Marchenko methods can retrieve Green’s functions and focusing functions from single-sided reflection data and a smooth velocity model, as essential components of a redatuming process. Recent studies also indicate that a modified Marchenko scheme can reconstruct primary-only reflection responses directly from reflection data without requiring a priori model information. To provide insight into the artifacts that arise when input data are not ideally sampled, we study the effects of subsampling in both types of Marchenko methods in 2D earth and data — by analyzing the behavior of Marchenko-based results on synthetic data subsampled in sources or receivers. With a layered model, we find that for Marchenko redatuming, subsampling effects jointly depend on the choice of integration variable and the subsampling dimension, originated from the integrand gather in the multidimensional convolution process. When reflection data are subsampled in a single dimension, integrating on the other yields spatial gaps together with artifacts, whereas integrating on the subsampled dimension produces aliasing artifacts but without spatial gaps. Our complex subsalt model indicates that the subsampling may lead to very strong artifacts, which can be further complicated by having limited apertures. For Marchenko-based primary estimation (MPE), subsampling below a certain fraction of the fully sampled data can cause MPE iterations to diverge, which can be mitigated to some extent by using more robust iterative solvers, such as least-squares QR. Our results, covering redatuming and primary estimation in a range of subsampling scenarios, provide insights that can inform acquisition sampling choices as well as processing parameterization and quality control, e.g., to set up appropriate data filters and scaling to accommodate the effects of dipole fields, or to help ensuring that the data interpolation achieves the desired levels of reconstruction quality that minimize subsampling artifacts in Marchenko-derived fields and images.

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与收购相关的二次抽样对马尔琴科聚焦、重定和初步估计的影响分析

Marchenko 方法可以从单面反射数据和平滑速度模型中检索格林函数和聚焦函数，作为重定标过程的基本组成部分。最近的研究还表明，修改后的 Marchenko 方案可以直接从反射数据重建仅初级反射响应，而无需先验模型信息。为了深入了解当输入数据采样不理想时出现的伪影，我们研究了二维地球和数据中两种类型的马尔琴科方法中子采样的影响——通过分析基于马尔琴科的结果对源中子采样的合成数据的行为或接收器。通过分层模型，我们发现对于马尔琴科重定标，子采样效应共同取决于集成变量和子采样维度的选择，源于多维卷积过程中被积函数的聚集。当反射数据在单个维度上进行二次采样时，在另一个维度上进行积分会产生空间间隙和伪影，而在二次采样维度上进行积分会产生混叠伪影但没有空间间隙。我们复杂的盐下模型表明，二次采样可能会导致非常强烈的伪影，由于孔径有限，这可能会进一步复杂化。对于基于 Marchenko 的初级估计 (MPE)，在完全采样数据的某个部分以下进行二次采样会导致 MPE 迭代发散，这可以通过使用更强大的迭代求解器（例如最小二乘 QR）在一定程度上缓解。我们的结果，涵盖了一系列子抽样场景中的重定点和初步估计，