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Linear Programs for the Reconstruction of 2D Images from Geophysical Electromagnetic Measurements

机译:从地球物理电磁测量重建二维图像的线性程序

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摘要

In this paper we present an approach for constructing vertical sections of the electrical conductivity of the earth on the basis of surface measurements. We assume that the conductivity of the earth varies with depth and laterally but not along the third dimension or strike. Electromagnetic measurements are effected every few meters across strike using pairs of horizontal and vertical coils, with the separation between source and receiver varying in order to sample different depths. The data thus provides information about the vertical and horizontal distribution of electrical conductivity of a section of the earth. Recovering the true conductivity distribution from the measurements is a nonlinear inverse problem that allows some useful linear approximations, which we exploit here using linear programming techniques. We apply a regularization approach using ε-insensitive functions for both, the fitness to the data and the penalizing function. This representation enforces a model structure of blocks immersed in a homogeneous basement, a useful model in many practical instances. Applications of the technique to synthetic and field data in one and two dimensions illustrate the usefulness of the technique.
机译:在本文中,我们提出了一种基于表面测量值构造地球电导率垂直部分的方法。我们假设地球的电导率随深度和横向变化,但不沿三维或走向变化。电磁测量是通过使用成对的水平和垂直线圈每隔几米进行一次电磁测量,并且源和接收器之间的距离会有所不同,以便对不同深度进行采样。因此,数据提供了有关地球某一部分的垂直和水平方向电导率分布的信息。从测量中恢复出真实的电导率分布是一个非线性反问题,它允许一些有用的线性近似,我们在这里使用线性编程技术进行了研究。对于数据的适应度和惩罚函数,我们使用使用ε不敏感函数的正则化方法。这种表示法增强了浸没在均质地下室中的砖块的模型结构,这在许多实际情况下都是有用的模型。将该技术应用于一维和二维综合数据和现场数据说明了该技术的实用性。

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