Multipath propagation of underwater sound gives rise to both constructive and destructive interference. The sound which originates from a surface or a submerged source is reflected multiple times by the surface and the seabed before reaching the sensor. The summation of the many delayed replicas of the original signal results in an interference pattern specific to the current multipath environment. In passive underwater surveillance the multipath interference pattern can be detected using time-frequency analysis such as spectrograms. If the multipath environment can be approximated to some extent the patterns found in the spectrogram can be linked to certain source parameters, such as depth and speed. The theoretical modeling of underwater sound propagation in a multipath environment starts with the physical modeling of sound in the form of differential equations. These differential equations can be studied to give more approachable theories for sound propagation, most notably ray and normal mode theories. One of the most important aspects in modeling the multipath environment is refraction, or bending of sound imposed by the unavoidable temperature gradient found in all large bodies of water. Ray and normal mode theories are both capable of modeling the propagation of sound in vertical temperature gradients.In this thesis numerical models of ray and normal mode theories are used to estimate the interference patterns created by a submerged vessel. This thesis includes the developement of a numerical ray model which is evaluated in together with third party ray and normal mode models. The evaluation is done using real hydrographic data to give realistic sound speed profiles at three locations on the Finnish coast. Further, the seabed reflection is assessed in the context of using Lloyd's mirror effect for passive detection.
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