Depth estimation of gravity anomalies by S-transform of analytic signal

The S-transform has widely been used in the analysis of non-stationary time series. A simple method to obtain depth estimates of gravity field sources is introduced in this study. We have developed a new method based on the spectral characteristics of downward continuation to estimate depth of structures. This calculation procedure is based on replacement of the Fourier transform with the S-Transform in traditional downward formula. We expect the localized estimation of the depth of anomalies using the S-transform spectrum rather than FFT spectrum. Likewise in the wavelets which don’t have a direct relationship with wave numbers, the S-Transform corresponds to wave number instead of scale or pseudo wavenumber. This is the main advantage of using S-transform instead of wavelets. This advantage will lead to easier and more precise calculation of depth estimation. Synthetic examples indicate the usefulness of this method. The method was applied to field examples producing reasonable results comparable to some common methods such as wavelet-based source characterization and Euler deconvolution. It is possible to average the local spectra over the wavenumber axis that leads to the spectrum referenced to position axis. The depth of anomaly can be computed in any point of the profile by using localization of spectrum. Thereby, we can analyze distinguished traces of shallow and deep anomalies while the lateral effects are also considered.