Several joint and fault patterns were mapped a,t differm'tt scales (frmtt 1 cm to 100 kin) on the sedimentary cover of Saudi Arabia. They were analyzed using a new multifractM algorithm improved to correct for irregular geometry of ntapped donnains and finite size effects. Moreover, a new technique (the Opti•ta! Anisotropic Wavelet Coefficient method) was conceived. It, a,llows transformation to large scales maps from smaller scales ones and quantifies the multiscale behavior of h...ulting anisotropy. It consists of finding •t each point on a fault map an optimism filter 1hat 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 lirnited ranges, separated by clta. racterislic scales. X•,k• can observe a one-to-one correspondence between those characteristic scales and the depths of the •nain lithological or rheological interfaces in the Arabian crust. Fracturing and faulting can thus be better modeled a,s a hierarchical process, controlled in large part by the layering of the crust. field observations and experinmnts [Nagan, 1991' Mandelbrol et al., 1984; Scholz and A•iles, 1986; Herrmann and Rou•:, 1990; Sor'nette et al., 1990]. O•t the one hand, power law distributions are claimed to characterize tlte statistics of earthquake sizes and fault lengt, hs and, o•t the other }rand, the geo•netrical structure of faulting is found to be fractal within well-defined bou•lds. Power law distributions do not imply necessarily a fractal geometry ms they can emerge solely from dynat•ical or kinematic rules [Bak et al,, 1988; Carlson a•{d Langer, t989; Somelie, 1992]. Conversely, a fractal geoi•letry does not result in general from large fluctuations [Stan. le'y and Ostrowsky, 1986]. The i•tterplay and possible I Also at Bureau des Recherches G&:dogiques et Minit?,res, ()rl•;ans, France 2Also at relar, ionship bet, ween these two classes of properties is probably one of the most in•portant proble•ns in the physics of earthquakes and faul'ting [Soraetle and Sornette, 1989; Sornelte and Virieux, 1992; Sometie, 199!]. Recently, freq•mncy-size distributions for earthquakes [Pacheco et al., 1992] and relationships between opening displacement att•l fracture length [Hattou ctal., 1994] have been fo•nd to display a cross.t)ver from sn•all large events. Are s'i•tilar crossovers i•lentifiable in the geometry of fa•lt. ing? Wltat are o•r •tterstattdi•g cff tim n•echat•ics eft h•lting? Here we address t,l•cse questions and rel•r•rt o•t a detailed a•talysis of fra, ct•re and h•lt patterns front the tenflatterer re) the h,tndred-kilox•eter scale in a we!l-defined natural setting, i,}lt' western Arabian plate, using satellitei•t•age interpretation, aerial phot, ograph study, a•d field str•c,l•ra, l •na, t•.ping, The geo•tetrica, l selLsintilarity tested with box-co•lntitlg it•ult ifractal tools, correct for the irreg•lar geot•etry of mapped don'rains a•td finite size effect. s, 'Fhis global •wt..hod is co•n...