Abstract A time-frequency spectrum of a time signal generated by transforming the scalogram from the Continuous Wavelet Transform (CWT), called TFCWT, was studied earlier primarily with the Morlet wavelet, which promises high frequency resolution at low frequencies and high time resolution at high frequencies. However, the Ricker wavelet has often been used for spectral decomposition with different methods in seismic data analysis. In this study, we use the Paul wavelets of fourth order, which closely resembles the Ricker wavelet, and of 40th order as a proxy for the Morlet wavelet to analyze their time-frequency resolution with TFCWT. The lower-order Paul wavelets have high time resolution and low frequency resolution, whereas the higher-order Paul wavelets show high frequency resolution at low frequencies and high time resolution at high frequencies, which is desired in seismic data analysis. We have performed a comparative study for spectral analysis with TFCWT in RGB blending technique using the 4th order Paul wavelet and the Morlet wavelet. 3D seismic data from the Gandak depression of the Ganga Valley basin in India was scrutinized for detecting concealed paleo-river channels and related depositional systems using the responses from the Paul wavelets of different orders. The Morlet wavelet better delineates the paleo-river channels on RGB blended images within the Siwalik formation of Tertiary age. Furthermore, the Regional Unconformity, which has relatively lower frequencies, shows finer details with the Morlet wavelet in the shallow marine depositional environment from the pre-Tertiary compared to the Paul wavelet of 4th order. Thus, the Paul wavelets of different orders with TFCWT can be used for geological feature enhancement from seismic data with associated time-frequency resolution. Research highlights <UnorderedList Mark="Bullet"> <ItemContent> Time-frequency continuous wavelet transform (TFCWT) with Paul wavelet. </ItemContent> <ItemContent> The Paul wavelet of order 4 closely approximates waveform and characteristics of the Ricker wavelet. </ItemContent> <ItemContent> Lower order Paul wavelets represent high time resolution and low frequency resolution. </ItemContent> <ItemContent> Higher order Paul wavelets represent high frequency resolution at low frequencies and high time resolution at high frequencies. </ItemContent> <ItemContent> The RGB blending technique with the TFCWT enhances concealed subsurface features that help characterize pre-Tertiary and Tertiary depositional environment in the Ganga Valley Basin. </ItemContent> </UnorderedList>

Evaluation of Paul wavelet based TFCWT in comparison to Ricker and Morlet wavelets for seismic spectral analysis

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发表日期：

2026年1月29日

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Jitendra Argal,
Satish Kumar Sinha

摘要

Abstract

A time-frequency spectrum of a time signal generated by transforming the scalogram from the Continuous Wavelet Transform (CWT), called TFCWT, was studied earlier primarily with the Morlet wavelet, which promises high frequency resolution at low frequencies and high time resolution at high frequencies. However, the Ricker wavelet has often been used for spectral decomposition with different methods in seismic data analysis. In this study, we use the Paul wavelets of fourth order, which closely resembles the Ricker wavelet, and of 40^th order as a proxy for the Morlet wavelet to analyze their time-frequency resolution with TFCWT. The lower-order Paul wavelets have high time resolution and low frequency resolution, whereas the higher-order Paul wavelets show high frequency resolution at low frequencies and high time resolution at high frequencies, which is desired in seismic data analysis. We have performed a comparative study for spectral analysis with TFCWT in RGB blending technique using the 4^th order Paul wavelet and the Morlet wavelet. 3D seismic data from the Gandak depression of the Ganga Valley basin in India was scrutinized for detecting concealed paleo-river channels and related depositional systems using the responses from the Paul wavelets of different orders. The Morlet wavelet better delineates the paleo-river channels on RGB blended images within the Siwalik formation of Tertiary age. Furthermore, the Regional Unconformity, which has relatively lower frequencies, shows finer details with the Morlet wavelet in the shallow marine depositional environment from the pre-Tertiary compared to the Paul wavelet of 4th order. Thus, the Paul wavelets of different orders with TFCWT can be used for geological feature enhancement from seismic data with associated time-frequency resolution.

Research highlights

Time-frequency continuous wavelet transform (TFCWT) with Paul wavelet.

The Paul wavelet of order 4 closely approximates waveform and characteristics of the Ricker wavelet.

Lower order Paul wavelets represent high time resolution and low frequency resolution.

Higher order Paul wavelets represent high frequency resolution at low frequencies and high time resolution at high frequencies.

The RGB blending technique with the TFCWT enhances concealed subsurface features that help characterize pre-Tertiary and Tertiary depositional environment in the Ganga Valley Basin.