Bulletin of the Seismological Society of America, Vol. 87, No. 6, pp. 1685-1690, December 1997 Fractal Pattern of the Sumatra Fault Seismicity and Its Possible Application to Earthquake Prediction by Sigit Sukmono, M. T. Zen, L. Hendrajaya, W. G. A. Kadir, D. Santoso, and J. Dubois Abstract It has been noted that the characteristics of earthquakes occurring on an active fault are closely related to the irregularity of fault geometry. Because of their rough appearances over many length scales, faults can be regarded as fractal sets and their geometrical irregularity can be quantified using fractal dimension values. Pre- vious observations show that the Sumatra fault system (SFS) consists of 11 active fault segments with geometric fractal dimension values (D) ranging from 1.00 ___ 0.03 to 1.24 ___ 0.03. In this article, the relationships between D values and large shallow earthquakes (5.0 _-< mb ~ 7.0, depth _-< 50 km) occurring between 1965 and 1994 are analyzed. The results show that there is a repetitive pattern, which we call the fractal pattern, of the SFS seismicity, correlating the times of earthquake recur- rence with fault segment geometric D values. Based on this fractal pattem and the relationship between segment D values and seismogenic crustal models along the SFS, the 11 segments of the SFS can be divided into two groups of three classes in which each segment class has a specific earthquake recurrence interval. The recur- rence interval then may be used to predict future large earthquakes in the segment classes as we have done before in predicting the 7 October 1995 Kerinci earthquake and 10 October 1996 Torn earthquake. Introduction The Sumatra fault system (SFS) is a 1650-kin-long NW- trending dextral strike-slip fault zone that accommodates the oblique convergence between the Indo-Australian and Eu- rasian plates. It extends in a succession of at least 11 seg- ments and connects northward to the Andaman extensional back arc basin and southward to the extensional fault zone of the Sunda strait (Fig. 1). Although the SFS is widely known as one of the world's great active dextral faults and has generated many destructive earthquakes (Table 1), its seismic behavior is largely unknown. The seismic behavior of a fault can be correlated with the fault's geometrical irregularity. Certain faults or fault segments always rupture in "characteristic" earthquakes governed by their geometrical irregularity (Schwartz and Coopersmith, 1984). A detailed knowledge of fault-system geometry is requisite to an understanding of the mechanics of faulting in terms of the concentrations of stress and other departures from stress homogeneity that arise from compli- cated fault geometries (Segall and Pollard, 1980). Because of their rough appearances over many length scales, faults can be regarded as fractal, and a fault's geometrical irregu- larity can be quantified by the fractal dimension D: larger D values are associated with more irregular geometry. The D values then can be related to some faulting mechanics pa- rameters such as stress condition, degree of faulting, and fracturing energy density. The definition of a fractal distribution is given by (Man- delbrot, 1982) Ni = C/~, (1) where Ni is the number of objects with a linear dimension r;, D is the fractal dimension, and C is a constant of propor- tionality. In an earlier article (see Sukmono et al., 1996), we calculated the fractal dimension D for SFS fault segments using the method outlined in Okubo and Aki (1987). D val- ues for the 11 active segments of the SFS ranged from D = 1 + 0.03 to 1.24 + 0.03 (Fig. 1). By making inferences on the complexity of the geometry of mapped faults and its relation to fault mechanics, we assume that the complexity mapped at the surface is representative of the structural detail at depth, as suggested by Eaton et aL (1970). Based on maximum SFS aftershock depths (Harjono et al., 1994), we chose an upper fractal cutoff of 15 km with a lower fractal cutoff of 1 km as suggested in Okubo and Aki (1987). With the upper cutoff of 15 kin, only active fault traces lying within a 30-km-wide band centered about the primary fault trace are included in the D value determina- tions. Sukmono et al. (1996) observed also that there are six fractal discontinuities along the segments that are reflected 1685