We combine qualitative analysis of Wiechert seismograms with quantitative analysis of Galizin-Wilip and Press-Ewing seismograms from Europe to draw conclusions regarding simplicity/complexity of P waveforms of large, shallow earthquakes since 1907 which occurred along the Mexican subduction zone. These seismograms are compared with LP WWSSN seismograms of recent earthquakes. It is found that the earthquakes in Oaxaca are simple with two exceptions. The earthquake of 15 January 1931 (MS = 8.0) was a complex, intraplate event with normal or strike-slip faulting. Some earthquakes are simple, and others are complex in the subregions of Guerrero and Michoacan. All three earthquakes in Jalisco are complex. The depths of the events are shallow (10 ≲ H ≲ 20 km) with the majority being at 16 km. The simplicity of events, the evidence of a characteristic magnitude of MS ≃ 7.8, and the ratio of surface wave to P-wave seismic moment of about 1.5 in Oaxaca suggest rather homogeneous asperities of nearly equal dimension separated by barriers. Elsewhere, the interface of the plates is characterized by smaller asperities of differing sizes separated by areas where aseismic deformation may occur. The earthquakes of 22 February 1943 (MS = 7.7) and 14 March 1979 (MS = 7.6) which were supposed to have broken the same area show drastically different P waveforms. It appears that the location of the 22 February 1943 earthquake is in error. Alternatively, the same area may have been broken with entirely different rupture processes.