基于空间离散烈度点椭圆模型的历史地震参数估计方法研究
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摘要
由于地震仪器记录的历史较短,不足以在短时间、小尺度范围内弄清楚地震活动性规律,因而对历史地震的研究非常重要。地震史料只有转换成用现代地震参数(如震级、震中位置等)的形式来表达,才有可能用于地震科学的各种研究。已出版的各版本历史地震目录里地震参数估算方法主观经验性较强,不确定性较大；现有新方法多以圆烈度衰减关系为基础,忽略了烈度分布的椭圆特征。本文通过建立椭圆烈度分布模型,联立椭圆数学方程,直接带入原始烈度点信息来估算历史地震基本参数,并以蒙特卡洛方法对参数估定的不确定性进行定量分析,以提高历史地震参数估计的科学性,减少主观判断带入的不确定性。
本文首先分析了历史地震资料的特点,认为我国历史地震记录虽然跨度时间长,资料丰富,但受历史条件所限,在时、空、强上分布均不均匀,地震记录与烈度点都存在着不完整性,而且历史地震参数不确定性较大。
针对历史地震资料的特点,我们基于宏观影响场的图像特征来建立地震烈度椭圆分布模型。引入空间统计分析的概念,从空间数据的角度给出了离散烈度点的定义,阐述了空间离散烈度点建模理论。以原始烈度点空间分布为基础用最小二乘法拟合各地震各烈度区椭圆烈度估计线,进而对烈度估计线统计回归得到椭圆烈度分布模型。依据所能获取的地震烈度信息,本文建立了适用于中国南北地震带、东部地区和新疆地区的椭圆烈度分布模型。该模型的建立充分利用了大量原始离散烈度点信息,通过数学手段得到烈度估计线,避免了等震线圈定过程中的主观经验因素。
根据所建立的椭圆烈度分布模型,联立考虑中心点和方向性的椭圆数学方程,建立了地震参数估计方程,给出了参数求解的基本条件,并用既有仪器测定记录又有宏观考察数据的现代地震进行了内符验算和外推验算,证明了算法的可行性。采用蒙特卡洛方法,通过大量的抽样模拟,定量分析了所得参数的不确定性,并进一步讨论了本文所提算法的稳定性和适用性。
本文建立了一套估算地震震中与震级的方法,旨在用此方法来估算只有烈度记载且烈度数据点相对较少的历史地震参数。以云南地区和山西地区为例,将此方法应用于有真实历史记载的地震进行了试算。历史地震算例表明,此方法对烈度数据点较少、等震线不易勾画的历史地震颇为有效。处理过程直接明了,一定程度上减少了主观不确定性,可重复和再现。同时证明了该方法对烈度信息空间分布散乱的稳定性。
由于单烈度点地震占了历史强震总数的近1/3,本文单独对这类地震进行了讨论分析。研究表明,历史强震目录里单烈度点地震的震级可能存在普遍偏小的问题,尤其是在新疆、西藏和青海等地广人稀而又地震活动频繁的地方,可能会造成大量历史大震的漏记或者错记。
最后对研究工作进行了总结,讨论了存在的问题,并给出了使用历史地震资料的若干建议与研究展望。
本文建立了椭圆烈度分布模型和地震参数估计方程,直接利用全部烈度点的空间分布信息来估算地震震级和震中,为历史地震参数的确定提供了新的思路与方法,进一步提升了地震史料的可用性,提高了历史地震参数的可靠性,对于历史地震的重建和历史地震参数的校核具有重要意义。
Due to the short history of seismic instruments record, it is insufficient to know well of the law of seismic activity in a short time and within a scope of small-scale, thus it's very important to study on the historical earthquakes. Historical earthquake materials only converted into the form of modern seismic parameters (such as magnitude, epicenter, etc.), are possible for a variety of earthquake science research. The methods of earthquake parameters estimation in published historical earthquake catalogs partly are subjectively empirical with great uncertainty; Existing new methods are mostly based on circle intensity attenuation relationship, ignored the elliptical distribution characteristic of intensity. This paper established elliptical intensity distribution model, combined with ellipse mathematic equation, used the information of origial intensity points derectly to calculate historical earthquakes'basic parameters, and used the Monte Carlo method for quantitative analysis of the uncertainty of parameter estimation. These works are in order to improve the scientific and reduce the subjective uncertainty of the paramters'estimation of historical earthquakes.
Firstly, this paper analyzed the characteristics of historical earthquake materials. Although Chinese historical earthquake records span a long time and are information rich, but due to the historical conditions, they are unevenly distributed in time, space and magnitude. The earthquake records and intensity data points are both not integrated, and the parameters of historical earthquakes have great uncertainty.
According to the characteristics of historical earthquake materials, this paper established elliptical intensity distribution model based on the image feature of macro earthquake influence field. We introduced the concept of spatial statistical analysis, gave the definition of the discrete intensity points from the perspective of spatial data, and elaborated spatial modeling theory about discrete intensity point. Based on the spatial distribution of original intensity points, we used the least-square method to fit elliptical intensity estimation lines of different earthquakes of different intensity zones, then regressed the elliptical intensity distribution model. According to the seismic intensity information that can be obtained, this article established elliptical intensity distribution models that apply to the Chinese north-south seismic belt, the eastern region and the Xinjiang region. These models take advantage of the spatial distribution of large numbers of original discrete intensity points, use mathematical means to get intensity estimated lines to avoid subjective factors in the process of isoseismal plotting.
Substituting the established elliptical intensity distribution model into the ellipse mathematic equation which considers the center point and the direction, we established the earthquake parameters estimation equation, and gave the basic conditions for solving, did internally checking and extrapolation checking on modern events with both instrument records and macro investigation records, proved the feasibility of the algorithm. Using the Monte Carlo method, we quantitatively analyzed the uncertainty of calculated parameters by simulating a large number of sampling and further discussed the stability and applicability of the algorithm.
This paper has established a method to estimate earthquakes' epicenter and magnitude aimed on using this method to estimate the historical earthquake parameters that have only intensity information and the intensity data points relatively few. In Yunnan and Shanxi Province as an example, this method is applied to real historical earthquakes. Historical earthquake examples show that this method is quite effective for historical earthquakes with less intensity data points and difficulty to delineate isoseismal. The process of our method is straightforward. It can reduce the subjective uncertainty to some extent, and can be repeatable and reproduced. This work has also proved that the method is stability for the scattered spatial distribution of intensity information.
As the historical earthquakes with a single intensity point account for nearly1/3of the total historical record, we discussed such earthquakes alone. Studies have shown that the magnitude of such earthquakes in historical earthquake catalog may generally smaller than the real, especially in Xinjiang, Tibet and Qinghai such frequent seismic activity but sparsely populated areas, it may cause a lot of large historical earthquakes omission or wrong noted.
Finally, the research works are summarized, problems are discussed and a few recommendations are given on how to use historical earthquake materials.
This paper has established elliptical intensity distribution model and seismic parameters estimation equation. This method directly uses the spatial distribution information of all intensity points to estimate seismic parameters, provides new idea for historical earthquake parameters determination, further enhances the availability of historical earthquakes and improves the reliability of the historical seismic parameters. For the reconstruction and parameters'checking of historical earthquakes, it has important significance.
本文首先分析了历史地震资料的特点,认为我国历史地震记录虽然跨度时间长,资料丰富,但受历史条件所限,在时、空、强上分布均不均匀,地震记录与烈度点都存在着不完整性,而且历史地震参数不确定性较大。
针对历史地震资料的特点,我们基于宏观影响场的图像特征来建立地震烈度椭圆分布模型。引入空间统计分析的概念,从空间数据的角度给出了离散烈度点的定义,阐述了空间离散烈度点建模理论。以原始烈度点空间分布为基础用最小二乘法拟合各地震各烈度区椭圆烈度估计线,进而对烈度估计线统计回归得到椭圆烈度分布模型。依据所能获取的地震烈度信息,本文建立了适用于中国南北地震带、东部地区和新疆地区的椭圆烈度分布模型。该模型的建立充分利用了大量原始离散烈度点信息,通过数学手段得到烈度估计线,避免了等震线圈定过程中的主观经验因素。
根据所建立的椭圆烈度分布模型,联立考虑中心点和方向性的椭圆数学方程,建立了地震参数估计方程,给出了参数求解的基本条件,并用既有仪器测定记录又有宏观考察数据的现代地震进行了内符验算和外推验算,证明了算法的可行性。采用蒙特卡洛方法,通过大量的抽样模拟,定量分析了所得参数的不确定性,并进一步讨论了本文所提算法的稳定性和适用性。
本文建立了一套估算地震震中与震级的方法,旨在用此方法来估算只有烈度记载且烈度数据点相对较少的历史地震参数。以云南地区和山西地区为例,将此方法应用于有真实历史记载的地震进行了试算。历史地震算例表明,此方法对烈度数据点较少、等震线不易勾画的历史地震颇为有效。处理过程直接明了,一定程度上减少了主观不确定性,可重复和再现。同时证明了该方法对烈度信息空间分布散乱的稳定性。
由于单烈度点地震占了历史强震总数的近1/3,本文单独对这类地震进行了讨论分析。研究表明,历史强震目录里单烈度点地震的震级可能存在普遍偏小的问题,尤其是在新疆、西藏和青海等地广人稀而又地震活动频繁的地方,可能会造成大量历史大震的漏记或者错记。
最后对研究工作进行了总结,讨论了存在的问题,并给出了使用历史地震资料的若干建议与研究展望。
本文建立了椭圆烈度分布模型和地震参数估计方程,直接利用全部烈度点的空间分布信息来估算地震震级和震中,为历史地震参数的确定提供了新的思路与方法,进一步提升了地震史料的可用性,提高了历史地震参数的可靠性,对于历史地震的重建和历史地震参数的校核具有重要意义。
Due to the short history of seismic instruments record, it is insufficient to know well of the law of seismic activity in a short time and within a scope of small-scale, thus it's very important to study on the historical earthquakes. Historical earthquake materials only converted into the form of modern seismic parameters (such as magnitude, epicenter, etc.), are possible for a variety of earthquake science research. The methods of earthquake parameters estimation in published historical earthquake catalogs partly are subjectively empirical with great uncertainty; Existing new methods are mostly based on circle intensity attenuation relationship, ignored the elliptical distribution characteristic of intensity. This paper established elliptical intensity distribution model, combined with ellipse mathematic equation, used the information of origial intensity points derectly to calculate historical earthquakes'basic parameters, and used the Monte Carlo method for quantitative analysis of the uncertainty of parameter estimation. These works are in order to improve the scientific and reduce the subjective uncertainty of the paramters'estimation of historical earthquakes.
Firstly, this paper analyzed the characteristics of historical earthquake materials. Although Chinese historical earthquake records span a long time and are information rich, but due to the historical conditions, they are unevenly distributed in time, space and magnitude. The earthquake records and intensity data points are both not integrated, and the parameters of historical earthquakes have great uncertainty.
According to the characteristics of historical earthquake materials, this paper established elliptical intensity distribution model based on the image feature of macro earthquake influence field. We introduced the concept of spatial statistical analysis, gave the definition of the discrete intensity points from the perspective of spatial data, and elaborated spatial modeling theory about discrete intensity point. Based on the spatial distribution of original intensity points, we used the least-square method to fit elliptical intensity estimation lines of different earthquakes of different intensity zones, then regressed the elliptical intensity distribution model. According to the seismic intensity information that can be obtained, this article established elliptical intensity distribution models that apply to the Chinese north-south seismic belt, the eastern region and the Xinjiang region. These models take advantage of the spatial distribution of large numbers of original discrete intensity points, use mathematical means to get intensity estimated lines to avoid subjective factors in the process of isoseismal plotting.
Substituting the established elliptical intensity distribution model into the ellipse mathematic equation which considers the center point and the direction, we established the earthquake parameters estimation equation, and gave the basic conditions for solving, did internally checking and extrapolation checking on modern events with both instrument records and macro investigation records, proved the feasibility of the algorithm. Using the Monte Carlo method, we quantitatively analyzed the uncertainty of calculated parameters by simulating a large number of sampling and further discussed the stability and applicability of the algorithm.
This paper has established a method to estimate earthquakes' epicenter and magnitude aimed on using this method to estimate the historical earthquake parameters that have only intensity information and the intensity data points relatively few. In Yunnan and Shanxi Province as an example, this method is applied to real historical earthquakes. Historical earthquake examples show that this method is quite effective for historical earthquakes with less intensity data points and difficulty to delineate isoseismal. The process of our method is straightforward. It can reduce the subjective uncertainty to some extent, and can be repeatable and reproduced. This work has also proved that the method is stability for the scattered spatial distribution of intensity information.
As the historical earthquakes with a single intensity point account for nearly1/3of the total historical record, we discussed such earthquakes alone. Studies have shown that the magnitude of such earthquakes in historical earthquake catalog may generally smaller than the real, especially in Xinjiang, Tibet and Qinghai such frequent seismic activity but sparsely populated areas, it may cause a lot of large historical earthquakes omission or wrong noted.
Finally, the research works are summarized, problems are discussed and a few recommendations are given on how to use historical earthquake materials.
This paper has established elliptical intensity distribution model and seismic parameters estimation equation. This method directly uses the spatial distribution information of all intensity points to estimate seismic parameters, provides new idea for historical earthquake parameters determination, further enhances the availability of historical earthquakes and improves the reliability of the historical seismic parameters. For the reconstruction and parameters'checking of historical earthquakes, it has important significance.
引文
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