As oil and gas exploration moves toward complicated geological environments, high-resolution and true-amplitude seismic imaging becomes increasingly important for detecting and evaluating hydrocarbon reservoirs. Traditional ray-based and wave-equation imaging methods can be considered as the adjoint operator of seismic forward modeling, which are difficult to produce high-quality images in complicated structures because of limited frequency band, unbalanced illumination, and irregular acquisition. Least-squares migration (LSM) generates an inverse solution for subsurface reflectivity model with high image resolution and balanced amplitudes. Previous studies on LSM mainly focused on the developments of theoretical and practical strategies, but few on error and uncertainty analysis. We present a quantitative analysis method to evaluate the errors of LSM results. The ϕdata\phi _{\mathrm{ data}} and ψdata\psi _{\mathrm{ data}} functions are first computed based on the local similarity and L2L_{2} -norm misfit between observed and synthetic data. They are used as data-domain kinematic and dynamic errors, respectively. Then, these local functions are mapped to the subsurface using a Kirchhoff-integral relation to calculate image-domain errors. Numerical examples for synthetic and field data demonstrate that as the iteration of LSM increases, the total kinematic and dynamic errors are reduced, and they vary in different locations. For low signal-to-noise-ratio (SNR) field data, LSM might enlarge image errors at large iterations because of the overfitting issue, and proper regularization is very important to facilitate the convergence of LSM to a good solution.

中文翻译：

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最小二乘成像的定量误差分析


随着油气勘探走向复杂的地质环境，高分辨率、真实振幅的地震成像对于油气藏的检测和评价变得越来越重要。传统的射线成像方法和波动方程成像方法可作为地震正演模拟的伴随算子，但由于频带有限、光照不平衡、采集不规则等原因，难以在复杂结构中生成高质量图像。最小二乘偏移 (LSM) 生成具有高图像分辨率和平衡振幅的地下反射率模型的反演解。以往对LSM的研究主要集中在理论和实践策略的发展上，而对误差和不确定性分析的研究很少。我们提出了一种定量分析方法来评估 LSM 结果的误差。首先根据观测数据和合成数据之间的局部相似性和 L2L_{2} 范数失配来计算 ψdata\phi _{\mathrm{ data}} 和 ψdata\psi _{\mathrm{ data}} 函数。它们分别用作数据域运动学和动态误差。然后，使用基尔霍夫积分关系将这些局部函数映射到地下，以计算图像域误差。合成数据和现场数据的数值例子表明，随着 LSM 迭代次数的增加，总运动学和动态误差减少，并且它们在不同位置有所不同。对于低信噪比（SNR）场数据，LSM可能会因过拟合问题而在大迭代时放大图像误差，而适当的正则化对于促进LSM收敛到良好的解决方案非常重要。