Automatic fault detection in seismic images using deep learning-based methods has attracted great interest in recent years. Detecting faults by deep learning methods is generally considered a supervised learning task, which requires numerous diverse training samples and corresponding accurate labels. Because field data with faults labeled by experienced interpreters are difficult to acquire, training samples are usually generated synthetically, in which the 1D seismic wavelets are convolved with reflectivity models. However, the 1D-convolution-based synthetic seismic images still differ from the real seismic images. Therefore, the network trained by such samples may fail to detect some faults in the field data. Full-wavefield approaches are the optimal seismic modeling methods, but they cannot be widely used at present due to the high cost. In this paper, we present an efficient approach to generate realistic synthetic seismic images by using a point-spread function (PSF)-based convolution. Because the size of a seismic sample used for deep learning training is a small range relative to the field seismic data, assuming the background velocity is close to homogeneous in such a small range, we can efficiently construct the PSF using the analytical Green’s function. With an Intel Core i9-10900K CPU, the PSF approach takes approximately 15 min to generate a seismic image of size 128 × 128 × 128, whereas it takes approximately 20 h to generate a seismic image of the same size using reverse time migration. The examples of one synthetic image and two field seismic images demonstrate that the network trained with the PSF convolution samples can predict more accurate and continuous faults than that trained with the 1D convolution samples.

The ray-tracing technique under the high-frequency assumption has been widely used in seismic wave propagation and migration. However, the practical use of conventional ray tracing is limited in complicated media especially when seismic data are band limited. Besides, the ray-tracing method also suffers from shadow zones in complex media. To alleviate these problems, we have developed a band-limited beam propagator and we apply it in seismic wave propagation and migration, which is flexible to implement and can be friendly to extract angle gathers. To derive the band-limited beam propagator, the band-limited ray-tracing method is adopted to compute the central ray of the beam. These rays in the first Fresnel zone are weighted to obtain the band-limited ray based on the assumption of a local plane wave. Then, the band-limited ray is extended to the band-limited beam propagator using the paraxial approximation. Because the beam propagator has a certain beam width perpendicular to the central ray, it has better illumination than the conventional ray-tracing method, and it could partially alleviate the problem of shadow zones. Finally, we use the band-limited beam propagator to develop a band-limited beam migration and analyze the angle gathers in complicated areas. Numerical examples on synthetic models indicate that the proposed band-limited beam propagator outperforms the conventional ray method in terms of illumination. Its applications in migration determine that it could enhance the imaging quality and produce better angle gathers in a complex area.

Accurately injecting and extrapolating multicomponent seismic data is a major step in elastic reverse time migration (RTM) and full-waveform inversion. The theoretical basis of this process is the seismic representation theorem. We propose a numerical approach based on the collocated-grid MacCormack finite-difference (FD) scheme to implement the injection and extrapolation. The MacCormack FD scheme defines wavefield parameters on the same grid. When dealing with the boundary condition in the representation theorem, it is more advantageous than the commonly used staggered-grid FD scheme which defines the stress and velocity on offset grids; thus, interpolations are required to link the boundary values to nearby nodes. In contrast, with the MacCormack scheme, the traction and particle velocity data can be directly injected into the boundary nodes as equivalent concentrated forces, force dipoles, and double couples. The accuracy of this approach is validated by comparing the regenerated wavefield with the original wavefield. Our primary purpose is to develop an injection method for elastic RTM, but this approach also can be used to numerically investigate other interesting issues in the elastic wave injection, including errors and artifacts caused by injection from unclosed boundaries, incomplete boundary values, and uncertain velocity models. In particular, seismic data are usually acquired on the ground surface where the traction-free condition is naturally maintained. We simulate a land acquisition scenario by generating a synthetic multicomponent data set on a traction-free surface. The reconstructed wavefields from velocity data are compared with the original forward-propagated waves to evaluate the accuracy of the boundary treatments. Two multicomponent elastic RTM examples are presented to demonstrate the applications of the proposed injection method. By combining the regenerated receiver-side wavefield and the vectorized imaging condition, the PP, PS, SP, and SS images are calculated.

Angle domain common image-point gathers (ADCIGs) can alleviate the limitations of common image-point gathers in offset domain, and have been widely used for velocity inversion and amplitude variation with angle (AVA) analysis. We propose an effective algorithm for generating ADCIGs in transversely isotropic (TI) media based on the gradient of traveltime by Kirchhoff pre-stack depth migration (KPSDM), as the dynamic programming method for computing the traveltime in TI media would not suffer from the limitation of shadow zones and traveltime interpolation. Meanwhile we present a specific implementation strategy for ADCIGs extraction via KPSDM. Three major steps are included in the presented strategy: (1) traveltime computation using dynamic programing approach in TI media; (2) slowness vectors calculation by the gradient of traveltime table calculated previously; (3) construction of illumination vectors and subsurface angles in migration process. Numerical examples are included to demonstrate the effectiveness of our approach, which hence shows its potential application for subsequent tomographic velocity inversion and AVA.

Obtaining high-resolution images of the subsurface requires advanced migration methods and high-quality seismic data. Least-squares migration (LSM), as an inversion-based method, aims to produce a high-precision subsurface reflectivity model by minimizing the misfit between observed and modeled data. However, the high computational cost associated with large-scale data sets and the convergence challenges encountered with complex data limit the widespread application of LSM. In this study, we reframe the fundamental theory of LSM within the framework of linear system analysis. We identify the point spread function (PSF) of the underground scattering points as the impulse response of the linear seismic imaging system, with the conventional imaging result regarded as the zero-state response of the same system. In this case, the inversion imaging problem can be expressed as the estimation of the corresponding stimulation function of the imaging system, leveraging the known impulse response and zero-state response. Specifically, we introduce the Gaussian beam propagator to generate PSFs as the impulse response of the inversion imaging system. Subsequently, Gaussian beam migration (GBM) is used for the zero-state response of this imaging system. After that, a broadband GBM can be accomplished by a deconvolution with the estimated impulse response and the zero-state response of this system. The deconvolution is implemented by the division in wavenumber domain with a stabilization factor. Numerical examples demonstrate the effectiveness and potential applications of the developed broadband imaging method based on the impulse response of the linear imaging system.