Buried pipelines are “lifelines” for cities; therefore, it is vital to understand their location and depth before municipal construction to prevent them from being damaged. Magnetic methods have been applied to detect buried ferrous metal pipelines such as steel and cast-iron pipes. We have developed a positioning method for buried pipelines from magnetic data, which is based on a combination of the tilt angle and the downward continuation. The magnetic tilt angle can provide information about the location and depth of buried pipelines, which can easily be calculated by the horizontal and vertical magnetic field gradients. We prove that the tilt angle for the magnetic field that has been reduced to the pole is independent of the magnetization direction given by the pipeline direction with respect to the inducing field. A tilt angle of 90° marks the location of a buried pipeline, whereas the depth is the distance between the location of the 90° and its adjacent 0°. The iterative Tikhonov regularization method for downward continuation, while separating the superimposed anomalies and enhancing the horizontal resolution, also reduces the influence of fast Fourier transform-induced noise and other noise that is intrinsic to the data set. We use the derivative of the Tikhonov regularization result as a regularization term of the minimization function and a constraint for the regularization parameter choice to obtain a more stable and accurate downward-continued result. This positioning method is applicable to single and parallel pipeline detection.

中文翻译：

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根据磁数据确定地下管道的位置

地下管线是城市的“生命线”。因此，至关重要的是在市政建设之前了解它们的位置和深度，以防止它们受到损坏。磁性方法已被用于检测地下的黑色金属管道，例如钢管和铸铁管道。我们已经开发了一种基于磁数据的地下管道定位方法，该方法基于倾斜角和向下延伸的组合。磁倾角可以提供有关埋地管道的位置和深度的信息，可以通过水平和垂直磁场梯度轻松计算出该信息。我们证明，减小到极点的磁场的倾斜角与管道方向相对于感应场的磁化方向无关。90°的倾斜角标记了地下管线的位置，而深度是90°的位置与其相邻的0°之间的距离。向下连续的迭代Tikhonov正则化方法在分离叠加的异常并提高水平分辨率的同时，还减少了快速傅立叶变换引起的噪声和数据集固有的其他噪声的影响。我们将Tikhonov正则化结果的导数用作最小化函数的正则化项以及对正则化参数选择的约束，以获得更稳定和准确的向下连续结果。该定位方法适用于单流水线和并行流水线检测。向下连续的迭代Tikhonov正则化方法在分离叠加的异常并提高水平分辨率的同时，还减少了快速傅立叶变换引起的噪声和数据集固有的其他噪声的影响。我们将Tikhonov正则化结果的导数用作最小化函数的正则化项以及对正则化参数选择的约束，以获得更稳定和准确的向下连续结果。该定位方法适用于单流水线和并行流水线检测。向下连续的迭代Tikhonov正则化方法在分离叠加的异常并提高水平分辨率的同时，还减少了快速傅立叶变换引起的噪声和数据集固有的其他噪声的影响。我们将Tikhonov正则化结果的导数用作最小化函数的正则化项以及对正则化参数选择的约束，以获得更稳定和准确的向下连续结果。该定位方法适用于单流水线和并行流水线检测。还减少了快速傅立叶变换引起的噪声和数据集固有的其他噪声的影响。我们将Tikhonov正则化结果的导数用作最小化函数的正则化项以及对正则化参数选择的约束，以获得更稳定和准确的向下连续结果。该定位方法适用于单流水线和并行流水线检测。还减少了快速傅立叶变换引起的噪声和数据集固有的其他噪声的影响。我们将Tikhonov正则化结果的导数用作最小化函数的正则化项以及对正则化参数选择的约束，以获得更稳定和准确的向下连续结果。该定位方法适用于单流水线和并行流水线检测。