Title: A Deep-Learning-Driven Optimization-Based Inverse Solver for Accelerating the Marchenko Method Show Chinese title

Title: 基于深度学习的优化反演求解器，用于加速马尔琴科方法

Abstract: The Marchenko method is a powerful tool for reconstructing full-wavefield Green's functions using surface-recorded seismic data. These Green's functions can then be utilized to produce subsurface images that are not affected by artifacts caused by internal multiples. Despite its advantages, the method is computationally demanding, primarily due to the iterative nature of estimating the focusing functions, which links the Green's functions to the surface reflection response. To address this limitation, an optimization-based solver is proposed to estimate focusing functions in an efficient way. This is achieved by training a network to approximate the forward modeling problem on a small subset of pre-computed focusing function pairs, mapping final up-going focusing functions obtained via the conventional iterative scheme to their initial estimates. Once trained, the network is fixed and used as the forward operator within the Marchenko framework. For a given target location, an input is initialized and iteratively updated through backpropagation to minimize the mismatch between the output of the fixed network and the known initial up-going focusing function. The resulting estimate is then used to compute the corresponding down-going focusing function and the full Green's functions based on the Marchenko equations. This strategy significantly reduces the computational cost compared to the traditional Marchenko method based on conventional iterative scheme. Tests on a synthetic model, using only 0.8% of the total imaging points for training, show that the proposed approach accelerates the imaging process while maintaining relatively good imaging results, which is better than reverse time migration. Application to the Volve field data further demonstrates the method's robustness and practicality, highlighting its potential for efficient, large scale seismic imaging. Show Chinese abstract

Abstract: 根据地表记录的地震数据，Marchenko方法是一种用于重建全波场格林函数的强大工具。 这些格林函数随后可用于生成不受内部多次反射引起的伪影影响的地下图像。 尽管该方法具有优势，但由于估计聚焦函数的迭代性质，该方法计算量较大，这将格林函数与地表反射响应联系起来。 为解决这一限制，提出了一种基于优化的求解器，以高效的方式估计聚焦函数。 这是通过训练一个网络来近似一个小部分预计算的聚焦函数对的正演问题，将通过传统迭代方案获得的最终上行聚焦函数映射到其初始估计值。 一旦训练完成，网络就被固定，并作为Marchenko框架内的正演算子使用。 对于给定的目标位置，初始化输入并通过反向传播进行迭代更新，以最小化固定网络的输出与已知初始上行聚焦函数之间的不匹配。 然后利用得到的估计值，根据Marchenko方程计算相应的下行聚焦函数和完整的格林函数。 与基于传统迭代方案的传统Marchenko方法相比，这种策略显著降低了计算成本。 在合成模型上的测试表明，仅使用总成像点的0.8%进行训练，所提出的方法在保持相对良好的成像结果的同时加速了成像过程，效果优于逆时偏移。 在Volve油田数据上的应用进一步证明了该方法的鲁棒性和实用性，突显了其在高效大规模地震成像方面的潜力。