Summary We present a method for inverting total-field anomaly data to estimate the geometry of a uniformly magnetized 3-D geological source in the subsurface. The method assumes the total-magnetization direction is known. We approximate the source by an ensemble of vertically juxtaposed right prisms, all of them with the same total-magnetization vector and depth extent. The horizontal cross-section of each prism is a polygon defined by a given number of equi-angularly spaced vertices from 0○ to 360○, whose polygon vertices are described by polar coordinates with an origin defined by a horizontal location over the top of each prism. Because our method estimates the radii of each polygon vertex we refer to it as radial inversion. The position of these vertices, the horizontal location of each prism, and the depth extent of all prisms are the parameters to be estimated by solving a constrained nonlinear inverse problem of minimizing a goal function. We run successive inversions for a range of tentative total-magnetization intensities and depths to the top of the shallowest prism. The estimated models producing the lowest values of the goal function form the set of candidate solutions. To obtain stabilized solutions, we impose the zeroth- and first-order Tikhonov regularizations on the shape of the prisms. The method allows estimating the geometry of both vertical and inclined sources, with a constant direction of magnetization, by using the Tikhonov regularization. Tests with synthetic data show that the method can be of utility in estimating the shape of the magnetic source even in the presence of a strong regional field. Results obtained by inverting airborne total-field anomaly data over the Anitápolis alkaline-carbonatitic complex, in southern Brazil, suggest that the emplacement of the magnetic sources was controlled by NW-SE-trending faults at depth, in accordance with known structural features at the study area.

中文翻译：

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用于 3-D 源几何估计的磁径向反演

总结 我们提出了一种反演总场异常数据的方法，以估计地下均匀磁化 3-D 地质源的几何形状。该方法假设总磁化方向已知。我们通过一组垂直并列的直棱镜来近似源，所有这些棱镜都具有相同的总磁化矢量和深度范围。每个棱柱的水平横截面是一个多边形，由给定数量的从 0○ 到 360○ 等角度间隔的顶点定义，其多边形顶点由极坐标描述，原点由每个棱柱顶部的水平位置定义棱镜。因为我们的方法估计了每个多边形顶点的半径，所以我们将其称为径向反演。这些顶点的位置，每个棱镜的水平位置，所有棱镜的深度范围是通过求解最小化目标函数的约束非线性逆问题来估计的参数。我们对一系列暂定的总磁化强度和深度进行连续反演，直至最浅棱镜的顶部。产生目标函数最低值的估计模型形成候选解集。为了获得稳定的解，我们对棱镜的形状施加零阶和一阶 Tikhonov 正则化。该方法允许通过使用 Tikhonov 正则化来估计具有恒定磁化方向的垂直和倾斜源的几何形状。使用合成数据进行的测试表明，即使在存在强区域磁场的情况下，该方法也可用于估计磁源的形状。