Assessment of the reliability of 2D inversion of apparent resistivity data

The reliability of inversion of apparent resistivity pseudosection data to determine accurately the true resistivity distribution over 2D structures has been investigated, using a common inversion scheme based on a smoothness-constrained non-linear least-squares optimization, for the Wenner array. This involved calculation of synthetic apparent resistivity pseudosection data, which were then inverted and the model estimated from the inversion was compared with the original 2D model. The models examined include (i) horizontal layering, (ii) a vertical fault, (iii) a low-resistivity fill within a high-resistivity basement, and (iv) an upfaulted basement block beneath a conductive overburden. Over vertical structures, the resistivity models obtained from inversion are usually much sharper than the measured data. However, the inverted resistivities can be smaller than the lowest, or greater than the highest, true model resistivity. The substantial reduction generally recorded in the data misfit during the least-squares inversion of 2D apparent resistivity data is not always accompanied by any noticeable reduction in the model misfit. Conversely, the model misfit may, for all practical purposes, remain invariant for successive iterations. It can also increase with the iteration number, especially where the resistivity contrast at the bedrock interface exceeds a factor of about 10; in such instances, the optimum model estimated from inversion is attained at a very low iteration number. The largest model misfit is encountered in the zone adjacent to a contact where there is a large change in the resistivity contrast. It is concluded that smooth inversion can provide only an approximate guide to the true geometry and true formation resistivity.