Investigation of sound pressure waveforms helps the selection of appropriate metrics to evaluate their effects on marine life in relation to noise thresholds. As marine animals move farther away from a sound source, the temporal characteristics of sound pressure may be influenced by interactions with the sediment and the sea surface. Sound pressure kurtosis and root-mean-square (rms) sound pressure are quantitative characteristics that depend on the shape of a sound pulse, with kurtosis related to the qualitative characteristic “impulsiveness.” After verifying the propagation modeling approach using selected test cases from the JAM Workshop held in Cambridge, UK, in 2022, the time dispersion values of pressure signals produced by an individual airgun shot across various sediment types are analyzed. The results reveal that there is significant pulse dispersion when the seabed consists of predominantly sand-type sediments: i.e., the airgun signal duration increases considerably over long distances, thus decreasing the kurtosis of a sequence of pulses, whereas the pulse dispersion is more limited for clay and silt-type sediments. The range variations of frequency weighted kurtosis and rms sound pressure differ from those of the unweighted kurtosis, depending on the corresponding lower and upper roll-off frequencies corresponding to different marine animal groups.