Fractal characteristics of earthquake occurrence in Al Hoceima city and its adjoining region, Morocco

Abstract

• Geographic and temporal correlation of the fractal dimension and the seismic b-value. • Three approaches for estimation of the fractal dimension. • Negative correlation between d -value and b-value in spatial approaches, positive correlation in temporal approaches. • The anomaly zone 4.39°W-3.14°W, 35.04°N-35.22°N shows the increased seismic activity. Al Hoceima region is one of the most seismically vulnerable areas in northern Morocco due to its proximity to the Africa–Eurasia plate convergence. This study presents an examination of geographic and temporal variations of the correlation fractal dimension (Dc value) and the seismic b-value in the Al Hoceima city and adjoining region, Morocco. The data file is prepared from the International Seismological Center (ISC) catalog spanning from September 1965 to April 2023, which includes 1301 earthquakes having magnitude of completeness Mc = 3.6. The maximum likelihood technique is used to estimate the b-value of the Gutenberg-Richter law, and the correlation integral technique to estimate the Dc value. Among the three approaches used for estimation, the first involves a temporal window that shifts in five-year increments. The second employs spatial sliding windows while keeping the latitude constant, and the third utilizes a spatial sliding window with a fixed longitude. The average value of the parameters b was estimated to be (1.1 ± 0.1) from the first approach, (1.45 ± 0.1) from the second approach and (1.52 ± 0.15) from the third approach. The average values of the spatial fractal dimension estimated from the three techniques are respectively (0.68 ± 0.04), (0.62 ± 0.04) and (0.37 ± 0.11). According to our results, the Dc/b ratio is smaller than 0.54 for Approach 1, smaller than 0.6 for Approach 2, and greater than 0.33 for Approach 3. This study found a strong positive correlation in the temporal approach while weak positive and negative correlations between the Dc value and the b-value for both the spatial approaches. The outcome of this study offers new understanding of the fractal characteristics of earthquake distribution in the Al Hoceima region of Morocco.