Amplitude calibration of a fast S-transform algorithm

Christopher W. Bird, Kristopher A. Innanen, Mostafa Naghizadeh

The S-transform is a time-frequency decomposition technique with a wide range of applications in seismic signal analysis but has been under-used due to the high computational cost needed to employ it. In this paper we present a fast, non-redundant S-transform (FST). The ability of the FST to provide high fidelity estimates of the amplitudes is tested in this paper. Where the FST cannot provide accurate estimates of amplitudes, we calibrate it by normalizing the unit impulse response of the algorithm. Due to the low resolution at low frequency nature of the FST algorithm, the spectra of individual events will interfere with each other at low frequencies and limit the ability of the FST to estimate amplitudes. We discuss the limits of the calibrated S-transform to estimate amplitudes and we propose a set of standards for the fidelity of estimated amplitudes as a function of proximity in time to other events.