Sparse Velocity Analysis: Deconvolution of Velocity Spectrum Based on Sparse Inversion

In this study, for the problems of poor energy aggregation and low resolution of velocity direction in the velocity spectrum obtained by stacking or semblance velocity analysis, we propose a sparse velocity analysis strategy, which is a secondary processing of the velocity spectrum based on sparse inversion method. In this approach, we assume that velocity spectrum at each time instant is formed by the convolution of a spike function with a window function, which reduces the resolution of the velocity spectrum in velocity direction due to the presence of a blurry window function. Accordingly, we use hyperbolic events with known velocities to extract a deconvolution operator in velocity direction, and then use the sparse inversion theory to perform deconvolution with velocity spectrum at each time instant to remove the effect of the blurry window function. In deconvolution, we apply nonnegative constraints and use the alternating direction method of multipliers (ADMM) for making all the high-resolution velocity spectrum values positive, and obtain a high-resolution velocity spectrum after “de-window,” that is, the sparse velocity spectrum. The algorithm is a secondary processing of velocity spectrum, which is computationally efficient, and can accomplish high-resolution analysis and modeling of velocity.