Comparison of the stability of the downward continuation of gravity field by using the Tikhonov regularization and improved regularization operators

Downward continuation of potential field data plays an important role in interpretation of gravity and magnetic data. For its inherent instability,many methods have been presented to downward continue stably and precisely. The Tikhonov regularization approach is one of the most robust. It is based on a lowpass filter derivation in the Fourier spectral domain, by means of a minimization problem solution. In this manuscript,we propose an improved regularization operator for downward continuation of potential field data. First, we simply define a special wavenumber named the cutoff wavenumber to divide the potential field spectrum into the signal part and the noise part based on the radially averaged power spectrum of potential field data. Next, we use the conventional downward continuation operator to downward continue the signal and the Tikhonov regularization operator to suppress the noise. Moreover, the parameters of the improved operator are defined by the cutoff wavenumber which has an obvious physical significance. For computing the α parameter, it is necessary that the C-norm of the potential field must be calculated. The improved operator can not only eliminate the influence of the high-wavenumber noise but also avoid the attenuation of the signal.
Experiments through synthetic gravity and real gravity data from Kohe Namak region, Ghom province, Iran show that the downward continuation precision of the proposed operator is higher than the Tikhonov regularization operator.