Seismic resolution enhancement with variational modal based fast matching pursuit decomposition

Enhancing vertical resolution and signal-to-noise ratio are key objectives in the seismic data processing. Considering the underground medium is inhomogeneous and incompletely elastic, seismic wave energy attenuation occurs during underground propagation, which has a significant impact on seismic data resolution and signal-to-noise ratio. Traditional fast-matching pursuit algorithms make it difficult to separate valid signals and noise effectively while reconstructing the noisy signals. Therefore, an improved fast-matching pursuit algorithm that combines the variational modal decomposition (VMD) strategy is developed. The VMD algorithm is used to obtain intrinsic mode functions with varying amplitudes, frequencies, and center times. It can achieve a multi-scale decomposition of non-stationary seismic data. Based on the intrinsic mode functions of different scales, the fast matching pursuit algorithm can reconstruct prior information of the amplitude, frequency, and center time of valid signals and noise signals in the mode functions. Thus, the high-resolution sparse representation of intrinsic mode functions is achieved. The numerical results indicate that the proposed method not only separates the effective signal and noise but also preserves the valid signal as much as possible. In addition, the feasibility of the method is further verified by field exploration data. The results show that this strategy can enhance the resolution of seismic data while restoring the attenuated energy using multi-scale seismic data.