Wavelet extraction and local seismic phase correction using normalized first-order statistics

Abstract

© 2016 Geophysical Press Ltd. In this paper wavelet phase is extracted using normalized first-order statistics, which are introduced as an indicator of localized seismic signal phase. The analysis demonstrates sharpness of the probability distribution of a discrete time series, which is more robust than that obtained by applying higher-order statistics. The normalized first-order statistical value of the zero phase signal is higher than that of the non-zero phase signal, hence it is used as a signal phase correction controller to produce zero-phase signals. The most important parameter for correctly estimating the phase pertains to the best length of time window used for local phase correction. Incorrect window length creates non-zero phase wavelets. To choose the correct time window length, a continuous wavelet transform is applied, using a Morlet wavelet to decompose signals to wavelets. Based on the time-distance between maximum energy of wavelet coefficients normalized by the scale, it is possible to choose the best window length for local phase correction. Synthetic and real data examples are used to demonstrate the effectiveness of this method in both wavelet extraction and for local correction of signal phase. Results of the seismic phase correction using this method demonstrate superiority over the local Kurtosis and local skewness methods, because of high stability and dynamical range. Normalized first-order statistics permit a short window length not only as a phase correction controller but also as a thin layer detector.