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 $\phi _{\mathrm{ data}}$ and $\psi _{\mathrm{ data}}$ functions are first computed based on the local similarity and $L_{2}$ -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

随着油气勘探向复杂地质环境发展，高分辨率和真振幅地震成像对于油气藏的探测和评价变得越来越重要。传统的基于射线和波方程的成像方法可以看作是地震正演的伴随算子，在复杂结构中，由于频带有限、光照不平衡、采集不规则等问题，难以产生高质量的图像。最小二乘偏移 (LSM) 为具有高图像分辨率和平衡幅度的地下反射率模型生成逆解。以往对 LSM 的研究主要集中在理论和实践策略的发展上，很少关注误差和不确定性分析。我们提出了一种定量分析方法来评估 LSM 结果的误差。这 $\phi _{\mathrm{ 数据}}$和 $\psi _{\mathrm{ 数据}}$首先根据局部相似性计算函数，然后 $L_{2}$- 观察数据和合成数据之间的范数不匹配。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示例表明，随着 LSM 迭代次数的增加，总运动学和动态误差会减少，并且它们在不同位置会有所不同。对于低信噪比 (SNR) 的场数据，LSM 可能会因为过拟合问题而在大迭代中扩大图像误差，适当的正则化对于促进 LSM 收敛到一个好的解决方案非常重要。