Seismic diffractions from small-scale discontinuities or inhomogeneities carry key geologic information and can provide high-resolution images of these objects. Because diffractions characterized by weak energy are easily masked by strong reflections, diffraction-enhancement processing is essential before subwavelength information detection. Therefore, a novel diffraction-separation method is developed that uses the Fourier-based geometric-mode decomposition (GMDF) algorithm to remove reflections and separate diffractions in the common-offset or poststack domain. The key idea of our method is that, in the frequency-wavenumber (f-k) domain, strong reflections concentrate linearly along a certain dip direction, whereas weak diffractions are distributed over a wide range of wavenumbers owing to their variable dips in the time-space domain. The GMDF algorithm can effectively represent reflections with directional and linear geometric features by adaptively decomposing seismic data as a combination of the band-limited modes consisting of linear characteristics in the f-k domain. The alternating direction method of the multipliers algorithm is used to solve the GMDF optimization problem and obtain linear reflections. Because this method considers the energy sparsity property and linear geometric features of reflections in the f-k domain, kinematic and dynamic differences between reflections and diffractions are exploited to separate diffractions. Applied synthetic and field examples demonstrate the good performance of our method in removing strong reflections and separating weak diffractions, providing interpreters with detailed structural and stratigraphic information.

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