Active faults sources for the Pátzcuaro–Acambay fault system (Mexico): fractal analysis of slip rates and magnitudes M w estimated from fault length

Abstract. The Patzcuaro–Acambay fault system (PAFS), located in the central part of the Trans-Mexican Volcanic Belt (TMVB), is delimited by an active transtensive deformation area associated with the oblique subduction zone between the Cocos and North American plates, with a convergence speed of 55 mm yr −1 at the latitude of the state of Michoacan, Mexico. Part of the oblique convergence is transferred to this fault system, where the slip rates range from 0.009 to 2.78 mm yr −1 . This has caused historic earthquakes in Central Mexico, such as the Acambay quake ( M s  = 6.9) on 19 November 1912 with surface rupture, and another in Maravatio in 1979 with M s  = 5.6. Also, paleoseismic analyses are showing Quaternary movements in some faults, with moderate to large magnitudes. Notably, this zone is seismically active, but lacks a dense local seismic network, and more importantly, its neotectonic movements have received very little attention. The present research encompasses three investigations carried out in the PAFS. First, the estimation of the maximum possible earthquake magnitudes, based on 316 fault lengths mapped on a 15 m digital elevation model, by means of three empirical relationships. In addition, the Hurst exponent H w and its persistence, estimated for magnitudes M w (spatial domain) and for 32 slip-rate data (time domain) by the wavelet variance analysis. Finally, the validity of the intrinsic definition of active fault proposed here. The average results for the estimation of the maximum and minimum magnitudes expected for this fault population are 5.5 ≤  M w  ≤ 7. Also, supported by the results of H at the spatial domain, this paper strongly suggests that the PAFS is classified in three different zones (western PAFS, central PAFS, and eastern PAFS) in terms of their roughness ( H w  = 0.7,  H w  = 0.5,  H w  = 0.8 respectively), showing different dynamics in seismotectonic activity and; the time domain, with a strong persistence H w  = 0.949, suggests that the periodicities of slip rates are close in time (process with memory). The fractal capacity dimension ( D b ) is also estimated for the slip-rate series using the box-counting method. Inverse correlation between D b and low slip-rate concentration was observed. The resulting D b  = 1.86 is related to a lesser concentration of low slip-rates in the PAFS, suggesting that larger faults accommodate the strain more efficiently (length  ≥ 3 km). Thus, in terms of fractal analysis, we can conclude that these 316 faults are seismically active, because they fulfill the intrinsic definition of active faults for the PAFS.