三维复杂速度模型中地震事件震源轨迹的计算

Calculation of hypocentral loci of seismic events in a 3-D complex velocity model

地球内部三维速度图像的广泛建立为进行高精度的地震定位提供了良好条件.使用震源轨迹确定震源位置不仅稳健而且直观,但三维复杂速度模型中的震源轨迹难以给出解析解.为此,本文提出了一种较准确地计算三维复杂速度模型中震源轨迹的数值方法.根据震源轨迹在残差场中的特点:(1)震源轨迹位于残差正负极性彼此不同的邻点之间;(2)绝对梯度在震源轨迹的法线方向最大;(3)在法线方向上越靠近震源轨迹残差绝对值越小,对于每个模型节点分别和残差正负极性与其不同的邻点组成的点对,将其中绝对梯度最大的点对作为震源轨迹法线点对,选取法线点对中残差绝对值较小的点(即震源轨迹所在模型单元的节点)作为震源轨迹代表点;在绝对残差场中数值较小的连通区域(可能有多个)内,利用最小走时树算法依次计算出每个连通区域中地震波从绝对残差最小点至同一连通区域内震源轨迹代表点的射线路径作为震源轨迹.算例表明:本文方法适用于三维复杂速度模型,对震源轨迹的稳定性及构成段数没有限制,计算的震源轨迹精细且较完整、可用于高精度的地震定位.

Availability of wide three-dimensional(3-D)velocity images of the Earth′s interior enables earthquake location with high accuracy.The earthquake location using hypocentral loci is robust and visual.However,hypocentral loci can hardly be expressed analytically when the velocity model is complex.In this study,a ray tracing-based numerical method is presented for accurately calculating hypocentral loci in a 3-D complex velocity model.As for each node in the residual field,it is combined with its adjacent nodes differing from it in residual polarity(positive,zero,or negative)into node pairs.Among these node pairs,the one with maximum absolute gradient is referred to as a normal node pair and its node with smaller absolute residual is selected as a focal locus reference point(FLRP),which is based on the facts that(1)the hypocentral locus lies between such adjacent nodes that they have different residual polarity;(2)the absolute gradient of residual is maximum along the normal to the hypocentral locus;(3)in a normal direction,the closer to the hypocentral locus,the smaller the absolute residual.In low absolute residual connected regions of which each completely contains only one of the segments constituting a hypocentral locus,the ray paths from the separate regional minimum points to their respective FLRPs within the same connected regions are calculated with a minimum traveltime tree algorithm to represent the hypocentral locus.Numerical examples show that the presented method is adapted to complex velocity models,and has no restrictions in the stability and the number of hypocentral locus segments.The calculated hypocentral loci are fine and complete enough for accurate earthquake location.