RATES OF AFTERSHOCK DECAY AND THE FRACTAL STRUCTURE OF ACTIVE FAULT SYSTEMS

Aftershock activity on frequency decay against time is characterized b y a power law (the modified Omori formula) of an exponent p, which dif fers with each aftershock sequence. A theoretical study suggested that p, which is a rate constant of aftershock decay, is related to the fr actal dimension of a pre-existing fault system. This has however never been checked. Aftershock activity on size distribution is also charac terized by an exponential distribution against magnitude (the Gutenbeg -Richter relation) with a slope b. Although p is expected to be relate d to b, which is related to the partitioning rate of earthquake energy , the relationship has never been established. Here the relation betwe en the p-values and the fractal dimensions of the pre-existing fault s ystems, and that between the p-values and the b-values are explored, u sing natural seismicity data and data of the observable fault systems. The p- and B-values were estimated for fifteen aftershock sequences w hich occurred in Japan. In this paper aftershocks were identified on t he basis of a phenomenological definition in the seismicity data. The fractal capacity dimensions D-0 are estimated for the pre-existing act ive fault systems observed on the surface in the aftershock regions. I n the present paper the standard box-counting method was adopted to ge t the Do. Negative correlations between (1) p and D-0, and (2) p and b were observed with some scattering. Observation (1) shows that the ra te of aftershock decay p decreases systematically with increasing occu pancy rate of the pre-existing active fault system Do and suggests tha t aftershock decay dynamics is constrained by the pre-existing fractur e field. Observation (2) shows that p certainly has a relation with b. Moreover, we offer possible interpretation on these negative correlat ions and some scatters in both observations; the scatters are interpre ted as the scatter of the difference of two fractal dimensions between 3-D fracture construction in the crust and 2-D cross-sectional surfac e (observed active fault system). Supported by further tests, this pap er strongly suggests that the scaling for a natural fracture system is self-affine (with different fractal scalings in different directions) rather than self-similar, which would be a manifestation of regional anisotropy of the fracture system, and that the seismic parameters p a nd b depend on the 3-D construction of the fracture System in the crus t. (C) 1998 Elsevier Science B.V. All rights reserved.