Least-square reverse time migration (LSRTM) can obtain high-resolution and high-amplitude preserved imaging results. Compared to the traditional migration methods, LSRTM can be robust and free of low-frequency artefacts. Under the first-order Born approximation, the corresponding scattering wave equation can only describe the wavefield under the approximate of weak perturbation. Nevertheless, in complicated media, weak scattering potential and small scatter assumptions are generally difficult to be satisfied. For inversion, with full wavefield information, the inversion results can be contaminated by artefacts caused by a strong scattering interface that to high-order scattered waves from strong scattering interfaces. To handle this problem, the first-order scattering wave equation is introduced as a penalty term to the LSRTM objective function, which can suppress the artefacts caused by the weak scattering hypothesis of the Born approximation. As a result, the LSRTM converts to an alternative optimisation problem: firstly, we need to find the optimal solution in the first-order scattered wavefield space. That is, by calculating a virtual source corresponding to the time-domain augmented wave equation, reconstructing an accurate first-order scattered wavefield based on the first-order scattering wave equation; secondly, an updated gradient of the reflectivity is then calculated based on the reconstructed first-order scattered wavefield. Therefore, the inverted reflectivity calculated according to the first-order scattered wavefield can be capable of obtaining the imaging results with high precision and high-amplitude preservation. Synthetic and real dataset results illustrate the effectiveness of the proposed method.

中文翻译：

---

具有一阶散射波动方程惩罚的最小二乘逆时偏移

最小二乘逆时偏移 (LSRTM) 可以获得高分辨率和高幅度的保留成像结果。与传统的迁移方法相比，LSRTM 可以稳健且没有低频伪影。在一阶Born近似下，对应的散射波动方程只能描述弱微扰近似下的波场。然而，在复杂介质中，弱散射势和小散射假设通常难以满足。对于反演，使用完整的波场信息，反演结果可能会被强散射界面引起的伪影污染，而强散射界面对高阶散射波的影响。为了解决这个问题，引入一阶散射波动方程作为 LSRTM 目标函数的惩罚项，这可以抑制由 Born 近似的弱散射假设引起的伪影。因此，LSRTM 转换为一个替代优化问题：首先，我们需要在一阶散射波场空间中找到最优解。即通过计算时域增广波动方程对应的虚拟源，根据一阶散射波动方程重构准确的一阶散射波场；其次，然后基于重建的一阶散射波场计算更新的反射率梯度。因此，根据一阶散射波场计算出的反演反射率可以得到高精度、高幅度保存的成像结果。