We consider the problem of image-domain least-squares migration (LSM) based on efficiently constructing the Hessian matrix with sparse beam data. Specifically, we use the ultra-wide-band phase space beam summation method, in which beams are used as local basis functions to represent scattered data collected at the surface. The beam domain data are sparse. One can identify seismic events with significant contributions so that only beams with nonnegligible amplitudes need to be used to image the subsurface. In addition, due to the beams’ spectral localization, only beams that pass near an imaging point need to be taken into account. These two properties reduce the computational complexity of computing the Hessian matrix — an essential ingredient for LSM. As a result, we can efficiently construct the Hessian matrix based on analyzing the sparse beam domain data.

中文翻译：

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一种用于图像域最小二乘迁移的压缩数据方法

我们考虑了基于使用稀疏波束数据有效构建 Hessian 矩阵的图像域最小二乘迁移 (LSM) 问题。具体来说，我们使用超宽带相空间波束求和方法，其中波束用作局部基函数来表示在表面收集的散射数据。波束域数据是稀疏的。人们可以识别具有重要贡献的地震事件，以便只需要使用振幅不可忽略的波束来对地下进行成像。此外，由于光束的光谱定位，只需要考虑通过成像点附近的光束。这两个属性降低了计算 Hessian 矩阵（LSM 的基本要素）的计算复杂度。其结果，