The theory of compressed sensing (CS), offering a novel perspective beyond the Nyquist-Shannon sampling theorem, has garnered significant attention from geophysicists. It enables the reconstruction of ideal high-density seismic signals using cost-effective random undersampling, provided that the seismic signals can be sparsely represented. However, the near-surface noise challenges the sparse representation of seismic reflection signals. To suppress near-surface noise and achieve a better sparse representation of seismic reflection signals within the CS framework, this article develops a method for CS-based near-surface noise suppression, centered on 3-D conical Radon transform (CRT) combined with the CS theory. First, this study introduces the 3-D CRT into seismic signal processing, exploiting the “conical surface” characteristic of near-surface noise in 3-D CMP records. A method for extracting seismic signals and suppressing noise in the 3-D conical Radon domain is proposed. Subsequently, an adaptive filtering strategy is integrated with the 3-D CRT to develop a method for adaptive near-surface noise suppression in the 3-D conical Radon domain. Finally, combining CS theory, adaptive filtering strategies, and the 3-D Radon transform, this article proposes a method for adaptive near-surface noise suppression in the 3-D conical Radon domain based on CS. Numerical examples demonstrate that the integration of the CS random undersampling framework, adaptive filtering strategies, and the 3-D CRT significantly mitigates the impact of near-surface noise on seismic reflection signal reconstruction within the CS framework. This effectively addresses the issue of the 3-D CRT’s unsuitability for near-surface noise suppression within the CS framework.

Seismic velocity is crucial for seismic waveform inversion in geological exploration. An accurate velocity model is a key prerequisite for reverse time migration and other high-resolution seismic imaging techniques. Traditional methods perform well in seismic wave velocity modeling, but there are issues such as lack of low-frequency components, low computational efficiency, and subjective factors, which result in low accuracy in modeling seismic wave velocity containing noise. In addition, mid-to-low frequency data is crucial for velocity model inversion, but existing methods often overlook this. In this paper, we present a Multi-scale Fusion Network with Shot-Record attention module (MFNSR), which can construct velocity models directly from the original seismic record. The proposed network can obtain finer-grained complete semantic information in the shot record by multi-layer fusion operation. SR-attention is proposed to reveal the medium-low frequency information in the shot record. The proposed Random Noise Block enables better generalization of the model and higher accuracy in modeling the shot record speed of the entrained noise. The results of extensive numerical experiments on synthetic models show that our method acquires outstanding performance, which verifies the positive effect of MFNSR on the inversion of medium-low frequency data. The visualizations of outputs show that the proposed method can obtain more accurate velocity models.

In marine seismic exploration, the ocean bottom cable can receive both reflected P- and S-wave information from sub-seabed structures. Recently, a water-land dual-detector observation system has been developed to record acoustic pressure fields using water detectors and elastic displacement wave fields using land detectors. These water-land dual-detector data sets are commonly used to suppress multiples. However, the conventional elastic least-squares reverse time migration (LSRTM) based on single elastic wave equations cannot simultaneously utilize the ocean bottom dual-sensor (OBD) data. To solve the acoustic-elastic joint inverse problem by simultaneously using observed pressure and displacement records in the OBD data, we propose an OBD-data-based joint acoustic and decoupled-elastic LSRTM (JADE-LSRTM). This method constructs a new joint acoustic and decoupled-elastic misfit function, acoustic-elastic wave backward-adjoint operators and demigration operators in the curvilinear system, and gradient directions with respect to P- and S-wave velocity. In these acoustic-elastic coupled wavefield propagation operators, acoustic equations are used to calculate forward-propagated and backward-propagated pressure wavefields in the seawater based on water detector data sets, while decoupled elastic equations are applied to produce the displacement wavefields in the underlying elastic medium, with a higher computational efficiency than the traditionally combining individual acoustic and decoupled-elastic wavefield operators. Comparing to the conventional elastic LSRTM, the proposed method enables the use of acoustic data, which is crucial for OBD data. Two numerical examples demonstrate that the proposed curvilinear coordinated JADE-LSRTM based on water-land dual-detector data can produce accurate images in P- and S-component with higher efficiency and accuracy.

Most least-squares migration imaging methods use iterative gradient update methods to approximate the inverse of the Hessian matrix, but such approximations are not accurate and require a large amount of computational time. The point spread function (PSF) is an optical imaging method, defined as the response of an imaging system to a point source of light. In optics, the image of a complex object is considered to be a degenerate result obtained by convolving the PSF with the real object, which is analogous to the definition of seismic imaging using Hessian operator. To accurately calculate the inverse of the Hessian matrix, solve the PSF sparsity selection problem, and eliminate migration noise, we propose a velocity -adaptive irregular PSF deconvolution imaging using a Gaussian smoothing X-shaped denoising diffusion filtering operator. The velocity-adaptive irregular grid selection strategy allows for adaptive selection of the grid size based on the velocity of the different layers, ensuring maximum imaging accuracy and avoiding the risk of interference among PSFs. The Gaussian smoothing X-shaped denoising diffusion filtering operator eliminates migration noise and also prevents the introduction of deconvolution noise. We use the Marmousi model and a field data set to compare the performance of our proposed method with other common methods, demonstrating that our proposed method has clearer seismic events, more balanced amplitude, higher resolution, higher signal-to-noise ration than others.

Prismatic waves carry steeply dipping structural information that primaries cannot contain. Therefore, prismatic waves are separately used in some migration methods to improve the illumination and imaging effect on steeply dipping structures. Least-squares reverse time migration of prismatic waves (LSRTM-P) can produce high-resolution images with improved steeply dipping structures. However, viscoelasticity exists widely on the Earth, which poses great difficulty for imaging. The effect of attenuation on prismatic waves is difficult to be compensated when conducting LSRTM-P because prismatic waves have three propagation paths. To overcome this problem, a$Q$-compensated LSRTM ($Q$-LSRTM)-P method is proposed by deriving$Q$-compensated forward-propagated operators and backward-propagated adjoint operators of prismatic waves, which compensates for$Q$attenuation along all the three propagation paths of prismatic waves. The proposed$Q$-LSRTM-P is conducted to update the image after applying the conventional$Q$-LSRTM. Besides, the proposed method can be adapted to the irregular surface media. Numerical examples on two synthetic and a field datasets verify that our method can produce better imaging results with clearer steeply dipping structures, higher signal-to-noise ratio (SNR), higher resolution, and more balanced amplitude than noncompensated LSRTM-P and conventional$Q$-LSRTM.

Curvilinear-grid-based least-squares reverse time migration (LSRTM) can produce an accurate image of complex subsurface structures. However, a huge amount of computational cost of LSRTM makes it difficult in real data applications, especially in 3-D cases. We propose a wavefield continuation operator in a new curvilinear-$\tau $domain to make the sampling space in the vertical direction to be uniform by stretching and compressing the low- and high-velocity zones, respectively. An objective function based on a conical wave encoding and student’s$T$distribution is constructed to improve the computational efficiency and robustness of LSRTM. The gradient formula is derived based on the objective function, and to correct the unbiased random estimation error, the idea of random optimization is introduced to obtain a weighted gradient. Demigration and adjoint wave equations in the curvilinear-$\tau $domain are derived to calculate the synthetic records and the backward-propagated wavefields. Numerical examples on synthetic and field datasets suggest that the proposed 3-D LSRTM method produces better images with a higher signal-to-noise ratio (SNR), more improved resolution, and more balanced amplitude than the conventional 3-D LSRTM and greatly improves the computational efficiency of 3-D LSRTM.

In the deep-marine environment, seismic data contain multiples and are seriously affected by$Q$attenuation. Multiples have been used in migration to image the shadow zones and improve the resolution. However, the effect of attenuation on multiples is more serious than primaries because multiples have longer propagation paths. Therefore, we compensate the forward-propagated source-side and backward-propagated receiver-side wavefields along all the propagation paths of multiples. To fully use the primaries and multiples, we construct an objective function of least-squares reverse time migration of joint primaries and multiples (LSRTM-J) to update the imaging results by jointly using primaries and different-order multiples. In practice in a seawater medium, seismic waves can hardly be affected by attenuation. To decrease the computational cost, we divide the medium in the deep-marine environment into an acoustic medium part and a viscoacoustic medium part and derive the acoustic–viscoacoustic coupled compensated forward continuation operator, compensated adjoint operator, attenuated demigration operator, and gradient formula of joint primaries and multiples. To eliminate the severe scattering and diffracted noise caused by the strong-reflected irregular seabed interface, we mesh the velocity and$Q$models into curvilinear grids to perfectly match the seabed structure and realize the proposed viscoacoustic LSRTM-J in the curvilinear domain. Numerical examples on two typical models and a real data test suggest that the proposed method produces images with high SNR, high resolution, balanced amplitude, clear imaging structures, and strong deep region energy, and the total computational cost is the least of the other four conventional methods.