基于指数函数的川滇地区余震序列衰减规律研究

Decay law of aftershock sequences in the Sichuan-Yunnan region based on an exponential function

摘要:

较大的余震可能造成额外损失并有二次触发建筑物受灾的风险。为研究余震序列衰减规律,文章尝试采用指数衰减模型拟合分析5个不同地区余震序列,并借助修正赤池信息准则、贝叶斯信息准则与调整后R²,分析其与传统余震衰减模型的性能。结果表明,指数模型描述余震序列衰减规律的能力与修正的大森余震模型、修正的拉伸指数模型接近。尤其对于四川长宁M_S6.0余震序列和云南彝良M_S5.7余震序列,指数模型表现优于其他两种模型。指数模型参数具有明确的物理意义:参数A与r之和能够准确代表强震后的实际初始余震数,5个余震序列初始余震数偏差均小于1.70%;参数k可作为反映余震序列衰减快慢的特征值,k值越大则余震序列衰减越慢,其值与主震震级呈反比例关系。

Abstract:

Large aftershocks can cause additional losses and trigger the risk of building damage. To study the decay law of aftershock sequences, this paper attempts to use the exponential decay model to fit and analyze five aftershock sequences in various regions. The performances of the exponential and traditional aftershock decay models were analyzed using the corrected Akaike information criterion, Bayesian information criterion, and adjusted R². The results show that the ability of the exponential model to describe the decay law of aftershock sequences is close to that of the modified Omori aftershock model and the stretched exponential model, especially the M_S6.0 aftershock sequence in Changning, Sichuan Province, and the M_S5.7 aftershock sequence in the Yiliang county of the Yunnan Province. In these two sequences, the exponential model performed better than the other two models, and the exponential model parameters showed clear physical meanings. The sum of parameters A and r can accurately represent the number of initial aftershocks after a strong earthquake. The deviations in the initial aftershock number of the five aftershock sequences are all less than 1.70%. The parameter k can be used as a characteristic value that reflects the decay rates of the aftershock sequences. The larger the value of k, the slower the decay of the aftershock sequence; and its values are inversely proportional to the magnitude of the main shock.