基于布谷鸟算法的马尔可夫链蒙特卡洛反演方法  

Markov chain Monte Carlo inversion with cuckoo algorithm

作　　者：李进 张怀 石耀霖 LI Jin;ZHANG Huai;SHI YaoLin(National Key Laboratory of Earth System Numerical Modeling and Application,College of Earth and Planetary Sciences,University of Chinese Academy of Sciences,Beijing 101408,China;Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai),Zhuhai Guangdong 519080,China;Beijing Yanshan Earth Critical Zone National Research Station,University of Chinese Academy of Sciences,Beijing 101408,China)

机构地区：[1]地球系统数值模拟与应用全国重点实验室,中国科学院大学地球与行星科学学院,北京101408 [2]南方海洋科学与工程广东省实验室(珠海),广东珠海519080 [3]北京燕山地球关键带国家野外科学观测研究站,中国科学院大学,北京101408

出　　处：《地球物理学报》2025年第4期1511-1520,共10页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(U2239205);国家杰出青年科学基金项目(41725017);科技部国家重点研发计划重点项目(2020YFA0713400)联合资助。

摘　　要：由于地球物理重、磁、电、震等实际勘测数据不够完备,部分数据信噪比较低,使得传统的以吉洪诺夫(Tikhonov)正则化为基础的反演理论存在分辨率较低、适定性较差等问题.近年来,以贝叶斯(Bayesian)反演为代表的随机反演日趋成熟.该方法具备反演结果分辨率更高、全局收敛性更好、更易于与人工智能(AI)结合等优势,弥补了传统算法的不足.贝叶斯反演方法最主要的瓶颈在于马尔可夫链蒙特卡洛采样算法计算量大、收敛速度慢且不稳定.本文在贝叶斯反演框架下构建了地球物理反演的目标参数,利用数据与待反演参数之间存在的物理关系,基于马尔可夫链蒙特卡洛算法,引入布谷鸟算法优化采样,实现了对重力场和地震波平均速度的反演,并与传统反演方法进行了对比.结果表明,我们提出的方法比传统马尔可夫链蒙特卡洛反演方法具有更高的准确率、更快的收敛速度和更好的稳定性,为今后在地球物理反演中实现吉洪诺夫正则化与随机反演相结合的非线性反演理论提供了新思路和新途径.Due to the incompleteness of actual geophysical survey data,including geophysical gravitational,magnetic,electrical and seismic measurements,and low signal-to-noise ratio of partial data,the traditional inversion theories based on Tikhonov regularization face issues such as low resolution and poor adaptability.In recent years,stochastic inversion,represented by Bayesian inversion,has become increasingly mature.This method offers advantages of the higher resolution of inversion results,better global convergence and easier combination with artificial intelligence(AI),compensating for the shortcomings of traditional algorithms.The main bottleneck of the Bayesian inversion method lies in a large amount of calculation,slow and unstable convergence of the Markov chain Monte Carlo sampling algorithm.In this paper,the target parameters of geophysical inversion are constructed under the framework of Bayesian inversion.By the physical relationship between the data and the parameters to be inverted,based on the Markov chain Monte Carlo algorithm,the cuckoo algorithm is introduced to optimize sampling,and the inversion of the gravity field and the average velocity of seismic wave is realized,and compared with traditional inversion methods.The results show that method we proposed has higher accuracy,faster convergence and better stability than the traditional Markov chain Monte Carlo inversion method,which provides a new idea and a new approach for realizing the nonlinear inversion theory combining Tikhonov regularization and stochastic inversion in geophysical inversion in the future.

关 键 词：随机反演 贝叶斯反演 马尔可夫链蒙特卡洛算法 布谷鸟算法 重力反演 地震波反演 

分 类 号：P313[天文地球—固体地球物理学] P315[天文地球—地球物理学]