Massimo Di Stefano
Transmission losses and target strength related to compressional waves ·at near-normal incidence on the water- sediment interface are computed by acoustic measurements both in a controlled environment and at sea (Portsmouth Harbor); these latter permitted to investigate three largely different sediment types (mud, sand, and rock). Comparisons with bottom losses values based on several works published demonstrate the need to evaluate also other parameters related to the backscattering process (i.e. surficial roughness, volume backscatter) in the target strength estimation.
This research focus on the adoption of the active sonar equation as a method to compute trasmission loss and target strenght (in dB) of an acoustic wave propagating underwater. The compressional wave was generated by a trasmitteer oriented in a near-normal direction to the sea-sediment interface. The computations are based on measured values of source level collected during an experiment in a controlled environment (experiment 1), and source level values collected at-sea in a open ocean environment (experiment 2). at different locations. The data collected in a controlled environment (Deep Tank of the Jere A. Chase Ocean Engineering Laboratory at the University of New Hampshire), experiment 1, were used for calibration, and also as terms of reference for the data collected at-sea. The data collected at-sea, experiment 2, were collected using an active sonar system in two different configuration, the first to evaluate the Range dependency of an Acoustic wave as it propagates (configuration a) and the second (configuration b) to compute the target strength for different kind of sediments.
Introduction - The term "sonar" is the acronym for sound navigation and ranging. It indicates a generic projector that transmits a pulse of sound, and a hydrophone that waits to receive the same pulse after it propagates out into the water, reflects on some target, and travels back. If the projector and the hydrophone are integrated on the same transducer, this configuration is called monostatic, otherwise bi-static or multi-static sonars.
Sonar equation - The active sonar equation represents a useful mean for making predictions (e.g. estimate the maximum range of target detection) and sonar design (e.g. definition of some specific sonar capabilities)[!]. It is based on the use of decibel (dB), a logarithmic unit that indicates the ratio of a physical quantity over a reference level. The sonar equation describes the acoustic pulse propagation process, estimating how much of acoustic signal get back from the target. The Source Level (SL) term describes the generation of the transmitted pulse, the Transmission Losses are related to the propagation to and from the target, and the Target Strength represents how much signal is reflected and scattered off the target in the direction of the hydrophone. The resulting Echo Level represents the received intensity from the targer:
$$ EL = SL - 2TL + TS \quad (1) $$Source Level - Conventionally, the effective amplitude $P_0$ of a spherical pressure wave generated by a projector is measured at the distance of 1 meter as a reference to predict its amplitude at any distance [2]. The Source Level is calculated in decibel making the ratio between $P_0$ and the underwater acoustic reference pressure $P_{ref}$ (where $\rho$ is the density of the medium, and $c$ is the sound velocity):
$$ SL = 10 \cdot \log_{10} \frac{P_{0}^2 /\ \rho c}{P_{ref}^2 /\ \rho c} = 20 \log_{10} \frac{P_0}{1 \mu Pa} dB \ re \ 1 \mu Pa \ @ \ 1m \quad (2) $$Transmission Losses -- They are related to the attenuation of the amplitude of the acoustic signal for geometrical spreading and absorption. In the sonar equation, they are estimated as a ratio of intensities I in function of the range R:
$$ TL = 10 \log_{10} \frac{I_{(1m)}}{I_r} \quad (3) $$The spreading effect on the intensity is function of the inverse of the range, for a wave propagating cylindrically, and o f the square o f the range, for a spherical wave. The absorption is usually modeled with a logarithmic absorption coefficient a, with units of dB/m and frequency dependent. For a spherical wave, the resulting transmission losses can be calculated as:
$$ TL = 20 \log_{10} R + \alpha R \quad (4) $$The three main mechanisms related to the absorption are: viscous dissipation, heat conduction, and molecular relaxation. The effects of the absorption increase with the frequency (Figure 1).
from oms import *
from IPython.display import Image
Image(filename='/var/www/html/shared/OM/sound_absorption.png', width=300, height=400)
Target Strength - When an acoustic wave emitted by a projector insonifies a target, only a portion of the energy is redirected toward the receiver. The Target Strength describes this portion as a ratio between the scattered intensity at a distance of l meter $I_s$, and the incident acoustic signal $I_i$ [3]:
$$ TS = 10 \log_{10} \frac{I_s}{I_i} \quad (5) $$The scattered intensity $I_x$ depends on the characteristics of the incident acoustic wave (e.g. frequency, pulse length) and the target (e.g. material, rugosity, orientation between the projector and the target). If the intensity is scattered back in the direction-of the original source of spherical acoustic waves (usually evaluated at the distance r of l meter), it is possible to define the backscattering cross section $\sigma_{bs}$ and the resulting target strength as [4]:
$$ \rho_{bs} = r^2 \frac{I_{bs}}{I_i} ; \quad TS = 10 \log_{10} \frac{\sigma_{bs}}{r_2} \quad (6) $$If the target is an area of seafloor, the target strength is usually modeled as composed by two terms: the surface backscattering strength per unit area $S_s$ and the surface effectively insonified $A$ [5]:
$$ TS = S_s + 10 \log_{10} \frac{A}{A_{ref}} \quad (7) $$Signal-to-noise ratio (SNR) - This ratio permits to evaluate the echo detection, assuming the axis of the transducer is pointed in the direction of the echo target:
$$ SNR = SL - 2TL + TS - (NL- DI) \quad (8) $$Noise Level - The Noise Level (NL) represents all the acoustic waves measured, but not generated by the sonar. Sources of ambient noise are the movement of water due to tides, the shipping, the seismic activity, breaking waves, etc. This background noise does not have usually a preferred direction (i.e. isotropic noise). It differs from the acoustic waves generated from the transducer, but coming from objects different from the target (i.e. reverberation) [6, 7].
Directivity Index - Usually a transducer has much more sensitivity from a limited range of directions. This permits to decrease the isotropic environmental noise in the measures.
Sound levels - The most generally used logarithmic scale for describing sound levels is the decibel [8].
Decibel - A Decibel (sB) is a unit-less quantity used for attenuation in I0-base logarithm. Since it is based on a ratio, a quantity expressed in dB has meaning only if a reference is given.
Intensity Level - It is defined as:
$$ IL = 10 \log_{10} \left|\frac{I}{I_{ref}}\right| dB \ re \ I_{ref} \quad (9) $$Sound Pressure Level - n underwater acoustics, the pressure of l $\mu Pa$ is usually adopted as a reference for the logarithmic ratio. The result, called Sound Pressure Level, is:
$$ SPL = 20 \log_{10} \left| \frac{P_e}{1 \mu P a} \right| dB \ re \ 1 \ \mu Pa \quad (10) $$The measure of a SPL by an electronic device is usually obtained from the voltage root mean square $V_{rms}$, the sensitivity of the hydrophone receiving sensitivity $M_x$, and the gain $G$ applied in reception.
$$ SPL = \left| M_x \right| - G + 20 \log_{10} V_{rms} \quad (11) $$Simple reflection model - Among the various models present in literature, a simple one is based on a harmonic plane wave incident on a plane boundary. The reflection is due to a change in the product of velocity $c$ and density $\rho$ (hereinafter, acoustic impedance) for the t_wo mediums involved. The mathematical derivation - present in several textbooks (e.g. [8]) - from the appropriate equations is not reported in the present paper. For this model, the Rayleigh reflection coefficient at normal incidence represents the ratio of the pressures of a reflected wave to that ofthe incident wave [9]:
$$ R = \frac{\rho_2 c_2 - \rho_1 c_1}{\rho_2 c_2 + \rho_1 c_1} \quad (12) $$The Bottom Loss (BL) of a plane wave at normal incidence (on a peak pressure basis) can be expressed in dB by the following formula:
$$ BL = -20 \log_{10} R \quad (13) $$Using the formula (13), values of BL can be computed using sediment and seawater average properties present in oceanographic tables. Implicit in this computation is that at normal there is little or no dependence of reflection coefficients and bottom loss on frequency. However, in most cases, BL must be measured in situ due to the variability of values of sediment and water densities and velocity at different temperature and pressure [9]. Due to different models applicable (specular reflection and incoherent scattering), the seafloor can be represented as a mirror or composed by several sources of acoustic waves. This provides two slightly different formulas to calculate the TL from the SPL (where D is depth):
$$ TS = SPL - SL + 20 \log_{10} (2D) + 2 \alpha D \quad (14) \\ TS = SPL - SL + 40 \log_{10} (D) + 2 \alpha D \quad (15) $$The BL is related to the TS, but for the simple formula applied (13) the results are not related to the frequancy of the incident signal as well as the area of seafloor insonified.
Introduction - An active sonar system (Figure 2) was configured in two different experiment to study the behaviour of underwater acoustic wave propagation:
Image(filename='/var/www/html/shared/OM/schema.png', width=400, height=200)
In experiment 1 the signal generator sent an electric impulse to the transducer (projector) which converted the electric signal in a pressure (acoustic) wave. The hydrophone received the acoustic wave and converted it back to an electric signal which was then amplified and filtered with a band-pass filter by the preamplifier and finally sent to the oscilloscope where the signal has been analyzed. The acoustic signal was sent by a transmitter mounted on a rigid frame attached to one side of the testing tank, the receiver (hydrophone) was positioned at a distance of 5 meter from the transmitter. To avoid signal reflection both projector and receiver were opportunately positioned far from the tank boundaries and submerged at an opportune depth of ~1m. The sonar equation was used to study the dinamic of the system and to calculate the sound pressure level (SPL) registerd by the receiver (hydrophone) and to perform range measurments validated by direct measurments of the distance between transmitter and hydrophone.
The experiment was repeated 20 times using acoustic signals at fixed voltage and different frequency (from 45 to 56 kHz) and at different volatges with fixed frequence (from 1 to 8V). At the end of the experiment number 1 an automatized method to evaluate the "acoustic resonance frequency of the hydrophone" has also been developed. A similar eaxperiment with transmitter and receiver at distance of 1 meter and fixed frequency was repeated 8 times at different voltages. The SL data collected was used as reference in experiment 2.
Experiment number 2 was conducted in open ocean in the Porthsouth bay area. The active sonar system was configured and made operative on the Research Vessel Gulf Challanger in two different configurations:
a) transmitter fixed on a rigid frame and hydrophone lowered at different depth (-3, -6, -9, -12) m
b) transmitter and hydrophone fixed side by side on the same rigid frame
In experiment 2 configuration 'a' (hydrophone and transmitter positioned at different ranges) the displacement in sea water of source transducer was obtained by a fiberglass structure of about 4 meters length and 1 meter wide submerged at ~1.5 meters, the hydrophone was instead connected to a cable and deployed at diffeternt depths (-3, -6, -9, -12).
The sonar equation was adopted to compute the SPL from the data collected and validate experimentally that the amplitude of acoustic wave that propagates in time along a medium is inversely proportional to the distance traveled by the wave.
Experiment number 2 configuartion 'b' (transmitter and hydrophone positioned side by side on the fiberglass structure) was repeated in 3 different locations (Table 1, Map 1) with different depth and seafloor characteristics. In this particular example the 'Acvtive sonar equation' was used to derive TS (target strength) used to identify substarate complexity and sediment caractherization. For each location a sediment sampling was performed to validate the substrate classification with direct measurments.
from IPython.display import HTML
link = 'http://bl.ocks.org/d/93dbeb4bf157178a64eb'
print(link)
HTML('<iframe frameborder="0" width="100%%" height="300" src="%s"></iframe>' % link)
http://bl.ocks.org/d/93dbeb4bf157178a64eb
from oms import *
station = {'Station 1': {'Longitude':'-70.7074', 'Latitude':'43.0719', 'Depth':'31.3944'},
'Station 2': {'Longitude':'-70.6975', 'Latitude':'43.0227', 'Depth':'18.288'},
'Station 3': {'Longitude':'-70.6429', 'Latitude':'43.0263', 'Depth':'8.2296'}
}
Dict2Table(station, title='Station location at sea',
caption='Table 1 - Average positions (WGS 84) and depth of stations')
Depth | Longitude | Latitude | |
---|---|---|---|
Station 1 | 31.3944 | -70.7074 | 43.0719 |
Station 3 | 8.2296 | -70.6429 | 43.0263 |
Station 2 | 18.288 | -70.6975 | 43.0227 |
Experiment 1
The operations in the Deep Tank permitted the definition of the Source Level at different voltages and of an optimal frequency for the hydrophone.
Data format description - The signal recorded by the data logger was in the form of a csv (comma separated value) text file with (Table 2) a column for each of the following variables : Sample number, Time related to trigger point, Value Ch1, Value Ch2, Value Ref1, Value Ref2 :
%matplotlib inline
import matplotlib.pyplot as plt
#import qgrid
data = loadwave('http://epinux.com/shared/OM/data/sonar/at-tank/delta-f/02_51khz2vN40.DAT')
#qgrid.show_grid(data)
data.head()
SN | TTP | CH1 | CH2 | REF1 | REF2 | |
---|---|---|---|---|---|---|
0 | -5000 | -0.01000 | 0.010743 | 0.003906 | 0.002441 | 0.002441 |
1 | -4999 | -0.01000 | 0.008789 | 0.007813 | 0.002441 | 0.002441 |
2 | -4998 | -0.01000 | 0.008789 | -0.007813 | 0.002441 | 0.002441 |
3 | -4997 | -0.00999 | 0.009766 | 0.003906 | 0.002441 | 0.002441 |
4 | -4996 | -0.00999 | 0.008789 | 0.011719 | 0.002441 | 0.002441 |
The pressure levels recorded for the source (transmitted signal) and for the hydrophone (received signal) were stored respectiveley in the $CH1$ and $CH2$ field. The overlay between the waveform of transmitted and received signals for a given measurment (Figure 3) shows clearly the distance in time (milliseconds) from when the acoustic wave was genereted to the time when the wave reached the receiver.
chplot(data)
Deep Tank Operations - Estimation of the optimal frequence $\phi$ for the hydrophone. This estimation was operated evaluating the different frequency responses to individuate the optimal frequency for the adopted source array. The SPL was computed for a wide spectrum of frequencies (Figure 3) with transmitter and receiver at a fixed range of 5 meters. The results of this operation permitted to determine $\phi$ at 51 kHz.
$V_{rms}$ and $SPL$ were computed on the portion of the CH2 signal at the time when the receiver detected the CH1 signal. This selection was performed by cross correlation the two signals (Figure 4, code block 2)
nstep=350
lag, newdata = lagcut(data, nstep=nstep, plot=True)
For an accurate computation of the $V_{rms}$ value, the resulting selected received signal (Figure 5) was cutted at the extremity to evaluate $V_{rms}$ only on the steady state area (Figure 6).
fig = plt.figure(figsize=(12,7))
ax = fig.add_subplot(211)
ax.grid()
ax.plot(data.CH2[data.CH2.shape[0]/2+data.CH2.shape[0]-lag-40: data.CH2.shape[0]/2+data.CH2.shape[0]-lag+nstep+200]);
restyle(ax)
plt.show()
filtered = newdata[findSteadyStateStart(newdata):]
fig = plt.figure(figsize=(12,7), dpi=60)
ax = fig.add_subplot(211)
ax.grid()
ax.plot(filtered.index.values,filtered.values,'-');
restyle(ax)
Finally $SPL$ is calculated using $Eq.(11)$, with: $$ V_{rms} = \frac{CH2_{norm}}{\sqrt{N_{CH2}}}$$
mx = 158
rms=Sci.linalg.norm(newdata.values)/np.sqrt(newdata.shape[0]) # calculate rms
spl=mx-10+20*np.log10(rms) # calculate spl using eq. (11)
print('rms : ', rms)
print('spl : ', spl)
rms : 3.06920757624 spl : 157.740525231
The previous computation was generalized in a code function which execution was iterated over a set of 20 different dataset each one corriponding to a specific frequence varing from 45 kHz to 56 kHz (Figure 6)
import urllib.request
filelist1 = 'http://epinux.com/shared/OM/data/sonar/at-tank/delta-f-filelist.txt'
datalink1 = 'http://epinux.com/shared/OM/data/sonar/at-tank/delta-f/'
listafile1 = urllib.request.urlopen(filelist1).read().decode('utf-8').strip().split('\n')
storedict1, allspl = {}, []
fort = [splcalc(os.path.join(datalink1,i), storedict=storedict1) for i in listafile1]
freqplot(storedict1)
The second part of experiment one, Sorce Level was computed for a set of measurments at different voltages and with fixed frequancy $\phi = 50 kHz$. Using the formula reported in (11), the set of measurments were converted in SPL. This operations in the Deep Tank permitted the definition of the Source Level $SL$ (at 1 meter) at frequency $\phi$ of the hydrophone. This experiment showed an expected trend with an increasing value of $SPL$ for bigger values of voltage (Figure 7) except for the $SPL$ computed for voltage $V=2$ that present an anomaly in the data maybe related to some noise in the test tank, or more probably to an change in the oscilloscope settings)
filelist2 = 'http://epinux.com/shared/OM/data/sonar/at-tank/delta-v-filelist.txt'
datalink2 = 'http://epinux.com/shared/OM/OM_tank/SL/'
listafile2 = urllib.request.urlopen(filelist2).read().decode('utf-8').strip().split('\n')
storedict2={}
vort = [splcalc2(os.path.join(datalink2,i), storedict=storedict2) for i in listafile2]
x,y = np.arange(1,9), [i['spl'] for i in vort]
fig = plt.figure(figsize=(12,4), dpi=60) ; ax = fig.add_subplot(111)
ax.plot(x,y,'-bo', lw=2) ; ax.grid()
restyle(ax)
plt.xlim(min(x)-1, max(x)+1) ; plt.ylim(min(y)-1, max(y)+1)
(119.48494700864407, 132.31475560362324)
Experiment 2 :
Configuration a - A set of measurments at station 1 were used to compute transmission Losses (TL) at different ranges $r$ between transmitter and receiver. The measured values of $V_{rms}$ at different ranges were collected and converted in $SPL$. The obtained SPL, fitted with the theoretical transmission loss, were computed from the Source Level registered during the experiment in the controlled environment using the formula (11).
Data analysis for a representative measurement - The transmitted and received signals for a given measurement at-sea are presented in figure 8.
filelist3 = 'http://epinux.com/shared/OM/data/sonar/at-sea/st1_filelist.txt'
datalink3 = 'http://epinux.com/shared/OM/data/sonar/at-sea/ST1'
ST1 = urllib.request.urlopen(filelist3).read().decode('utf-8').strip().split('\n')
files = [os.path.join(datalink3,i) for i in ST1]
sampledata = loadwave(files[3])
chplot(sampledata)
The cross-correlation was used to define the signal received from the transmitter. The experiment was completed plotting range and trasmission loss for each measurments and overlayed on the teorethical transmission loss (Figure 9) given by : $$TL = SL - 20 \log_{10} r $$
xy = rtloss(files, plot=True)
Configuration b - transmitter and hydrophone fixed side by side on the same rigid frame, the acoustic wave traveled all the way down to the seafloor and the reflected signal was recorded by the hydrophone allowing to compute TS (target strength) for station 2 and station 3. The TS value was then used to identify substarate complexity. The values of TS found for two station are shown in table 3 and 4.
ST2_filelist = "http://epinux.com/shared/OM/data/sonar/at-sea/st2_filelist.txt"
ST3_filelist = "http://epinux.com/shared/OM/data/sonar/at-sea/st3_filelist.txt"
ST2 = urllib.request.urlopen(ST2_filelist).read().decode('utf-8').strip().split('\n')
ST3 = urllib.request.urlopen(ST3_filelist).read().decode('utf-8').strip().split('\n')
path2 = 'http://epinux.com/shared/OM/data/sonar/at-sea/ST2'
path3 = 'http://epinux.com/shared/OM/data/sonar/at-sea/ST3'
TS_ST2 = bottomloss(path=path2, filelist=ST2)
TS_ST3 = bottomloss(path=path3, filelist=ST3)
table = ListTable()
table.append(['Num sample', 'TS'])
for i, v in enumerate(TS_ST2):
table.append([i+1, v])
table
Num sample | TS |
1 | -61.929471642406995 |
2 | -60.65368229707518 |
3 | -60.8446995975996 |
4 | -61.59236361915734 |
5 | -61.39352978745313 |
6 | -62.163049091542774 |
7 | -59.452457203042556 |
8 | -61.4737713030205 |
9 | -61.58604425306257 |
table = ListTable()
table.append(['Num sample', 'TS'])
for i, v in enumerate(TS_ST3):
table.append([i+1, v])
table
Num sample | TS |
1 | -54.826948547140375 |
2 | -57.36380477597717 |
3 | -58.12755240675142 |
4 | -56.453903146013914 |
5 | -57.1080432298763 |
Both exmeriments showed how to study underwater acoustic waves using the sonar equation. In particular experiment 1 demostarte how to use the sonar equation to test and calibrate the hardware before to acquire data in the field. With Experiment 2 (configuration a) computation of trasmission loss of undewater acoustic wave has been demostrate. In experiment 2 configuration b was used to derive important information about the seafloor needed for its caractherization using remote sensing technique. However, in configuration b a series of neglection were made. Loss due to absorption was not considered and also other factors like non-normality of the incident wave, approssimate value for the sound speed, missed information about signal gain and the use of a suboptimal frequency for the hydrophone. Also the importance to evaluate other factor as the area insonified (in order to normalize the measured data and obtain a more general 'backscattering coefficient') This consideration emerged from the executed analysis and comparison with the BL computed and the BL values reported in published works. It also appeared clearly the need to involve the characteristics of the acoustic signal (e.g. the frequency adopted) for a better theoretical estimation of the TS values. In the end, the high variability in the results suggested the necessity to increase the number of measures for each station.
All the code and data used in this report are available on line at [*]. Also the report itself is a executable paper and can be run to reproduce the results found during this experiments.
Source code used in this report:
!/usr/local/bin/gist -p oms.py
https://gist.github.com/9ef470c612f62b9a293e
This notebook:
notebook = !/usr/local/bin/gist -p Ocean_Measurments_SONAR.ipynb
print(notebook[0].replace('https://gist.github.com','http://nbviewer.org'))
http://nbviewer.org/89a98bdb0d7d0465862b
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[2] Au, W.W.L., The sonar ofdolphins. 1997, New York (USA): Springer-Verlag.
[3] Clay, C.S. and H. Medwin, Acoustical Oceanography and Applications. 1977, New York (USA), London (UK), Sydney (Australia), Toronto (Canada).
[4] Pierce, A.D., Acoustics: an introduction to its physical principles and applications. 1989: Acoustical Society of America.
[5] Lurton, X., An introduction to underwater acoustics : principles and applications. 2nd ed. 20 I0, Heidelberg ; New York: Springer, published in association with Praxis Publishing, Chichester, UK. xxxvi, 680 p.
[6] Brekhovskikh, L.M. and I.U.P. Lysanov, Fundamentals ofocean acoustics. 3rd ed. Modern acoustics and signal processing. 2003, New York: AIP Press/Springer. xiv, 278 p.
[7] Bruneau, M., Fundamentals o f acoustics. 2006, ; Newport Beach, CA: ISTE Ltd. 636 p.
[8] Kinsler, L.E., et al., Fundamentals o f acoustics. 4th ed. 2000, New York (USA): Wiley. xii, 548 p.
[9] Hamilton, E.L., Reflection coefficients and bottom losses at normal incidence computed from Pacific sediment properties. Geophysics, 1970. 35(6): p. 995- 1004.