Spatial Distribution, Scaling and Self-similar Behavior of Fracture Arrays in the Los Planes Fault, Baja California Sur, Mexico

Abstract

We present a case of detailed analysis of fracture arrays spanning four orders of magnitude in length; all of them measured at a single natural site by acquiring images at progressively larger scales. There is a high dispersion of cumulative-length exponents, box dimensions and fracture densities. However, the fractal analysis supports the fractal nature of fracture arrays. Our data indicate the existence of an upper limit for the density parameters, as similarly reported by other authors. We prove that box dimension is in inverse relation with fracture concentration and in direct relation with fracture density. These relations are also observed in our data and additionally there is an upper limit for the box dimensions. We interpret the dispersion in our results as more fundamental than methodological problems. It represents a truncation in the complete evolution of the fracture systems because in natural cases strain initiates overprinting of previous fracture arrays. Considering that larger fractures accommodate strain more efficiently than small fractures, the generation of small fractures is inhibited in the presence of preexisting larger fractures. Maximum values of fracture density prevent accommodating an excess of strain in a single or restricted range of scales; we claim this condition produces migration of fracturing to larger scales originating fracture scaling.

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

“…The Hurst exponent shows a strong persistence, meaning close periodicities in time for groundrupturing in the PAFS. D b = 1.86 is consistent with the values obtained by Nieto-Samaniego et al (2005; D b = 1.87 upper limit), who proved that the box dimension is in inverse relation to fracture concentration and in direct relation to fracture density. The high value of the fractal dimension might indicate the possibility of a major earthquake (Aviles et al, 1987) in the PAFS faults.…”

“…The TMVB developed within an extensional tectonics setting resulting from the subduction of the Rivera and Cocos plates beneath the North American plate. The central TMVB is characterized by the Tula-Chapala fault zone (Johnson and Harrison, 1990), where the kinematics is extensional and transtensional from the Miocene (Johnson and Harrison, 1989;Martínez-Reyes and Nieto-Samaniego, 1990;Garduño-Monroy et al, 2009) with a left strike slip component (Suter et al, 1992(Suter et al, , 1995(Suter et al, , 2001Ego and Ansan, 2002;Norini et al, 2006).…”

“…Self-similarity was studied by Nieto-Samaniego et al (2005) in the Los Planes fault, Baja California Sur, Mexico, using a detailed fractal analysis of fracture arrays. Their sampled fracture traces have box dimensions between 1.51 and 1.87.…”

“…The Environmental Seismic Intensity scale ESI 07 (Michetti et al, 2007) is a new intensity scale, with 12 degrees of intensity, based only on earthquake environmental effects (EEEs). The ESI 07 scale integrates traditional intensity scales, and allows to define seismic intensity based on the entire scenario of effects.…”

Integral Methods in Science and Engineering

“…General aspects of fracture systems in geological media with scaling laws were considered in [BoEtAl01], where the principal concern focused on the spatial distribution of fractures, the fracture intensity, and their self-similar appearance in different scales (see also [LaEtAl02], [NSEtAl05], [OrMaLa06]). To the best of our knowledge the perspectives that arise from our present discussion are new, since they may be considered a first step towards an approach that in a long term may open pathways for a dynamical fracture pattern genesis simulation beyond the phenomenological implementation, presented in this work.…”