Compared with traditional adjoint-based migration, least-squares migration (LSM) can reduce finite-frequency effects, remove acquisition footprints and improve spatial resolution by solving a linear inverse problem for subsurface reflectivity. One important requirement for the success of LSM is having an accurate migration velocity model. Because of low signal-to-noise ratio (SNR), inaccurate traveltime picking, lack of low-frequency signals and limited acquisition aperture, it is still challenging to build an accurate velocity model using ray-based tomography or full waveform inversion. LSM with large velocity errors results in erroneous reflector locations, strong swing artifact and even non-convergence. To mitigate these issues, we develop a novel least-squares imaging framework in the subsurface half-opening angle domain. Instead of using high-wavenumber velocity perturbations as the reflectivity model as in traditional LSM, we parameterize the wave equation with an angle-dependent reflectivity, and derive the corresponding linearized forward modeling and adjoint migration operators. Because Gaussian Beam migration naturally incorporates propagation directions in wavefield extrapolation, we compute the Green’s function using the Gaussian beam summation method. To improve the common-image gather (CIG) quality for low-fold and low-SNR data, a shaping regularization over the half-opening angles is introduced in the conjugate gradient scheme to iteratively update the angle-dependent reflectivity model. A flattening-enhanced summation is used to compute the stacked images by accounting for the depth moveout of CIGs caused by velocity errors, and produces constructive stacking results. Numerical experiments for benchmark models and a land survey demonstrate that the proposed method can improve LSM convergence and produce high-quality angle-dependent and stacked images even with inaccurate migration velocity models.

与传统的基于伴随的偏移相比，最小二乘偏移 (LSM) 可以通过解决地下反射率的线性逆问题来减少有限频率效应、消除采集足迹并提高空间分辨率。LSM 成功的一个重要要求是拥有准确的迁移速度模型。由于信噪比 (SNR) 低、旅行时拾取不准确、缺乏低频信号和有限的采集孔径，使用基于射线的断层扫描或全波形反演建立准确的速度模型仍然具有挑战性。具有大速度误差的 LSM 会导致错误的反射器位置、强烈的摆动伪影甚至不收敛。为了缓解这些问题，我们在地下半张角域中开发了一种新颖的最小二乘成像框架。我们不像在传统 LSM 中那样使用高波数速度扰动作为反射率模型，而是使用与角度相关的反射率参数化波动方程，并推导出相应的线性化正演建模和伴随偏移算子。因为高斯光束偏移在波场外推中自然地结合了传播方向，所以我们使用高斯光束求和方法计算格林函数。为了提高低倍和低 SNR 数据的公共图像聚集 (CIG) 质量，在共轭梯度方案中引入了半张角上的整形正则化，以迭代更新角度相关反射率模型。通过考虑由速度误差引起的 CIG 的深度时差，使用平坦增强求和来计算堆叠图像，并产生建设性的叠加结果。基准模型的数值实验和土地调查表明，即使迁移速度模型不准确，所提出的方法也可以提高 LSM 收敛并产生高质量的角度相关和堆叠图像。