高维局部数据体中线性信号预测基本理论与方法

Basic theory and method of linear signal prediction in high-dimensional local data volume

1.同济大学海洋与地球科学学院波现象与智能反演成像研究组(WPI),上海200092;
2.中国石油东方地球物理公司研究院,河北涿州072751

1. Wave Phenomenon and Intelligent Inversion Imaging Research Group (WPI),School of Ocean and Earth Sciences,Tongji University,Shanghai 200092,China;
2. Research Institute,BGP Inc.,CNPC,Zhuozhou 072751,China

首先,提出了若干线性结构(可以视为局部平面波)飘在具有不同概率分布特征的、实测的局部高维数据体中是地震信号处理的核心概念模式,认为对局部高维数据体中的线性结构进行建模及最佳预测,从而解决去噪、数据规则化和解混叠(Deblending)等问题是地震数据处理中的基本环节;认为对线性信号进行最佳的建模和预测包括模型驱动和数据驱动的方法。前者是由预先选定的局部平面波基函数的线性叠加表示局部高维数据体中包含的信号;后者由数据矩阵(张量)分解的方法推断局部高维数据体中包含的线性结构。然后,全面分析了频率空间域高维Wiener滤波方法、自相关矩阵及Hankel矩阵正交分解方法(SSA方法)、高维线性Radon变换方法(高维Beamforming方法)和张量分解方法的基本理论,为进行局部高维数据体中线性信号预测及各种应用奠定了理论基础。最后,指出山前带及其他复杂地表探区实际数据中的相干噪声和非相干噪声往往不符合线性信号建模及预测的理论假设条件,因而必须发展非线性去噪方法。

This article first proposes that several linear structures (which can be regarded as local plane waves) float in local high-dimensional data volume with different probability distribution characteristics,which is the core conceptual mode of seismic signal processing.It is believed that modeling and optimal prediction of linear structures in local high-dimensional data volumes,in order to solve the problems such as denoising,data regularization,and deblending,are the very basic steps in seismic data processing.It is considered that the optimal modeling and prediction of linear signals include model-driven and data-driven methoel.The former represents the signals contained in the local high-dimensional data volume by the linear superposition of pre-selected local plane wave basis functions.The latter uses the data matrix (tensor) decomposition method to infer the linear structure contained in the local high-dimensional data volume.Then,the basic theories of high-dimensional Wiener filtering method,autocorrelation matrix and Hankel matrix orthogonal decomposition method (SSA method),high-dimensional linear Radon transform method (high-dimensional Beamforming method),and tensor decomposition method in the frequency space domain were comprehensively analyzed,and a theoretical foundation for linear signal prediction and various applications in local high-dimensional data volume is built.Finally,it is pointed out that the coherent noise and incoherent noise in the real data of the piedmont zone and other complex surface exploration areas often seriously deviate from the theoretical assumptions of linear signal modeling and prediction,developing nonlinear denoising methods is also inevitable.

中石油集团前瞻性基础性项目“物探岩石物理与前沿储备技术研究”(2021DJ3501)、国家自然科学基金(42474142,42304124,42174135,42074143)、中国博士后科学基金(2023M732633)和国家重点研发计划变革性技术关键科学问题重点专项(2018YFA0702503)共同资助。

10.12431/issn.1000-1441.2025.64.01.001