Multifractal images of the seismicity in the Ibero-Maghrebian region (westernmost boundary between the Eurasian and African plates)

• The seismicity of the Ibero-Maghrebian region is analyzed by multifractal analysis.
• Positions and energies of earthquakes are considered as fractal sets.
• We study the fractal dimensions of capacity, entropy, correlation and spectral slope.
• The fractal geometry of the plate boundary is addressed.

The earthquake occurrence has a scale-invariant behavior that can be analyzed by means of a set of non-integer dimensions. The capacity dimension is related to the number of spatially distributed earthquakes, that is, to what extent the data space is full; while the dimensions of entropy and correlation are related to the mode in which the data fill the space, i.e. how data are ordered and how data are clustered, respectively. The behavior of the multifractal spectrum is asymptotic at the ends of its variation range. The difference between the extreme values of the spectrum, called multifractal spectrum slope, is used to investigate how the earthquakes and its energy are spatially distributed. In this paper we explain the fractal geometry of the seismicity in the Ibero-Maghrebian region, which is located in the westernmost end of the contact between the Eurasian and African plates. This region presents an unevenly spatially distributed seismic activity with areas of strong earthquakes beside others where the seismicity is weaker. The present-day stress field, the fault systems and the characteristic seismicity of the zone make the contact between the Eurasian and African plates an open problem. To address this issue, we have mapped the spatial variation of the fractal dimensions of capacity, entropy, correlation and the multifractal spectrum slope, which are calculated from positions and energies of earthquakes with focal depth between 0 and 120 km. The multifractal approach allows shedding light on the filling, ordination and clustering of the spatially distributed earthquakes and the released energy. The existence of lithospheric faults in response to the strong interaction between plate edges seems to be the cause of the observed shallow and intermediate seismicity and the rupture of the plate boundary in the Betic–Rif–Alboran area.

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