基于加权平均导数的频率-空间域正演模拟及GPU实现  

Frequency-space domain acoustic modeling based on an average-derivative and GPU implementation

作　　者：唐祥德[1,2] 刘洪[1] 张衡[3] 

机构地区：[1]中国科学院地质与地球物理研究所,中国科学院油气资源研究重点实验室,北京100029 [2]中国科学院大学,北京100049 [3]国土资源部海底矿产资源重点实验室,广州海洋地质调查局,广州510075

出　　处：《地球物理学报》2015年第4期1341-1354,共14页Chinese Journal of Geophysics

基　　金：国家高技术研究发展计划(863计划)项目(2012AA061202);国家油气重大专项(2011ZX05008-006-50);国家油气重大专项(2011ZX05003-003);国家自然科学青年基金(41204073)联合资助

摘　　要：传统基于旋转坐标系的频率-空间域正演模拟方法仅适用于方形网格,而实际生产中矩形网格广泛存在,本文提出一种适用性广的正演差分算子,不仅适用于方形网格而且适用于矩形网格.通过综合运用平均导数法、加速项加权平均、模拟退火法压制频散和减少单个波长所需网格点数,从而提高算法精度和减少计算量.在该方法的基础上采用不完全LU分解作为求解Helmholtz方程的预条件,并利用图形处理器加速计算速度,很大程度上提高了频率域正演的效率.Full-waveform inversion （FWI） can supply accurate velocity model for seismic imaging and is becoming a very important technology in seismic exploration. The frequency domain modeling is the base of frequency domain FWI and can be used for each iteration. In this case, accurate and fast frequency domain modeling is very necessary. The traditional frequency domain modeling methods can only be used in square grid and the memory and computation requirements are huge. We present a high efficient and adaptable frequency domain modeling technique in this paper.We design a 17-point scheme to perform the frequency domain modeling and use the average-derivative method to overcome the disadvantage that the traditional frequency domain modeling method can not be used in rectangular grid. Our operator can not only be applied in the condition of square grid but also rectangular grid, which is very useful in the real world situation because the rectangular grid is very popular in field work. Therefore, our operator is of greater applicability than the traditional methods. In order to reduce the dispersion and the number of grid points per shortest wavelength, we combine the mass acceleration term into the point calculation and get the optimal coefficients through simulated annealing algorithm. As the program Matlab provides the large scale optimization method, we use fmincon in this program to further optimize the coefficients. At last, the number of grid points per shortest wavelength is reduced to 2.5 comparing to 4 in 9-point method which is the most common frequency domain modeling method with phase velocity errors no larger than 1%. Therefore, the requirements of calculation amount and memory are reduced greatly. There are two main ways in solving Helmholtz equation which is the algorithm of frequency domain acoustic modeling, including direct method and iterative method. The direct method is LU decomposition while the matrix of LU decomposition in our algorithm usually is huge in 2D data and is difficult to solve usin

关 键 词：频率-空间域正演 矩形网格 不完全LU分解 GPU加速 

分 类 号：P631[天文地球—地质矿产勘探]