Conventional seismic migrations are often suitable for structural imaging of the subsurface, but have quantitative limitations. We proposed an imaging strategy for obtaining true-amplitude imaging results within the framework of least-squares migration. Gaussian beam migration and demigration operators are developed to produce two images, which are used to estimate the approximate inverse of the Hessian in the imaging domain by introducing a non-stationary filter operator. By applying an image correction with the estimated inverse Hessian to a conventional Gaussian beam migration result, the resulting image is much closer to the true-amplitude image. Benefiting from the Gaussian beam propagator, which is a one-way beam propagator, the proposed method has more flexibility than the method based on two-way wave equations, and it can be adapted to higher frequency imaging with less computational cost compared to a two-way wave equation method. Some numerical examples are shown to demonstrate the effectiveness and efficiency of the proposed method.

中文翻译：

---

一种基于高斯光束偏移和反偏移的真幅成像方法

传统的地震偏移通常适用于地下结构成像，但存在数量上的局限性。我们提出了一种在最小二乘偏移框架内获得真实振幅成像结果的成像策略。开发了高斯光束偏移和反偏移算子以产生两个图像，通过引入非平稳滤波器算子来估计成像域中 Hessian 的近似逆。通过将估计的逆 Hessian 图像校正应用于传统的高斯光束偏移结果，得到的图像更接近于真实幅度的图像。受益于高斯光束传播器，它是一种单向光束传播器，所提出的方法比基于双向波动方程的方法具有更大的灵活性，并且与双向波动方程方法相比，它可以以更少的计算成本适应更高频率的成像。一些数值例子证明了所提出方法的有效性和效率。