中国震灾的分维及其灾情的分形模型

根据分形理论在相关领域中的研究进展，分析了公元前1831年至公元1979年间中国东北区、华北区、华中区、华南区、西南区、内蒙古区、西北区、青藏区等8大自然区内地震活动的强度-频度关系对长时段中国地震资料的适用性和中国地震活动分维在空间上的变化情况，建立了中国震灾灾情的分形模型.研究结果表明：(1)根据现有长时段统计资料建立起来的中国地震强度-频度关系式是合理的；(2)中国震灾的分维为1.485 8，在中国的8大自然区中，以华中区地震活动分维值相对最大，为1.225 8，华南区地震活动分维值其次，为1.207 2，而以东北区地震活动分维值最小，仅为0.635 2；(3)震灾分维大小与不同区域地震数目之间并不能建立较好的联系，而是在总体上与我国东部地震带、台湾地震带、喜马拉雅地震带与西部地震带的空间分布(这些地震带地震活动较为强烈)是相对应的；(4)中国震灾灾情(死亡人数)的分形模型为lg N=0.632 6 lg r+3.839(式中r为标度，N为标度r之上的灾情出现频次).

The Fractal Character of China Earthquakes

According to the fractal theory,the fractal character of earthquakes in China is preliminarily discussed in this paper.The fractal model of conditions of earthquakes in China is also discussed.Some conclusions can be drawn as follows.(1) The formula of Gutenberg-Richter(lg N=-bM a) is tenable for the data in China during a long period.(2) The fractal dimension of earthquakes for China is 1.485 8,that of Northeast China is 0.635 2,that of North China is 1.137 2,that of Center China is 1.225 8,etc.The fractal dimension of earthquakes of Center China is the largest among 8 natural regions,that of Northeast China is the smallest among 8 natural regions.(3) The fractal dimensions of earthquakes of China answer to their spatial distribution.(4) The fractal model of conditions of China earthquakes(more than 1 000 deaths) is also established,the formula is lg N=-0.632 61g r 3.839(where r is the scale,N is the frequency above r).