In 2002 and 2003, tagged sperm whales (Physeter macrocephalus) were experimentally exposed to airgun pulses in the Gulf of Mexico, with the tags providing acoustic recordings at measured ranges and depths. Ray trace and parabolic equation (PE) models provided information about sound propagation paths and accurately predicted time of arrival differences between multipath arrivals. With adequate environmental information, a broadband acoustic PE model predicted the relative levels of multipath arrivals recorded on the tagged whales. However, lack of array source signature data limited modeling of absolute received levels. Airguns produce energy primarily below 250 Hz, with spectrum levels about 20-40 dB lower at 1 kHz. Some arrivals recorded near the surface in 2002 had energy predominantly above 500 Hz; a surface duct in the 2002 sound speed profile helps explain this effect, and the beampattern of the source array also indicates an increased proportion of high-frequency sound at near-horizontal launch angles. These findings indicate that airguns sometimes expose animals to measurable sound energy above 250 Hz, and demonstrate the influences of source and environmental parameters on characteristics of received airgun pulses. The study also illustrates that on-axis source levels and simple geometric spreading inadequately describe airgun pulse propagation and the extent of exposure zones.