Seismic Filtering Using the S-Transform Method

The S-Transform method is a powerful time-frequency analysis technique widely employed for seismic signal filtering and enhancement. Unlike conventional Fourier transforms, the S-Transform provides frequency-dependent resolution while maintaining absolute time reference, making it particularly suitable for non-stationary seismic signals. In implementation, the S-Transform can be computed using a windowed Fourier transform approach with Gaussian windows whose width varies inversely with frequency. A typical MATLAB implementation would involve: 1. Decomposing the seismic signal into time-frequency representations 2. Applying thresholding or masking operations in the S-Transform domain 3. Reconstructing the filtered signal through inverse transformation Key algorithmic advantages include superior time-frequency localization, precise spectral decomposition, and effective noise suppression capabilities. The method has demonstrated exceptional performance in critical seismological applications such as earthquake detection through weak signal extraction, subsurface structure mapping via reflection enhancement, and reservoir characterization using attenuation analysis. The S-Transform's mathematical formulation combines Fourier transform advantages with wavelet-like multiresolution analysis, typically implemented through convolution operations in the frequency domain. This approach enables researchers to isolate specific seismic components (e.g., P-waves, S-waves, or surface waves) while suppressing ambient noise and multiple reflections, significantly improving signal-to-noise ratios in processed seismic data. Practical implementations often incorporate optimization techniques for computational efficiency, including fast algorithms for discrete S-Transform calculation and parallel processing for large-scale seismic datasets. These enhancements make the method particularly valuable for modern seismic interpretation workflows, contributing substantially to advances in subsurface imaging and geophysical research.