Geostatistical analysis of the power-law exponents of the size distribution of earthquakes, Quaternary faults and monogenetic volcanoes in the Central Trans-Mexican Volcanic Belt

The Trans Mexican Volcanic Belt (TMVB) is related to the convergence between the Cocos and Rivera plates beneath the North American plate by the Middle America Trench (MAT). Moreover, there is also intraplate faulting within the TMVB, which is responsible of important earthquakes like the Acambay in 1912 (Mw 7.0) and Maravatío in 1979 (Mb 5.3). In this tectonic scheme, monogenetic volcanoes, active faulting and earthquakes configure a complex tectonic frame where different spatial anisotropy featured this activity. This complexity can be characterized by the power-law of the frequency-size distribution of the monogenetic volcanoes, the faults and the earthquakes. This power-law is determined by the b-value of the Gutenberg-Richter law in case of the earthquakes. The novelty of this work is the application of geostatistics techniques (variograms) for the analysis of spatial distribution of the b-values obtained from the size distribution of the basal diameter for monogenetic volcanoes in the Michoacán-Guanajuato Volcanic Field (bmv), surface area for faults in the Morelia-Acambay fault system (bf) and the seismicity in the Central TMVB (beq). Therefore, the anisotropy in each case was compared and a geometric tectonic model was proposed. The evaluation of the spatial distribution of the b-value maps gives us a general interpretation of the tectonic stress field and the seismic hazard in the zone. Hence, the beq-value map for the seismic catalog shows anomalously low and high values, reveling two different processes, one related to a typical tectonic rupture (low b-values) and the other one related to hydraulic fracturing (high b-values). The resulting bmv-map for the diameter basal cones indicates us the locations of the ages of the monogenetic volcanoes, giving important information about the volcanic hazard. High bmv-values are correlated with the presence of young cinder cones and an increasing probability of a new volcano. For the Morelia-Acambay fault system, the bf-map shows the strongest locations along the system where tectonic stress accumulates.