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Analytical and graphical determination of the trajectory of a fireball using seismic data

机译：使用地震数据对火球轨迹进行分析和图形确定

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摘要

In this paper we discuss two methods, one analytical and the other graphical, to determine the trajectory of a fireball using the arrival times of atmospheric shock waves recorded by a seismic network. In the analytical method the trajectory and the raypaths are assumed to be straight and we solve for the fireball velocity, the azimuth (φ) and elevation angle (δ) of the trajectory, the coordinates of the intersection of the trajectory with the earth's surface, and the corresponding intersection time (t_0). Because the problem is nonlinear, we solve it iteratively. The fireball velocity cannot be determined uniquely, and trades off with t_0. The graphical method is based on the drawing of contours of arrival times, which should be elliptical for fireball shock waves. If the distribution of seismic stations is appropriate, the horizontal projection of the fireball is given by the axis of symmetry of the contours, which allows the estimation of φ, while δ can be estimated from the spacing between contours along the symmetry axis. Application of the two methods to data from four fireballs shows that the graphically derived parameters can be within a few degrees of the analytical parameters. In addition, a fireball recorded in the Czech Republic has reliable trajectory parameters derived from video recordings, which allows an independent assessment of the quality of the parameters determined analytically. In particular, φ and δ have errors of 1.7° and 1.3°, respectively, which are not particularly large considering that the station distribution was not favorable.
机译：在本文中，我们讨论了两种方法，一种是分析方法，另一种是图形方法，它利用地震网络记录的大气冲击波的到达时间来确定火球的轨迹。在分析方法中，假设轨迹和射线路径是笔直的，我们求解了火球速度，轨迹的方位角（φ）和仰角（δ），轨迹与地球表面的交点的坐标，以及相应的交叉时间（t_0）。因为问题是非线性的，所以我们迭代地解决它。火球速度无法唯一确定，因此需要与t_0权衡。图形方法基于到达时间的轮廓图，对于火球冲击波，该时间应为椭圆形。如果地震台的分布适当，则火球的水平投影由轮廓的对称轴给出，这可以估算φ，而δ可以从沿对称轴的轮廓之间的间距估算。两种方法对来自四个火球的数据的应用表明，以图形方式得出的参数可以在分析参数的几度之内。此外，在捷克共和国录制的火球具有可靠的轨迹参数，这些参数是从视频记录中得出的，从而可以独立评估通过分析确定的参数的质量。尤其是，φ和δ分别具有1.7°和1.3°的误差，考虑到站分布不利，误差不是特别大。

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