马尔琴科理论、算法与应用综述
Marchenko Theory, Algorithms, and Applications: A Review
中文总结 AI 辅助
本综述介绍源于量子逆散射的马尔琴科方法，涵盖其理论推导、多维扩展、各类应用及实用技术，还评估了当前的局限性与开放问题。
中文摘要 AI 辅助
地表采集的地震反射数据携带了地下各个深度的信息，包括常规偏移成像视为噪声或伪影的内部多次波。马尔琴科方法可直接从这些单侧测量结果中提取地下格林函数，它仅需的模型信息是平滑的宏观速度模型，用于估算从地表到深度虚拟点的直达波走时。该方法源于一维量子力学逆散射，过去二十年已通过声互易定理推广到三维声学介质，通过相应的弹性动力学和麦克斯韦互易定理推广到弹性和电磁介质。本综述涵盖经典的格尔范德-列维坦-马尔琴科方程及其通过薛定谔散射形式的推导、推动多维扩展的地震干涉测量结果，以及高维波聚焦的耦合马尔琴科方程。应用方面涉及马尔琴科重定位、单侧和双侧成像条件、内部多次波消除、面向目标的处理及全波形反演，还包括对耗散介质、弹性动力学、电磁场和平面波采集的扩展，以及最小二乘实现、GPU加速、压缩感知采集和近期预测聚焦函数的机器学习方法等实用主题。综述总结了海洋、陆地、盐下及时移监测场景的野外数据结果，最后评估了当前的局限性和开放问题，包括弹性多分量扩展、联合反演及神经网络加速器。
英文摘要
Seismic reflection data collected at the Earth's surface carry information from every depth in the subsurface, including the internal multiples that conventional migration treats as noise or artefacts. The Marchenko method retrieves subsurface Green's functions directly from these single-sided measurements. The only model information it requires is a smooth macro-velocity model, used to estimate the direct-wave traveltime from the surface to a virtual point at depth. The method originates in one-dimensional quantum mechanical inverse scattering and has been generalised over the past two decades to three-dimensional acoustic media using acoustic reciprocity theorems, and to elastic and electromagnetic media using the corresponding elastodynamic and Maxwell reciprocity theorems. This review covers the classical Gelfand--Levitan--Marchenko equation and its derivation through the Schrodinger scattering formalism, the seismic interferometry results that motivated the multidimensional extension, and the coupled Marchenko equations for wave focusing in higher dimensions. On the application side it treats Marchenko redatuming, single- and double-sided imaging conditions, internal multiple elimination, target-oriented processing, and full-waveform inversion. Extensions to dissipative media, elastodynamics, electromagnetic fields, and plane-wave acquisition are also covered, along with practical topics such as least-squares implementations, GPU acceleration, compressive-sensing acquisition, and recent machine-learning approaches to predicting the focusing functions. Field-data results from marine, land, sub-salt, and time-lapse monitoring settings are summarised. The review closes with an assessment of current limitations and open problems, among them elastic multi-component extensions, joint inversion, and neural-network accelerators.
