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Nonlinear Analysis of the Frequency-magnitude Relationship in the Western Circum-Pacific Region

机译：西部环太平洋地区频率量级关系的非线性分析

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— It has long been realized that the linear Gutenberg-Richter model arduously describes the frequency-magnitude relationship for the magnitude span ranging from small to large earthquakes because of the breakdown of the self-similarity rule due to the changing scaling of the magnitude. Three different segments should be observed from small (usually M < 3.0), through moderate (M < M c , where M c is the frequency-magnitude turning point caused by the seismogenic thickness), to large earthquakes (M ≥ M c ). We will only concentrate on the moderate and large earthquakes due to their importance. The breakdown of the self-similarity rule from moderate to large earthquakes occurs where the earthquake is big enough to cut through the entire seismogenic layer. A nonlinear ‘hyperbolic’ model, which fits two linear relations smoothly, is studied in the present paper, where N is the cumulative number of earthquakes with magnitudes larger than or equal to M; a 1 to a 5 are constants to be calculated. The G-R linear relation is actually a special case of the present nonlinear model, i.e., a 3 or a 5 equal to zero. The nonlinear form, with the support of a reasonable physical mechanism, can generally give a better fitting with comparatively minor errors for complete data sets, especially for the areas where large earthquakes are numerous. In order to demonstrate its superiority to the linear G-R relation, thirteen seismogenic zones are examined around the western part of the Circum-Pacific region and western part of China and it is found that the fitting errors from this nonlinear model are, as expected, generally much smaller than those for G-R. Furthermore, the parameter a 4 is believed to relate with the saturated magnitude M c, which to some extent reflects the mean thickness of the seismogenic layer.
机译：－人们早已意识到，线性线性古腾堡-里希特（Gutenberg-Richter）模型很难描述从小地震到大地震的震级跨度的频率-震级关系，这是由于震级的变化导致自相似性规则失效的缘故。从小（通常为M <3.0）到中等（M ，其中M c 是由地震发生厚度引起的频率幅度转折点）到大，应观察到三个不同的部分。地震（M≥M c ）。由于地震的重要性，我们将只关注中度和大地震。自相似性规则从中等地震到大地震的破坏发生在地震大到足以穿透整个地震发生层的地方。本文研究了一个非线性的“双曲线”模型，该模型可以平滑地拟合两个线性关系，其中N是震级大于或等于M的地震累积数； 1 到5 是要计算的常数。 G-R线性关系实际上是当前非线性模型的一种特殊情况，即3 或5 等于零。非线性形式在合理的物理机制的支持下，通常可以以相对较小的误差更好地拟合完整的数据集，尤其是在发生大地震的地区。为了证明它优于线性GR关系，在环太平洋地区的西部和中国西部检查了13个地震带，发现该非线性模型的拟合误差与预期的一样，通常比GR的要小得多。此外，参数a 4 被认为与饱和强度M c有关，在某种程度上反映了震源层的平均厚度。

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