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## Avcohfarlne ELectronics UNDERWATER SOUND TRANSMISSION (1962)

### Citations

142 | Wave Propagation in a Turbulent Medium - Tatarski - 1961 |

79 |
Statistical properties of a sine wave plus random noise
- Rice
- 1948
(Show Context)
Citation Context ...r interest and will be disregarded. We are concerned with the behavior of the derivatives of F near a turning point. Using higher order terms as z -. Z, we may derive the relationship sin d(IF -sin 0 =-=(59)-=- as 0 - , which yields il(t •-kr)( / q -- > e i(-r) ni (60).'2rs 's001sFrom Equation (60) we obtain (2012i (w t - kr + •/12 1/6 -V - qJ (•) " •/3 (5 /3 r' sin 0 cos2 80 We note in passing that if N2 =... |

48 | Absorption and Dispersion of Ultrasonic Waves - Herzfeld, Lovitz - 1959 |

34 |
Physical properties of marine sediments
- Nafe, Drake
- 1963
(Show Context)
Citation Context ...er, no useful results can be obtained. In case the sound speed is a linear function of depth, and if =11 dcl 'Y c dZ (37) then the diffraction field pressure is nearly equal to S'A -3 (-' ) (H + 21 V =-=(38)-=- p L e H and V are the horizontal and vertical distances shown in Figure 11 and PL is the pressure at the limiting ray. 53 LLI LLJ LAJ LALLLU 2cLLJ 54 There appear to be few instances that Equation (3... |

17 |
Propagation of sound through a liquid containing bubbles
- Carstensen, Foldy
- 1947
(Show Context)
Citation Context ...ce, H= [(D + L)] 2 kyd is defined for water depth D anct layer depth L in feet. If the range R between source and receiver is less than H, then the propagation loss is N = ZO log R + aR + 60 - kL db; =-=(66)-=- kL , the near field anomaly, represents the mean contribution to the field of the multiple bottom and surface reflections. It is a function of bottom loss and surface loss such that kL = 10 log(l + Z... |

12 | Phase Velocity and Absorption Measurements in Water Containing Air Bubbles - Curley |

10 |
Speed of Sound in Sea Water as a Function of Temperature , Pressure and Salinity
- Wilson
- 1960
(Show Context)
Citation Context ...ts made by diluting the samples with distilled water. The first equation has a standard error of about 0. 22 m/sec and the second a value of 0. 30 m/sec. Equation 1, C = 1449.22 + CT + CP + CS + CSTP =-=(4)-=- where: CT = 4. 6233T - 5. 4585 x 10"2T 2 + 2. 822 x 10- 4 T 3 - 5. 07 x 0-7 TT4, Cp = 0.6 0 518x 10"1 P + 1. 0 279x 10-'P2 + 3.451x 10 9 P 3 - 3.5 0 3x 10" 2 pP 4 CS = 1.391(S-35) - 7.8 x 10 z (S-35)... |

10 |
Equation of Sound in Sea Water
- Wilson
(Show Context)
Citation Context ... sej water from Newton' s formula. Cz _ pP (5) where y is the ratio of specific heats, p is the density, and P is the isothermal compressibility. The density was computed from the formula PO P (1- P) =-=(6)-=- where p. is the mean compressibility as defined in Equation (8) below. The true compressibility, P , was found from the mean compressibility by the relation, 1 dv _ .~p. (dP'/dp) V dP 1 - Pp( It may ... |

9 |
Bottom Reverberation for 530 and 1030cps Sound in Deep Water
- Mackenzie
- 1948
(Show Context)
Citation Context ...leading to Equation (29) is applicable in principle to the present situation. However, no useful results can be obtained. In case the sound speed is a linear function of depth, and if =11 dcl 'Y c dZ =-=(37)-=- then the diffraction field pressure is nearly equal to S'A -3 (-' ) (H + 21 V (38) p L e H and V are the horizontal and vertical distances shown in Figure 11 and PL is the pressure at the limiting ra... |

8 |
Waie Propagation in a Randomly Inhomogeneous Medium, III
- Mintzer
- 1954
(Show Context)
Citation Context ...nomaly, represents the mean contribution to the field of the multiple bottom and surface reflections. It is a function of bottom loss and surface loss such that kL = 10 log(l + Zr arb + ra + rb ) db, =-=(67)-=- ra and rb being the surface and bottom intensity-reflection coefficients, respectively. The absorption coefficient in sea water (in kyd) is a and is discussed in references 9 and 14. N = 15 logR + aR... |

8 | Diagrams and the V, Method - Cole |

6 |
Propagation of Radiation in a Medium with Random Inhomogeneities
- Bergmann
- 1946
(Show Context)
Citation Context ...er of rays reaching a field point in - creases as the range increases. Hence the total field ultimately follows a cylindrical spreading law. More precisely, if N is the number of rays, then N Ipl _R2s=-=(64)-=- The quantity N can be determined by constructing a field diagram (Figure 5) , or can be estimated as follows. Let r0' and r 0 ' 'be the maximum and minimum cycle ranges for all possible angles. Then ... |

6 | Forward Scattering of Sound in the Sea and Its Correlation with the Temperature Microstructure", The - Whitmarsh, Skudrzyk, et al. - 1957 |

5 |
Scattering of underwater sound by a sea surface
- Marsh, Schulkin, et al.
- 1961
(Show Context)
Citation Context ...ial case where the origin is at one of the depths. These depths will be denoted Z+ and Z.. It is obvious, then, that Z+ * Z < Z.. Let z F z = cot Od• (19) Here E may be + or -. r = 2F+ (0) + 2F._ (0) =-=(20)-=- has been termed the "cycle range" by Cole," 7 and is twice the skipdistance defined by Marsh and Schulkin2 .l Equation (18) can now be written r [ .F+(0) - F+ (z)] + .-. (0) - F (z)] + 2mF+ (0) + ZnF... |

5 | Scattering of sound in a turbulent medium - Kraichnan - 1953 |

5 | The Effect of Temperature Inhomogeneities in the Ocean on the Propagation of Sound - Liebermann - 1951 |

4 |
Fundamentals of Sonar
- Horton
- 1961
(Show Context)
Citation Context ...omplex superposition). The solution for the sound field may be obtained with the aid of ray geometry. Corresponding to Equation (12) , there is a set of surfaces determined by the equation IV0Iz = nzs=-=(16)-=- where n £QC, and is the index of refraction relativc to the reference c speed co. The surfaces, where 0 is constant, constitute a set of wave fronts. Orthogonal to these wave fronts are skew curves, ... |

4 |
Density and Porosity of Sea-Floor Surface Sediments off San Diego", Bulletin Assoc. Petroleum Geologists 40
- Hamilton, Menard
- 1956
(Show Context)
Citation Context ...he additional fact that the scattering should level off at high frequencies. The irreversible conversion of acoustic to thermal energy, or absorption, is represented by the term e , in which A = lads =-=(34)-=- 2. 4. 4 Scattered Field Sound scattering, as a propagation effect, produces three basic effects. These include: a) contribution to the primary field b) creation of sound energy in shadows c) contribu... |

4 |
Transmission of 24-Kc Underwater Sound from a Deep Source
- Sheehy
- 1950
(Show Context)
Citation Context ...he behavior of the derivatives of F near a turning point. Using higher order terms as z -. Z, we may derive the relationship sin d(IF -sin 0 (59) as 0 - , which yields il(t •-kr)( / q -- > e i(-r) ni =-=(60)-=-.'2rs 's001sFrom Equation (60) we obtain (2012i (w t - kr + •/12 1/6 -V - qJ (•) " •/3 (5 /3 r' sin 0 cos2 80 We note in passing that if N2 =1- 1 ' Z, the case discussed by Marsh12 7 when 2a= a 2 sin ... |

4 | Acoustic Intensity Fluctuations and Temperature Microstructure in the Sea - Sagar - 1960 |

4 |
Range Dependence of Acoustic Fluctuations in a Randomly Inhomogeneous Medium
- Stone, Mintzer
- 1962
(Show Context)
Citation Context ...nce along the ray increases. This is trivially true for non-cyclic rays, or for reflected, non-refracted rays. For cyclic rays the result is true because, as r increases, r = mr 0 + E dr dro mo dO0 + =-=(63)-=- r dO+p in which e, c 1, and ez have maximum values, independent of r. Hence for points chosen at random along a ray, the probability that r - mrI < E tends to 1 as r increases, where E is any preassi... |

4 |
Note on the scattering of radiation in an inhomogeneous medium, Phys
- Pekeris
- 1947
(Show Context)
Citation Context ... N can be determined by constructing a field diagram (Figure 5) , or can be estimated as follows. Let r0' and r 0 ' 'be the maximum and minimum cycle ranges for all possible angles. Then + R<N L<1+ R =-=(65)-=- r 0s2 r01, 2. 5. 3 Shallow-Water Transmission 5Z Accounts of shallow-water transmission have recently appeared in the literature. In particular, references 2, 55, 58, 122, 128 discuss the 64 boundary... |

3 |
Speed of Sound in Water by a Direct Method
- Greenspan, Tschiegg
- 1957
(Show Context)
Citation Context ...y (980 cm/sec2 ) , s is the wind speed in cm/sec and w the angular freqnency in rad/sec. In addition, the relation hz = 2. 42 x 10-6a5 cm 2s(2) is employed for the mean square wave height, H = 1. 77h =-=(3)-=- for the average trough to crest wave height. 17 The sea is presumed to be isotropic, or rather, the average scattering over all azimuths is considered in developing the sound field. 0 2. 2. 2. 2 Chem... |

3 |
Formulas for the Computation of Sound Speed in Sea Water
- Mackenzie
- 1960
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Citation Context ...ssibility by the relation, 1 dv _ .~p. (dP'/dp) V dP 1 - Pp( It may be seen from this equation that the mean compressibility is defined by I (v-V) (8) Vo (P Po) where P = 0. Substituting Eqs. (6) and =-=(7)-=- into Eq. (5) , we obtain cz V (I - p )z a = F rP(di/TdP)- 2z The object in writing the equation for sound speed in terms of ii instead of P was to allow the use of an empirical equation obtained by V... |

3 |
Sound Absorption in Sea Water
- W, Schulkin
(Show Context)
Citation Context ...gat's pressure measurements. Therefore, the effect of pressure on the speed of sound in water should have the same characteristics regardless of whether Ekman's or Amagat' s data is used. In Equation =-=(9)-=- , p. can be obtained either from Equation (8) and Amagat's data, or from Ekman' s empirical equation. If Equation (8) and Amagatt s data are used, the second derivative of sound velocity in distilled... |

3 |
Factors Affecting Compressional Wave Velocity in Unconsolidated Marine Sand Sediments
- Brandt
- 1960
(Show Context)
Citation Context ...2 /' A) +. 25 , the number of trapped modes. When Marsh's equations" 0° are evaluated in detail the following form results for the product of the depth functions: U Y (ta). U (t = (MIM ), F(ta,tb )/D =-=(39)-=- D will be discussed later. F(ta, tb) takes one of three possible forms as follows: Case I - when both source and receiver are in the channel; i. e. ta -< tb -< 1 A(ta). A(tb) (40) Case II- when both ... |

3 |
On the propagation of waves in a medium with ran- dom inhomogeneities of the index of refraction. Akusticheskii Zhurnal
- Obukhov
- 1956
(Show Context)
Citation Context ...nce is exhibited. We would expect scattered rays to suffer greater loss because they are steeper. The simplest expression satisfying this requirement and the observed data was rt = ra rb +(I - r.) rb =-=(70)-=- where rt is the fraction of energy transmitted down the channel when a bottom event is coupled with each surface reflection, at - - lOlogl 0 rt (shallow-water attenuation constant, db/bounce) , rb is... |

3 |
On Wave Propagation in a Random Inhomogeneous Medium
- Potter, Murphy
- 1957
(Show Context)
Citation Context ...g [2z+ (ratio equivalent of boundary loss) 23db (71) This overestimates the situation, but is a proper estimate for conservative calculations. At the other extreme, we have simply 1 = [32 + q'Sz+ 'B] =-=(72)-=- as an example of the minimum variance of the propagation loss for a field dominated by surface and bottom reflected paths, and T Sz,' Bz being the variances associated with single refractions at surf... |

3 | Attenuation of Sound in Water Containing Air Bubbles - T, Kendig - 1952 |

3 | Absorption of Sound in Fluids", Rev - Beyer, Markiiam, et al. - 1951 |

2 |
The Propagation of Sound
- Schulkin
- 1969
(Show Context)
Citation Context ...2 Sound Absorption in Sea Water The recommended expression9 for absorption, a, in sea water 24 as a function of temperature, pressure and salinity is: SSAfT fZ B2 - Uf - 6. 54 x 10- 4 P) nepers/meter =-=(10)-=- fT? + fz T wher e: S is the salinity in parts per thousand fT is the temperature dependent relaxation frequenc in kc at atmospheric pressure = 21.9 X 10 -6 "1520 /(T at f is the acoustic frequency in... |

2 |
Measuremerts of the Backscattering of Underwater Sound from the Sea S-urface
- Garrison, Murphy, et al.
- 1960
(Show Context)
Citation Context ...plex sum p = .i pi over all rays reaching the field point. The equation for Pi will be stated, 44 p-Jl -j Lu LU2 cn .4c LhJ LLLU L16 0~LL. =4 and then the individual terms discussed. pi qJ( m ) Bnm-A =-=(26)-=-e e Each term in this equation is a function of the ray parameters and so a subscript (i) is implicit. The quantity q represents the optical approximation to the pressure, and is equivalent to the pre... |

2 |
Sound Velocities at the Surface of Deep Sea Sediments
- Fry, Raitt
- 1961
(Show Context)
Citation Context ...y MarshIl, who developed a correction to the optical limit, taking into account the finite wave length. For J( ), we have J(9 ei(2 5;/3-5 7r/12) ir /Z q /6 2V '/3 3D "/ ý '3 (9 in which ko(dr/deo )3= =-=(30)-=- 2 sin 0o (d2 r/d0 02)z and h? is the modified Hankel function as defined in reference 119. The quantity qJ (5) is not applicable when both d' r/dOoZ and dr/dO0 are zero. However, this can happen only... |

2 |
Effect of Transducer Velocity on the Structure of Signals Reflected from the Ocean Bottom", Paper W3, Meeting ASA
- Hurdle, Ferris
- 1962
(Show Context)
Citation Context ...istic equation Ph 2 C(B). B- hz' (B 1) o A(1) = 0 (47) In the case of strong trapping the following approximation to the roots may be us eful. Re(MXI)= 2 ( Im (MX~),= ~ Re (MY.,~' exp (M -3sReMXn)/z} =-=(48)-=- The velocity potential 4 is given by - ie NZ HO(077 r) Un (ta). Un(tb) (49) Ar) G-,, i Tri 0- K - r Re(MXn) 59 r I (MXQ k = Co The damping coefficient is given by T'r7 while 17,7 is needed in the pha... |

2 |
Study of Acoustic Propagation in a TwoLayered Model
- Williams, Ely, et al.
- 1960
(Show Context)
Citation Context ...f 0' is zero, we have the case of an internal (depressed) channel. The two are exactly equivalent with respect to the present analysis. Let Z be the depth of a turning point, so that n' (Z) = cos' 00 =-=(57)-=- In the vicinity of Z, %-.,hen z ;s slightly less than Z, we may always write n(z) = cos 0, +a(Z- z), a >o (58) 62 If a - o we have a relative maximum in the sound speed; if a = O0 we have a cusp in t... |

2 |
Fluctuations of Amplitude and Phase in a Spherical Wave", Soviet Phys
- Karavainikov
- 1957
(Show Context)
Citation Context ...z respectively, then the actual variance <T2 %hould be bounded Z - " O <O-. An expression for the variance of the propagation loss in db is: 1 G_= 10 log [2z+ (ratio equivalent of boundary loss) 23db =-=(71)-=- This overestimates the situation, but is a proper estimate for conservative calculations. At the other extreme, we have simply 1 = [32 + q'Sz+ 'B] (72) as an example of the minimum variance of the pr... |

2 | Theoretical and Experimental Study of Underwater Sound Reverberation - Cron, Schumacher |

2 | Acoustic Intensity Anomalies Introduced by Constant Velocity Gradients - Pedersen - 1961 |

2 | An Acoustical Interferometer for the Measurement of Sound Velocity in the Ocean - Urick |

1 |
Geological Society of America, Memoir 27 (1948) a) "Explosion Sounds in Shallow Water
- Worzel
(Show Context)
Citation Context ...ere c =4. 8 x 104 cm 2 sec , g is the acceleration of gravity (980 cm/sec2 ) , s is the wind speed in cm/sec and w the angular freqnency in rad/sec. In addition, the relation hz = 2. 42 x 10-6a5 cm 2s=-=(2)-=- is employed for the mean square wave height, H = 1. 77h (3) for the average trough to crest wave height. 17 The sea is presumed to be isotropic, or rather, the average scattering over all azimuths is... |

1 |
Equation for the Speed of Sound in Sea Water
- Wilison
- 1960
(Show Context)
Citation Context ...t other pressures, a review was made of the method used for computing sound speeds from specific volume0 data. Kuwahara and Matthews computed sound speeds in sej water from Newton' s formula. Cz _ pP =-=(5)-=- where y is the ratio of specific heats, p is the density, and P is the isothermal compressibility. The density was computed from the formula PO P (1- P) (6) where p. is the mean compressibility as de... |

1 |
Convergence Zone Propagation in the North-East Pacific
- Maunsell, Scrimger
- 1961
(Show Context)
Citation Context ...tio of specific heats, p is the density, and P is the isothermal compressibility. The density was computed from the formula PO P (1- P) (6) where p. is the mean compressibility as defined in Equation =-=(8)-=- below. The true compressibility, P , was found from the mean compressibility by the relation, 1 dv _ .~p. (dP'/dp) V dP 1 - Pp( It may be seen from this equation that the mean compressibility is defi... |

1 | Dependence of Sound AbsOarption on Concentration, Frequency, and Temperatur e n MgSO 4 Solutions Equivalent to Sea Water - Grosso, A |

1 |
Measurements of Sound Absorption
- Kurtze, Tamm
- 1954
(Show Context)
Citation Context ...l be listed and developed where necessary. The excess pressure P is the variable to be used in describing the sound field, and the fundamental equation governing P is the wave equation aZ p at 2 Ct . =-=(12)-=- In Equation (12) , 7 is the Laplacian operator and c the speed of sound. For a unique determination of P, boundary conditions and initial conditions must be stated. The boundary conditions require th... |

1 |
Sound Ab> sorption as a Function of Frequency from Direct Transmiiasion Measurements
- Murphy, Garrison
- 1957
(Show Context)
Citation Context ...l conditions. In the following developments, the source will be taken as an isotropic, point source, with a simple harmonic angular frequency of w. 33 In this case, Equation(lZ) becomes 17 p +k'p = 0 =-=(14)-=- iWt where k - and p = Pe t Near the source, if R is the distance to C the source, i(kR - wt)i = _e (15) R For other initial conditions, results may be obtained by Fourier synthesis, (i. e., complex s... |

1 |
Formulas for Sound Velocity ir-i Sea Water
- Beyer
- 1954
(Show Context)
Citation Context ...h a simple harmonic angular frequency of w. 33 In this case, Equation(lZ) becomes 17 p +k'p = 0 (14) iWt where k - and p = Pe t Near the source, if R is the distance to C the source, i(kR - wt)i = _e =-=(15)-=- R For other initial conditions, results may be obtained by Fourier synthesis, (i. e., complex superposition). The solution for the sound field may be obtained with the aid of ray geometry. Correspond... |

1 |
Measurement of Attenuation of Low Frequency Underwater Sound
- Sheehy, Halley
(Show Context)
Citation Context ...titute a set of wave fronts. Orthogonal to these wave fronts are skew curves, which are the rays of the sound field. If s is the arc length measured along a ray, the equation of the ray is d (n dx-an =-=(17)-=- ds \ -ds ) aTx and similarly for y and z. From the manifold of rays, those rays connecting specific points may be selected by integrating Equation (17) and applying boundary conditions. The selected ... |

1 |
An Equivalent Network for aMcoustical Transmission in Sea Water", Report SP-45, T"MPO, General Electric
- Peterson
- 1961
(Show Context)
Citation Context ...ed here. Temporarily, take the origin of cylindrical coordinates (r, z) to be at the source, and the source inclination to be 00. Then the equation of a point on the ray may be written z r =f cot 6 d =-=(18)-=- 0 0 is the inclination of the ray at the point ,. In Equation (18) , cot 0 must be finite and continuous throughout the interval of integration. In general, there will be points at which one of these... |

1 |
Sound Transrn~ission between 2 and 25 Kilocycles per Second
- Marsh, Schulkin
- 1954
(Show Context)
Citation Context ...predominant, and in which the deepest fiducial point is a turning point. In other words, the range is several multiples of the cycle ranges, and the influence of the ocean bottom is ignored. Equation =-=(21)-=- shows that, when the source and receiver depths are equal, the range is r = 2mF+ (o) + 2nF -(o) m tro + 2(n- m )F_(o) Hence when the range is an integral multiple of the cycle range, (54) r mr 0 dr m... |

1 |
Sound Reflection and Scattering from the Sea Starface
- Marsh
(Show Context)
Citation Context ...If 00 >0, m >- n and vice versa. In any case, rm- nj -< 1. In addition to the purely geometrical properties of the rays the eikonal K is important. We have K =ds ds (I+icL) TiA (z*ids c(-ia)f 0-s+ iA =-=(22)-=-0 €(1 - i a' 0 c T is the "Travel time, " and A represents absorption. Corresponding to the quantity FE , define zEZE G= j sin cos' H f sin 0 cos 0 z z Then, a -T Y+ [G +(0) - G+ (z)] + r_[G_(0)- G(zj... |

1 | Sea Surface Statistics deduced from Underwater Sound Measurements", manuscript submitted to N. Y. Academy of Sciences - Marsh |

1 |
The Processes of Sound Scattering at the Ocean Surface and Bottom", j
- Uricki
- 1956
(Show Context)
Citation Context ... FE , define zEZE G= j sin cos' H f sin 0 cos 0 z z Then, a -T Y+ [G +(0) - G+ (z)] + r_[G_(0)- G(zjCos 80 + 2mG + (0) + 2Y G_ (0) So A = +[H+ (0) -H+ (z)] +nr_ [Hs_(0) - H (z)] + Zm H+(0) + 2r H_(0) =-=(24)-=- 43 It is of interest to note that, by virtue of the mean value theorem of the calculus, T r (25)C. Cos 0 where c and cos 0 correspond to some point along the ray. This equation shows the extreme poss... |

1 |
Backscattering of Sound From the Sea Surface: Its Measurements, Causes, and Application to tha Prediction of Reverberation Levels
- Urich, Hoover
(Show Context)
Citation Context ...(zjCos 80 + 2mG + (0) + 2Y G_ (0) So A = +[H+ (0) -H+ (z)] +nr_ [Hs_(0) - H (z)] + Zm H+(0) + 2r H_(0) (24) 43 It is of interest to note that, by virtue of the mean value theorem of the calculus, T r =-=(25)-=-C. Cos 0 where c and cos 0 correspond to some point along the ray. This equation shows the extreme possible departure of the travel time from that which would be associated with the corresponding refr... |

1 |
Sound Transmission in the Arctic Ocean
- Kutshxale
- 1961
(Show Context)
Citation Context ...pressure, and is equivalent to the pressure reduction due to geometrical divergence of the ray bundle as discussed by Horton16, among many other s. Explicitly, -icw(t - T) ( Iq = e (-rn tano dr/de0 ) =-=(27)-=- Again, T is the "Travel time". T ds •(28)f c The quantity qJ ( ) has been discussed by MarshIl, who developed a correction to the optical limit, taking into account the finite wave length. For J( ), ... |

1 |
The Effect of Ice on Long Range Underwater
- son, D
- 1962
(Show Context)
Citation Context ...e reduction due to geometrical divergence of the ray bundle as discussed by Horton16, among many other s. Explicitly, -icw(t - T) ( Iq = e (-rn tano dr/de0 ) (27) Again, T is the "Travel time". T ds •=-=(28)-=-f c The quantity qJ ( ) has been discussed by MarshIl, who developed a correction to the optical limit, taking into account the finite wave length. For J( ), we have J(9 ei(2 5;/3-5 7r/12) ir /Z q /6 ... |

1 |
Underwater Sound Propagation i n the Arctic Ocean
- Mellen, sh, et al.
- 1962
(Show Context)
Citation Context ...inish exponentially in proceeding away from the limiting ray. In Figure 11 there are two limiting rays, and there will be a diffraction field associated with each. The development leading to Equation =-=(29)-=- is applicable in principle to the present situation. However, no useful results can be obtained. In case the sound speed is a linear function of depth, and if =11 dcl 'Y c dZ (37) then the diffractio... |

1 |
NcousLic and Other Physical Properties of Shallow Water Sedirnimnts off San Diego
- Menard
- 1956
(Show Context)
Citation Context ...ough Mackenzie 35 has shown that the acoustic properties of sediments may be reduced to first principles when sufficiently detailed knowledge of the material- is available. We write B = B (w, 0B, C), =-=(31)-=- 0 B being the grazing angle at the bottom and e indicating potential environmental dependency. G2 is the specular scattering coefficient of the sea surfacez. For small scattering, 3/A l•0S= I -0. 485... |

1 |
Sound Speed and Absorption Studies of Marine Sedir.nents by a Resonance Method
- Shunm-way
- 1960
(Show Context)
Citation Context ...he grazing angle at the bottom and e indicating potential environmental dependency. G2 is the specular scattering coefficient of the sea surfacez. For small scattering, 3/A l•0S= I -0. 485 b H sin 08s=-=(32)-=- where H is wave height in feet, b is equal to w H/27r, and 0s is the grazing angle at the sea surface. We take the same parametric depen - dence to hold for large scattering, so that, in general, a =... |

1 |
Low Velocities in High-Porosity Sediments
- Hamilton
- 1956
(Show Context)
Citation Context ...t in feet, b is equal to w H/27r, and 0s is the grazing angle at the sea surface. We take the same parametric depen - dence to hold for large scattering, so that, in general, a = Q (b 3/ H V/osin 09) =-=(33)-=- Figure 8 shows measured values from many sources,72 with Equation (32) plotted as a solid curve in the form, surface loss = - 10 log Q. 47 a A114 .... .... j+[f 4 4 ...44 ....... 44hl= ft JT V4 I -i ... |

1 |
Reflection of Sound from Coastal Bottoms", J.Acoust
- Mackenzie
(Show Context)
Citation Context ..., and for an incident plane wave. In terms of the geometry of Figure 9, Marsh gives, for small scattering, 49 LLAh ULLLU LUJ I-z C.> LU ULLU LU CD LUJ C.0 U50 S-/ r 0. 098H 4 (1 -i ) exp(- 1/a') ai 2 =-=(35)-=- where: '= 6. 33H / b(l - v1 ) (1-v) = 2 - (v -Y -2 cos I = rdkdp. as the ratio of scattered intensity in the direction (X, p.) to incident intensity. For application to a definite calculation, integr... |

1 |
Long Range, Shallow Water Bottom Reverberation
- Mackenzie
- 1962
(Show Context)
Citation Context ...opagation. Thus, the total scattered intensity will equal that lost from the specularly reflected ray. Accordingly, the scattered field due to the primary ray in question is approximately 2 re aR SRz =-=(36)-=- where C f 2/2 I sin d = 0 51 0 LU C2.) UD LUJ C= LUJ LU LA0( L&LU CsLLJ 52 The results 7 give empirical expressions for the sound field below the isothermal layer, which should be equivalent on the a... |

1 |
Preliminary Investigation of Echo Strength Received from the Sea Floor," 63rd Meeting Acoust. Soc. Am
- Breslan, Hersey, et al.
- 1962
(Show Context)
Citation Context ...(MIM ), F(ta,tb )/D (39) D will be discussed later. F(ta, tb) takes one of three possible forms as follows: Case I - when both source and receiver are in the channel; i. e. ta -< tb -< 1 A(ta). A(tb) =-=(40)-=- Case II- when both source and receiver are below the channel; i.e. 1 -< ta-4tb rhA (B1) h 2 (Bta) h2 (Btb) (41) Case MI - when one is in and one below the channel; i. e. ta < 1 - tb A (ta) hz (Btb) (... |

1 |
Acoustic Reflection Studies of the Continental Shelf and Slope off Southern California
- Moore
- 1960
(Show Context)
Citation Context ... I - when both source and receiver are in the channel; i. e. ta -< tb -< 1 A(ta). A(tb) (40) Case II- when both source and receiver are below the channel; i.e. 1 -< ta-4tb rhA (B1) h 2 (Bta) h2 (Btb) =-=(41)-=- Case MI - when one is in and one below the channel; i. e. ta < 1 - tb A (ta) hz (Btb) (42) 58 where A (t) = h,(MX YJ))h,(MX T)- Mt) - h2 (Mr) h, (MXr,- M/t) (43) The h, and hz functions are solutions... |

1 |
Ocean Basin Structure as Revealed by Seismic Profiles Studies
- Ewing, Ewing
- 1961
(Show Context)
Citation Context ...) Case II- when both source and receiver are below the channel; i.e. 1 -< ta-4tb rhA (B1) h 2 (Bta) h2 (Btb) (41) Case MI - when one is in and one below the channel; i. e. ta < 1 - tb A (ta) hz (Btb) =-=(42)-=- 58 where A (t) = h,(MX YJ))h,(MX T)- Mt) - h2 (Mr) h, (MXr,- M/t) (43) The h, and hz functions are solutions of Stokes' equation and are discussed at length and tabulated in reference 119. First deri... |

1 |
3., "Back Scattering of Sound from a Harbor Bottom
- Urick
- 1954
(Show Context)
Citation Context ...-< ta-4tb rhA (B1) h 2 (Bta) h2 (Btb) (41) Case MI - when one is in and one below the channel; i. e. ta < 1 - tb A (ta) hz (Btb) (42) 58 where A (t) = h,(MX YJ))h,(MX T)- Mt) - h2 (Mr) h, (MXr,- M/t) =-=(43)-=- The h, and hz functions are solutions of Stokes' equation and are discussed at length and tabulated in reference 119. First derivatives of these f unctions are designated as hl' and hz'. MX7 is the c... |

1 |
Backscattering of Explosive Sound by the Deep Sea Bottom, paper C4, 63rd Meeting of Acoust. Soc. Am
- Saling
- 1962
(Show Context)
Citation Context ...at length and tabulated in reference 119. First derivatives of these f unctions are designated as hl' and hz'. MX7 is the complex eigen value and will be given presently. Bt = pz(MX M _ M) + (M - Mt) =-=(44)-=- P A (1) and B 1 are obtained by setting t = 1 in the above expressions. D =(P 3 - I) [Bz +(MXr7- M) AZ(1)] - 2.1242930 (45) where the negative constant is the square of the Wronskian, W (hlh 2 ) and ... |

1 |
The Reflection of Sound from Coastal Sea Bottoms
- Liebernann
- 1948
(Show Context)
Citation Context ...mplex eigen value and will be given presently. Bt = pz(MX M _ M) + (M - Mt) (44) P A (1) and B 1 are obtained by setting t = 1 in the above expressions. D =(P 3 - I) [Bz +(MXr7- M) AZ(1)] - 2.1242930 =-=(45)-=- where the negative constant is the square of the Wronskian, W (hlh 2 ) and B is defined by B = h, (MXn)hz'(MXIK - M)- hz(MX?)h 1 tMXr- M) (46) MX- is a complex root of the characteristic equation Ph ... |

1 |
An Acoustic Survey of the b-,a Floor
- Lloyd
- 1961
(Show Context)
Citation Context ...ressions. D =(P 3 - I) [Bz +(MXr7- M) AZ(1)] - 2.1242930 (45) where the negative constant is the square of the Wronskian, W (hlh 2 ) and B is defined by B = h, (MXn)hz'(MXIK - M)- hz(MX?)h 1 tMXr- M) =-=(46)-=- MX- is a complex root of the characteristic equation Ph 2 C(B). B- hz' (B 1) o A(1) = 0 (47) In the case of strong trapping the following approximation to the roots may be us eful. Re(MXI)= 2 ( Im (M... |

1 |
uund Exploration in Reports of the Swedish Deep-Sea Expedition
- Weibull
(Show Context)
Citation Context ...the square of the Wronskian, W (hlh 2 ) and B is defined by B = h, (MXn)hz'(MXIK - M)- hz(MX?)h 1 tMXr- M) (46) MX- is a complex root of the characteristic equation Ph 2 C(B). B- hz' (B 1) o A(1) = 0 =-=(47)-=- In the case of strong trapping the following approximation to the roots may be us eful. Re(MXI)= 2 ( Im (MX~),= ~ Re (MY.,~' exp (M -3sReMXn)/z} (48) The velocity potential 4 is given by - ie NZ HO(0... |

1 |
Long-Range Shallow-Water, Transmission
- Mackenzie
- 1961
(Show Context)
Citation Context ... trapping the following approximation to the roots may be us eful. Re(MXI)= 2 ( Im (MX~),= ~ Re (MY.,~' exp (M -3sReMXn)/z} (48) The velocity potential 4 is given by - ie NZ HO(077 r) Un (ta). Un(tb) =-=(49)-=- Ar) G-,, i Tri 0- K - r Re(MXn) 59 r I (MXQ k = Co The damping coefficient is given by T'r7 while 17,7 is needed in the phase determination. For sufficiently large values of r HO2 (x - -r)-( 2 /Zexp ... |

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Signal-Level Fluctuation and Frequency Spreading
- Mackenzie, Long-Range
- 1962
(Show Context)
Citation Context ...i 0- K - r Re(MXn) 59 r I (MXQ k = Co The damping coefficient is given by T'r7 while 17,7 is needed in the phase determination. For sufficiently large values of r HO2 (x - -r)-( 2 /Zexp i( rr- -) TrJ =-=(50)-=- The transmission loss H is given by H = - 10 log j4.j From Equations (49) and (50) Z4, A77 cos 09 7 +[Z Ar7 sin 07 ]21r (51) wher e we= IU(ta) Ur(tb)I e Tr (52) 07= LJý 77 dr =arg - ( U 7(ta) Uri (tb... |

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Further Remarks on Long-Range, ShallowWater Transmission
- Mackenzie
- 1962
(Show Context)
Citation Context ...n. For sufficiently large values of r HO2 (x - -r)-( 2 /Zexp i( rr- -) TrJ (50) The transmission loss H is given by H = - 10 log j4.j From Equations (49) and (50) Z4, A77 cos 09 7 +[Z Ar7 sin 07 ]21r =-=(51)-=- wher e we= IU(ta) Ur(tb)I e Tr (52) 07= LJý 77 dr =arg - ( U 7(ta) Uri (tbfj. 2. 5 Practical Calculation of the Sound Field 2. 5. 1 General Considerations For detailed and precise calculation, the me... |

1 | Study of LowFrequency Sound Propagation in Hartlin Point Region of the ScotianShelf', J.Acoust - MacPherson, Fothergell |

1 |
Acoustic Attenuation in a Liquid Layer over a '"low' Viscoeiastic Solid", j
- Jr, Ely
(Show Context)
Citation Context ...f integral multiple of the cycle range. In the latter case, if the field point is at the depth of a fiducial point then the ray divergence is determined by 16 1 m2 r 0 n tan 0 dro/ dO0 provided r MEL =-=(55)-=-4 if 0 is zero, qJ ( mu) st be evaluated for the limit • -- 0, and we have = mg 0, 9 0 being the value of 1 corresponding to r = r 0 /4; z o. This gives I( 9o) tan0' m5/3 tan 0 (56) 0' being the ray a... |

1 |
Act.ustic Propagatinn in a Two-Layered Model-Transverse Wave in Bottom
- Eiy
(Show Context)
Citation Context ...dO0 provided r MEL (55)4 if 0 is zero, qJ ( mu) st be evaluated for the limit • -- 0, and we have = mg 0, 9 0 being the value of 1 corresponding to r = r 0 /4; z o. This gives I( 9o) tan0' m5/3 tan 0 =-=(56)-=- 0' being the ray angle at the point r = ro/4L It can be seen that either 0' or 0 i,. zero, and hence a further limit must be determined. If 0 is zero we have the case of a surface bounded sound chann... |

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Shallow-Water Test of the Theory of Layered Wave Guides
- Tolstoy
- 1958
(Show Context)
Citation Context ...to the present analysis. Let Z be the depth of a turning point, so that n' (Z) = cos' 00 (57) In the vicinity of Z, %-.,hen z ;s slightly less than Z, we may always write n(z) = cos 0, +a(Z- z), a >o =-=(58)-=- 62 If a - o we have a relative maximum in the sound speed; if a = O0 we have a cusp in the speed profile. The case o <a<Do can include relative maxima if the slope of the speed-depth curve is discont... |

1 |
received from a Source at Sea", J.Acoust
- 5-kc
(Show Context)
Citation Context ...l conditions. In the following developments, the source will be taken as an isotropic, point source, with a simple harmonic angular frequency of w. 33 In this case, Equation(lZ) becomes 17 p +k'p = 0 =-=(14)-=- iWt where k - and p = Pe t Near the source, if R is the distance to C the source, i(kR - wt)i = _e (15) R For other initial conditions, results may be obtained by Fourier synthesis, (i. e., complex s... |

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Wave Propagation in a Random Medium, McGraw-Hill Book Co
- A
(Show Context)
Citation Context ...ter (in kyd) is a and is discussed in references 9 and 14. N = 15 logR + aR + aT(R/H - 1) + 5 logH +60 - kL db. (68) For long ranges, R >_ 8 H, N = 101ogR + aR + aT(R/H - 1) + 10 logH 1- 64. 5- kLdb. =-=(69)-=- These equations represent the gradual transition from spherical spreading in the near field to cylindrical spreading in the far field. The loss coefficient at (db per cycle of bottom and surface refl... |

1 | On the Diffusion of Wound Waves in a Turbulent Atmosphere - Lyon - 1959 |

1 | Scattering in an Inhomogeneous Medium", ORL Contract NOrd - Skudrzyk - 1960 |

1 | Theoretical Development of Volume Reverberation as a First Order Scattering Phenomenon - Carletoi- |

1 | The IsothemnFollowe - Lafond - 1961 |

1 | Slicks and Temperature Structure in the Sea - Lafond |

1 | Effect of an Internai Wave on Sound in the Ocean - Lce - 1961 |

1 | L_, "Measurement of the Transverse Correlation Coefficient of a - Gershman, Tuzhilkin - 1961 |

1 | The Velocity of So.d in Sca Water at Zero Depth - Grosso, A |

1 | Sound Speed Measurements Utilizing the Bathyscapth Tiieste - Mackenzie - 1961 |

1 | Comparison of Directly Measured Sound Velocities with Values Calculated from Hydrographic Data - Hays |

1 | Report HD282, Hydro. Dept. British Admiralty - Matthews - 1939 |

1 | Measurement of Sound Absorption in Aqueous Salt Solutions by a Resonator Method - unknown authors - 1951 |

1 | Effect of Pressure on Sound Propagation in Water - Litovitz, Carnevale - 1955 |

1 | Effects of Pressure on Ultrasonic Relaxation in Liquid - Litovitz, Carnevale, et al. - 1957 |

1 | Theory of the Anomolous Propagation of Acoustic Waves in the Ocean - Marsh |

1 | Tracing on the IBM - Gardner |

1 | The Uses of Ray Tracing in the St udy ot Underwater Acoustic Propagation", Symposium un Sonar Systems - Daintith - 1962 |

1 | et al., "Ray Tracing with an LGP-30 - Dosso - 1960 |

1 | Tracing Program Key (Program II) ", Repc-t No - Cole, Puravs - 1958 |

1 | The Use of Ray Methods and First-Order Diffraction Corrections - Marsh |