基于射线追踪技术计算地震定位中震源轨迹的改进方法

Improvement of the ray-tracing based method calculating hypocentral loci for earthquake location

使用震源轨迹确定震源位置不仅稳健而且直观,但当介质复杂时震源轨迹难以给出解析解.基于最小走时树射线追踪技术计算震源轨迹的方法(以轨迹所在的残差场中残差最小的点(初始点)至残差较小的点(震源轨迹代表点)的射线路径表示震源轨迹)适用于复杂速度模型,但尚不能正确计算由多段组成的震源轨迹,同时兼顾计算轨迹的完整性和精细性较为困难,计算参数设置烦琐不适于大批量数据的自动处理.针对该方法存在的问题,本文对其进行了改进:(1)采用一种"削皮"算法选取震源轨迹所经过的模型单元的节点作为轨迹代表点;(2)将残差较小的区域作为震源轨迹计算区域(该区域依轨迹分布自适应地划分为若干个连通区域),从未计算的轨迹代表点中选取残差最小者作为射线路径初始点,利用最小走时树算法依次计算所有连通区域内的震源轨迹;(3)通过去掉较短的不再分叉的射线路径使震源轨迹更为精细.虚拟和真实事件的算例表明,改进方法有效克服了原方法的不足,可便捷地计算复杂速度模型中事件的震源轨迹,计算的轨迹精细且较完整.

Hypocentral loci are very useful for reliable and visual earthquake location,but they can hardly be analytically expressed when the velocity model is complex.There is a ray-tracing based numerical method to calculate them,in which a focal locus is represented in terms of ray paths from the minimum point（namely initial point）to low residual points（referred as hypocentral locus reference points,HLRPs）in its residual field.It has no restrictions on the complexity of the velocity model and can produce quite fine results.However,this method is incapable of addressing multi-segment loci and inadequate for processing large quantity of data.Additionally,it is rather laborious and difficult to set its controlling parameters for obtainingboth fine and complete hypocentral loci.This paper presents an improvement of the ray-tracing based method.The method for calculating hypocentral loci is based on the minimum traveltime tree algorithm for tracing rays.It consists of three steps：（1）HLRPs are selected from nodes of the model cells that the hypocentral locus runs through by means of a so-called peeling method.（2）The calculation domain of a hypocentral locus is defined as such a low residual area that its connected regions each include one segment of the locus and then all the focal locus segments are respectively calculated with the minimum traveltime tree algorithm for tracing rays by repeatedly assigning the minimal point among those HLRPs that have not been traced as an initial point.（3）Short ray paths without branching are removed to make the calculated locus finer.The improved method is applied to a virtual seismic event and a real earthquake.The virtual event takes place in a 300km×60km complex velocity model with a background of Yunnan area.It is covered well by 9seismic stations.The real earthquake occurred in North China and its epicenter and three seismic stations are located in an approximately straight line.Considering the lateral heterogeneity along the line is weak,a horizontally homogeneous crustal model is employed for calculating theoretical travel times.The differences between the observed and the calculated traveltimes are no more than 0.1sfor P waves and 0.4sfor S waves.For the two events,we calculate their hypocentral loci constrained with arrival times and those with arrival time differences when only P waves are used and both P and S waves are used.As for the arrival time constrained hypocentral loci of the virtual event,we investigate them in six different cases：（a）all stations,（b）sparse stations;（c）near stations;（d）far stations;（e）right-side stations;and（f）noisy arrival times.The numerical tests show that one-segment and multi-segment hypocentral loci are calculated correctly and their intactness is maintained well.For the same event,resultant fine hypocentral loci intersect exactly at the hypocenter when the velocity model and the observed arrival times are accurate.The parameters controlling the quality of outputting results can be chosen within a quite wide range and require little adjusting once they are set properly.Hypocentral loci associated with near stations have strong constraints on hypocenters.Additional use of S-wave data can improve the azimuth distribution and the stability of hypocentral loci.The improved method is capable of efficiently calculating hypocentral loci with good completeness and fineness for earthquakes in a complex model.Arrival times from near stations are critically important for determining hypocenters.S-wave data are helpful in strengthening the constraint on hypocenters,especially when the observation is incomplete.