Feature Extraction of a Non-Stationary Seismic–Acoustic Signal Using a High-Resolution Dyadic Spectrogram

Abstract

Using a novel mathematical tool called the (Formula presented.) -gram, researchers analyzed the energy distribution of frequency components in the scale–frequency plane. Through this analysis, a frequency band of approximately 12 Hz is identified, which can be isolated without distorting its constituent frequencies. This band, along with others, remained inseparable through conventional time–frequency analysis methods. The (Formula presented.) -gram successfully addresses this knowledge gap, providing multi-sensitivity in the frequency domain and effectively attenuating cross-term energy. The Daubechies 45 wavelet function was employed due to its exceptional 150 dB attenuation in the rejection band. The validation process encompassed three stages: pre-, during-, and post-seismic activity. The utilized signal corresponds to the 19 September 2017 earthquake, occurring between the states of Morelos and Puebla, Mexico. The results showcased the impressive ability of the (Formula presented.) -gram to surpass expectations in terms of sensitivity and energy distribution within the frequency domain. The (Formula presented.) -gram outperformed the procedures documented in the existing literature. On the other hand, the results show a frequency band between 0.7 Hz and 1.75 Hz, which is named the planet Earth noise.