary array summing variable For each array point, temp(i), the array is sampled over ip points centered on the midpoint ipmid=i and each sample is multiplied by the weight, wgt/norm. The range bias is removed by multiplying each term by the ratio of its range index divided by the range index of the midpoint. The sum of the samples replaces the original array value at the point i. Presently, the SE program is configured to average over a 9 point window, with weights [1,2,3,4,5,4,3,2,1] and normalization 25. DRDC Atlantic CR