Compressive sensing principles applied in time and space for three‐dimensional land seismic data acquisition and processing

Abstract Compressive sensing introduces novel perspectives on non‐uniform sampling, leading to substantial reductions in acquisition cost and cycle time compared to current seismic exploration practices. Non‐uniform spatial sampling, achieved through source and/or receiver areal distributions, and non‐uniform temporal sampling, facilitated by simultaneous‐source acquisition schemes, enable compression and/or reduction of seismic data acquisition time and cost. However, acquiring seismic data using compressive sensing may encounter challenges such as an extremely low signal‐to‐noise ratio and the generation of interference noise from adjacent sources. A significant challenge to this innovative approach is to demonstrate the translation of theoretical gains in sampling efficiency into operational efficiency in the field. In this study, we propose a spatial compression scheme based on compressive sensing theory, aiming to obtain an undersampled survey geometry by minimizing the mutual coherence of a spatial sampling operator. Building upon an optimised spatial compression geometry, we subsequently consider temporal compression through a simultaneous‐source acquisition scheme. To address challenges arising from the recorded compressed seismic data in the non‐uniform temporal and spatial domains, such as missing traces and crosstalk noise, we present a joint deblending and reconstruction algorithm. Our proposed algorithm employs the iterative shrinkage‐thresholding method to solve an ℓ 2 – ℓ 1 optimization problem in the frequency–wavenumber–wavenumber ( ω – k x – k y ) domain. Numerical experiments demonstrate that the proposed algorithm produces excellent deblending and reconstruction results, preserving data quality and reliability. These results are compared with non‐blended and uniformly acquired data from the same location illustrating the robustness of the application. This study exemplifies how the theoretical improvements based on compressive sensing principles can significantly impact seismic data acquisition in terms of spatial and temporal sampling efficiency.