During a 1960 experiment on long-range ocean acoustic propagation, the signals of explosive shots made near Perth, Australia were recorded by a hydrophone array at Bermuda. The acoustic paths followed by those pulses are recalculated using a modern atlas for global ocean sound speed. The blocking or refractive effects of topographic features, besides continents, are ignored in this simple calculation. No direct path to the hydrophone array is obtained, and the array is found to be in the acoustic shadow by 300–400 km. The large energy of the 300-lb explosive sound sources required for adequate SNR at the receiver also points to a shadowed reception. Given nominal estimates for temperature warming on the sound channel axis due to climate change, the experiment repeated today would give signals that arrive 12 s earlier, but this signal could not be reliably measured because of intra-annual variability.
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 Some years ago, there was renewed interest in a long-range acoustics experiment conducted in 1960 in which sound from explosive shots propagated from Perth, Australia half way around the earth to a hydrophone array south of Bermuda [AGU, 1960; Shockley et al., 1982; Munk et al., 1988; Heaney et al., 1991; Munk et al., 1995]. The two aims of the analysis were the determination of the propagation paths of the acoustic energy and the explanation of the observed double arrivals (Figure 1). Munk et al. , based on ray tracing confined to the sound channel axis, found the direct path to be blocked by the African continent. Longuet-Higgins  showed theoretically that double arrivals were to be expected near the antipode of an acoustic source, since the acoustic paths converge at the antipode of a “slightly oblate spheroid” to create caustics. Heaney et al. , employing a more accurate approach than Munk et al. , calculated the paths by ray tracing using acoustic mode phase speeds derived from an atlas for global ocean properties with 5° spatial resolution [Gorshov, 1979] and from the DBDB5 ocean topography [National Geophysical Data Center, 1985]. Two acoustic paths, resulting from acoustic interactions with the bathymetry and the refractive properties of ocean sound speed, appeared to account for the double arrivals. Munk et al.  summarized the results of these analyses.
 This paper searches for direct, non-bottom interacting, propagation paths using the 2005 World Ocean Atlas (WOA05) [Antonov et al., 2006; Locarnini et al., 2006] The same conclusion as Munk et al.  is reached; no direct acoustic paths are found. The 2005 atlas has 1° spatial resolution and used considerably more data than were available for the 1979 atlas; the ocean sound speed gradients affecting horizontal refraction are more accurately represented. A consideration of the 300-lb yield of the 1960 acoustic shots, compared to the much weaker yields employed in similar long-range tests, shows that the recordings at Bermuda were indeed in the acoustic shadow of the African continent. Part of the motivation of this study was to assess whether a repeat of this experiment would result in a meaningful measure of global ocean warming over the past 50 years [Munk and Forbes, 1989].
 A significant difficulty in this analysis is that neither the data acquired in 1960, nor a precise description of the experimental parameters, are available. There are two original, if indirect, sources, however. First, Bryan et al.  described the results of long-range acoustics experiments during 1959–1960 in the South Atlantic using 3- and 48-lb shots deployed from the R/V Vema. These experiments culminated in the Perth-to-Bermuda experiment in March 1960, so the experimental methods described by Bryan et al.  are relevant. Second, Shockley et al.  relied on unpublished notes by C. Hartdegen, from which they derived the data and other information used for their study (Figure 1). Only the primitive oscilloscope scans of what appear to be pressure amplitude from hydrophones (Figure 1) are available as data. de Groot-Hedlin et al.  describe some of the acoustic properties of explosive shots.
2. Mode Phase Speeds and Acoustic Propagation in the 2005 World Ocean Atlas
Heaney et al.  calculated mode properties using modes that decayed to zero at depth in the open ocean. In shallow water they allowed for the effects of the ocean bottom by employing a standard semi-infinite sponge layer (K. D. Heaney et al., personal communication, 2008). The ocean bottom introduces refractive effects on mode propagation, in addition to sound speed gradient [Munk and Zachariasen, 1991]. They also invoked the adiabatic approximation, so that scattering of acoustic energy between modes was assumed not to occur. These assumptions will be discussed further below.
 Here the Heaney et al. approach was repeated using sound speeds and mode properties calculated from the WOA05, but the influence of the ocean bottom was ignored. Direct, non-bottom interacting paths were sought in this simplified calculation. The ray equations used for this calculation are those of Munk et al. . Figure 2 shows the latitudinal gradient of mode-1 phase speed at 30-Hz frequency for the world's oceans calculated from the WOA05; the dominant feature is the Antarctic circumpolar front. The figure also shows the acoustic paths determined by shooting, that is, it shows the paths obtained from a set of initial azimuthal angles. Figure 3 shows the locations of the arriving rays near Bermuda for the unrefracted case (zero horizontal sound speed gradient) and for modes 1 and 3. The unrefracted case shows part of Longuet-Higgins' predicted caustic near the antipode to the northwest of Bermuda. The direct arrivals for modes 1 and 3 are a few hundred kilometers to the southwest of Bermuda. As was found by Munk et al.'s  simpler calculation, the direct paths to Bermuda are blocked by Africa.
3. Horizontal Refraction With Rays
 The horizontal refraction of the acoustics can also be calculated using vertically-cycling rays which can model deeper-turning acoustic energy. (High-order modes should give an equivalent result.) Low-order acoustic modes are confined near the sound channel axis. Deep-turning rays are expected to be more weakly refracted than low-order modes or shallow rays because they mostly travel below the regions of large, near-surface sound speed gradients.
 The calculation of horizontal refraction using two-dimensional geometric ray code involves iterative steps to achieve an approximate solution for the three-dimensional problem. Acoustic paths can be determined this way without having to resort to more computationally-expensive, three-dimensional ray tracing. To avoid confusion in describing these steps, the horizontal path in latitude and longitude with azimuthal launch angle will be distinguished from a vertically-cycling ray along a depth-range section of sound speed with vertical launch angle. First, a ray with a given vertical launch angle is calculated, using an initial path determined by the unrefracted geodesic. This ray gives the approximate vertical cycling of rays near the geodesic path. Using that ray, the horizontal refraction of a path with a given azimuthal launch angle is calculated using the local sound speed gradient at the ranges and depths of the ray. A new path for the ray is thus determined, and the sound speed section along the new path is then used to recalculate the ray at the given vertical launch angle. This iterative procedure converges to a consistent path and ray for a given azimuthal launch angle after about three iterations.
 Paths from Perth to Bermuda for acoustic rays were determined using this procedure in a manner similar to the search for mode paths. The results were also similar in that no direct paths from Perth to Bermuda were found (Figures 3d–3f).
4. Acoustic Arrivals in the Shadow of Africa
 Considerations of the intensity of the acoustic signals support the conclusion that the 1960 receptions at Bermuda were in the shadow of Africa. The telling piece of information is that the signals from the series of 200-lb TNT shots from the R/V Vema were weak, so the HMAS Diamantina was asked to repeat the experiment a few weeks later using 300-lb TNT shots [Shockley et al., 1982]. Even at the time, it was known that shots as weak as 4-lb TNT could be detected at distances of 10,000 km or more [Ewing and Worzel, 1948; Bryan et al., 1963]. During the Acoustic Thermometry of Ocean Climate (ATOC) program [The ATOC Consortium, 1998] 20-min coded acoustic signals from a broad-band, 250-W acoustic source located off California were detected at New Zealand (10,000 km range) by a single hydrophone (M. Dzieciuch, personal communication, 2008). While 300-lb of TNT has an energy yield of 630 × 106 J [see also Munk, 2006], the coded ATOC signals had a total energy of 0.3 × 106 J. de Groot-Hedlin et al.  recently conducted long-range acoustic tests employing SUS charges in the Southern Ocean for the Comprehensive Test Ban Treaty Organization. The 4-lb shots were easily detected at 9,500-km range. These considerations suggest that the 1960 tests employed explosives that were much larger than was necessary; hence they support the notion that the arrivals recorded at Bermuda were indirect.
 The calculations reported here, and those reported previously, rely on a number of dubious assumptions. Obviously, the influence of the sea floor on mode properties, acoustic blocking, or scattering must be taken into account. Heaney et al.  employed a standard semi-infinite sponge layer to model the effects of the bottom, but an accurate calculation of mode properties relies on knowing properties of the ocean bottom (e.g., sand, basalt or mud). In addition, for estimating attenuation caused by bottom interaction, the bulk attenuation of a sponge layer accounts for a straight conversion to shear in the loss caused by a fluid bottom, but does not account for loss due to coupling to the interface (Stoneley/Scholte) waves. Coupling to interface waves is responsible for anomalously large bottom loss at low grazing angles [Hawker, 1978]. Large peaks in the attenuation are also observed at regularly spaced frequencies, depending on frequency and sediment thickness [Hughes et al., 1990].
 The calculations here have ignored the direct blocking of the acoustics by sea floor topography, such as the likely interaction of the acoustics with the Kerguelen plateau and tablemounts (Figure 4). The calculation of acoustic bottom scattering, which is beyond the scope of this paper, would require an accurate knowledge of global topography. Heaney et al.  employed the DBDB5 atlas with 9-km resolution, while even the best presently available data for sea floor topography [Smith and Sandwell, 1997] (1-km resolution) may not be up to the task. In order to model topographic scattering, accurate calculations of horizontal refraction would be required, so that the exact location and angle of approach of the acoustic energy to topography could be determined.
 The assumption of adiabatic mode propagation is now known to be unrealistic; the acoustic modes are fairly vigorously coupled in long-range acoustic propagation, particularly across sharp fronts such as the Antarctic circumpolar front [McDonald et al., 1994; Wage et al., 2005]. Therefore, calculating the acoustic propagation assuming a fixed mode is unrealistic. With ubiquitous mode coupling and horizontal refraction that depends on mode number, calculation of the exact path of a particular mode seems a hopeless quest. Nevertheless, calculations assuming a fixed mode number provide a first order estimate of the path of acoustic energy.
 Horizontal refraction depends critically on the horizontal gradients of sound speed. These and previous calculations have employed a smoothed ocean atlas, however, and the circumpolar front is likely to be significantly sharper than is given by an ocean atlas. Munk et al.  also discussed the issues of scattering and refraction from the mesoscale environment, particularly in the area of the Agulhas Retroflection [Gordon, 2003]. Some of the recent high-resolution numerical ocean models (e.g., [Maltrud and McClean, 2005] would likely give a more accurate ocean environment for calculating the paths. While such models would not accurately estimate the ocean state in 1960, they would at least better represent the characteristics of the sound speed gradients.
 The discussion here suggests that the Heaney et al.  explanation for the arrivals recorded at Bermuda, requiring topography to influence the acoustic path, is plausible, but not definitive. Another possibility is the horizontal diffusion of the acoustic energy by diffraction or random refractive effects, as discussed by Munk et al. . The two arrivals are suggestive of multipaths, but such multipaths appear to be inherently contradictory to diffusive, shadowed arrivals. Evidence supporting bottom-interacting multipaths over diffusive multipaths may be found in the results reported by Bryan et al. . During the 1959–1960 experiments, shots deployed in the Indian Ocean were effectively blocked by Africa and not recorded by receivers in the South Atlantic (Ascension Island and Fernando de Noronha at 5–6 Mm range). To within 3° horizontal angle, no receptions were observed within the acoustic shadow of Africa, hence to that extent diffusive acoustic energy may be ruled out. In any case, techniques for the numerical calculation of horizontally diffusive acoustic propagation do not yet exist [see Collins et al., 1995].
Munk et al.  and Heaney et al.  offered different explanations for the fact that two arrivals were recorded on hydrophone JULIET, while only one arrival was recorded on nearby hydrophone GOLF (Figure 1) Munk et al.  argued the difference was due to a bottom reflection near the receivers, while Heaney et al.  suggested that a high noise level masked a second arrival on GOLF. It should be noted that, in the nature of antipodal acoustics, south of Africa the geodesic path to GOLF lies about 400-km to the north of the geodesic path to JULIET. Although the receivers at Bermuda are nearby, accounting for their acoustic arrivals appears to be two entirely separate problems.
Munk and Forbes  suggested that globally the ocean sound channel was warming at a nominal rate of about 5° mC/yr [see also Levitus et al., 2000]. At that rate, the temperature near the sound channel axis would have increased 0.24°C over the past 48 years. If the 1960 shots were repeated today, such warming would cause the signals to travel some 12 s faster out of 13,382 s. While this number is easily measurable acoustically, Chiu et al.  found seasonal peak-to-peak travel-time variability of about 7 seconds from simulated acoustic propagation from Heard Island to California using an eddy-resolving general circulation model [Semtner and Chervin, 1990, 1992]. Therefore, a repetition of the Perth-Bermuda experiment does not seem likely to result in a meaningful measurement of ocean warming over the past 48 years. A better understanding of acoustic propagation over global distances is still a worthy goal, however.
 The author is supported by Office of Naval Research award N00014-06-1-0152. M. Dzieciuch, K. Heaney, P. Worcester, and R. Odom provided helpful discussion. M. Dzieciuch provided the computer code for calculating mode phase speeds.