We develop a method to find the conductivity distribution of the ground from measurements taken with horizontal or vertical coplanar loops that work in the resistive limit or, equivalently, at low induction numbers. The method is based on an equation where the apparent conductivity and the true conductivity are linearly related by a weighting function. This equation can be used for inverting data from 3D or 2D structures. This method is an approximation for low conductivity contrast. However it works for moderated and high contrast. The inverse problem is solved using quadratic programming, minimizing the quadratic norm of residuals as well as the quadratic norm of spatial derivatives of the conductivities. With this, we can get conductivity images of the ground with minimum structure that also fit the data.


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