IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 22, NO. 2, APRIL 1997 219 Interpretation of Frequency-Dependent Transmission-Loss Interference Patterns Mohsen Badiey, Kevin P. Bongiovanni, and William L. Siegmann, Senior Member, IEEE Abstract— Experimental observations of broad-band acoustic propagation in a known geological region of the Atlantic Gener- ating Station (AGS) site [1] has prompted a new approach to understanding frequency-dependent behavior in shallow-water regions. A modal-based theory is presented to explain quan- titatively the interference patterns of transmission loss versus frequency observed in the experimental data. It is shown that the higher modes are responsible for observed interference patterns and that these can be related to modal group velocities using an ideal waveguide model. This may provide new insights applicable to existing inverse techniques. Index Terms— Broad-band propagation, frequency depend- ence, transmission loss. I. INTRODUCTION S HALLOW-WATER acoustic propagation is notoriously difficult to predict accurately for several reasons. Principal among these are the multiple boundary encounters that an acoustic front typically undergoes before arriving at a receiver. Often these distort and otherwise corrupt the original wave- form. Topographical variability and sediment composition changes over range and depth further complicate the problem. Much work is being done to interpret shallow-water acoustic experimental data (see, e.g., [1]–[4]) and currently techniques are being developed to extract environmental information from acoustic propagation in these scenarios [5], [6]. The principal thrusts in these areas employ CW transmissions. One reason for this is that in shallow-water environments, modal decomposition is convenient since for many situations of interest, only a relatively few modes propagate. Over short ranges, though, the arrivals may not be easily distinguishable. Broad-band signals, on the other hand, may provide a means of characterizing oceanic structure and phenomena by exploiting features unique to frequency-dependent propaga- tion. Broad-band acoustics techniques have been used for applications such as determining the optimum frequency [8], source localization [9]–[11], and waveform inversion [12]. Yet the interpretation of the intensity interference structure over frequency has not attracted widespread use. The aim of this paper is to demonstrate the potential usefulness of this phenomena for investigating shallow-water acoustics. Manuscript received June 6, 1996; revised January 7, 1997. This work was supported in part by the Office of Naval Research. M. Badiey is with the Graduate College of Marine Studies, University of Delaware, Newark, DE 19716 USA. K. P. Bongiovanni is with TASC, Reading, MA 01867 USA. W. L. Siegmann is with the Department of Mathematical Sciences, Rens- selaer Polytechnic Institute, Troy, NY 12180 USA. Publisher Item Identifier S 0364-9059(97)03401-8. A series of experiments performed in a very shallow- water site off the shore of New Jersey using an airgun source [1] prompted an effort to interpret broad-band signals recorded over relatively short distances for a variety of fixed source–receiver positions. Observation of transmission-loss (TL) variations over frequency, for a fixed range, contained many features typical of TL patterns over range for fixed frequency. Thus, our initial interest is to develop an interpre- tation of the frequency-dependent interference structure which could provide a plausible physical explanation for the observed patterns. The methodology applied here is to cast the problem in its simplest modal form which corresponds to an isospeed ideal waveguide formulation. This approach has the advantage of clearly illustrating the underlying phenomena and can be extended to more complicated stratified media. It will be seen that it is the separable formulation which permits this extension. Next, we determine if a physically based repre- sentation of the actual frequency-dependent TL phenomena can be obtained. Following the procedure for determining TL over range patterns, we find that a simple explanation begins with the modal dispersion relation and its role within the asymptotic form of the Hankel function. Interestingly, it is not the lowest modes which dominate the interference structure, but the highest propagation modes. Furthermore, the behavior predicted by this formulation is clearly seen in the broad-band acoustic data. Additionally, a simple formula is constructed for approximating the interference wavelength in a given frequency band which provides relatively accurate predictions of observed behavior when compared with the collected acoustic data. In Section II, we briefly discuss the experiment and its role in this investigation. The next section develops the theory of frequency-dependent TL patterns within an ideal waveguide and an approximation method for estimating the interference wavelength, which also relates it to the group velocities, is also developed. Section IV assesses the quantitative behavior of the theory using comparisons with some collected acoustic data. The paper concludes with a summary in Section V. II. EXPERIMENTAL ACOUSTIC DATA In the summer of 1992, a week-long series of broad- band acoustic experiments were performed at the AGS site which lies five miles offshore of southern New Jersey [1]. The airgun source provided the broad-band signal which was recorded at a fixed array of hydrophones distributed at 1-m intervals throughout the water column. The initial motivation 0364–9059/97$10.00  1997 IEEE