Modeling and simulation of marine mammal generated sound. I. Stochastic modeling of marine mammal spatial distributions, collective motions, and vocalization occurrence times

Stochastic models and algorithms are developed for representing and simulating marine mammal spatial distributions, collective motions, and vocalization occurrence times. A general class of Markov‐process models of collective motion is first identified. Within this class, particular representations are constructed that incorporate interaction mechanisms of the type developed in distributed behavior modeling [C. Reynolds, Comput. Graph. 21, 25 (1987)]. Collective motion is represented by a Markov process with a stationary probability density defined in terms of an ‘‘energy’’ function that expresses the propensity for clustering and polarization within groups of individuals. Computer‐generated sample functions of the Markov processes, based on variants of the Metropolis algorithm, provide for simulation of a variety of collective motions. These range from nearly independent motions of solitary individuals to motions in highly clustered and polarized configurations simulating motions of marine mammals in pods. Occurrence times of vocalizations are represented by Markov processes and associated simulation algorithms. Simulations of patterned click sequences (codas) [Watkins and Schevill, J. Acoust. Soc. Am. 62, 1485 (1977)] produced by sperm whales (Physeter catodon) are presented as an example. Potential applications to sonar systems and marine mammal acoustic surveys are briefly discussed. [Work supported by ONR and NRL.]