Båth's law and its relation to the tectonic environment: A case study for earthquakes in Mexico

• The mainshock-aftershock magnitude difference depends on the types of earthquakes.
• 96–97% of the mainshock-aftershock energy sequence is related to the mainshock.
• Seismic energy and energy-to-moment ratio estimates agree with global studies.
• A dependence of stress drop on focal mechanism is observed.
• A statistically differentiated behavior for source parameters is observed.

We studied 66 mainshocks and their largest aftershocks in the Mexican subduction zone and in the Gulf of California with magnitudes in the range of 5.2 < Mw < 8.0 from 1932 to 2015. Three different types of earthquakes were analyzed: shallow thrust interplate, intermediate-depth inslab and transform strike-slip earthquakes (26, 19 and 21 events, respectively). We focus on observational aspects of the Båth's law. By studying the magnitude difference, energy ratios and energy partitioning of the mainshock-largest aftershock sequences, we analyze the physics of the mainshock-largest aftershock relationship (Båth's law). The partitioning of energy during a mainshock-aftershock sequence shows that about 96–97% of the energy dissipated in a sequence is associated with the mainshock and the rest is due to aftershocks. Our results for radiated seismic energy and energy-to-moment ratio are partially in agreement with worldwide studies supporting the observation of mechanism dependence of radiated seismic energy. The statistical tests indicate that the only significant difference is for shallow thrust and strike-slip events for these parameters. The statistical comparison of stress drop of shallow thrust versus that of inslab events shows a strongly significant difference with a confidence better than 99%. The comparison of stress drop of shallow thrust events with that of strike-slip events, also indicates a strongly significant difference. We see no dependence of stress drop with magnitude, which is strong evidence of earthquake self-similarity. We do not observe a systematic depth dependence of stress drop. The results also reveal differences in the earthquake rupture among the events. The magnitude difference between the mainshock and the largest aftershock for inslab events is larger than interplate and strike-slip events suggesting focal mechanism dependence of Båth's law. For the case of this parameter, only that for inslab and strike-slip events present a significant difference with 95% confidence.