Analysis of modeled time series data is presented to provide insight into propagation physics of horizontally refracted sound in the Catoche Tongue region of the Gulf of Mexico. The analysis is motivated by the observation of out-of-plane arrivals in measured time series data. In particular, the extended duration of the refracted arrivals is shown to be caused by interaction with multiple locations along the steep sides of the Tongue. Comparison of the modeled time series is made to previous work by Sturm [J. Acoust. Soc. Am. 117(3), 1058-1079 (2005)], who examined the frequency dependence of out-of-plane modal arrivals for the wedge-shaped ocean.