基于L-BFGS理论求解复程函方程的地震波复走时计算方法  

A fast algorithm for computing complex traveltime based on L-BFGS method

作　　者：黄兴国[1,2] 孙建国[1,2] 孙章庆[1,2] 王乾龙[1,2] HUANG Xing-Guo SUN Jian-Guo SUN Zhang-Qing WANG Qian-Long(College for Geoexploration Science and Technology, Jilin University, Changchun 130026 Laboratory for Integrated Geophysical Interpretation Theory of the Ministry for Land and Resources of China -- Laboratory for Wave Theory and Imaging Technology, Changchun 130026)

机构地区：[1]吉林大学地球探测科学与技术学院,吉林长春130026 [2]国土资源部应用地球物理综合解释理论开放实验室-波动理论与成像技术实验室,吉林长春130026

出　　处：《物探与化探》2016年第5期961-967,共7页Geophysical and Geochemical Exploration

基　　金：国家自然科学基金项目(41274120;41404085)

摘　　要：地震波复走时在处理几何射线理论面临的焦散问题有着重要作用。为了获得一种精度高且更为高效的复走时计算方法,将L-BFGS最优化理论引入分离的复程函方程中用于求取等效虚慢度,直接利用复走时实部、虚部正交的条件为目标函数,减少了梯度矩阵的一次乘积,利用计算梯度的正演部分作为复走时计算部分,得到了一种求解复程函方程的L-BFGS快速推进复走时计算方法。通过对解析法、动力学射线追踪法、高斯牛顿—共轭梯度快速推进法、L-BFGS快速推进法计算结果的精度和效率分析,表明L-BFGS快速推进法在精度和效率上均具有一定的优越性,也能适应在实际应用中的大规模计算需求。Complex traveltime of seismic wave plays an important role in dealing with caustics with which geometric ray theory faces. To obtain a higher accuracy and a more efficient method for calculating the complex traveltime,the authors introduce the L-BFGS optimization method to calculate the imaginary slowness. In addition,orthogonal condition of the real part and imaginary part of complex traveltime are taken as the objective function,and then a new L-BFGS-FMM method is obtained for computing complex traveltime. The numerical examples demonstrate the effectiveness of L-BFGS-FMM used in this paper. An analysis of accuracy and efficiency of the results obtained by using the analytical method,dynamic ray tracing method,Gauss-Newton-conjugate gradient method and L-BFGS-FMM method shows that the L-BFGS-FMM method introduced in this paper is superior to all the other methods,and hence the method introduced in this paper can meet the large- scale computing requirement in practical applications.

关 键 词：复程函方程 复走时 快速算法 L-BFGS理论 快速推进法 

分 类 号：P631.4[天文地球—地质矿产勘探]