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Compressive sensing for land seismic acquisition and processing
Titova, Anna
Titova, Anna
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2025
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2026-11-11
Abstract
Compressive sensing (CS) is a framework with which signals are acquired using far fewer measurements than the Nyquist sampling theorem allows. Reducing the cost of seismic surveys is essential, but it is not the only open problem that requires attention and affects the quality of land seismic data. In this dissertation, I demonstrate how CS-based mathematical techniques mitigate shortcomings of seismic acquisition and tackle the challenges of processing land datasets. I address the classical problem of estimating the spectrum of discrete signals that are not perfectly periodic over the observation interval by forming the Fourier basis functions using signal-adjusted wavenumbers. I further extend this approach to nonuniformly sampled nonstationary signals by developing the floating window Fourier transform (FWFT). With FWFT, I show that the error of spectrum estimations is dominated by the sparsity defects of the signal rather than by specific sequences of samples in the sampling patterns, which is an invaluable insight for research on CS-based sampling. I review the Fourier analysis and synthesis by considering another classical problem of irregularly sampled signals. Its practical relevance to apparent velocity filtering of irregularly spaced seismic traces to separate the surface and reflected waves allows me to put filtering artifacts in the context and compare those with cultural and other seismic noise observed in land seismic records. In addition, the task of surface wave removal provides me with an opportunity to test mathematical models and evaluate numerical algorithms using raw seismic signals and sampling patterns directly related to the station spacing of receivers (or sources) deployed in the field for the production type survey. I apply the principles of CS to reduce the cost of seismic acquisition and develop the two-step sampling approach by explicitly invoking theoretical considerations of the CS framework. With two-step sampling, I show that theory-based sampling schemes can also be used for CS-based reconstruction of seismic data.
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