Least-squares reverse-time migration (LSRTM) attempts to invert the broadband-wavenumber reflectivity image by minimizing the residual between observed and predicted seismograms via linearized inversion. However, rugged topography poses a challenge in front of LSRTM. To tackle this issue, we present an unstructured mesh-based solution to topography LSRTM. As to the forward/adjoint modeling operators in LSRTM, we take a so-called unstructured mesh-based “Grid Method.” Before solving the two-way wave equation with the Grid Method, we prepare for it a velocity-adaptive unstructured mesh using a Delaunay Triangulation plus Centroidal Voronoi Tessellation algorithm. The rugged topography acts as constraint boundaries during mesh generation. Then, by using the adjoint method, we put the observed seismograms to the receivers on the topography for backward propagation to produce the gradient through the cross-correlation imaging condition. We seek the inverted image using the conjugate gradient method during linearized inversion to linearly reduce the data misfit function. Through the 2D SEG Foothill synthetic dataset, we see that our method can handle the LSRTM from rugged topography.

中文翻译：

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基于自适应非结构​​化网格的地形最小二乘逆时迁移

最小二乘逆时偏移 (LSRTM) 试图通过线性化反演最小化观测和预测地震图之间的残差来反演宽带波数反射率图像。然而，崎岖的地形给 LSRTM 带来了挑战。为了解决这个问题，我们提出了一种基于非结构化网格的地形 LSRTM 解决方案。对于 LSRTM 中的前向/伴随建模算子，我们采用了一种所谓的基于非结构化网格的“网格方法”。在使用网格方法求解双向波动方程之前，我们使用 Delaunay 三角剖分加质心 Voronoi 镶嵌算法为其准备速度自适应非结构​​化网格。崎岖的地形在网格生成过程中充当约束边界。然后，通过使用伴随方法，我们将观测到的地震图放在地形上的接收器上进行反向传播，以通过互相关成像条件产生梯度。我们在线性化反演过程中使用共轭梯度法寻找反演图像，以线性减少数据错配函数。通过 2D SEG Foothill 合成数据集，我们看到我们的方法可以处理崎岖地形的 LSRTM。