Study On Parameters Estimation Method Of Historical Earthquakes Based On Discrete Intensity Points And Elliptical Model

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.