基于动态规划旅行时场的海森矩阵计算方法及其应用  

Computation of Hessian Matrix Based on Dynamic Programming Traveltime Field and Its Application

作　　者：晁吉荣 王通 倪文军 Chao Jirong;Wang Tong;Ni Wenjun(School of Geophysics and Geomatics,China University of Geosciences,Wuhan Hubei 430074,China;Jianghan Logging Company Sinopec Matrix Corporation,Wuhan Hubei 430073,China)

机构地区：[1]中国地质大学地球物理与空间信息学院,湖北武汉430074 [2]中石化经纬有限公司江汉测录井分公司,湖北武汉430073

出　　处：《工程地球物理学报》2024年第2期354-362,共9页Chinese Journal of Engineering Geophysics

基　　金：国家自然科学基金面上项目(编号:42374139);中国石化地球物理重点实验室开放基金(编号:36750000-23-FW0399-0003)。

摘　　要：地震波反演成像是经典偏移成像在最小二乘反演框架下的延伸,其核心在于消除偏移成像系统中海森矩阵的影响,得到更高分辨率的成像结果。海森矩阵规模巨大,对其的高效计算可有力推动地震波反演成像方法的进步。本文首先从一次反射波的偏移和反演成像的对比出发,推导出海森矩阵的表达及其简化形式,通过分析表达式,指出旅行时场是海森矩阵计算的关键问题。接着,提出利用点扩散函数(PSF,Point Spread Function)来近似表达海森矩阵,并引入动态规划旅行时计算,获取了旅行时场表征的PSF,从而实现对一阶海森矩阵的高效表达,并分析计算所得的PSF性态,对比计算效率。最后,基于传统偏移成像结果,利用计算得到的PSF进行了成像校正,对计算得到的近似海森矩阵的有效性进行了测试和应用。数值实验表明,基于动态规划旅行时场可以高效稳定地计算近似海森矩阵。通过对比海森矩阵分辨率校正前后的成像结果,验证了本文发展的高效近似海森矩阵计算方法的有效性和应用潜力。The seismic data inversion imaging is an extension of classic migration imaging within the least squares inversion framework.Its core lies in eliminating the impact of the Hessian matrix in the migration imaging system to achieve higher-resolution imaging results.The immense scale of the Hessian matrix makes its efficient computation crucial in advancing seismic data inversion imaging methods.This paper compares the migration of a reflection wave with inversion imaging,deriving the expression and simplified form of the Hessian matrix.By analyzing the expression,it identifies the traveltime field as a key issue in Hessian matrix computation.Next,it proposes an approximation of the Hessian matrix using the point spread function(PSF)and introduces dynamic programming for traveltime computation,obtaining the PSF representing the traveltime field.This approach achieves efficient representation of the first-order Hessian matrix and analyzes the properties of the computed PSF while comparing computational efficiency.Finally,utilizing the PSF computed based on traditional migration imaging results,it corrects the resolution in the imaging domain and tests and applies the effectiveness of the computed Hessian matrix.Numerical experiments demonstrate that the Hessian matrix computes efficiently and stably based on dynamic programming for the traveltime field.By comparing imaging results before and after Hessian matrix resolution correction,it validates the effectiveness and application potential of the developed efficient Hessian matrix computation method.

关 键 词：旅行时 最小二乘法 海森矩阵 点扩散函数 反褶积 

分 类 号：P631.4[天文地球—地质矿产勘探]