A precise theory exists, based on an integral equation, by which acoustic signal attenuation versus frequency, due to a known bubble-density distribution versus bubble radius, may be calculated. Lacking a simple inversion scheme for the integral equation, an approximation which accounts only for attenuation due to resonant bubbles is available (and often applied) to calculate a bubble distribution. An iterative approach for improving on that resonant bubble approximation is presented here. That new approach is based on alternating calculations and corrections between attenuation data and the bubble distribution presumed to have produced it. This iterative technique is tested, first, on two simulated data sets of bubble distributions. It is then applied to attenuation data measured as a function of frequency from 39 to 244 kHz during the Scripps Pier Experiment [Caruthers et al., Proc. 16th Int. Cong. on Acoust., pp. 697–698 (1998)]. The results of the simulations demonstrate the validity of the method by faithfully reproducing the initial distributions for the simulated attenuation data. When applied to the real data, the method leads to a bubble distribution whose use in a direct solution of the integral equation reproduces the measured data with greater accuracy than does the resonant bubble approximation alone.
FIGURE 1. Multi-beam echo sound survey of the site and location relative to the island of Kauai (inset). FIGURE 2. Equipment lay down for KauaiEx. The principal sound source located at the southern end (left) broadcast to VLA' s distributed along the track. Acoustic sensors were interleaved with environmental sensors including thermistor strings along the entire propagation path. FIGURE 4. Deployment of the telesonar testbed (left). Track of the towed transmitter (T1) relative to the receiver testbed (T3) (right). FIGURE 5. Matched-filter response or replica correlogram showing the impulse response of the channel in 3 separate frequency bands.
An experiment was performed just off the research pier at the Scripps Institute of Oceanography to determine the acoustic effects of small bubbles in very shallow water (∼6 m depth). The distance offshore was ∼300 m. The propagation lengths were 2–10 m, and the frequency range was from 39 to 244 kHz. During the experiment, rip currents passed through the field of measurement instruments. These rip currents were laden with bubbles created in the surf between the instruments and the shore. The effects of these rip currents on the spatial distributions of the resulting acoustic attenuation are discussed. From the attenuation data, the bubble distributions are calculated using a new iterative approach [Caruthers et al., in press, J. Acoust. Soc. Am.] that is based on the well-known resonant bubble approximation. Calculated bubble distributions varied from an essentially uniform lack of bubbles during quiescent periods to highly inhomogeneous and dense bubbly regions within rip events. Such observed distributions were consistent with measurements made by other investigators during the experiment.
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