稳健回归模型在地震烈度衰减关系中的应用

Application of Robust Regression Model in Seismic Intensity Attenuation Relationship

摘要:

通过分析地震烈度衰减关系的模型与方法，设计了一种稳健回归模型。结合区域历史震害资料，应用该模型拟合地震烈度衰减关系，对新疆地区的烈度衰减关系进行分区分析，并与前人研究的结果进行对比分析。结果表明本文设计的稳健回归模型能对衰减关系拟合中提高回归分析的抗差性，衰减曲线更接近原始数据的优势分布。

Abstract:

The traditional intensity attenuation relationship was analyzed using the least squares method fitting.When every observation value is assigned the same weight，outliers are unreasonably treated. Minimizing the sum of squared residuals is the objective in the error checking of the least squares regression model，and the variance is not a robust statistical unit. Therefore，this method is unstable for intensity attenuation. A stable regression for the M estimation method is proposed in this paper.The method was applied to study 117 earthquake macroscopic isoseismic lines，as well as a joint attenuation model.All selected earthquakes from 1716 to 2011 were greater than MS5.0. The results are as follows：Near the epicenter, the intensity attenuation curves in the long axis were close to those in the short axis.With an increase in epicentral distance，the decay of intensity increased along the long and short axis，and along the long shaft it was faster than that along the short shaft. In the far field，the curves of the long axis coincided with those of the short axis.Compared with historical seismic survey data，the simulated intensity of the long and short axial was consistent with the field data in the epicentral region and the far field.Under the same magnitude，the intensity of Tianshan was a slightly higher than that of Arkin and the West Kunlun Mountains in meizoseismal area，which may relate to regional site conditions.In the near field and with the same epicenter distance region, the intensity of Tianshan area was slightly higher than that of Arkin and the West Kunlun Mountains region. In the far field，in the same epicenter distance，the intensity attenuation speed in the Tianshan area was greater than that in the Altun Mountains and West Kunlun Mountains area，which was more obvious when the magnitude was greater than 7.In the far field and under the same magnitude，the attenuation curves of both shafts were similar and tended to be similar in shape to those of the Altun and West Kunlun Mountains.In the same epicenter location near the epicenter，the intensity of West Kunlun Mountains was slightly higher than that of Elgin area.In contrast，the intensity of Altun area was slightly higher than that of KunLun area in the far field position of larger magnitude.By contrast，the actual average rupture scale determined by three regression models indicated that the robust regression model was better than least squares regression and multivariate regression，and it could accurately reflect geological background and attenuation law in the Tianshan area.Therefore，it was the most fit for simulation of the actual value.In short，the robust regression model significantly improved the simulation of seismic intensity attenuation relationship for large magnitudes and has a strong practical significance for earthquake prediction in the region.Furthermore，this method provides reasonable intensity attenuation for regional seismic hazard analysis and seismic zoning.