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Utilizing CTBT Hydroacoustic Stations
paths, and from this, we can expect that dispersion depends on the oceanography. One consequence of refraction are shadow zones, areas where rays do not pass and sound from the source is not heard.
In comparing the two environments, note how the midlati- tude sound speed profile adds a component of downward refraction, further isolating the signal from sea-surface reflec- tions. The IMS station hydrophones are moored at an optimal depth, both to minimize the effect of shadow zones and to maximize the reception of all paths. In the midlatitudes, the optimal depth occurs at the axis of the well-known sound duct (see Figure 1), the SOFAR channel, named after the 1940s SOund Fixing And Ranging triangulation system that was developed to rescue downed pilots. The SOFAR system triangulated impulsive signals from bombs or “implosion discs” deployed by downed pilots. The discs were set with a fuse to detonate at a prescribed depth, geographically chosen to be at the SOFAR axis, to maximize the chance of detec- tions by at least three search and rescue monitoring stations (Bureau of Naval Personnel, 1953, p. 282).
In the deep ocean, rays with steep angles sample higher sound speeds, and although having longer paths, this deep diving portion of the wave front actually travels faster than the part initially traveling horizontally. Thus, as a signal propagates further and further away from its source, its wave front elon- gates, with the steep rays arriving first, followed eventually by the horizontal rays. An important observation (see Figure 4) is that rays at ±Ѳ follow the same path, albeit with a spatial offset near the source corresponding to the initial surface reflection (or refraction) of the positive angles. This pair of up-and-down rays arrive at the same time, and depending on frequency (f), the folded wave front here may reinforce through constructive interference. These pairs of up-and- down going rays define the propagating modes, and through a ray-mode analogy, these specific frequency-dependent ray launch angles correspond to a mode angle. As modes may not be familiar, let us take a minute to discuss what an oce- anic mode is, and afterward, the advantage of decomposing a signal, like that from the San Juan, into a discrete set of modal arrivals should be clear.
Oceanic Mode Propagation
To introduce modes, let us consider vibration of a guitar string (see Figure 5). Modes are standing waves, waves not propagating in the direction in which they are defined. (e.g., along the guitar string), but are a description of the ampli-
tude of the oscillations. When a guitar string is plucked, it is very clear that the motion resembles a half sine wave, pinned at one end by the nut (Figure 5, top) and the bridge at the other end (Figure 5, bottom). This is mode-1, the most basic motion that satisfies the boundary condition that the string does not move at the bridge or nut. Mode-2 may not be obvious; it resembles a full sine wave with a node or zero point of motion at the midpoint of the string (the 12th fret). To excite mode-2 and not mode-1, one can (with some practice) excite “the harmonic” by placing a finger lightly on the string at the half-way point and pluck the string on either side with the other hand. The light finger touch sup- presses motion at the midpoint, letting only those modes with a node there vibrate (mode-2).
Mode shapes of a sound duct are also sinusoid-like. The mode shape describes the amplitude of a standing wave in depth, which propagates down the duct (away from the source) at its propagation speed. Revisiting the ray mode analogy, a pair of rays are associated with each mode. The plus or minus ray launch angles establish the mode angle, mathematically representing the trajectory of two interfering up-and-down- going plane waves (wave fronts with no curvature) that form the mode. The trajectory of the analogous rays sweep through the vertical (depth) extent of the mode shape. Also, the aver- age propagation speed of the ray over one “ray cycle” (or the distance before the ray trajectory repeats) is equal to the mode propagation speed.
For the modes in a deep-ocean duct, mode angles are between the horizontal and the limiting rays. In shallower oceans, the physics of bottom reflection must be considered, and the mode angle is limited to within the critical angle, the shallow angle where total reflection occurs, and no energy is
Figure 5. Mode-1 (black) and mode-2 (white) of guitar string. The shaded areas represent the area swept out by the string vibration of mode-1 or mode-2 (displacement is exaggerated). Note the node, or stationary point of mode-2, at the 12th fret. See animation at
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