Modelling shallow water sound transmission by using a simple analytical formula based on the effective depth approximation

Understanding and modelling the transmission of underwater sound is critical for predicting the performance of acoustic sensing systems. Complicated mathematical models based on various approaches have been developed in past decades to predict sound transmission in the complex underwater environments. These complex models require detailed environmental inputs, longer execution time, and do not always show explicitly the effects of specific environment factors. For quick engineering assessments or sonar operations analysis, it would be advantageous to develop simple parameterised sound transmission formulas that capture the main features of underwater sound propagation using the fewest possible parameters. In this paper, we give a simple formula for incoherently averaged transmission loss in shallow water environments by taking into account the effects of energy spreading, absorption, and leakage out of boundaries. The formula is based on extension of earlier work by using the concept of effective depth to include the effect of normal mode penetration into the seafloor on modal attenuation. Comparison with measurement data at several shallow water sites worldwide shows that the formula are capable of producing the main features of shallow water sound propagation in environments with different types of seafloors. The formulas are useful for estimating sound transmission losses in generic yet representative underwater environments where detailed environmental knowledge is lacking or the fine details of underwater sound propagation is not required.