The mean of the sensitivity kernel in the electrical resistivity method

Abstract:

While the electrical resistivity method is sensitive to the resistivity structure of the ground everywhere, it is useful to define a centre of the region of sensitivity. A useful starting point is to consider the sensitivity kernel for an infinite half-space of constant resistivity. In the past, the peak and median have been considered as estimates of the region of sensitivity. However, there does not exist a simple formula for either the peak or the median. In this contribution it will be shown that there does exist a simple mathematical formula for the mean of the sensitivity kernel. It will also be shown that when the mean of the sensitivity kernel is used as the pseudodepth, that depth soundings are significantly smoother and easier to interpret than when using a fixed ratio of the total array length. A formula for the horizontal mean of arrays is also derived which gives the appropriate horizontal pseudoposition for asymmetric arrays like pole-dipole arrays.