C. ALLAN BOYLES and GERALDINE W. JOICE COMPARISON OF THREE ACOUSTIC TRANSMISSION LOSS MODELS WITH EXPERIMENTAL DAT A The use of sound is a basic part of antisubmarine warfare. One factor affecting submarine detec­ tion is transmission loss, which is a measure of the extent to which sound is weakened in passing from one point to another. In the deep ocean, an important propagation mode is convergence zone propagation. When it exists, the sound intensity does not decay as fast with range because the sound energy is partially focused. This article compares the latest theoretical models with measured trans­ mission loss data taken under the conditions of convergence zone formation. INTRODUCTION Since acoustic or sound waves propagate more readily than electromagnetic waves through water, the use of sound has become a basic part of antisub­ marine warfare technology since World War II. There are always many different ways in which equipment can be designed and used, and an intelli­ gent choice among the alternatives depends on accu­ rate knowledge of the different factors affecting per­ formance. One of these factors is the extent to which sound is weakened in passing from one point to another. This weakening is called transmission loss. Figure 1 - The RIV Seismic Explorer was used to tow the It is possible to arrive at a suitable choice of equip­ receiving hydrophone. ment and operational doctrine experimentally by trial-and-error methods, but this can be extremely costly and time consuming. Different equipment must be designed, built, taken to sea, and tested under a wide range of weather and oceanographic conditions. It is much quicker and less expensive if theoretical models can be used to guide the decision as to which is the optimum type of equipment and operational doctrine to be employed for any circum­ stance. The theoretical predictions, of course, cannot be divorced from the experimental data. A limited number of sea tests must be conducted in order to confirm the validity of the theoretical models. This article describes one phase of a sea test con­ ducted in April 1976 in the Pacific Ocean. The major Figure 2 - The USNS DeSteiguer was used to tow the acoustic projector and perform various oceanographic objective of that phase was to make detailed, accu­ measu rements. rate transmission loss measurements and supporting oceanographic measurements so that values derived using the latest theoretical models could be compared phone used to measure the transmission loss was a with the measured values. simple omnidirectional hydrophone. (Omnidirection­ Two ships participated in the test: the R/ V Seismic al means that the response of the hydrophone to an Explorer (Fig. 1), which towed the receiving hydro­ arriving sound wave is independent of the arrival di­ phone, and the USNS DeSteiguer (Fig. 2), which rection.) The acoustic projector (Fig. 3) is quite towed the acoustic projector and took extensive large, weighing approximately 2600 pounds in air. A oceanographic measurements. The receiving hydro- series of eight tonals or sine waves and a linear fre- Volume 3, Number 1, 1982 67 Figure 3 - The acoustic projector used to generate the comb of eight sine waves and the linear frequency-modu­ lated signal. The projector is quite large and weighs about 2600 pounds. quency-modulated signal were radiated by the pro­ jector. In this article, only the 550-hertz tonal and the linear frequency-modulated signal are discussed. The oceanographic parameters measured during the test were temperature and salinity as functions of depth, and the speed of sound measured directly. Very few direct measurements of the sound speed were made because the ship had to remain stationary for several hours while a velocimeter was lowered by cable to the bottom. Figure 4 shows the velocimeter Figure 4 - The Navy oceanographer aboard the USNS being lowered. Temperature measurements can be DeSteiguer prepares to lower a sound velocimeter. This in­ made from a moving ship by using a temperature strumentation package measures the speed of sound di­ probe called an expendable bathythermograph. The rectly as a function of depth and also measures tempera­ ture and salinity. probe is launched from a tube and trails a very fine wire over which the signal carrying the temperature information is continually transmitted. Figure 5 shows a temperature probe being launched during the separated by only a few nautical miles open the range test. Because the speed of sound depends on tempera­ between them until they are about 185 kilometers ture, salinity, and pressure (or, equivalently, depth), apart. There are three convergence zones within a .it can be computed from measurements of tempera­ range of 185 kilometers. Figure 6 is an artist's con­ ture and salinity. Since seawater is nondispersive at ception of a typical run. In this article, we will only frequencies of interest in antisubmarine warfare examine the data taken in the first convergence zone. (through the megahertz range), the speed of sound discussed above is the phase velocity. CONVERGENCE ZONE FORMATION Prior to World War II, only crude listening devices In order to gain some understanding of deep ocean and echo ranging devices were in use. That war gave acoustic propagation and convergence zone forma­ the real impetus to research in underwater acoustics. tion, consider the simplified sound speed profile Since then, some remarkable advances have been shown in Fig. 7. Here we have plotted the speed of made in the field of underwater sound. One such area sound versus water depth from the sea surface to the has been a detailed investigation of the temperature bottom of the water column. structure of the deep ocean and the many different Suppose there is a point source at a depth of 100 propagation paths available to sound energy over meters. (A point source has dimensions much smaller very long ranges (hundreds of kilometers). One im­ than the wavelength being radiated and emits spheri­ portant mode of propagation is called convergence cal wave fronts.) Figure 8 shows two infinitesimal ray zone propagation. Where convergence zones exist, bundles leaving the source in a downward direction. sound energy does not decay as rapidly with range as Rays are curves that are always perpendicular to it otherwise would because the energy is partially wave fronts and, in the limit of vanishing wave­ refocused. The physics of convergence zone forma­ length, energy is transported in the direction of the tion will be discussed in the next section. rays. It is incorrect to speak about intensity or power In order to measure transmission loss in a converg­ per unit area along a single ray. Therefore, associated ence zone environment, two ships that are initially with each ray is an infinitesimal area of the wave 68 Johns Hopkins A PL Technical Digest O~-----.~----.-------r------.------. 400 en 800 j .r:. 0. ~ 1200 1600 2000~-----L------~----~------~----~ 1480 1496 1512 1528 1544 1560 Velocity (meters/second) Figure 7 - Sound velocity as a function of depth. This sim­ plified profile is used to illustrate the formation of conver­ gence zones. 0.-----------,-----------,,----------, Figure 5 - An expendable bathythermograph probe imme­ diately after launch. Notice the very fine wire, trailing from the probe, over which data are transmitted to a recorder. In en contrast to the sound velocimeter shown in Fig. 4, these Q) 400 'E:) probes can be launched from a moving ship. .§. .r:. 600 0. Q) Cl 800 1000 0 9 18 27 Range (kilometers) Figure 8 - Example of how two (of many) ray bundles focus to create local regions of high intensity. front about that ray and perpendicular to it. The col­ lection of all rays that go through this small area of wave front is called the infinitesimal ray bundle asso­ ciated with the original ray. The trajectory of the ray bundle describes how a small but finite area of the wave front is refracted. In the ray theory approxima­ tion, the energy is confined to a ray bundle. Leakage of energy out of the bundle is called diffraction. Ray bundles leaving a point source initially start out along a radial line from the source because the wave fronts are spherical close to the source and the rays are perpendicular to the wave fronts. Before long, they are bent or refracted by the inhomoge­ neous medium. Why this refraction takes place is easy to see. Consider, for example, a bundle leaving the source horizontally at a depth of 100 meters. Ref­ erence to Fig. 7 shows that the speed of sound is de­ creasing with depth in that region. The top of the small wave front subtended by the bundle is moving Figure 6 - An artist's conception of an opening run to at a faster speed than the bottom of the wave front. measure transmission loss. Hence, the rays through the wave front would tend to Volume 3, Number 1,1982 69 be refracted downward. The same reasoning can be used to explain upward refraction if the speed of sound is increasing with depth. The diameters of the bundles shown in Fig. 8 have been greatly exaggerated for clarity. Bundle 1 focuses relatively soon after its lower vertex. (Focusing means that the small portion of the wave front sub­ en 800 tended by the ray bundle collapses to a point and CIl t then expands as it moves away from the focal point.) E Bundle 2, leaving the source at a steeper grazing ..r:; 0. CIl angle (the angle between the ray and the horizontal), Q 1200 focuses later at a shallower depth. Ray bundles leav­ ing the source at angles between those of bundles 1 and 2 will have focal points located between the focal 1600 points of bundles 1 and 2.