The Auxiliary S-Transform Adewale Amosu and Yuefeng Sun, Department of Geology and Geophysics, Texas A&M University Summary The traditional S-transform combines the advantages of the Short Time Fourier Transform and wavelet transform by mak- ing use of a frequency-dependent Gaussian window, however, its resolution may still be inadequate for certain seismic in- terpretation applications. Coherency-based spectral decom- position methods rely on multi-trace coherency attributes to improve spectral decomposition results. We propose a new coherency-based spectral decomposition method, the Auxil- iary S-transform, which significantly improves on the reso- lution of the S-transform. The Auxiliary S-transform maps a seismic section into the time-frequency-slowness domain where the properties of coherent seismic signals are more eas- ily accessible and coherency information can be harnessed. In this domain, the most coherent signals are better resolved us- ing a percentile coherency filter obtained from the slant-stack transform. We apply the Auxiliary S-transform to synthetic and real seismic data and evaluate its performance. Compared to the S-transform, the Auxiliary S-transform demonstrates improved temporal resolution at all frequencies. Introduction Spectral decomposition methods transform seismic data into the time-frequency domain to reveal the variation of frequency content with time. Several spectral decomposition methods have been developed. Cohen (1995) used a fixed preselected window length in implementing the Short Time Fourier trans- form (STFT). Charkraborty and Okaya (1995) introduced the Continuous Wavelet Transform (CWT), which produces a time- scale map called a scalogram. The S-transform introduced by Stockwell et al. (1996) makes use of a frequency-dependent Gaussian window and has better resolution at low frequen- cies than the CWT. Several studies have introduced improve- ments to the S-transform by modifying its window function (Mansinha, 1997; Pinnegar and Mansinha, 2003; Sejdic et al., 2008; Pei and Wang, 2010; Li and Castagna, 2013; Cheng et al., 2016; Wang and Gao, 2017; Agustianto and Sun, 2018). Other approaches include casting spectral decomposition as an inverse problem (Portniaguine and Castagna, 2004; Puryear et al., 2012) and coherency-based methods (Amosu and Sun, 2016; Amosu and Sun, 2018). While the methods differ, each method is suitable for specific requirements (Castagna et. al, 2003). Various spectral decomposition methods have been widely applied to seismic data (Sinha et al., 2005; Qi and Castagna, 2013; Barbato et al., 2014; Chopra and Marfurt, 2015; Chopra and Marfurt, 2016; Castagna et al., 2016; Jahan and Castagna, 2017; Wu and Castagna, 2017; Lin et al., 2018; Lyu et al., 2019; Murtazin and Butorin, 2020). In this study, we introduce a new coherency-based method, the Auxiliary S-transform (AST). The AST is an invertible integral transform that maps a seismic section into the time-frequency- slowness domain. In the time-frequency-slowness domain, co- herent signals are more concentrated and more easily separa- ble. For example, linear signals sum to a point. To ensure the most coherent signals are preserved, percentile filtering is ap- plied. The data is then mapped into the time-frequency-space domain. The results show significant improvement over the traditional S-transform. Theory The Auxiliary S-transform is defined for a seismic section d(x, t ), where x is trace number and t is time as follows: A( f , η , p)=  ∞ -∞  ∞ -∞ d(x, t = τ + px) | f | √ 2π w(η -τ , f )e -i2π f τ dxdτ (1) where τ is intercept time, η is a parameter that controls the po- sition on the time axis, p is slowness and w(η , f ) is the Gaus- sian window defined as: w(η , f )= 1 √ 2πσ ( f ) exp  - η 2 2σ 2 ( f )  (2) with the constraint that:  ∞ -∞ w(η - τ , f )dτ = 1 The inverse of the Auxiliary S-transform is defined as: d(x, t )=  ∞ -∞  ∞ -∞  ∞ -∞ A( f , η , p)e i2π f τ dη dfdp (3) A percentile coherency filter can be applied in the time-frequency- slowness domain, in this case, the inverse is given as: d Filter (x, t )=  ∞ -∞  ∞ -∞  ∞ -∞ A( f , η , p)F (η , p)e i2π f τ dη dfdp (4) where F (η , p) is a percentile coherency filter defined as: F (η , p)=  1, if m( p, η ) ≥ m( p, η ) percentile 0, otherwise (5) and m( p, η )=  ∞ -∞ d(x, τ + px)dx (6) m( p, η ) is the linear Radon transform or slant-stack transform (Thorson and Claerbout, 1985) which is obtained by summing the seismic section along the linear trajectory (η = τ + px). Methodology We apply equation (1) to a seismic section to map it into the time-frequency-slowness domain. We perform percentile fil- tering in this domain by multiplying the data with the coherency 10.1190/segam2021-3593408.1 Page 1106 © 2021 Society of Exploration Geophysicists First International Meeting for Applied Geoscience & Energy Downloaded 09/03/21 to 54.144.218.150. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/page/policies/terms DOI:10.1190/segam2021-3593408.1