ABSTRACT A new theory of echolocation is described that explains in detail the sonar systems employed by Cetaceans and other marine mammals. One unusual feature of the method is the use of phase encoded angular coordinate information. The fatty melon of the dolphin phase encodes angular coordinate information into the outgoing signal train as a dispersive distortion. Clicks from the nasal sacs in pairs or greater number constitute the member signals of the outgoing train. Each click is an omnidirectional spread-spectrum signal of monophasic character. Decoding of the received signal and location of reflective targets is accomplished in real time by a phase invariant (or equivalently a Doppler invariant) quadrature matched filter processor that complements the signal design. Timing measurements give target ranges and relative velocities. Phase measurements convey target angular coordinates, while amplitude and polarity measurements express target quality or character. Generalizations of the theory are presented along with results from both computer simulations and laboratory physical model studies. These works suggest that a new class of acoustic echolocation systems may be developed with important advantages in terms of effectiveness, simplicity of operation, and economy. Such systems could perform important services in the offshore, both in exploration and production context where the location of reflectors is the objective. Several applications of such nature are discussed. INTRODUCTION The remarkable echolocation feats of Cetaceans naturally have stimulated many research studies. How can it be possible to resolve targets in three positional coordinates when only one signal source and two receivers (ears) are available? Further, how is the ambiguity between target relative motion and target range so effectively resolved? Explanations of several biosonars by Altes, Busnel et al. and Dreher illustrate the unsatisfactory state of our knowledge in this area. A new theory of echolocation is presented here that answers in detail the questions posed. Perhaps the single most distinctive feature of this theory is the encoding of angular coordinate information as phase distortions by dispersion. No other method of echolocation deliberately disrupts the phase coherence of a propagating signal wave field. We shall recognize the unusual anatomy of the dolphin head as a simple system that accomplishes the dispersive-phase encoding of angular coordinate information. The distinctive character of dolphin echolocation clicks will be noted as endowing them with immunity to Doppler distortions while enabling them to resolve adequately both target range and relative velocity parameters. Results of computer modeling and physical simulation are offered in support of the theory. Generalizations of the theory lead to specifications of echolocation systems that should function well in high noise environments, in the face of deliberate jamming, and in the presence of a dispersive propagation medium. The role of echolocation devices such as marine radars and sonars is quite well defined. It follows then that a new approach we shall describe here must be of practical significance, particularly in view of its cited advantages.