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Stochastic Branching Models of Fault Surfaces and Estimated Fractal Dimensions

机译：断面的随机分支模型和分形维数估计

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摘要

We discuss simulations of nonplanar fault structures for a variant of the geometric stochastic branching model of Kagan (1982) and perform fractal analyses with 2-D and 3-D box-counting methods on the simulated structures. One goal is to clarify the assumptions associated with the geometric stochastic branching model and the conditions for which it may provide a useful tool in the context of earthquake faults. The primary purpose is to determine whether typical fractal analyses of observed earthquake data are likely to provide an adequate description of the underlying geometrical properties of the structure. The results suggest that stochastic branching structures are more complicated and quite distinct from the mathematical objects that have been used to develop fractal theory. The two families of geometrical structures do not share all of the same generalizations, and observations related to one cannot be used directly to make inferences on the other as has frequently been assumed. The fractal analyses indicate that it is incorrect to infer the fractal dimension of a complex volumetric fault structure from a cross-section such as a fault trace, from projections such as epicenters, or from a sparse number of representative points such as hypocenter distributions.
机译：我们讨论了Kagan（1982）的几何随机分支模型的变体的非平面断层结构的模拟，并对模拟结构进行了二维和三维盒计数方法的分形分析。一个目标是弄清楚与几何随机分支模型有关的假设，以及在地震断层的情况下可以提供有用工具的条件。主要目的是确定观察到的地震数据的典型分形分析是否可能对结构的基本几何特性提供足够的描述。结果表明，随机分支结构更加复杂，并且与用于发展分形理论的数学对象截然不同。几何结构的这两个族并没有共享所有相同的概括，并且与一个假设相关的观察不能像经常被假定的那样直接用于对另一个推断。分形分析表明，从断层（如断层迹线），投影（如震中）或稀疏的代表点（如震中分布）推断复杂体积断层结构的分形维数是不正确的。

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