HR: 10:20h
AN: U52A-01 INVITED    [Abstracts]
TI: Tokunaga fractals: Stream networks, DLA, aftershocks, and biology
AU: * Turcotte, D L
EM: turcotte@geology.ucdavis.edu
AF: Donald L. Turcotte, Department of Geology University of California, Davis, CA 95616, United States
AU: Newman, W I
EM: win@ucla.edu
AF: William I. Newman, Department of Earth and Space Sciences, University of California, Los Angeles, CA 90095, United States
AB: A Tokunaga fractal is a self-similar branching topology that includes both primary and side branching. It was developed in terms of the self-similar branching of stream networks. It was subsequently shown that the branching topology of diffusion limited aggregation (DLA) clusters is also a Tokunaga fractal. The epidemic type aftershock sequence (ETAS) model has been widely used to model the statistics of seismicity. A self-similar version of ETAS is the branching aftershock sequence (BASS) model (GRL, 34, L12303,2007). The aftershocks of the main shock represent a primary branching structure. The aftershocks of aftershocks represent the side- branching structure. We show that deterministic BASS simulations give a Tokunaga fractal structure. The primary branching ratio is given aby the b-value of the aftershocks. The characteristic earthquake magnitude is given by the modified form of Bath's law. The average branching ratio of all parent-daughter is unity. Tokunaga fractals can also be found in biology. A specific example is the vein structure of leaves.
DE: 1242 Seismic cycle related deformations (6924, 7209, 7223, 7230)
DE: 1824 Geomorphology: general (1625)
DE: 3252 Spatial analysis (0500)
DE: 4440 Fractals and multifractals
DE: 4485 Self-organization
SC: Union [U]
MN: 2007 Fall Meeting