S-transform with maximum energy concentration: Application to non-stationary seismic deconvolution

Abstract The S-transform is known as an efficient method for analyzing seismic signals in the time–frequency (TF) domain. However, it provides a TF map with high energy diffusion due to inflexibility of the window function used in its analysis or synthesis formulas. In this paper, an optimization algorithm for S-transform is proposed to find the optimum Gaussian windows for providing a TF map with maximum energy concentration. Afterwards, we show the possibility of obtaining the desired TF map from two different perspectives: generating the TF map from a time-windowed signal or from a frequency-windowed signal. Through the optimization algorithm and by using an energy concentration measure (ECM), the optimum windows are selected instantaneously, for each time or frequency sample. Testing the proposed method on variety of signals shows its good performance to provide a well concentrated TF map, compared with other TF analysis methods. Application of the proposed method to perform non-stationary deconvolution of synthetic and field seismic data sets presents a better performance than short-time Fourier transform (STFT) and standard S-transform (SST) in improving the temporal resolution of the data.