Analysis of numerical differentiation methods applied to time domain electromagnetic (TDEM) geophysical data in the S-layer differential transform

The S-layer differential transform produces subsurface conductivity-depth images from Time Domain Electromagnetic (TDEM) data. It is a very fast method, but suffers from high noise levels due to the implementation of two consecutive numerical differentiations that are performed in the algorithm. In this paper, twelve numerical differentiation strategies are compared in order to find the most efficient differentiation scheme, specifically for TDEM data and the S-layer differential transform. The twelve strategies are made up through combinations of three differentiation methods, optional smoothing of data and optional resampling of data to equally spaced intervals. Comparisons are made on analytical, synthetic and field data.