Continuous wavelet transformation of seismic data for feature extraction
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Continuous wavelet transformation of seismic data for feature extraction Amjad Ali1 · Chen Sheng‑Chang1 · Munawar Shah2 Received: 1 June 2020 / Accepted: 1 October 2020 © Springer Nature Switzerland AG 2020
Abstract Continuous wavelet transformation (CWT) as a new mathematical tool has provided deep insights for the identification of localized anomalous zone in the time series data set. In this study, a three-layer geological model is investigated by CWT to locate seismic reflections temporally and spatially. This model consists of three layers, where the third layers of the anticline structure are assumed to act as a pure sandstone hydrocarbon reservoir with 10% porosity. The equation of Gassmann has been implemented for the pore fluid substitution in the reservoir. Synthetic seismic data are generated for the three-layer geological model. Due to the presence of noise, it is always difficult to interpret seismic data. But, CWT has the ability of noise reduction, improving the visualization of a data set and locating the anomalies in terms of scalogram and 3D CWT coefficients. Synthetic seismic data of the geological structure are transformed by CWT. The successful transformation of P-wave velocity, synthetic seismic data and acoustic impedance inversion provided evidence to distinguish different interfaces accurately. CWT has successfully located seismic reflections by localizing high-energy spectrum within the cone of influence. Three high-energy spectrums have been identified at 0.8 s, 1 s and 1.07 s, and it exactly matches the seismic data and three-layer geological model. Keywords Gassmann’s equation · P-wave velocity · Synthetic seismic trace · Acoustic impedance inversion · Continuous wavelet transformation
1 Introduction Seismic reflection data are non-stationary in nature, because of their frequency variation with time. The geoscientist has great interests in the trends and periodicities generated by complex subsurface geological structures. Generally, the Fourier transform is used to study these trends and periodicities in the geophysical time series. It is a mathematical tool that breaks down a time series signal into its component frequencies. Therefore, Fourier transform is a mathematical depiction of signal amplitudes of discrete components that construct it. Frequencydomain representation of the signal and the process of transformation from time to frequency domain are called
Fourier transform [28]. Initially, Fourier transform was first introduced for spatial fringe pattern analysis [22, 23]. It has been mainly implemented profilometry [24] and for the measurement of wave front shape [25]. But in Fourier transform, it has been assumed that the underlying processes in the geophysical time series are stationary. There are various techniques have been used to analyze the non-stationary time series signal. For time–frequency mapping, [11] illustrated the data-adaptive method and [5] implemented the short-time Fourier transform. The spectral decomposition of the seismic signal has also been used to
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