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MODELING A SONAR DETECTION PREDICTION SYSTEM IN A DISCRETE
AND HETEROGENEOUS OCEAN
SDPS-DH
Odmir Aguiar
ODMIR AGUIAR
MODELING A SONAR DETECTION PREDICTION SYSTEM IN A DISCRETE AND HETEROGENEOUS
OCEANSDPS-DH
1st Edition
Sao Vicente - SP - BrazilFundacao Plural
2014
i
Copyright Odmir Aguiar, 2013Cover: Odmir Aguiar Cover Image: Graphic generated by the SDPS-DH using XBT data, with correction TS factor, in active mode.
Review: xxxxxDiagramming: Odmir Aguiar
Catalogue Interoperability Protocol Data (CIP)(Brazilian Book Chamber, SP, Brazil)
2014All rights of electronic publications PLURAL FOUNDATIONAv. Presidente Wilson 1.033 - Itarare11.320-001 - Sao Vicente, SP - [email protected]
ii
Aguiar, Odmir.Modeling a Sonar Detection Prediction System in a Discrete and
Heterogeneous Ocean / Odmir Aguiar. - Sao Vicente: Fundacao Plural, 2014.
ISBN 978-85-667700-02-x
1. Underwater Acoustic. 2. Acoustic Models. 3. Acoustical Oceanography
CDD-551.47
A282s
Introduction1
This book presents a process of developing a model of acoustic
propagation from a new approach of the Raytracing
Theory, or simply Rays Theory. It also develops a model of sonar detection prediction for naval
use, with programming blocks in MATLAB to some relevant
stages of development.
Oceanography, or Ocean Science, is the generic name given to the scientific study of the oceans and has among its objectives to get a behavior description of water masses that make up the oceans and its biogeochemical processes.
This science tries to gain enough knowledge to be able to estimate sea future behavior, without forgetting that the oceans have a mutative natural process, which depends on a huge amount of parameters and relationships, and, therefore, can never be fully modeled.
Classically composed with four areas (physical, chemical, geological and biological), oceanography is, among other sciences, a new science that has had significant advances in recent decades.
4
1.1 OceanographyHow to gather in a single block of contributions all the scientific branches of Physics, Chemistry,
Biology and Geology?... More objective, therefore, would be to emphasize the main topics covered in oceanographic science, and that there would be none other than those arising from the application of
knowledge physical, chemical, biological and geological characteristics of the sea.(Diegues, 1974)
The underwater acoustics, a physical oceanography area, dedicated to the study of the behavior of sound waves that propagate in the oceans, and seeks to describe the path followed by the sound wave, its interaction with the environment and especially the history and scope of this wave.
The option to acquire information on the liquid medium by means of mechanical waves instead of electromagnetic waves is because the latter suer a large absorption during propagation.
Despite what George Pickard imagined in the middle of the last century (Pickard, 1968), beyond distance (depth) and sound speed information, nowadays we can generate three-dimensional images of the seabed using acoustic models, due to the deepening of the research and technological achievements obtained in the last three decades of the twentieth century.
5
The sonar (Sound Navigation and Ranging) is a set of electromechanical equipment that has as main purpose, in active mode, determining the distance of an object or of the seabed, to the vessel its installed.
Despite its many uses, the sonar system will be treated as a device for military use, that aims to detect ships and submarines during a naval operation.
The use of sonar as a military equipment shown to be important during World War II, allowing the localization of submarines, main weapon to attack the ship convoys, making it an essential tool in the maintenance of naval power (N.A.S., 1998).
6
1.2 Underwater AcousticsThe sound propagation in sea water depends on the values of temperature, salinity and pressure found in the medium. Among these three variables, temperature is one that exerts an influence
markedly dominant pattern of sound propagation beans. Thus, the record of temperature against depth, obtained from a bathythermogram, provides, through certain calculations, with a good
approximation, the vertical distribution of the sound speed in the sea. (Diegues, 1974)
The study of sound wave propagation in the oceans was initially developed based on Rays Theory, which is based on the path followed by rays belonging to the sound beam and with these rays traced, apply the eects of interactions with the environment.
At low frequencies (below 1 kHz) the Rays Theory gave way to the Normal Modes Theory and solutions with the Parabolic Equations (Robinson & Lee, 1994), which have a simpler implementation, therefore faster processing and mainly because these theories can contemplate the destructive/constructive eect interaction of wave fronts.
On the other hand, the teaching and development of the Rays Theory never have been abandoned, because it provides a more eective way to visually represent the propagation process, but has not been used to its full potential for the study of propagation in shallow water, because the complexity of the equipment demand more powerful algorithms for processing.
The naval sonar (military) uses frequencies ranging typically between 3 kHz and 14 kHz for active sonar, and frequencies between 1.5 kHz and 2.5 kHz as listening priority to passive sonar, aiming at the acquisition of reliable information on an area of about 10 nautical miles radius around the user, in shallow and deep water.
The development of algorithms of this book, based on Rays Theory, allows a good representation of the eects of the sound waves propagation at sea associated with computers with high processing capacity and allows the use of Rays Theory is resumed for the study of sound propagation.
7
1.3 SDPS-DHThe compressible sound wave propagation in the ocean presents therefore as a very important chapter
of Oceanography. (Diegues, 1974)
Since the early studies, scientists sought to develop a reliable and fast processing sonar range forecasting system, for installation in warships, to support decision process in naval operations involving antisubmarine actions.
This system is a 3/4 perspective model of sonar range prediction from a new approach to Rays Theory, which is presented in Chapter 3, having attached to it a database of georeferred oceanographic information.
In the chapters of this book, will be presented separately the theoretical, the methodologies and the main lines of programming each block described in Figure 1,
8
the algorithm employed in the development end of the Sonar Detection Prediction System (SDPS).
Figure 1 - Block diagram of the Sonar Detection Prediction System
Propagation Model Loss Model
Prediction Model
Sonar Parameters Model
Oceanographic Parameters User inputs
In Chapter 2, will be present the database architecture with the parameters required for the processing of oceanographic Propagation and Loss Models, describing their main characteristics and the methodology used for treatment.
The new approach developed for the application of the Rays Theory will be presented in Chapter 3.
Chapter 4 presents the Sonar Parameters Model.
Statements based on physical laws, are presented in Chapter 5, the Loss Model, including losses involving scattering, absorption, reflection and refraction.
The codes presented in Chapters 2 to 5 are part of the SDPS-DH, whose sonar detection prediction model will have its methodology present in Chapter 6.
9
The system mentioned in this book was developed for about five years and is the result of a personal interest developed in the area of acoustic propagation by the author, who saw the possibility to generate and compile this type of knowledge in Brazil, with the basic motivation contribute to the development of the necessary technology for the modernization of the Brazilian Navy ships.
It can be argued that the system developed in this work has a holistic perspective and is an isolated system does not open because it has properties that are not only fruits of their individual models and presents exchange relationships with the environment where the propagation occurs.
According to the classification Chorley & Kennedy (apud Chirstofoletti, 1999) the system can be considered a process response, that is, indicates the process and represents the response form for a particular purpose, as to type, it is certainly analogous abstract, mathematical and stochastic, as based on the perspective to represent a specific phenomenon, taking his models were developed separately, the understanding of the parties seeking to model the whole being included therein applying idealizations of acoustic phenomena and adding random components, observed data, and experiments.
The system described in this book, although it presents new methodologies, uses classical instruments on the subject, showing how to highlight the suitability of Rays Theory and calculation of transmission losses for an ocean heterogeneous.
The point of innovation of this system are contained in all chapters, it is important to highlight the data processing methodology oceanographic (Chapter 2), the formulation based on x for the wave propagation (Chapter 3), the establishment of formulas some sonar parameters (Chapter 4), the envelope of the Loss Model (Chapter 5) and the method of calculation and presentation of the forecast range (Chapter 6).
10
Oceanographic Parameters
2 The term heterogeneous and discrete ocean, in the title of this book supports the methodology of use of oceanographic parameters in this sonar detection prediction system, which seeks to express as faithfully as possible
the variability of the oceanic environment during the sound
wave propagation.
Since Sturm & Colladon first sound propagation studies in Lake Geneva, for almost two centuries (Clay & Medwin, 1977), through the development of the first device to detect targets through sound waves in the sea, designed by Richardson in 1912 (Urick, 1983), knowledge of the oceanographic parameters proved vital for obtaining an estimate of the behavior of sound waves in the oceanic environment.
With the appearance of computer technology and the development of databases that support iterative process, it was possible to better access to information available oceanographic parameters.
The raw data used in SDPS-DH not undergone any treatment or filtration, to preserve the characteristics of the Brazilian coast, which has a great variability of oceanographic parameters.
Treatments based on standard deviation or maximum and minimum limits of oceanographic parameters were not reliable when it has a mass of data that contains information of the entire Brazilian coast (Aguiar, 1998), such treatments are shown only valid with a coastal less variability as shortest non tropical coasts.
This chapter is devoted to the knowledge of the structure and manipulation of these parameters for use in Propagation and Loss Models presented in Chapters 3 and 5.
12
2.1 Temperature & SalinityOne of the main features of the temperature distribution at sea is to be your average vertical gradient in absolute value, much higher than the average horizontal gradient. At the equator, for example, the temperature can fall 25oC, on the surface, 5oC at the depth of 1,000 m. But it would require a shift of
5,000,000 m for the North or the South, from the equator to find a temperature of 5oC. (Diegues, 1974)
The raw data of temperature and salinity of the entire Brazilian Continental Margin were provided by the Brazilian National Oceanographic Data Bank (BNDO), which is operated by the Brazilian Navy Hydrographic Center (CHM), which is subordinate to the Brazilian Navy Directorate of Hydrography and Navigation (DHN), corresponding to approximately 2,000,000 information collected, received in the following format:
DATE - LATITUDE - LONGITUDE - DEPTH - TEMPERATURE - SALINITY
Latitude and longitude are given in degrees, minutes and seconds, the depth in meters, the temperature in degrees Celsius, and salinity in parts per thousand.
13
Figure 2 - Division of the Brazilian coast were used to built the database
14
To use the data in Propagation and Loss Models initially was made conversion date, preserving only the information about the month in which it was collected.
Because there are few data available, the system uses the calculation of quarterly averages, which represent the seasons at south hemisphere, that is, the months of December, January, and February are the ones that make up the summer, and so on.
Values were converted latitude and longitude in degrees, minutes and seconds to degrees with thousandth of accuracy, that is, the value supplied from 2335'30S was converted to -23.592.
Depth values were tabulated in multiples of five meters, and this value resulting from tests with various intervals greater than five meters which did not provide satisfactory results for the reassembly of the average profiles of temperature and salinity, because they could not properly represent the vertical variability related to seasonal thermoclines and the eect generated by the mouths of rivers and sea arms.
After this patterning, there was a separation of data regions as shown in Figure 2, with the intention of reducing the processing time because the system reads all the database to select which will be used in processing, based on the studies of Union Scale Macrodiagnostic of the Brazilian Coastal Zone (MMA, 1996).
Due to the models using the average values of parameters oceanographic not made any additional treatment in the database of temperature and salinity to minimize the probability of exclusion of significant data in the calculation of the average values during processing.
The system used for the establishment of oceanographic parameters to be processed, a technique that could be called moving average (Aguiar, 2004), which is to obtain averages around certain geographical points, which in this case is the trajectory of the wave.
15
The values of the database used to calculate the mean are those which are contained in a square centered on the specific point and with side equal to one nautical mile (Figure 3).
Figure 3 - Schematic illustrating the areas used to obtain mean values for each point () from the database
The technique used for obtaining the mean values causes two distant points of a nautical mile present dierent values of temperature and salinity, thus ensuring a better characterization of the oceanic environment and therefore aspects of acoustic propagation.
16
The amount of these points, which will be used by the model propagation depends exclusively on the measured distance so that it calculates the wave propagation, and each of these two points determines a faixa (track), that is, a portion of the ocean which have their interpolated values.
Figure 4 - Temperature average profiles (red line) and reconstructed (blue line) temperature of a track end
0 5 10 15 20 25 30
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Temperature Profile
Degrees Celsius [C]
Dept
h [m
]
Direction 0
Such as variations in temperature and salinity are known behavior in a profile (such as the presence of thermoclines), its not necessary maintain during processing the
17
information associated with all depths, so information is stored TS specific depths that can reconstruct the profile (Figures 4 to 6).
Figure 5 - Salinity graphics of average profile (red line) and reconstructed profile based on average (blue line) of a track end
34 34.5 35 35.5 36 36.5 37 37.5
0
500
1000
1500
Salinty Profile
Parts Per Thousand [/oo]
Dept
h [m
]
Direction 0
The values of these depths are determined by an exponential sequence which is calculated from the maximum depth of the profile, thereby establishing what appears as corte (cut) in the programming lines, the region between two cuts is defined as a camada (layer) that has constant gradient.
Through testing, it was determined that the optimal number of cuts is between 6 and 9, depending on the maximum depth.
18
This exponential sequence was created so that they could preserve the characteristics of oceanic features (mixing layer and thermoclines) and could faithfully represent them.
Figure 6 - Temperature graphics of XBT profile (magenta line), average profile (red line) and reconstructed profile based on XBT (blue line) from a track end
The model in question obtains average values of oceanographic parameters every mile, away from the point where the wave generated in the directions north, east, south and west.
19
Interpolating these values, it can create a discrete and heterogeneous ocean, which will spread.
As it is a discrete analysis of acoustic propagation was necessary to establish a sampling interval, which is called the passo (step), after exhaustive tests had its optimum value set at about 34 meters.
A step value greater than 34 meters would allow a beam during propagation go through more than one layer, resulting in a failure in processing, and a little step would generate gains less than outweighed the overhead of processing time.
At this point it may ask what was the dierence between the innovative step approach of the range dependent classical approach, but we must consider the fact that the second approach requires several processing steps deem it with the same values of oceanographic parameters (see Chapter 3).
This fixed horizontal step will increase the time during the rays trajectory processing and determining losses during propagation, ensuring that oceanographic conditions are changed in each iteration, generating a discrete and heterogeneous ocean.
In addition, the propagation model developed may accept as average temperature profile for all areas, a value obtained by an expendable bathythermograph (XBT), which considerably improves the results of the detection prediction (Figure 6).
Using XBT does not compromise the heterogeneity inherent of this system, because even if the temperature profile is unique to all directions and distances, information of salinity and facies remain dierent at each passo in the processing.
20
% *************************************************************% OCEANOGRAPHIC FILE% from a S,T,Z,M,lat,long archive% (S in parts per thousand, T in Celsius and Z in meters)% (M month (dec. is 0), lat in g.ggg, long in g.ggg)disp('*** OCEANOGRAPHIC DATA ***');myarea=input('Input the area name where you stay: ','s');eval(['load ' myarea '.log'])eval(['oceano= ' myarea '(:,:);'])[...]% *************************************************************% POSITION AND COURSE DATA % will come direct from GPS device, on real-time operationdisp('*** POSITION AND COURSE DATA ***');input('Input latitute (D.DD, S is negative) ');lat = ans;lat = fix(lat*100)/100;input('Input longitude (D.DD, W is negative) ');long = ans;long = fix(long*100)/100;%input('Course of the ship (000 to 359)? ');%Rumo = ans;Rumo = -1; % if information is unknown% *************************************************************% GRAPHICS DATA - H-Fix increment model(r)dist = 18/EQP;% Distance to plot in nautical miles; multiple of 6% *************************************************************% GRAPHICS DATA - Number for results - Auxiliary step tablen_Qinter = 4;for Qinter = 1:n_Qinter Dir(Qinter) = 360*(Qinter-1)/n_Qinter; NSstep(Qinter) = cos(Dir(Qinter)*pi/180)/60; % related with n_faixas EWstep(Qinter) = sin(Dir(Qinter)*pi/180)/60; % one mile stependdsup = zeros(1,n_Qinter);dcp = zeros(1,n_Qinter);
21
dcs1 = zeros(1,n_Qinter);dcs2 = zeros(1,n_Qinter);dcs3 = zeros(1,n_Qinter);Ampp = zeros(1,n_Qinter);% *************************************************************% SELECT DEPTH DATA FOR 4 DIRECTIONS (n_Qinter = 4)EtSize = size(srf5); % lat, long, depthEtSize = EtSize(1);EtGrid = 0.08; % in degrees -> 4.8 NMAuxBat1 = 1;AuxBat2 = 1;for Et = 1:EtSize if srf5(Et,1) >= lat-EtGrid & srf5(Et,1) < lat+EtGrid if srf5(Et,2) >= long-2*dist/60 & srf5(Et,2) < long+2*dist/60 Bat1(AuxBat1,:) = srf5(Et,:); AuxBat1 = AuxBat1 + 1; end end if srf5(Et,1) >= lat-2*dist/60 & srf5(Et,1) < lat+2*dist/60 if srf5(Et,2) >= long-EtGrid & srf5(Et,2) < long+EtGrid Bat2(AuxBat2,:) = srf5(Et,:); AuxBat2 = AuxBat2 + 1; end end endAuxBat1 = AuxBat1 - 1; AuxBat2 = AuxBat2 - 1;% *************************************************************[...]% *************************************************************% GRAPHICS DATA - H-Fix increment model(r)n_faixas = dist/0.6 + 1; % 0.01 degrees length each; must be an intergern_passos = 32*(n_faixas-1); dx = 1852*dist/n_passos; % better less than 36 metersdistM = n_passos*dx; % distance in metersn_cortes = 6 + Acr; n_camadas = n_cortes - 1;
22
n_raios = abs(fix((EQP^3)*(angulo_I-angulo_F))); % 1 to passive and 0.125 to active% *************************************************************% AREA RANGE DATAsquad = 0.5; % in NM% *************************************************************% GRAPHICS CHOICESGRC = 1; %- only echo excess or emission level.... normal choice....%GRC = 5; % - all graphics% *************************************************************% MONTH DATA - arranging in seasons because the poor databasedisp('*** MONTH REFERENCE ***');input('Change the actual month? (0-no / 1-yes) ');otmes = ans;if otmes ~= 1 juliano=datenum(date); mes = str2num(datestr(juliano,5)); else input('Choose the month (1-JAN / 2-FEB /... / 12-DEC): '); mes = ans;endif mes == 12 | mes == 1 mes = 2;endif mes == 3 | mes == 4 mes = 5;endif mes == 6 | mes == 7 mes = 8;endif mes == 9 | mes == 10 mes = 11;end% *************************************************************[...]% *************************************************************% CHECK DATA if min(sbZ(Qinter,:)) > 0
23
% REFINE THE T,S,Z DATA - keep off blanks & average values for faixa = 1:n_faixas% *************************************************************% AUXILIARY LAB VARIABLES count = 1; for prof = 1:fix(max(oZ(:,faixa)))+1 if oE(prof,faixa) ~= 0 lS(count,faixa) = oS(prof,faixa)./oE(prof,faixa); lT(count,faixa) = oT(prof,faixa)./oE(prof,faixa); lZ(count,faixa) = oZ(prof,faixa); count = count+1; end end count = count - 1;% *************************************************************% CHECK DATA if count == 0 error('The oceanographic database do not have enough information to continue - #DB') end% *************************************************************% REBUILT THE Z DATA rZ(:,faixa) =sbZ(Qinter,faixa)*rlZ;% *************************************************************% REFINE THE T,S DATA for corte = 1:n_cortes flagSTZ = 0; for auxZ = 2:count if lZ(auxZ,faixa) >= rZ(corte,faixa) & flagSTZ == 0 rS(corte,faixa)=lS(auxZ-1,faixa)-(lZ(auxZ-1,faixa)-rZ(corte,faixa))*(lS(auxZ-1,faixa)-lS(auxZ,faixa))/(lZ(auxZ-1,faixa)-lZ(auxZ,faixa)); rT(corte,faixa)=lT(auxZ-1,faixa)-(lZ(auxZ-1,faixa)-rZ(corte,faixa))*(lT(auxZ-1,faixa)-lT(auxZ,faixa))/(lZ(auxZ-1,faixa)-lZ(auxZ,faixa)); flagSTZ = 1; end end
25
if rS(corte,faixa)== 0 & corte > 2 rS(corte,faixa) = 2*rS(corte-1,faixa)-rS(corte-2,faixa); end if rT(corte,faixa)== 0 & corte > 2 rT(corte,faixa) = 2*rT(corte-1,faixa)-rT(corte-2,faixa); end end if XBT == 1 for corte = 1:n_cortes flagSTZ = 0; if max(Tbt(:,1)) > 50 % first column is depth (Z,T,...) for auxZ = 2:count2 if Tbt(auxZ,1) > rZ(corte,faixa) & flagSTZ == 0 rT(corte,faixa)=Tbt(auxZ-1,2)-(Tbt(auxZ-1,1)-rZ(corte,faixa))*(Tbt(auxZ-1,2)-Tbt(auxZ,2))/(Tbt(auxZ-1,1)-Tbt(auxZ,1)); ZT = 1; flagSTZ = 1; end end else % second column is depth (T,Z,...) for auxZ = 2:count2 if Tbt(auxZ,2) > rZ(corte,faixa) & flagSTZ == 0 rT(corte,faixa)=Tbt(auxZ-1,1)-(Tbt(auxZ-1,2)-rZ(corte,faixa))*(Tbt(auxZ-1,1)-Tbt(auxZ,1))/(Tbt(auxZ-1,2)-Tbt(auxZ,2)); ZT = -1; flagSTZ = 1; end end end end end end% *************************************************************% CREATE THE MATRIXES - s,t and z Sij = zeros(n_cortes,n_passos); Tij = zeros(n_cortes,n_passos);
26
Zij = zeros(n_cortes,n_passos); for corte = 1:n_cortes if EQP == 2 for faixa = 1:n_faixas-1 Sij(corte,1+(faixa-1)*fix(n_passos/(n_faixas-1)):faixa*fix(n_passos/(n_faixas-1)))=linspace(rS(corte,faixa),rS(corte,faixa+1),fix(n_passos/(n_faixas-1))); Tij(corte,1+(faixa-1)*fix(n_passos/(n_faixas-1)):faixa*fix(n_passos/(n_faixas-1)))=linspace(rT(corte,faixa),rT(corte,faixa+1),fix(n_passos/(n_faixas-1))); Zij(corte,1+(faixa-1)*fix(n_passos/(n_faixas-1)):faixa*fix(n_passos/(n_faixas-1)))=linspace(rZ(corte,faixa),rZ(corte,faixa+1),fix(n_passos/(n_faixas-1))); end else for faixa = 1:n_faixas-1 Sij(corte,1+(faixa-1)*fix(n_passos/(n_faixas-1)):faixa*fix(n_passos/(n_faixas-1)))=linspace(rS(corte,n_faixas+1-faixa),rS(corte,n_faixas-faixa),fix(n_passos/(n_faixas-1))); Tij(corte,1+(faixa-1)*fix(n_passos/(n_faixas-1)):faixa*fix(n_passos/(n_faixas-1)))=linspace(rT(corte,n_faixas+1-faixa),rT(corte,n_faixas-faixa),fix(n_passos/(n_faixas-1))); Zij(corte,1+(faixa-1)*fix(n_passos/(n_faixas-1)):faixa*fix(n_passos/(n_faixas-1)))=linspace(rZ(corte,n_faixas+1-faixa),rZ(corte,n_faixas-faixa),fix(n_passos/(n_faixas-1))); end end Sij(corte,n_passos) = Sij(corte,n_passos-1); Tij(corte,n_passos) = Tij(corte,n_passos-1); Zij(corte,n_passos) = Zij(corte,n_passos-1); end% ************************************************************
27
Facies, in the context of geological oceanography, are all the lithological characteristics observable on a rock seen from the point of view of its genesis or even the set of structural and mineralogical characteristics of a rock (Belov & Komarov, 1998).
The geological database consists of approximately 2,500 samples, which originally had, besides the geographical coordinates of the place to get, the percentages of clay, silt, sand and gravel and its sample percentage analysis.
From this database we created a second database also geographically referred with values of density of the sample, and velocity of sound propagation in the sample, based on the values in the Table 1 (Clay & Medwin, 1977; Muehe, 1994).
28
2.2 FaciesOn the bottom of the sea lay a relatively soft layer that reaches on average 1-2 km thick, like a huge carpet. It consists of material from various sources, carried by rivers, transferred to remote areas by
ocean currents, scattered by the waves, sometimes coming from remains of pelagic animals, or even meteorite that reached Earth's atmosphere, and volcanic eruptions. This rug is made of
unconsolidated sediments, and below it there is another layer, has consolidated over millions of years. (Diegues, 1974)
Table 1 - Values of density and speed of sound propagation in sediments
DENSITY SOUND SPEED PROPAGATION
Clay 1,420 g/cm3 1,505 m/s
Silt 1,430 g/cm3 1,519 m/s
Sand 1,980 g/cm3 1,742 m/s
Gravel 2,030 g/cm3 1,836 m/s
This second database is operated during the processing of the templates using the procedure previously described for moving average to ensure propagation in an ocean discrete and heterogeneous.
The latitude and longitude values were treated in the same manner as described in Section 1 of this chapter.
If the system does not find enough data to get the values it assigns local average values of 1,820 g/cm and 1,675 m/s at that point, that these values represent the average global values on the Brazilian continental shelf.
29
for faixa = 1:n_faixas fRo(faixa) = fRo(faixa)./fE(faixa); fC(faixa) = fC(faixa)./fE(faixa); end% *************************************************************% CREATE LINE WITH VALUES OF fRo and fC RoFi = zeros(n_passos,1); CFi = zeros(n_passos,1); for faixa = 1:n_faixas-1 if EQP == 2 R o F i ( 1 + ( f a i x a - 1 ) * f i x ( n _ p a s s o s /( n _ f a i x a s - 1 ) ) : f a i x a * f i x ( n _ p a s s o s /(n_faixas-1)))=linspace(fRo(faixa),fRo(faixa+1),fix(n_passos/(n_faixas-1))); C F i ( 1 + ( f a i x a - 1 ) * f i x ( n _ p a s s o s /( n _ f a i x a s - 1 ) ) : f a i x a * f i x ( n _ p a s s o s /(n_faixas-1)))=linspace(fC(faixa),fC(faixa+1),fix(n_passos/(n_faixas-1))); else R o F i ( 1 + ( f a i x a - 1 ) * f i x ( n _ p a s s o s /( n _ f a i x a s - 1 ) ) : f a i x a * f i x ( n _ p a s s o s /(n_faixas-1)))=linspace(fRo(n_faixas+1-faixa),fRo(n_faixas-faixa),fix(n_passos/(n_faixas-1))); C F i ( 1 + ( f a i x a - 1 ) * f i x ( n _ p a s s o s /( n _ f a i x a s - 1 ) ) : f a i x a * f i x ( n _ p a s s o s /(n_faixas-1)))=linspace(fC(n_faixas+1-faixa),fC(n_faixas-faixa),fix(n_passos/(n_faixas-1))); end end RoFi(n_passos) = RoFi(n_passos-1); CFi(n_passos) = CFi(n_passos-1);% *************************************************************% Z AXIS zf_max = max(fix(Zij(n_cortes,:))+1); zfi_max = fix(Zij(n_cortes,:))+1; eixoZ = linspace(0,zf_max-1,zf_max); profundi = zeros(n_camadas+1, 2); % *************************************************************
31
While executing this model, it was noted the need for a separate base bathymetric for processing the propagation model.
Initially, it was attempted to use the maximum depth of the profile T-S chosen to obtain a moving average, which revealed an error due to variability of values that occur in continental shelf regions and submerged mountains chains.
A bathymetric a grid, with an interval of 4.8 NM, was built from the maximum depth profiles T-S, and based on this grid the system find the local depth for process the models.
The values of latitude and longitude in this grid are stored in degrees with precision to thousandths.
Despite all efforts, was not yet available in academia a georeferred grid with better precision for use in this system, mostly because this kind of data is classified.
32
2.3 DepthThe oceans are deposited in basins embedded in the surface of the earth. The basin is solid
container in which it is contained the liquid mass. [...] From the shore, the bottom begins to fall softly. Here is the beginning of the continental shelf, similar to an expansive terrace that surrounds all
continents. Has an average slope of 1:1,000. [...] The end of the continental shelf is indicated by a sudden and sharp increase in the slope of the bottom (between 1:4 and 1:6) called the platform edge.
(Diegues, 1974)
% *************************************************************% CHECK DATAif AuxBat1 == 0 || AuxBat2 == 0 error('The bathymetric database do not have enough information to continue - #BT')end% *************************************************************% DEPTH NS-EWfor bns = 1:AuxBat2/2 BatNS(bns,1) = Bat2(bns,1); BatNS(bns,2) = Bat2(bns,3)-(Bat2(bns,3)-Bat2(bns+AuxBat2/2,3))*(Bat2(bns,2)-long)/EtGrid;endfor bew = 1:2:AuxBat1 BatEW((bew-1)/2+1,1) = Bat1(bew,2); BatEW((bew-1)/2+1,2) = Bat1(bew,3)+(Bat1(bew,3)-Bat1(bew+1,3))*(Bat1(bew,1)-lat)/EtGrid;endcsbew = 1;for ib1 = 1:fix(AuxBat1/2 - 1) for ib2 = BatEW(ib1,1):0.01:BatEW(ib1+1,1)-0.01 sbew(csbew,1)= fix(ib2*100)/100; sbew(csbew,2)= BatEW(ib1,2) - (BatEW(ib1,1)-ib2)*(BatEW(ib1,2)-BatEW(ib1+1,2))/(BatEW(ib1,1)-BatEW(ib1+1,1)); csbew = csbew +1; endendcsbns = 1;for ib1 = 1:fix(AuxBat2/2 - 1) for ib2 = BatNS(ib1,1):0.01:BatNS(ib1+1,1)-0.01 sbns(csbns,1)= fix(ib2*100)/100; sbns(csbns,2)= BatNS(ib1,2) - (BatNS(ib1,1)-ib2)*(BatNS(ib1,2)-BatNS(ib1+1,2))/(BatNS(ib1,1)-BatNS(ib1+1,1)); csbns = csbns +1; endend
33
sbM1 = max(sbns(:,2));sbM2 = max(sbns(:,2));sbM3 = max([sbM1 sbM2]);Acr = 0;if sbM3 > 200 Acr = 1;endif sbM3 > 400 Acr = 2;endif sbM3 > 600 Acr = 3;endif sbM3 > 800 Acr = 4;endif sbM3 > 1000 Acr = 5;end% *************************************************************
34
2.4 Others ParametresThe waves formed within a zone of atmospheric turbulence, by the wind are called sea. The sea have
short crests, the direction of propagation is variable and confuse, the heights are irregular and variable lengths are fairly short. [...] As the sea move away from their place of origin, spreading to
remote areas where no longer felt the effects of wind that originated, its characteristics will be changing, slowly easing up. Denominate this case, swell. (Diegues, 1974)
During system startup, the user has to insert the values of sea state and wind speed, because these parameters directly influence the surface scattering.
Although there is a relationship between these parameters, the two values are requested to minimize possible errors of observation, since the user's perception about the state of the sea may be impaired due pitch and roll, thereby influencing decisively the quality of the result model.
From the information of the state of the sea can get the values for the wind speed and wave height by the following formulas (Apel, 1987):
Ws = 2.2966*SSB + 1.3412 [m/s] (1)
35
H = 0.6042*(SSB)2 + 0.5696*SSB + 0.7190 [ft] (2)
Wherein:
WS = wind speed, in m/s;
H = wave height, in feet; and
SSB = sea state, in the Beaufort scale.
If there is inconsistency between the sea state and wind speed, the system assumes an average value between the inserted and those obtained by the Formula 1.
The sound speed in water, fundamentally due parameter of temperature and salinity is calculated by Medwins formula (Clay & Medwin, 1977):
c = 1,449.2 + 4.6*T - 0.055*T + 0.00029*T + (1.34 - 0.010*T)*(S - 35) + 1.55.10-5**z [m/s] (3)
Wherein:
c = propagation speed of sound, in m/s;
T = temperature, in C;
S = salinity, in parts per thousand; and
z = depth, in m.
Medwin's formula was chosen because it is the only one in the range of parameter values used encompasses the variability of a coastline with a high degree of variability (Aguiar, 1998; Mikhin, 1996).
From the speed profile obtained from the database, the system can generate the graphic shown in Figure 7, which shows the values of sound speed as a function of depth in the ends of a passo (step), according to the following identification of colors from the source tuning: blue, magenta, green, and red.
36
Figure 7 - Sound speed profiles graphics generated by the system, in the ends of a passo
1485 1490 1495 1500 1505 1510 1515 1520 1525 1530 1535
0
50
100
150
200
250
300
350
400
450
500
Sound Speed [m/s]
Dept
h [m
]
Sound Speed Profiles Direction 0
The density of the water is required for the determination of the reflection coecient, it is calculate using the following formula (apud Robinson & Lee, 1994):
= 999.907 + 0.8149*S - 0.000482*S2 + 0.0000068*S3 [g/cm] (4)
Wherein:
= density of sea water in g/cm; and
S = salinity in parts per thousand.
37
% *************************************************************% ENVIRONMENTAL DATAdisp('*** METEOROLOGICAL DATA ***');input('Input sea state in Beaufort scale (0 to 12): ');beaufort = ans;w_ms = 2.2966*beaufort + 1.3412;input('Input wind Speed in knots: ');w_kn = ans;w_ms1 = w_kn*1852/3600;beaufort1 = fix((w_ms1 - 1.3412)/2.2966);if beaufort > beaufort1 beaufort = fix((beaufort + beaufort1)/2);endw_ms = 2.2966*beaufort + 1.3412;h_ft = 0.6042*beaufort^2 - 0.5696*beaufort + 0.719;% *************************************************************% AIR DATAro_ar = 1e-006;c_ar = 340; % *************************************************************[...]% *************************************************************% CREATE THE MATRIX c - Medwin formula C i j = 1449.2+4.6.*Tij-0.055.*(Tij.^2)+0.00029.*(Tij.^3)+(1.34-0.010.*Tij).*(Sij-35)+1.55.*0.00001*(1+0.001.*Sij).*Zij;% *************************************************************% CREATE THE MATRIX ro - Roij = 1000 + (-0.093 + 0.8149.*Sij - 0.000482.*Sij.^2 + 0.0000068.*Sij.^3);% *************************************************************
38
Propagation Model3
0 1 2 3 4 5 6 7 8 9
0
500
1000
1500
Ray Tracing
Distance [NM]
Dept
h [m
]
Direction 0
Knowing the vertical structure of the sound speed becomes
possible to establish a propagation model of the sound beam that will indicate, for their
part, quiet zones, scope and other elements that concern us know.
(Diegues, 1974)
Models based on Rays Theory were used extensively during the second half of the twenty century, however, lost ground to the models based on techniques that provided faster processing and function not obtain accurate results for the propagation at low frequencies.
Despite this, the models based on Rays Theory still are better suited for use in short distances, or when there are abrupt large variations of the characteristics of the environment in which the wave propagates.
The trajectory of the rays depends primarily on the eect of refraction and the boundary conditions on the surface and the bottom.
As will be seen in Chapter 5, the propagation model is the basis for the calculation of the losses, which provides the use of a heterogeneous ocean.
Robert J. Urick, one of the greatest scholars of underwater acoustics for naval use, on page 176 of his book Principles of Underwater Sound (1983) points out that:
Rays Theory is more convenient to use at short ranges, where the high-order images rapidly die out because of reflection losses and an increasingly great distance from the field point.
Urick also defines the desirable limit (r) for use Rays Theory through the following expression:
r = H2/ (5)
Wherein H is the local depth and is the wavelength.
From Formula 5 it can be seen that for a frequency of 3.5 kHz in an area with a depth of 80 m, Rays Theory may be used to model the propagation to a distance of 8.1 NM of the source, and the value of the speed of sound in water of 1,500 m/s.
40
The system was built with the hypothesis applying basic naval sonar, for frequencies greater than 1.5 kHz, trying to provide information on an area of 10 nautical miles radius around the user, in places where the depth is greater than 50 m.
The values in Table 2 in red represent situations where the SDPS-DH should not be used, if they were not implemented model innovations, presented in Chapters 3 to 5 of this book.
Table 2 - Maximum distance (NM) to be used for propagation models based on conventional Rays Theory
f - Frequency [kHz]---------------------------------------------------------------------------
- Wavelength [m]f - Frequency [kHz]
--------------------------------------------------------------------------- - Wavelength [m]f - Frequency [kHz]
--------------------------------------------------------------------------- - Wavelength [m]f - Frequency [kHz]
--------------------------------------------------------------------------- - Wavelength [m]f - Frequency [kHz]
--------------------------------------------------------------------------- - Wavelength [m]
1.5 2.5 3.5 7.0 14.0
1.00 0.60 0.43 0.21 0.11
H - Local Depth
[m]
60 m 1.9 3.2 4.5 9.1 18.1
H - Local Depth
[m]
80 m 3.5 5.8 8.1 16.1 32.2H - Local
Depth
[m]
120 m 7.8 13.0 18.1 36.3 72.6H - Local Depth
[m]
160 m 13.8 23.0 32.3 64.5 129.0
H - Local Depth
[m] 200 m 21.6 36.0 50.4 100.8 201.6
H - Local Depth
[m]500 m 135.0 225.0 315.0 630.0 1,259.9
H - Local Depth
[m]
1,000 m 540.0 899.93 1,259.9 2,519.8 5,039.6
The limits described in the basic hypothesis are the result of research done in Brazilian Navy agencies.
The conventional Rays Theory uses the depth values where changes occur in the velocity gradient (z) as tracing limits, holding constant the oceanographic parameters regardless of the variation in the x coordinate (x).
x = z/tan(ai) (6a)
Unlike the classical model (Figure 8a), the model uses to track boundaries of the step value (x) (Figure 8b), which is considered the variation of the parameters
41
oceanographic a discrete way, obtaining the z coordinate variation (z) according to the following expression, where ai is the angle of incidence of the ray:
z = x*tan(ai) (6b)
Figure 8 - Schematic of the rays path produced by a model based on iterative z (red line) and a model based on iterative x (green line)
Depending of z value, checks whether or not, there was a change of layers, represented by dashed lines in Figure 9, and then, if reflection occurred or not.
In case of a reflection, is rectified value of z recalculated and the value of z before further processing.
During processing the information stored value of angle of incidence (i), speed of sound (c), z, x and the distance the ray traveled.
42
Figure 9 - Graphic of the rays path produced by the model
0 1 2 3 4 5 6 7 8 9
0
500
1000
1500
Ray Tracing
Distance [NM]
Dept
h [m
]
Direction 0
Suppose an environmental in which the theoretical sound wave propagation had repeated reflections on the surface and the distance between the reflection points increase continuously due to the variation of the oceanographic parameters (Figure 10).
One can note that a propagation model that constantly alter their oceanographic parameters would draw the green path as a template dependent range, which would change the parameters oceanographic each nautical mile radius would draw the red one.
43
Looking to Figure 10, it can be concluded that the use of a value of x small enough to ensure propagation in a heterogeneous ocean is essential for the correct calculation of the wave behavior (beam).
Figure 10 - Schematic path of the rays produced by the step model (green line) and for a range dependent model (red line)
In the MATLAB programming lines, we can better understand the dynamics of the model and observe the insertion of random oscillations when the reflections occur, and Figure 11 can see propagation model simplified block diagram.
These oscillations were included in the model to try to reproduce some of the best eects, encoding extremely complex, which occur in it, and the decision result of reading the texts written by Belov & Komarov (1998), and Andronov (1998).
The random fluctuations, caused among other factors by the roughness of the interface, although the small maximum values, 0.375 for the surface reflection, and 0.125 for bottom reflection, may eventually lead to a collapse in the model.
44
1 NM
Figure 11 - Basic block diagram of the Propagation Model
Calculus of z to the next step
Did reflection occur?
Did layer change
occur?
Calculus of new ray parameters
Calculus of the reflection effects and
the new z, and oscillation insertion
YY
N N
1
1
Establishment of oceanographic and ray
parameters
Establishment of oceanographic for the
next step
The collapse of the model value occurred due to the random oscillation when the angle and the oscillation have the same order of magnitude and opposite signs, causing the ai to always remain very close to zero.
45
% *************************************************************% THE RAY TRACINGfor raio = 1:n_raios % *************************************************************% RESET PARAMETERS FOR A NEW RAY for camada = 1:n_camadas profundi(camada,1) = Zij(camada,1); profundi(camada,2) = Zij(camada+1,1); end z_fundo = max(Zij(:,1)); camada1 = ca_fonte; zmin = profundi(camada1,1); zmax = profundi(camada1,2); x1 = 0; z1 = z_fonte; a1 = angulo_I + dangulo*(raio-1); c1= c_fonte; soma_ds = 0; for passo = 1:n_passos;% *************************************************************% SET NEW PARAMETERS FOR THE NEXT STEP for camada = 1:n_camadas profundi(camada,1) = Zij(camada,passo); profundi(camada,2) = Zij(camada+1,passo); end zmin = profundi(camada1,1); zmax = profundi(camada1,2); z = Zij(:,passo); z = [z;z_fonte]; c = Cij(:,passo); c = [c;c_fonte]; dc = dcij(:,passo); z_fundo = max(Zij(:,passo));% *************************************************************% PREVIEW WHERE THE RAY IS GOING TO (Z) if a1 == 0 a2 = -1*asin(dc(camada1)/c1); dz = dx*tan(a2); c2 = c1 + dc(camada1)*dz; else
46
end else % z2 pass through the surface layer dz2 = z2-zmax; dz2 = dz2*c1/c(camada1+1); z2 = zmax + dz2; dz = z2 - z1; c2 = c(camada1+1) + dc(camada1+1)*(z2-z(camada1+1)); a2 = acos(cos(a1)*c2/c1)*sign(a1) + AngSctS; if (cos(a1)*c2/c1)>1 a2 = -a1 + AngSctS; end camada1 = camada1 + 1; end end end% *************************************************************% GOING TO DOWNER LAYER if z2 >= zmax% *************************************************************% NO BOTTOM REFLECTION if z2 < z_fundo if camada1 == n_camadas error('Problems in the ray tracing, check your data! - #RT') end dz2 = z2-zmax; dz2 = dz2*c1/c(camada1+1); z2 = zmax + dz2; dz = z2 - z1; c2 = c(camada1+1) + dc(camada1+1)*(z2-z(camada1+1)); a2 = acos(cos(a1)*c2/c1)*sign(a1); if (cos(a1)*c2/c1)>1 a2 = 0; end camada1 = camada1 + 1;% *************************************************************% BOTTOM REFLECTION else z2 = 2*z_fundo-z2;% this jump may cause a visual distortion
48
RefFun(passo,raio) = 1; k = 2*pi*freq/c(n_camadas); AngSctB = 0.5*(rand(1)-.5)*(pi/180)*k/120; % max 0.125 variation if z2 >= zmin c2 = c(n_camadas) + dc(n_camadas)*(z2-z(n_camadas)); a2 = -acos(cos(a1+aZi(passo))*c2/c1)*sign(a1+aZi(passo)) + AngSctB + aZi(passo); if (cos(a1+aZi(passo))*c2/c1)>1 a2 = -a1 + AngSctB + 2*aZi(passo); end else % z2 pass through the bottom layer if camada1 == 1 error('Problems in the ray tracing, check yuor data! - #RT') end dz2 = zmin-z2; dz2 = dz2*c1/c(camada1-1); z2 = zmin-dz2; dz = z2 - z1; c2 = c(camada1-1) +dc(camada1-1)*(z2-z(camada1-1)); a2 = -acos(cos(a1+aZi(passo))*c2/c1)*sign(a1+aZi(passo)) + AngSctB + aZi(passo); if (cos(a1+aZi(passo))*c2/c1)>1 a2 = -a1 + AngSctB + 2*aZi(passo); end camada1 = camada1 - 1; end end end% *************************************************************% CHECK Z DATA - to prevent errors caused by random angles if z1 < 0 z1 = 0; end if z1 > z_fundo z1 = z_fundo; end% *************************************************************
49
% ARCHIVE NECESSARY DATA raio_x(passo) = x1; raio_y(passo, raio) = z1; raio_a(passo, raio) = a1; raio_c(passo, raio) = c1; soma_ds = soma_ds + (dz*dz + dx*dx)^(0.5); raio_s(passo, raio) = soma_ds; % *************************************************************% PREPARE FOR NEXT STEP x1 = x2; z1 = z2; a1 = a2; c1 = c(camada1) + dc(camada1)*(z2-z(camada1)); endend% *************************************************************
50
3.1 Refraction ModelAnother mitigating factor is generated by the geometric effects on the sound rays projected from the
source. In this case, the loss in intensity caused by the scattering or dispersion of the rays is proportional to the square of the distance. (Diegues, 1974)
Refraction is a phenomenon that occurs when a ray changes medium, and the mediums have characteristics with similar values (c1c2 & 12), so that the direction of propagation will change (Figure 12).
There is, actually, no loss of energy to be applied because of the refraction what occurs is a change in the value of the sound pressure, which has the unit watts per square meter (W/m), due to the dispersion of ray in refraction (Hall, 1987; Parente, 1997).
Snell-Descartes Law statement: the ratio of the sine of the incident angle (1) and the sine of the refraction angle (2) is constant, and this constant is equal to the refraction index n21, for a given wavelength (Diegues, 1974).
51
0 1 2 3 4 5 6 7 8 9
0
100
200
300
400
500
600
700
800
900
1000
Ray Tracing
Distance [NM]
Dept
h [m
]
Direction 180
The variation of sound intensity is calculated based on the Rays Theory, with the framework of their calculations the path traveled by the rays, which delimit a beam in which losses occur due to the spread, this path being defined primarily by refraction.
Figure 12 - Ray refraction when it passes from one less refractive medium (1) to a more refractive medium (2).
The Propagation and Loss Models developed, unlike models using triangular meshes has as its basis the paths of the rays mesh and fixed horizontal step (Figure 13).
sin(1) = n21 = n2 (7)sin(2) n1
Wherein:
1 = incident angle (angle the incident ray makes with the normal);
52
medium
medium
2 = refracted angle (angle that the refracted ray makes with the normal);
n21 = relative refraction index;
n2 = refraction index of medium 2; and
n1 = refraction index of medium 1.
If considered only the eect of refraction would be right to say that A0*P0 = A1*P1 = A2*P2 = A3*P3 = ... = An*Pn, according to the Conservation of Energy Law, which does not characterize a loss itself.
A0, A1, A2, A3, and An are the areas of spherical caps whose center the origin of the sound pulse with a ray equal to the distance traveled by the wave.
In the model, is used only on the area of spherical cap circle base for the calculations.
The area A0 is computed with the radius as a distance of 1 meter from the source, which enables use the value of the sonar power measured converted to sound pressure as P0.
The model was built based on spherical dispersion alone; programing lines were not made for the specific case of waveguide, when the ray became confined between two parallel planes and presents cylindrical dispersion characteristics.
During the preparation of the SDPS-DH was discussed incessantly the need or not to generate a special algorithm for cylindrical dispersion, which was not necessary because the algorithm developed for spherical dispersion covers cases where there waveguide.
53
Figure 13 - Schematic of intensity variation sound
The cylindrical dispersion is nothing more than the special case of spherical dispersion, in which has specific boundary conditions.
54
3.2 Reflection ModelThe sound propagation depends on the local depth, of the sediments covering the seabed, and sea conditions. The mud, for example, reflects sound very badly, while the sandy bottoms absorb very little sound wave, constituting a great reflection element. In a sea very choppy also will effect the
propagation of incipient form, one cannot take advantage of all the possibilities of the device. (Diegues, 1974)
Reflection occurs when a wave meets along its trajectory, an interface in which the dierence between the medium densities is very high (Hall, 1987).
Let us take as a basis to Figure 14, in which we have an incident ray I, a reflected ray R, and a transmitted ray T, and the product of the propagation speed of the density of the medium 1 is much lower than that of the medium 2 (c1*1 c2*2).
We can observe in the scheme that part of the energy of the beam I is transmitted to medium 2, which generates the ray T, and other part of the energy remains in the first half, leading the ray R, the angles i and r has the same value when measured relative to normal, and t is smaller than i due to c1*1 be significantly lower than c2*2.
56
0 1 2 3 4 5 6 7 8 9
0
100
200
300
400
500
600
700
800
900
1000
Ray Tracing
Distance [NM]
Dept
h [m
]
Direction 180
There is a value of i from which it is no longer transmitted energy to the medium 2, this angle value is called the critical angle or grazing angle.
Figure 14 - Scheme of the ray reflection in the seabed
The Rayleigh formulas (apud Urick, 1983) for the reflection coecient to be applied to the sound pressure is (RR12)2, whereas in the model angles are measured relative the horizontal, we have:
RR12 = c2*2*sin(i) - c1*1*sin(t) (8) c2*2*sin(i) + c1*1*sin(t)
Wherein:
1 = density of the medium 1, in g/cm;
c1 = sound speed propagation in the medium 1, in m/s;
2 = density of the medium 2, in g/cm;
57
medium
medium
c2 = sound speed propagation in the medium 2, in m/s;
i = angle of incident ray, in rd;
r = angle of reflected ray, in rd; and
t = angle of transmitted ray, in rd.
The value of the grazing angle (gzg):
gzg = acos(c1/c2) [rd] (9)
These formulas (8 & 9) are applied to bottom and surface reflections.
58
% *************************************************************% SURFACE REFLECTION crit_a1 = acos(raio_c(passo,raio)/c_ar); % grazing angle ang_i1 = acos(cos(raio_a(passo,raio))); ang_t1 = c_ar*ang_i1/Cij(1,passo); RR_10 = -(ro_ar*c_ar*sin(ang_i1)-(Roij(1,passo))*Cij(1,passo)*sin(ang_t1))/(ro_ar*c_ar*sin(ang_i1)+(Roij(1,passo))*Cij(1,passo)*sin(ang_t1)); if RR_10 > 1 | RR_10 < 0.9 error('Problems to build the Surface Reflection Coefficient - #SR') end if crit_a1 >= ang_i1 RR_10 = 1; end% *************************************************************[...]% BOTTOM REFLECTION crit_a2 = acos(raio_c(passo,raio)/CFi(passo)); % grazing angle ang_i2 = acos(cos(raio_a(passo,raio))); ang_t2 = CFi(passo)*ang_i2/Cij(n_cortes,passo); RR_12 = (RoFi(passo)*CFi(passo)*sin(ang_i2)-(Roij(n_cortes,passo))*Cij(n_cortes,passo)*sin(ang_t2))/(RoFi(passo)*CFi(passo)*sin(ang_i2)+(Roij(n_cortes,passo))*Cij(n_cortes,passo)*sin(ang_t2)); if RR_12 > 0.5 | RR_12 < 0 error('Problems to build the Bottom Reflection Coefficient - #BR') end if crit_a2 >= ang_i2 RR_12 = 1; end% *************************************************************
59
Sonar Parameters Model
4The terms of the sonar equation
are called sonar parameters, which shows dierence between active and passive modes, due
the distance traveled by the sound wave. (Aguiar, 2005)
The sonar parameters are inherent characteristics of: the detection equipment, the environment where the propagation occurs, and the target to be detected.
The sonar equation using active sonar is (Urick, 1983):
EE = SL - 2*TL + TS - (NL - DI + DT) [dB] (10)
Wherein:
EE = echo excess, value that defines the amount of energy that is received after reflecting on target, expressed in dB.
SL = source level, value that defines the power of sonar equipment, measured at 1 meter distance from the source, expressed in dB re 1 Pa.
TL = transmission loss, value that defines the amount of energy lost during transmission, expressed in dB.
TS = target strength, value that defines the target reflectivity capacity, expressed in dB.
NL = noise level, is the sum of the values of self and environmental noises (NLS + NLE), expressed in dB re 1 Pa.
DI = directivity index, is the value for the power of discrimination in marking detection equipment, expressed in dB.
DT = detection threshold, is the value at which the sonar equipment is able to detect the target, expressed in dB.
The sonar equation for passive sonar is (Urick, 1983):
SE = SL - TL + TS - (NL - DI + DT) [dB] (11)
Wherein:
61
SE = signal excess, value that defines the amount of energy that is received due to noise generation from a target, expressed in dB.
Figure 15 - Basic block diagram of the Sonar Parameters Model
Calculus of active sonar parameters
Establish the equipment parameters
Is it in active mode?
Establish the oceanographic
parametersEstablish the target
parameters
Calculus of passive sonar parameters
Calculus of environmental noise
N
Y
62
4.1 EquipmentThere are countless tools for scientific research or practical application that rely on knowledge of
sound propagation in the sea. The sound emissions generated by ultramodern electronics are used in signaling underwater, under the most varied forms. The sound is used for depth measurement, the
distance determination and detection of underwater objects such as submarines or fish stocks. Hence their use in monitoring the trajectory of objects or instruments; measurement distance information
from objects drifting or installed on the seabed. (Diegues, 1974)
The parameters SL, DI, DT, and NLs are inherent of the detection equipment, the platform that transports it, and the operator experience, they are being supplied to the prediction system at the moment you insert the vessel or submarine code with which it will perform the processing.
A parameter often used in the Brazilian Navy is the Figure of Merit (FoM), which is expressed by (IPqM, 2000):
FoM = SL - (NLs - DI + DT) [dB] (12)
This parameter, if we consider only NLs (self noise), adds the detection equipment parameters, featuring a specific kind of sonar in a specific ship.
63
Important parameters, that are not part of the equation, are: the sonar source depth, width and positioning of the sonar transducer and the central transmission frequency to active sonar, whose values are reported directly to the system.
These important parameters are loaded from a file in which the ship code is the index being accountable to it the values of: the upper and lower angles of the sound beam, the central transmission frequency, cruise speed, source level, the source depth, the self noise level, DI and DT.
Along with these values, the file also provides information on whether the ship or submarine will operate in passive or active mode.
If processing is chosen in passive mode, the system assumes the angles values are -35 and 45, for upper and lower limits of the sound beam, respectively.
In passive sensing the values of source depth, source level and center frequency of the transmission depend of the target parameters.
64
% *************************************************************% SHIPS FILEload parametros.log% *************************************************************% SHIP DATAn_navios = size(parametros); n_navios = n_navios(1);disp('*** SHIP INFORMATION ***');input('Input the Ship Code? ');codnav = ans;for navio = 1:n_navios if codnav == parametros(navio,1) p_navio = parametros(navio,:); endendEQP = p_navio(2); % 1 for passive or 2 for activeif EQP == 2 z_fonte = p_navio(3); % Transducer depth in meters angulo_I = p_navio(4); % Superior angle of the beam in degrees angulo_F = p_navio(5); % Inferior angle of the beam in degrees freq = p_navio(6); % Central Frequency in kHz; freq = freq*1000; sl_e = p_navio(7); % Projector Source Level in dB re 1 Pa else angulo_I = -35; % ref p_navio(4) angulo_F = 45; % ref p_navio(5) freq = 0;endDI = p_navio(8); % Receiving Directivity Index in dBveloc = p_navio(9); % Your standard velocity in knots[...]DT = p_navio(11); % Detection Threshold in dB% *************************************************************[...]% *************************************************************% SOURCE LEVEL FOR CALCULUSif EQP == 1 SL = sl_t; % Target Source Level (PASSIVE) else SL = sl_e; % Projector Source Level (ACTIVE)end % *************************************************************
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4.2 Environmental NoiseAnimal populations generate noise in the marine environment, thereby creating problems in the use of acoustic instruments and joined in designing record often false echoes that need to be correctly
interpreted. (Diegues, 1974)
The environmental noise level, which is part of the NL, was modeled by Robert J. Urick as described in his book Principles of Underwater Sound (1983), which analyzes among other factors the wind and sea conditions.
Being directly proportional to the sea state and conversely the central frequency can get the equation:
66
Figure 16 - Graphic of self noise versus speed, which was the basis for the equation 12
30354045505560657075
1 10 100
Freqncia [KHz]
Niv
el d
o es
pect
ro [d
B re
1P
a]
NLE = 64.782 - 8.861*log(f) + SS [dB re 1Pa] (12)
Wherein:
NLE = environmental noise level, in dB re 1 Pa.
f = central frequency, in kHz.
SS = state of the sea, on the Beaufort scale.
67
Spec
trum
Lev
el
Frequency
% *************************************************************nl_e = p_navio(10); % Self-Noise Level in dB re 1 Pa% *************************************************************[...]% *************************************************************% AMBIENT-NOISE LEVEL nl_m = 64.782 - 8.861*log(freq/1000) + beaufort; % isotropic - pg 402 Urick% *************************************************************% NOISE LEVELNL = 10*Log10(10^(nl_e/10) + 10^(nl_m/10));% *************************************************************
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4.3 TargetEspecially for the Navy Officer, considering the need for their skills on the tactic and antisubmarine
warfare. You need to know to take advantage of the characteristics of sound propagation, using sonar or echo sounder. (Diegues, 1974)
During system startup, the user is prompted to choose which type of target is intending to detect, since this information is used to model the target strength (TS).
The choices consists of two pieces of information: whether the target is a surface or submarine and specific description.
Are given the following options: a) Submarine targets: - Nuclear submarine - Conventional submarine - Torpedo
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- Mine b) Surface targets: - Corvettes, frigates and destroyers, aircraft carriers, cruisers and battleships; - Small warships (coastal patrol craft, fast attack craft, ...); or - Merchant and passenger ships.
In the case of surface targets, modeling TS also depends on whether and if it is, or not, in a convoy.
For submarines, which are showing one broadside, TS depends directly on the radius of the target (a) and its length (L) and inversely wavelength () (Urick, 1983):
TS = 10*log10{(a*L2)/(2*)} [dB] (13)
If they are presenting bow or stern, has its value reduced to about half the calculated.
In the specific case of the mine TS is equal to 10 dB, and if the target is a torpedo TS is equal to -5 dB (Urick, 1983).
For surface targets, we used the data obtained in several campaigns during the World War II, where the values of TS were between 5 and 16 dB, depending on the type of ship (Urick, 1983).
The construction of the formula used the model was chosen based on a value for each of the classes listed above and included the number of vessels that are part of the convoy.
TS = 1 + Sc/2 + Nsc [dB] (14)
Wherein:
Sc = Class target area:
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10, for corvettes, frigates and destroyers; 20, for aircraft carriers, cruisers and battleship; 8, for small warships (coastal patrol craft, fast attack craft, ...); or 12, for merchant and passengers ships.Nsc = number of ships in the convoy
When seeking a passive detection, the target al.so provides information that enables the modeling of the source level, the depth of the source and the central frequency.
The values of the central frequency for the passive detection were determined based on an interview in the organ of the Navy responsible for training sonar operators were defined as values for the model the frequency of 1.5 kHz to submarine targets and 2.5 kHz for surface targets, that this choice is consistent with the observations made by Harrison (1998), in his article Underwater Acoustical Modeling.
Figure 17 - Graphic of self noise versus speed, which was the basis for the equation 15
100
105
110
115
120
125
130
135
140
145
0 2 4 6 8 10 12
Velocidade [ns]
Niv
el d
o es
pect
ro [d
B re
1P
a]
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Spec
trum
Lev
el
Speed [knots]
To obtain the value of SL for the passive detection was used based on the self-noise of the target (NLS), which essentially varies according to the speed (v), both as for ships and submarines. In the case of underwater target is a mine NLS is null, and if a torpedo, NLS is equal to 140 dB re 1 Pa (Urick, 1983).
Considering the available data (Urick, 1983) was obtained the graphic of Figure 17, applicable to submarine, which resulted in the following formula:
NLS = 3.24*v + 103 [dB re 1 Pa] (15)
A correction of -0.25 dB is applied to submarine targets, reducing NLS depending on the target depth, this correction is due to the increased pressure that causes the cavitation eect is smaller as increasing the operation depth.
From various graphics (Urick, 1983), one can formulate a single NLS equation that meets all surface ships and trains:
NLS = 0.05*v2 - 0.27*v + 110 + Nsc [dB re 1 Pa] (16)
In the passive mode, the source depth values are defined for submarine targets by the user information, and for surface targets according to the class of the target (Sc).
72
% *************************************************************% TARGET DATAdisp('*** TARGET DATA ***');input('Choose type of target (1-submarine target / 2-surface target)? ');info_T = ans;info_T = fix(info_T);if info_T < 1 || info_T > 2 info_T = 1; disp('The program set the value to 1 (submarine target) ');end% *************************************************************% SUB TARGET if info_T == 1 input('Choose class of target (1-nuclear sub / 2-conventional sub / 3-torpedo / 4-mine)? '); info_CL = ans; info_CL = fix(info_CL); if info_CL < 1 || info_CL > 4 info_CL = 2; disp('The program set the value to 2 (conventional sub) '); end if info_CL == 1 Comp_Sub=120; Raio_Sub=12; veloc_t=20; end if info_CL == 2 Comp_Sub=70; Raio_Sub=6; veloc_t=15; end if info_CL == 3 Comp_Sub=5; Raio_Sub=.3; veloc_t=45; end if info_CL == 4
73
Comp_Sub=1; Raio_Sub=.4; veloc_t=0; end cotaPer = Raio_Sub*2 + 5; cotaFun = Raio_Sub; if EQP == 1 input('Estimated target depth in meters? '); z_fonte = ans; db_cor = fix(-0.25*z_fonte); % pg 351 Urick freq = 1.5; freq = freq*1000; sl_t = fix(3.24*(veloc_t)) + 103 - db_cor; % pg 351 Urick TS = 10*log10((Raio_Sub*Comp_Sub^2)/(2*1500/freq))/2; % Average Target Strength - pg 315/324 Urick if veloc_t == 45; % is a torpedo sl_t = 140 - db_cor;% mean of measured values TS = -5; % pg 324 Urick - Aspect: Beam (-20dB Bow) end; if veloc_t == 0; % is a mine sl_t = 0; TS = 10; % pg 324 Urick - Aspect: Beam end else TS = 10*log10((Raio_Sub*Comp_Sub^2)/(2*1500/freq))/2; % Average Target Strength - pg 315/324 Urick end% *************************************************************% SURFACE TARGET elseif info_T == 2 input('Choose class of target (1-D, F or Cv / 2-A, C or B / 3-Small WS / 4-Cargo or Passenger)? '); info_CL = ans; info_CL = fix(info_CL); if info_CL < 1 | info_CL > 4 info_CL = 1; disp('The program set the value to 1-D or F or Cv '); end if info_CL == 1
74
snc = 10; end if info_CL == 2 snc = 20; end if info_CL == 3 snc = 8; end if info_CL == 4 snc = 12; end input('Estimated target speed in knots? '); veloc_t = ans; conv_nr = 0; input('The target have a convoy (0-no / 1-yes)? '); comboio = ans; if comboio == 1 input('How many ships are with it? '); conv_nr = ans; end if EQP == 1 freq = 2.5; freq = freq*1000; z_fonte = snc/2 - 1; sl_t = 0.05*veloc_t^2 - 0.27*veloc_t + 110 + snc + 2*conv_nr; % pg 346-348 Urick end TS = snc/2 + 1 + fix(rand(1)*5) + conv_nr; % Target Strength - pg 314 Urickend% *************************************************************
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Loss Model5 Sonar parameters are called the terms of members of the sonar
equation, which shows a dierence between active and
passive mode, due to the distance traveled by the sound
wave. (Aguiar, 2005)
Moving away from the transmitting source, the sound wave suers the phenomena of refraction, reflection, scattering, absorption, diraction and reverberation.
Figure 18 - Graphic of transmission losses produced by the model in passive mode
In this system, are considered only the first four phenomena, the sum of the eects of refraction and absorption account for nearly all the losses (Urick,1983).
The eects of reverberation were not considered to be of order of magnitude lower than the others, and the fact that its implementation in the model greatly increase the processing time.
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Diraction is a phenomenon by which a wave is distorted by an obstacle, it is a small object that is in its path, is a slot that allows only the passage of the wave front, as these obstacles are not common in the area of operation ships and submarines, the eect of this phenomenon was not considered explicitly (Vdovicheva et al., 1998).
Figure 19 - Graphic of transmission losses produced by the model in the active mode
The diraction, this system has its own design and its eects are contemplated by the algorithm and cut layers to establish the oceanographic parameters and creating
78
a heterogeneous ocean (Chapter 2), making it possible to establish the spread apart elevation of the seabed.
Because the model uses incoherent sum, that is, not yet can compute the phase variation in the sum wavefront, the eect isnt considered constructive/destructive these interactions.
Unlike other systems that use numerical meshes constructed independently of the phenomenon, this model is based on the mesh of the trajectories of the rays and the horizontal step fixed, which delimit the cells in which it applied the law of conservation of energy.
Figure 20 - Basic block diagram of the Loss Model
79
Calculus of absorption loss
Data from Sonar Parameters Model
Calculus of backscattering gain
N
Data from Propagation Model
YDoes a
reflexion occur?Calculus of reflexion
loss
Apply the losses
% *************************************************************% SURFACE SCATTERING / BOUNCE - pages 130-133 Burdic dB_10 = abs(-0.0021*marsh^2 + 0.331*marsh - 0.0046); Coef_ScS = 10^(-dB_10/10); if Coef_ScS > 1 | Coef_ScS < 0 error('Problems to build the Surface Scattering Coefficient- #SS') end% *************************************************************% APPLY SURFACE COEFFICIENTS if RefSup(passo,raio+1) == 1 I = I*RR_10^2; I = I*Coef_ScS^2; ScatS(passo) = ScatS(passo) + I*(1-Coef_ScS^2); end[...]
% *************************************************************% BOTTOM SCATTERING / VISCOUS LOSSES - page 136 Burdic Rr =(RoFi(passo)*CFi(passo))/(Roij(n_cortes,passo)*Cij(n_cortes,passo)); dB_12 = -20*log10((Rr-1)/(Rr+1)); Coef_ScF = 10^(-dB_12/10); if Coef_ScF > 1 | Coef_ScF < 0 error('Problems to build the Bottom Scattering Coefficient - #BS') end% *************************************************************% APPLY BOTTOM COEFFICIENTS if RefFun(passo,raio) == 1 I = I*RR_12^2; I = I*Coef_ScF^2; ScatF(passo) = ScatF(passo) + I*(1-Coef_ScF^2); end% *************************************************************% CALCULATE INTENSITY if t_sup == 0 & t_inf == 0 for prof = prof_sup:prof_inf-1
80
Intens(prof,passo) = Intens(prof,passo) + I; end end if t_sup == 1 for prof = 1:prof1-1 Intens(prof,passo) = Intens(prof,passo) + I*(Coef_ScS^2)*(RR_10^2); end for prof = 1:prof2-1 Intens(prof,passo) = Intens(prof,passo) + I; end end if t_inf == 1 for prof = prof1+1:Zij(n_cortes,passo) Intens(prof,passo) = Intens(prof,passo) + I; end for prof = prof2+1:Zij(n_cortes,passo) Intens(prof,passo) = Intens(prof,passo) + I*(Coef_ScF^2)*(RR_12^2); end end% *************************************************************% NEW VALUES I_feixe = I; Area_1 = Area_2;% *************************************************************% MIXING WITH AMBIENT NOISE - DESTRUCTIVE EFFECT if I_feixe < (10^(nl_m/10))/2 & EQP == 2 % 3dB below ambient noise for active detection I_feixe = 0; end % *************************************************************[...]% *************************************************************% CALCULATE ONE-WAY TRANSMISSION LOSSES TL = -10*Log10(Intens/I_SL);% *************************************************************
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5.1 Scattering ModelAt sea, also presents an energy loss due to the reflection effect they are responsible for particulate
matter. This effect is called in English language books of scattering. Such losses are very variable and introduce a degree of uncertainty in the performance of the sound equipment. (Diegues, 1974)
Scattering is a phenomenon which expresses the omnidirectional deviation of the sound energy of the wave front, when a reflection occurs.
A portion of the energy reflected and transmitted energy does not follow the predicted path calculated by Rayleigh Theory (Rayleigh, 1945), spreading around the point of reflection.
Although there being a total reflection of a wave front, there will still be a loss by scattering, this eect remains because the interface does not constitute a homogeneous layer, such that the higher the surface roughness and the impedance between media greater will be the scattering eect.
82
At the surface scattering, the eect is calculated based on the roughness of the sea surface which is estimated as a function of wave height (Burdic, 1984), which in turn is obtained by the sea state and the wind speed entered by the user, and depending on the frequency of the sound pulse.
However, the seabed scattering effect is calculated as a function of the composition of geological facies, depending on the impedance between the mediums (BURDIC, 1984).
The formulations below, which have been implemented in program lines, transcribe this phenomenon occurs when the reflection on the surface:
M = h.f (17)
AS = | 0.0021*M2 + 0.331*M - 0.0046| [dB] (18)CAS = 10(-As/10) (19)
Wherein:
M = Marsh coecient;
h = wave height, in feet;
f = central transmission frequency, in kHz;
As = attenuation due to scattering on the surface, in dB; and
CAS = attenuation coecient due to the surface scattering.
When the reflection occurs in the seabed are:
Rr = (CF*F.)/(A*CA) (20)
AF = -20.log{(Rr - 1)/(Rr + 1)} [dB] (21)
CAF = 10(-AF/10) (22)
Wherein:
Rr = seabed scattering coecient;
F = sediment density, in g/cm;
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CF = sound speed in the sediment, in m / s;
A = density of water, in g/cm;
CA = sound speed in the water. in m/s;
AF = attenuation due to seabed scattering, in dB; and
CAF = coecient of attenuation due to scattering in the background.
Routine was developed in MATLAB, used only for the active mode, which enables the reintegration part of the energy spread on the surface and the bottom.
Figure 21 - Graph of increased intensity sound due to scattering
84
Although the amount of scattered energy is very small, the routine ensures the backscattering eect is contemplated in the model as it is a well known eect of sonar operators.
Part of the amount of energy lost in the scattering back into the system by means of an algorithm initially calculates the overall coecient of propagation losses and applies to the amount of energy scattered in every place there was a reflection, trying thereby replicating all eects of propagation for this portion of energy.
This corrected value is returned as a spherical spreading energy, which has the center coordinates at which the reflections occur, with greater intensity at the center.
The sag amount of energy reentered into the system is regulated by half a normal curve, which has as a reference the largest amount of energy to be backscattered.
This ensures that the final summation of backscattered energy is equal to the sum of the energy spread multiplied by overall propagation losses.
A better understanding of the backscattering model can be obtained from the code reading system.
85
% *************************************************************% MARSH COEFFICIENTmarsh = h_ft*freq/1000;% *************************************************************[...]% *************************************************************% SCATTERING GAIN - AGUIAR's MODEL if EQP == 2 % only for active detection I_sc = zeros(fix(Zij(n_cortes,passo))+1,n_passos); I_i = mean(mean(Intens)); pap = I_i/I_SL; BoxD = hanning(fix(zf_max/dx)); distDS = conv(BoxD,ScatS); distDF = conv(BoxD,ScatF); convDS = size(distDS); convD = convDS(2); distDS = distDS(1,1+fix(convD/2)-fix(n_passos/2):convD); distDF = distDF(1,1+fix(convD/2)-fix(n_passos/2):convD); distDS = distDS(1:n_passos); distDF = distDF(1:n_passos); BoxZ = zeros(zf_max*2,1); BoxZ(1+zf_max/2:3*zf_max/2) = hanning(zf_max); distZS = BoxZ(zf_max+1:zf_max*2); distZF = BoxZ(1:zf_max); distZDS = (distZS*distDS); distZDF = (distZF*distDF); distZD = (distZDS+distZDF); distSS = distZDS/max(max(distZD)); distSF = distZDF/max(max(distZD)); I_scS = distSS.*mean(ScatS)*pap; I_scF = distSF.*mean(ScatF)*pap; for passo = 1:n_passos for prof = 1:fix(Zij(n_cortes,passo))+1 I_sc(prof,passo)=I_scS(prof,passo) + I_scF(prof+fix((max(Zij(n_cortes,:))-Zij(n_cortes,passo))),passo); end end Intens = Intens + I_sc; ISC = fix(max(max(10*log10(I_sc)))/10)*10 + 10; end% *************************************************************
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5.2 Absorption ModelHowever, it has been observed when using frequency is of the order of kilocycle, the value of the
attenuation coefficient obtained in experiments carried out directly on the sea appears to be approximately 100 times greater than that predicted in theory. This fact leads to the conclusion that in the sea are other mitigating effects than the viscous effects. Nowadays, this discrepancy is attributed to physicochemical reactions produced by pressure fluctuations. Magnesium sulfate was appointed
as the agent responsible for these reactions. (Diegues, 1974)
One way of attenuating acoustic energy is its conversion into heat, as proved the theory developed by Stokes-Kirchho, developed in the mid-nineteenth century (Clay & Medwin, 1997).
This transformation, which is produced by the friction generates an energy loss called absorption loss.
Then began compiling information for obtaining the absorption loss equation, using the described in Chapter 3 and Annex A.3.2 of the book Acoustical Oceanography (Clay & Medwin, 1977) which defines the value of the loss the absorption as:
s = F + rm + rb [dB/m] (23)
87
Wherein:
F = attenuation in freshwater;
rm = attenuation due to the molecular relaxation of magnesium sulfate; and
rb = attenuation due to molecular relaxation of boric acid.
Plots of absorption loss due to attenuation in freshwater is described in the literature as:
F = (1.71*10-8/F.cF)*((4F/3) + F')*f [dB/m] (24)
Wherein:
F = 1,000 Kg/m;
cf = propagation speed in the medium without salinity (S = 0), in m/s;
F = transverse (shear) dynamic viscosity coecient for freshwater;
F' = volumetric (compression) viscosity coecient for freshwater; and
f = frequency in kHz.
The value of cF can be obtained starting from the Medwin (1975) equation, as described in Formula 3, which replaces the value of salinity (S) to zero, due to the calculation being made for fresh water, thus leaving the following formulation:
cF 1,449.2 + 4.6*T - 0.055*T + 0.00029*T + (0.350*T - 46.9) + 1,55.10-2*Z [m/s] (25)
Wherein:
T = water temperature, in C; and
Z = local depth, in meters.
88
Figure 22 - Coecient of viscosity versus temperature (Clay & Medwin, 1977)
The equations for the coecients of viscosity were obtained by digitizing the graph and subsequent interpolation of the digitized points to obtain a polynomial equation (Figure 22).
The choice of an equation of the fifth degree was determined by obtaining a value lesser than 0.001 for RMS error.
By interpolation, were obtained equations for the coecients at sea level than inserted the corrections due to the depth, then getting:
89
Temperature
F (-6.10-10*T5 + 2.10-7*T4 - 2.10-5*T3 + 0.0015*T2 - 0.0625*T + 1.8084)*(1 - 1.1908*10-5*Z)/103 [Kg/s.m] (26)
F' (2.10-8.T5 - 2.10-6.T4 + 10-5.T3 + 0,0047.T2 - 0,2264.T + 5,5966).(1-1,1908.10-5.Z)/103 [Kg/s.m] (27)
The amount of loss due to absorption by molecular relaxation of magnesium sulphate is defined as:
rm = ((2.03*10-5*S*frm*f2)/(f2 + frm2))*(1 - 1.23*10-3*PA) [dB/m] (28)
Wherein:
S = salinity, ppm;
f = frequency, in kHz; and
PA = 9.9237*10-2*Z, ambient pressure, in atm
The value frm is obtained by the equation:
frm = 21.9*10[6 - 1,520/(T+273)] [kHz] (29)
Substituting the value of PA, which has:
rm ((2,03.10-5*S*frm*f2)/(f2 + frm2))*(1 - 1.22*10-4*Z) [dB/m] (30)
The amount of loss due to absorption by molecular relaxation of boric acid is defined as:
rb = (1.2*10-4*f2*frb)/(frb2 + f2) [dB/m] (31)
Where the value of frb is obtained by the equation:
frb = 0.9*(1.5)T/18 [kHz] (32)
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% *************************************************************% CALCULATE THE ALFA mi_F = (1-1.1908*10^(-5).*Zij).*(-6*10^(-6).*Tij.^5+2*10^(-7).*Tij.^4-2*10^(-5).*Tij.^3+.0015.*Tij.^2-0.0625.*Tij+1.8084)/(10^3); dmi_F = (1-1.1908*10^(-5).*Zij).*(2*10^(-8).*Tij.^5-2*10^(-6).*Tij.^4+10^(-5).*Tij.^3+.0047*Tij.^2-0.2264.*Tij+5.5966)/(10^3); freq_rm = 21.9*(10.^(6-1520./(Tij+273))); freq_rb = 0.9*(1.5.^(Tij/18)); alfa_rm = (1 - 1.22.*Zij*10^(-4)).*(Sij*2.03*(10^(-5)).*freq_rm.*((freq/1000)^2))./((freq/1000)^2+freq_rm.^2); alfa_rb = (1.2*(10^(-4))*freq_rb.*((freq/1000)^2))./((freq/1000)^2+freq_rb.^2); alfa_F = (1.71*(10^8)*(4*mi_F./3+dmi_F)*((freq/1000)^2))./(((Cij-(1.34-0.01*Tij).*(Sij-35)).^3)*1000); alfa = alfa_F + alfa_rm + alfa_rb; for passo = 1:n_passos Calfa(passo,:) = polyfit(Zij(1:n_cortes,passo),alfa(:,passo),5); alfa_nor(:,passo) = rot90(rot90(rot90(polyval(Calfa(passo,:),eixoZ)))); end% *************************************************************[...]% *************************************************************% ABSORPTION Am = alfa_nor(prof_sup,passo); dB_abs = (raio_s(passo+1,raio)-raio_s(passo,raio))*Am; Coef_abs = 10^(-dB_abs/10); if Coef_abs > 1 | Coef_abs < 0 error('Problems to build the Absorption Coeficient - #AB') end I = I*Coef_abs^2;% *************************************************************
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Prediction Model6
magenta-17m, cyan-60m, blue-120m, green-180m
Predict Detection Range [MN]
5.6667 11.3333 17
30
210
60
240
90270
120
300
150
330
180
0
It is the knowledge of this vertical structure, in its turn, that leads
us to the determination of a pattern of sound propagation,
that is, to obtain the corresponding sound field to that vertical speed structure.
(Diegues, 1974)
Having as basic information from the products generated by other modules of the system, the detection prediction model provides sonar range reaching into six dierent depths if a submarine target, or the dimension of 0 m if a surface target.
Using the Formula 10, presented in Chapter 4, are calculated for each point in the plane of propagation excess echo (EE) and mount figures (FIG) (Figure 23) with a color scale has a maximum level of source (SL) and the minimum zero of echo excess.
These figures actually are spatial arrays mounted by the system in which it searches the area where an excess amount of specific echo exists, this area has about three times the step, that is, about 100 m length and twice the diameter of the underwater target heigh
