Hierarchical geometry of faulting

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Abstract
Several joint and fault patterns were mapped at different scales (from 1 cm to 100 km) on the sedimentary cover of Saudi Arabia. They were analyzed using a new multifractal algorithm improved to correct for irregular geometry of mapped domains and finite size effects. Moreover, a new technique (the Optimal Anisotropic Wavelet Coefficient method) was conceived. It allows transformation to large scales maps from smaller scales ones and quantifies the multiscale behavior of faulting anisotropy. It consists of finding at each point on a fault map an optimum filter that reveals the local structure. Fault length distributions are also computed. Our main conclusion is that different geometrical power laws and anisotropic textures hold separately in distinct limited ranges, separated by characteristic scales. We can observe a one‐to‐one correspondence between those characteristic scales and the depths of the main lithological or rheological interfaces in the Arabian crust. Fracturing and faulting can thus be better modeled as a hierarchical process, controlled in large part by the layering of the crust.