Instantaneous frequency and phase without unwrapping

Abstract

The instantaneous phase of a complex trace is normally computed as an inverse tangent function of the ratio between its imaginary and real parts. This algorithm often produces a discontinuous function in the range [[Formula: see text], [Formula: see text]], as the principal value of the inverse tangent is assumed. The attempt of removing these discontinuities, called phase unwrapping, introduces uncertainties and some personal bias because it requires user-defined parameters. A new algorithm that does not require any of these parameters is presented with the related software code and some application examples. The results indicate a fair robustness of the estimates with respect to the noise, for the instantaneous phase and frequency. In addition, the median-averaged instantaneous frequency is a useful tool for the seismic stratigraphy analysis.