Angle domain common imaging gathers (ADCIGs) serve as not only an ideal approach for tomographic velocity modeling but also as a crucial means of mitigating low-frequency noise. Thus, they play a significant role in seismic data processing. Recently, the Poynting vector method, due to its lower computational requirements and higher resolution, has become a commonly used approach for obtaining ADCIGs. However, due to the viscoelastic properties of underground media, attenuation effects (phase dispersion and amplitude attenuation) have become a factor, which is important in seismic data processing. However, the primary applications of ADCIGs are currently confined to acoustic and elastic media. To assess the influence of attenuation and elastic effects on ADCIGs, we introduce an extraction method for ADCIGs based on fractional viscoelastic equations. This method enhances ADCIGs accuracy by simultaneously considering both the attenuation and elastic properties of underground media. Meanwhile, the S-wave quasi tensor is used to reduce the impact of P-wave energy on S-wave stress, thus further increasing the accuracy of PS-ADCIGs. In conclusion, our analysis examines the impact of the quality factor Q on ADCIGs and offers theoretical guidance for parameter inversion.

High resolution of post-stack seismic data assists in better interpretation of subsurface structures as well as high accuracy of impedance inversion. Therefore, geophysicists consistently strive to acquire higher resolution seismic images in petroleum exploration. Although there have been successful applications of conventional signal processing and machine learning for post-stack seismic resolution enhancement, there is limited reference to the seismic applications of the recent emergence and rapid development of generative artificial intelligence. Hence, we propose to apply diffusion models, among the most popular generative models, to enhance seismic resolution. Specifically, we apply the classic diffusion model—denoising diffusion probabilistic model (DDPM), conditioned on the seismic data in low resolution, to reconstruct corresponding high-resolution images. Herein the entire scheme is referred to as SeisResoDiff. To provide a comprehensive and clear understanding of SeisResoDiff, we introduce the basic theories of diffusion models and detail the optimization objective's derivation with the aid of diagrams and algorithms. For implementation, we first propose a practical workflow to acquire abundant training data based on the generated pseudo-wells. Subsequently, we apply the trained model to both synthetic and field datasets, evaluating the results in three aspects: the appearance of seismic sections and slices in the time domain, frequency spectra, and comparisons with the synthetic data using real well-logging data at the well locations. The results demonstrate not only effective seismic resolution enhancement, but also additional denoising by the diffusion model. Experimental comparisons indicate that training the model on noisy data, which are more realistic, outperforms training on clean data. The proposed scheme demonstrates superiority over some conventional methods in high-resolution reconstruction and denoising ability, yielding more competitive results compared to our previous research.

Staggered-grid finite-difference (SGFD) schemes have been widely used in acoustic wave modeling for geophysical problems. Many improved methods are proposed to enhance the accuracy of numerical modeling. However, these methods are inevitably limited by the maximum Courant-Friedrichs-Lewy (CFL) numbers, making them unstable when modeling with large time sampling intervals or small grid spacings. To solve this problem, we extend a stable SGFD scheme by controlling SGFD dispersion relations and maximizing the maximum CFL numbers. First, to improve modeling stability, we minimize the error between the FD dispersion relation and the exact relation in the given wave-number region, and make the FD dispersion approach a given function outside the given wave-number area, thus breaking the conventional limits of the maximum CFL number. Second, to obtain high modeling accuracy, we use the SGFD scheme based on the Remez algorithm to compute the FD coefficients. In addition, the hybrid absorbing boundary condition is adopted to suppress boundary reflections and we find a suitable weighting coefficient for the proposed scheme. Theoretical derivation and numerical modeling demonstrate that the proposed scheme can maintain high accuracy in the modeling process and the value of the maximum CFL number of the proposed scheme can exceed that of the conventional SGFD scheme when adopting a small maximum effective wavenumber, indicating that the proposed scheme improves stability during the modeling.