Owing to the proximity of an insulating ground surface, normal resistivity logging at shallow depths (less than 30 m) can yield an apparent resistivity that exceeds 200% of the formation resistivity for a homogeneous medium. The distortion is more acute for long‐normal than for short‐normal logging. Three examples from a landfill site in southern California are presented to show such distortion. The patterns of distortion are similar for logging devices consisting of either two point‐source electrodes or one point‐source and one finite length, line‐source electrode. The former electrode array is a generally accepted approximation of the latter. However, the simulated apparent resistivity for the line‐source array is greater than that for the point‐source array at any given depth. A resistivity contrast between the formation and the borehole fluid can shift the magnitude of the background apparent resistivity but does not significantly alter the pattern of distortion. The magnitude of the distortion can be reduced by placing the reference‐ground potential electrode at a radial distance that is about equal to the spacing between the downhole upper potential electrode and the upper current electrode. It can also be removed by including the radial distance in an array‐dependent geometric factor that accounts for the resistivity of the borehole fluid and the proximity of the logging device to the ground surface.
Space variant PSF parameterization in image space using printed point source arrays on the HiRez PET/CT
