Local quantum filtering and denoising of seismic data

The precise characterization and analysis of complex geologic targets in seismic reflection data are posing increasingly high demands on the capabilities of signal processing methods. A recent contribution to signal processing is the Schrödinger equation-based adaptive transformation, which projects seismic data onto a specific basis constructed by the wave functions derived from the Schrödinger equation. Each wave function corresponds to a specific energy and projection coefficient (PC), enabling the reconstruction of seismic data using these wave functions and their associated PCs. In this work, we investigate the filtering properties of the Schrödinger equation-based adaptive transformation. A specific quantum filtering approach, using the specific basis and PCs dynamically controlled by energy changes, is designed for extracting the local features from the seismic data. Furthermore, a quantum seismic data denoising approach, called local quantum denoising (LQD), is developed by integrating this specific quantum filtering approach with a threshold factor. Synthetic data examples indicate that the quantum filtering approach based on the Schrödinger equation outperforms adaptive decomposition tools such as variational mode decomposition (VMD) in highlighting distinct features within subcomponents, particularly when handling data with random near-surface velocity variations. The LQD method using the specific filtering properties exhibits stronger noise attenuation for seismic data with complex structures compared with the traditional Bayesian-based wavelet soft-thresholding method and the global quantum denoising (GQD) method. Field data applications demonstrate that, compared with VMD, the quantum filtering approach more effectively isolates the strong reflection amplitudes caused by the weathered crust and the gas reservoir in the different subcomponents of seismic data from a gas reservoir in China. Furthermore, for seismic data from a carbonate reservoir in the same region, the LQD method preserves more useful information related to dipping events compared with the traditional Bayesian-based wavelet soft-thresholding method and the GQD method.