Multistage matching pursuit Fourier interpolation with physics-based priors

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Summary The reduction of spatial sampling, as a strategy to reduce the cost of seismic acqusition, requires solutions within signal processing to support and minimise the impact of these geometries on the final data quality. We present an overview of a physics-based multistage interpolation solution that is capable of interpolating sparse and irregular spatially sampled data as a preconditioning step to support algorithms requiring regular and densely sampled input data. Our approach progressively models coherent seismic signal during the interpolation, where each stage focuses on different modes, starting with the strongest signal. Different sparsity-promoting prior information, to enhance the separability of the current strongest amplitude mode, is exploited to optimise the final interpolation output. We demonstrate the effectiveness of the workflow on synthetic land data that resolves several challenges related to the interpolation of spatially aliased data that exhibits a high dynamic range on input. These challenges, most notably the distortion of low-amplitude reflectivity within the vicinity of the high-amplitude surface waves, are eliminated using our multistage methodology providing improvements in the spatial continuity of both the low-amplitude reflectivity and high-amplitude surface waves. The advances observed provide uplift in handling sparse and irregular geometries within signal processing, and also potential opportunities for further seismic acquisition design optimisations enabled by this technology.

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