【摘要】 本文将拟牛顿法与信赖域法相结合的反演方法用于地震震中和一维速度结构的联合反演.通过数值试验比较发现:用拟牛顿法构造Hessian矩阵,虽然仅利用目标函数的一阶导数信息,但由于保证了正定性和拟牛顿条件,比解析求得Hessian矩阵更加高效稳定,通过与信赖域方法的结合,使得该联合反演方法与经典的联合反演方法相比不仅具有较高的计算效率和较高的反演精度,同时也具有更强的总体收敛性.利用本文方法对台湾集集地震重新定位结果(纬度23.86°N,经度120.80°E,深度10km,发震时刻1999年9月21日17:47:16.0)与前人主流结果一致.此外,该方法对不同初始速度模型以及不同的地震到时数据集均可给出较一致的结果,进一步表明该方法的优越性.本文还利用1998~2001年间华北遥测地震台网40个台站记录到的64次地震的971条P直达波和首波到时资料,采用本文提出的方法吩北京及其邻区的一维地壳P波速度结构进行联合反演,结果表明该地区浅层地壳速度较低,中部地壳速度较高,下部地壳速度逐渐递增.更多还原

【Abstract】 We propose a hybrid algorithm,which combines the quasi-Newton method and the trust-region method in a least square form,to simultaneously determine hypocenters and velocity structure.Our numerical tests indicate that the Hessian matrix constructed by the quasi-Newton method,with the positive definiteness and the satisfaction of the quasi-Newton condition,is more efficient and stable than the analytical one though only the first-order derivatives of the objective function are used in the quasi-Newton method.Furthermore,combining with the trust-region method,our algorithm of simultaneous determination of hypocenters and velocity structure has been proven to be more accurate and efficient and has better convergent property than the classic method.With our method,we relocate the hypocenter of the Chi-Chi earthquake of Taiwan and obtain the result: latitude 23.86°N,longitude 120.80°E,focal depth 10km,and origin time 17:47:16.0.This result is consistent with the credible previous result,and is robust with different initial values and different data sets.Finally,we apply our method to simultaneously determine hypocenters and 1-D velocity structure of the North China area by using the selected 971 high quality direct and refracted P arrivals of 64 earthquakes from 40 stations of the North China Seismic Network from 1998 to 2001.We find that the upper crust in this studied area has low velocity with a sharp increase at depth of 4km,the middle crust has high velocity (～6km/s),and the lower crust has a positive velocity gradient.更多还原