Acoustic propagation through subsurface bubble clouds in the ocean can exhibit signal travel times with enormous variations depending on the acoustic signal frequency, bubble size distribution, and void fraction. Recent theories have predicted large variations in phase speeds and attenuation that have been largely validated for frequencies well below and well above bubble resonance. However, great care must be exercised when theoretically treating signal propagation at frequencies near resonance, termed the ‘‘Anomalous Absorption Regime’’ nearly 100 years ago in the pioneering work of Sommerfeld [A. Sommerfeld, Physik. Z. 8, 841 (1975)] while investigating aspects of electromagnetic causality. We will discuss similarities between acoustic propagation in bubbly media and electromagnetic propagation in the presence of a conducting medium. We show that the signal travel time is dependent on the behavior of the dispersion formula in the complex frequency plane and place limits on the range of validity of these formulas, leading naturally to the necessary modifications to the current dispersion formulas to bring them into compliance with causality. Finally, we present theoretical results for the velocity of signals for a representative environment of experimental work carried out at the Naval Research Laboratory. [Work supported by the ONR.]
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