Research on Seismic Data Denoising Using Singular Value Decomposition

I conducted original research applying Singular Value Decomposition (SVD) for seismic data processing and noise reduction. The study provides comprehensive explanations of the methodology and results. The research begins with an introduction to SVD concepts, particularly focusing on how the algorithm decomposes seismic matrices into three components (U, Σ, V) where Σ contains the singular values representing signal energy. The implementation involves setting appropriate thresholds for singular value truncation to separate noise from meaningful seismic signals. The methodology section details how SVD was applied to seismic data matrices, with code examples showing the matrix organization where rows represent time samples and columns represent sensor channels. Key implementation aspects include computing the SVD using numpy.linalg.svd() or MATLAB's svd() function, followed by thresholding strategies where smaller singular values (typically associated with noise) are zeroed out before reconstruction. The dataset description covers both pre- and post-SVD processing data quality metrics, including signal-to-noise ratio calculations. Results demonstrate significant noise reduction while preserving essential seismic features, with visualizations comparing original and denoised seismic sections. The conclusion discusses implications for seismology and potential applications in earthquake detection and subsurface imaging, highlighting how this SVD-based approach provides a mathematical foundation for robust seismic signal processing. This research contributes significantly to the field of seismic data processing methodologies.