We are working on a project that we intend to estimate shallow temperature gradients from aeromagnetic and other support data using the spectral analysis procedure. We are having some technical problems and need some clarifications on the right procedure to follow because in literature, we have seen different approaches being used. We wish to use the same approach that Dolmaz et al. (2005) adopted in their work. But, we are have having some methodological challenges. In Fig. 4a, (see attached extract), a graph of Ln P1/2/|s| is plotted against wavenumbers, |s| and the centroid depth, zo is determined from the longest slope of the curve obtained. This is the familiar procedure of determining depth from spectral analysis technique except that the slope of the second longest wavelength is not determined from it as well. We need to be clarified on how they obtained Fig. 4b. The graph (Fig. 4b) suggests that they had to multiply their initial P1/2/|s| data by |s| in order to obtain P1/2 that they later used in plotting against |s|. Otherwise, how can we explain the fact that the data plotted on the y-axes of Fig. 4a is different from the data plotted on y-axes of Fig. 4b. Please we need someone to clarify as per whether to multiply our P1/2/|s| data by the wavenumbers to obtain P1/2 which is plotted again |s| in Fig. 4b. Its is from the second longest slope that zt is determined from.

Thank you.