ABSTRACT Because a vertical seismic profile (VSP) survey includes the installation of geophones into a borehole, the results of data processing are influenced by the deviation error of the borehole trajectory. In particular, when full waveform inversion (FWI) is applied to VSP data, receiver location errors distort the results of velocity inversion. Under this circumstance, we attempt to estimate the exact locations of receivers and resolve the distortion of the inverted velocity model by adding receiver locations to the inversion parameters. This makes the FWI process a multi-parametric inverse problem. In this case, it is desirable to invert each parameter group alternatively. Because receiver coordinates depend on borehole trajectory, the inverse problem is regularised by adding a term measuring the curvature of the borehole trajectory gradient to obtain a physically meaningful solution. In addition, we propose a grid search method to improve the estimation of receiver coordinates. In the case of VSP data, the inversion of receiver coordinates using the grid search method is more efficient and robust than using a local descent method. Through numerical examples, we verify that the proposed inversion algorithm can improve FWI results and mitigate velocity distortion. We also demonstrate that the convergence of FWI can be improved by applying the grid search method to the estimation of receiver coordinates.

中文翻译：

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通过垂直地震剖面数据的全波形反演估计速度和钻孔接收器位置

摘要 由于垂直地震剖面（VSP）测量包括在钻孔中安装检波器，数据处理的结果受到钻孔轨迹偏差误差的影响。特别是，当全波形反演 (FWI) 应用于 VSP 数据时，接收机位置误差会扭曲速度反演的结果。在这种情况下，我们尝试通过将接收器位置添加到反演参数来估计接收器的确切位置并解决反演速度模型的失真。这使得 FWI 过程成为一个多参数逆问题。在这种情况下，希望交替地反转每个参数组。因为接收器坐标取决于钻孔轨迹，通过添加测量井眼轨迹梯度曲率的项来对逆问题进行正则化，以获得物理上有意义的解。此外，我们提出了一种网格搜索方法来改进接收器坐标的估计。在 VSP 数据的情况下，使用网格搜索方法反演接收器坐标比使用局部下降方法更有效和稳健。通过数值例子，我们验证了所提出的反演算法可以改善FWI结果并减轻速度失真。我们还证明了通过将网格搜索方法应用于接收器坐标估计可以提高 FWI 的收敛性。使用网格搜索方法反演接收器坐标比使用局部下降方法更有效和更稳健。通过数值例子，我们验证了所提出的反演算法可以改善FWI结果并减轻速度失真。我们还证明了通过将网格搜索方法应用于接收器坐标估计可以提高 FWI 的收敛性。使用网格搜索方法反演接收器坐标比使用局部下降方法更有效和更稳健。通过数值例子，我们验证了所提出的反演算法可以改善FWI结果并减轻速度失真。我们还证明了通过将网格搜索方法应用于接收器坐标估计可以提高 FWI 的收敛性。