一维Burridge-Knopoff模型连续极限地震的时空相关性
Spatiotemporal correlations of earthquakes in the continuum limit of the one-dimensional Burridge-Knopoff model
摘要：
本文用计算机数值模拟的方法研究了一维弹簧-块体（Burridge-Knopoff）地震模型的时空相关性。通过系统地研究块尺寸参数a向\to 0变化的模型特性，检查模型的连续极限。引入Kelvin粘性项，使模型动力学具有明显的连续极限。在粘性项的存在下，尽管最小地震的大小随着α的减小而减小，但即使在连续极限下，原离散BK模型的许多性质仍保持定性不变。一个值得注意的例外是主震前甜甜圈状静止的存在/不存在。虽然原离散BK模型的大震伴随着地震加速度和在主震前的甜甜圈状平静，但随着a的减小，甜甜圈状平静的空间范围变窄，在连续极限，甜甜圈状平静可能完全消失。在离散BK模型中观察到的甜甜圈状静止是一种与模型的短长度截止尺度密切相关的现象。
英文摘要：
Spatiotemporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes, either with or without the viscosity term, are studied by means of numerical computer simulations. The continuum limit of the model is examined by systematically investigating the model properties with varying the block-size parameter a toward a\to 0. The Kelvin viscosity term is introduced so that the model dynamics possesses a sensible continuum limit. In the presence of the viscosity term, many of the properties of the original discrete BK model are kept qualitatively unchanged even in the continuum limit, although the size of minimum earthquake gets smaller as a gets smaller. One notable exception is the existence/non-existence of the doughnut-like quiescence prior to the mainshock. Although large events of the original discrete BK model accompany seismic acceleration together with a doughnut-like quiescence just before the mainshock, the spatial range of the doughnut-like quiescence becomes narrower as a gets smaller, and in the continuum limit, the doughnut-like quiescence might vanish altogether. The doughnut-like quiescence observed in the discrete BK model is then a phenomenon closely related to the short-length cut-off scale of the model.
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