Potential of Fractal Analysis of Earthquakes through Wavelet Analysis and Determination of b Value as an Aftershock Precursor: A Case Study Using Earthquake Data between 2003 and 2011 in Turkey

The b value of earthquakes is very useful to forecast the occurrence of aftershocks in a given region. The b value characterizes the release of energy due to stress accumulation in the rocks through an earthquake and is a direct indicator for the prediction of aftershocks in the region. Wavelet based fractal analysis is used in this study to determine the b value by calculating the fractal dimension. This method guarantees high accuracy results through a limited dataset. The objective of this work was to demonstrate an elegant method for the determination of the b value after an earthquake and predict the occurrence of aftershocks with high accuracy. Repeated earthquakes were analyzed between 2003 and 2011 in Turkey and the b value was found for these earthquakes. The results gave an indication that the b value of the mainshock and its aftershocks are different and aftershocks occur in the region when the b value of the mainshock deviates significantly from 0.5, and aftershocks keep occurring until the b value of the earthquake approaches close to 0.5 for this region. 1. Introduction Prediction of earthquakes is an important step in preventing large loss of life and property. Earthquakes mainly occur due to failure of rocks in activated faults. The rocks in the subsurface withstand high amount of stress and their ability to withstand stress depends on the rock type and varies from region. The increase in the stress levels beyond the threshold stress limits leads to failure of rocks. The b value has been calculated in the past from earthquakes [1–3] through many methods. Fractal analysis of earthquakes through wavelet analysis requires a limited number of datasets as compared to other methods. Fractal analysis of earthquakes has been done in the past [4, 5] and is a measure of the fracture scale in reactivated faults [6, 7] which often causes earthquakes. The fractals are the macrostructure characteristics which are discovered through microstructure studies. The characteristics do not change by changing the scale of observation. The b value of earthquakes has been found to be related to the fractal dimension in the past [8]. The b value is traditionally related to the Gutenberg-Richter Law [9]. The b value is dependent on the heterogeneity, rheology, thermal gradient, and stress conditions [10–12]. The b value has been found to increase with heterogeneity. For seismically active regions the b value is high (typically 1.0 and above), but after an earthquake the b value changes in the region [13] and the chances of aftershocks are related to this change in