震源体破裂行为的重整化群方法研究

应用重整化群方法对一维、二维和三维震源体的破裂问题进行了研究，得到了一维、二维和三辰原体破裂的临界概率值分别国０．２０６３、０．１７０７和０．１５９９，相关长度指数分别为１．４３８８、０．８０８４和０．５７５７。进而由此揭示了临界概率和相关长度指数随维数增大而减少的变化规律。

RENORMALIZATION GROUP APPROACH TO THE BREAK BEHAVIOR OF SEISMIC SOURCE BODIES

A seismic source body is treat as an array of asperities or blocks with a prescribed statistical distribution of strengths. When an asperity or a block fails the stress on the failed that is transferred to one adjecent that or more those. For linear array, the stress is transferred to a single adjecent asperity;for a two dimensional array to three adjecent asperities, and for a three dimensional array to seven adjecent blocks. Using a renormalization group approach, the break behavior of seismic source bodies is investigated. An extrapolation to arbitrarily large scales shows the existence of a critical applied stress at which the solutions bifurcate. The critical failure probability values of the linear, two and three dimensional seismic source bodies are 0. 2063, 0. 1707 and 0. 1599 respectively; the correlative length exponent values 1. 4388, 0. 8084 and 0. 5757. As being above that, the asperity or block failure cascades away from the nucleus, which is interpreted as an earthquake; below that the failure could not occur. At the same time, the change law of which critical probability and correlative length exponent values decrease with the increase in the dimensionality of a system is revealed.