摘要
为了充分利用矿区岩土体的三维速度结构,以正反演联用法为雏形,提出专门针对水平或倾斜分层介质的定位方法。推导水平分层介质中的波前曲面方程,并基于该方程,从任意观测系统角度,将发震时刻作为未知量引入非线性方程组求解,建立未知数个数等于非线性方程个数的适定非线性方程组,从而建立了波前正演法。不同于正反演联用法通过规则观测系统和曲线拟合确定发震时刻,波前正演法将发震时刻作为未知量,确定震源时空参数需要四个台站的非线性方程。为了简化波前正演法的非线性系统,采用变量代换法,减少了定位参数,从而减小了确定迭代初值的难度。通过将台站所在的原大地坐标系旋转至与介质分界面平行正交,使得新坐标系中的波前面推进方向与坐标轴z平行,从而将波前正演法推广应用于倾斜层状介质,有效解决了倾斜层状介质中的震源定位问题。对波前正演法的16个未知参数相对于3个速度结构参数的条件数进行计算,多种定位条件下的条件数计算结果表明,波前正演法的条件数均远小于10,波前正演法是良态的。
In order to make full use of 3-D velocity structure of the rock mass in the mining area, based on the combined method of forward and inversion as an embryonic form, a new method for positioning of seismic sources in multilayered horizontal or inclined media is put forward. The wave front surface equation in multilayered horizontal media is derived. From the perspective of any field setup, based on the equation, the original time of earthquake is substituted into the nonlinear equations as an unknown quantity. The nonlinear equation set is established, of which the unknowns are equal to the number of nonlinear equations, thus a method for positioning of seismic sources based on forward of wave front is established. The time when the earthquake happens is obtained through inversion and corrected by curve fitting based on regular field setup in the positioning model combined with forward and inversion. The positioning model, based on forward of wave front, which deals with the time of earthquake as an unknown quantity in the nonlinear equations, is different. It obtains spatiotemporal parameters of seismic sources through nonlinear equations of four stations. The number of source parameters is reduced using the method of variable substitution, so the nonlinear system of the positioning model based on forward of wave front is simplified. The determination of iterative initial value is easier. The original geodetic coordinates of stations are rotated into those which are orthogonal or parallel to the interfaces between different media. The forward direction of wave front in the new coordinate system is parallel to the axis z. Thus the positioning model based on forward of wave front is extended to multilayered inclined media. The positioning model based on forward of wave front is an effective method to solve the problem of source positioning in multilayered inclined media. The calculated results of conditional numbers of 16 unknown parameters corresponding to 3 parameters of velocity structure under different conditions show that the conditional numbers of positioning model based on forward of wave front are all far less than 10, and the positioning model based on forward of wave front is in good state.
引文
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