Shallow Water Acoustic Propagation at Arraial do Cabo, Brazil Antonio Hugo S. Chaves, Kleber Pessek, Luiz Gallisa Guimarães and Carlos E. Parente Ribeiro, LIOc-COPPE/UFRJ, Brazil Copyright 2011, SBGf - Sociedade Brasileira de Geofísica. speed profile, the region of Arraial do Cabo. Finally in the This paper was prepared for presentation at the Twelfth International Congress of the last section we discuss and summarize our main results. Brazilian Geophysical Society, held in Rio de Janeiro, Brazil, August 15-18, 2011. Theory Contents of this paper were reviewed by the Technical Committee of the Twelfth International Congress of The Brazilian Geophysical Society and do not necessarily represent any position of the SBGf, its officers or members. Electronic reproduction The intensity and phase of the sound field generated by a or storage of any part of this paper for commercial purposes without the written consent acoustic source in the ocean can be deduced by solving the of The Brazilian Geophysical Society is prohibited. Helmholtz wave equation. The complexity of the acoustic environment like sound speed profile, the roughness of Abstract the sea surface, the stratification of the sea floor and The Brazilian coastal region is a huge platform the internal waves introduce acoustic fluctuations during where the propagation is dominantly in a waveguide the sound propagation that decrease the signal finesse delimited by the surface and the bottom. The region (Buckingham, 1992). Nowadays several types of solutions near Arraial do Cabo is a place where there is a for the sound pressure field are available, in this work we special sound speed profiles (SSP) regimes related deal with two of them namely: normal mode and ray tracing to shallow waters. For some particular environmental techniques. The most important acoustical parameter and signal parameters, shallow water means a region of the ocean is the speed of sound and it depends on where the acoustic waveguide propagation occurs for the following oceanographic parameters, the temperature, low as well as intermediary frequencies. This work salinity and pressure (Clay, 1977). The average speed aims to describe some characteristics of waveguide at sea is approximately 1500 m/s and have spatial and propagation with typical sound speed profile of this temporal variations. Besides, based on experimental data place. The modal and ray tracing theories were of the above physical parameters, it is possible to obtain described with experimental results. Discussion about some empirical formulas for sound speed in the ocean how the fluctuations of environmental parameters (Clay, 1977), namely: would affect the waveguide in shallow waters were 2 introduced. c = 1449:2 + 4:6T − 0:055T + 3 Keywords: underwater acoustics, shallow water 0:00029T + (1:34 − 0:010T)(S − 35) + 0:016z (1) acoustics, waveguide propagation, ray tracing where c=speed(m/s),T=temperature(oC), S=salinity(parts Introduction per thousand), z=depth(meters). One of the characteristics of shallow waters are sound In the ideal waveguide normal mode propagation speed profile refracting downwards or nearly constant, framework, for a given frequency f , the harmonic pressure meaning that long range propagation takes place fields F(r)exp(−iwt) (w = 2p f ) propagating with speed c(z) exclusively via bottom-interacting paths, these shallow are solution of the Helmholtz’s wave equation: water environments are found on the continental shelf for 2 waters depths down to 200 meters. Sound is used widely w 52 + F(r) = 0 (2) in undersea applications because the ocean is essentially c(z)2 transparent to acoustic waves, whereas it is opaque to all types of electromagnetic waves. Applications of Besides, adopting the circular cylindrical coordinate system underwater sound include (Buckingham, 1992) active and (where the depth increases in the positive z direction) and passive detection of ships, submarines, seismic profiling, assuming the ocean a system with azimuthal symmetry, echo-sounding, high-resolution imaging, communications then the regular solutions of (2) can be written as: and acoustic tomography. In Low frequency regime, long range sound transmissions across oceans are possible. This ocean feature have been proposed as a mean of Z ¥ monitoring long-term global change (Buckingham, 1992), F(r) ≡ dk A(k)kJ0(kr)Y(z;k): (3) as well as the sound generated naturally at the surface is 0 being considered as the basis of remote sensing methods (Sommerfeld-Weyl Picture) for estimating weather conditions over ocean large scale. In the next sections we try to explain the widely used theories to sound propagation in shallow water. To this Where k is the radial wave number, J0 is the zero–th order end, we outline this work in the following form, first we Bessel function. In addition, “the vertical wave function” Y introduce the normal mode and ray tracing theories and satisfies the following wave equation: in the second section we show our experimental results in d2Y w2 a region of Brazil where there is a special regime of sound + − k2 Y = 0: (4) dz2 c(z)2 Twelfth International Congress of The Brazilian Geophysical Society SHALLOW WATER ACOUSTIC PROPAGATION AT ARRAIAL DO CABO 2 Applying Cauchy’s residue theorem, the Sommerfeld-Weyl For sound with a wavelength l propagating in an ideal integral (3) can be rewritten as: wave guide of depth d, it is possible estimate Rmax the maximum distance separation between the sound source and receiver (Katsnelson, 2002), namely: Z ¥ F(r) ≡ dk A(k)kJ0(kr)Y(z;k) R = 2d2=l (11) 0 max 2pi∑Residue Series + In general, due to wave guide geometry and bottom n | {z } geological features some frequencies are dropped. These Normal Modes: Discrete Spectrum allowed frequencies are limited by a cut off frequency fo, 1 Z ( ) where a roughly estimate (Brekhovskikh, 2002) to fo is dk A(k) k H 1 (kr)Y(z;k) (5) 2 0 given by: G2 cw C fo = ; (12) | {z } 4d sinqc Continuum Spectrum being the incident critical angle qc = arccos(cw=cb) and cw, cb the mean values of sound speed along the water column Asymptotic Ray Tracing expansion theory: and the sea bottom respectively. Notice that the frequency ¥ fo(12) is strongly depend on water depth. In another A j(r) F(r) = eiw t(r) (6) words, the f numerical value is a general feature of ducted ∑ (i ) j o j=0 w propagation and it occurs as a result of the evanescent wave propagation into the sea bottom. For instance, the efficiency of the duct to confine sound decreases as fo(12) 2 −2 2 j∇tj = c (r) + O(w )(Eikonal) increases. On the other hand, for a given frequency f the 2 number m of propagating modes in (9) is finite and satisfies 2∇t · ∇A0 + (∇ t)A0 = 0 + O(w) (Amplitud) the following inequality (Jessen, 1994): Rays are the wave front orthogonal curves family, w t(r) ≡ f Constant such that, m ≤ (2d cosqc) + 1=2 (13) cw d r = c∇t: (7) d s Equation(13) shows that as the frequency f increases the number of propagating modes increases (Jessen, 1994). Finally, it is necessary to calculated in dB the Transmission Keeping these ideas in mind, in the next section we analyze Loss (TL), given by: theoretically our experimental results. F(r) TL(r) = −20log (8) Results F0 The ray solution of wave equation(6) is a high frequency For instance, the normal mode solution in an ideal approximation (Buckingham, 1992) and this approach has waveguide where the surface is perfectly free and the a special significance for deep waters problems where only bottom perfectly rigid, the boundaries are perfect sound few rays are significant. The ray tracing methods are reflectors at all angles of incidence. The sound speed more suitable when the wavelength is very much less than cw and depth are constant. As a consequence of this any length scale related to the problem. These lengths particular situation, the values of the pressure reflection include bottom and surface roughness, the dimensions coefficient at the surface and at the sea bottom are ±1 of the campaign region as well as the distance over respectively (Jessen, 1994). In this framework, the residue measurable changes in the sound speed profile. There series in (5) gives the following sound pressure field as the is also some advantages in ray tracing, like velocity of following sum over all propagating modes (Jessen, 1994). computing rays can be traced through range-dependent sound speed profile and over complicated batimetry. The r Zm(z )Zm(z)exp(−ikmr) p = a exp[i(wt + p=4) 0 0 (9) difficulties are keeping the track of the phase at bottom 0 ∑ 1=2 m um(2pkmr) reflections, and computing shear waves contributions in an elastic bottom, but the principal disadvantage is that the In the present situation, where we assume harmonic fields, wave effects such as diffraction and caustics cannot be the above equation(9) is a explicit function of the angular handled satisfactorily. So, in order to obtain some physical frequency w = 2p f and the propagation time t. In addition, insight about the main features of the sound propagation, it the normal mode expression(9) of the sound pressure is is suitable analyze our results on both frameworks, the ray suitable to calculating sound field as a function of depth z tracing as well as normal mode theory. and range r, where the horizontal k and vertical g wave numbers satisfy the following equation: The sound speed profile sketched in Figure 1 is typical from Arraial do Cabo,RJ, Brazil. Here, it represents one month w2 averaged sound speed profile. In addition in this same k2 = k2 + g2 = : (10) m m c2 geographical region, assuming a constant depth of d= 80m, the structure of the water layer and the first sub bottom Besides, in (9) ao is a constant related to the source sediment are estimated by the following values of the 3 power, rw is the water density, z0 is the source depth, Zm constitutive parameters rw=1024 kg/m , cb=1750 m/s, rb = 3 is the vertical eigenfunction, while um is proportional to 1800kg=m respectively.