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全球和区域地震研究表明:用经验方法确定的古登堡-里克特分布中的b值相当稳定,一般限于-1±0.2。这里我用加利福尼亚、新西兰和日本的观测数据说明b值的稳定性是某一物理过程的表现,具体地讲,是地壳应变沿相对离散区组织的趋势的反映。若地壳某部分受位移场作用,位移就受遵从幂律分布的断层系调节。连续位移时,较长的而不是较短的断层开始发展,且承载越来越多的位移总量。区域位移方向的改变会逆转这个分布趋势。某区域长断层数与短断层数比值的变化会伴以断层长度和断层滑动率关系的变化。因为断层上地震的复发是断层长度和断层滑动率的函数,因而变形过程可能会产生一个反馈系统,使b值不受断层总量改变的影响。该想法的一个推论是,地震震级-频度统计关系可能归因于与控制板块构造边界发育和全球地震大致空间分布的同样的物理过程。
Global and regional seismic studies have shown that the b-value in the Gutenberg-Richter distribution, as determined empirically, is quite stable, generally limited to -1 ± 0.2. Here, I use observations from California, New Zealand and Japan to show that the stability of b is a manifestation of a physical process and, in particular, a reflection of the tendency of crustal strain to be organized in relatively discrete areas. If a part of the crust is affected by the displacement field, the displacement is regulated by a fault system that follows the power law distribution. With continuous displacement, longer, rather than shorter, faults begin to develop and carry more and more total displacement. Changes in the direction of the area displacement will reverse this distribution trend. The change of the ratio of the number of long faults to the number of short faults in a certain region will be accompanied by the change of the relationship between fault length and fault slip rate. Because the recurrence of an earthquake on a fault is a function of fault length and fault slip rate, a feedback system may be generated during the deformation so that the b value is not affected by the change in the total fault volume. A corollary of this idea is that the magnitude-frequency relationship of earthquakes may be attributed to the same physical process as the control plate tectonic boundary development and the general spatial distribution of global earthquakes.