Reverse time migration (RTM) has shown increasing advantages in handling seismic images of complex subsurface media, but it has not been used widely in 3D seismic data due to the large storage and computation requirements. Our prime objective was to develop an RTM strategy that was applicable to 3D vertical seismic profiling (VSP) data. The strategy consists of two aspects: storage saving and calculation acceleration. First, we determined the use of the random boundary condition (RBC) to save the storage in wavefield simulation. An absorbing boundary such as the perfect matching layer boundary is often used in RTM, but it has a high memory demand for storing the source wavefield. RBC is a nonabsorbing boundary and only stores the source wavefield at the two maximum time steps, then repropagates the source wavefield backwards at every time step, and hence, it significantly reduces the memory requirement. Second, we examined the use of the graphic processing unit (GPU) parallelization technique to accelerate the computation. RBC needs to simulate the source wavefield twice and doubles the computation. Thus, it is very necessary to realize the RTM algorithm by GPU, especially for a 3D VSP data set. GPU and central processing unit (CPU) collaborated parallel implementation can greatly reduce the computation time, where the CPU performs serial code, and the GPU performs parallel code. Because RBC does not need the same huge amount of storage as an absorbing boundary, RTM becomes practically applicable for 3D VSP imaging.

Elastic reverse time migration (RTM) has the ability to retrieve accurately migrated images of complex subsurface structures by imaging the multicomponent seismic data. However, the imaging condition applied in elastic RTM significantly influences the quality of the migrated images. We evaluated three kinds of imaging conditions in elastic RTM. The first kind of imaging condition involves the crosscorrelation between the Cartesian components of the particle-velocity wavefields to yield migrated images of subsurface structures. An alternative crosscorrelation imaging condition between the separated pure wave modes obtained by a Helmholtz-like decomposition method could produce reflectivity images with explicit physical meaning and fewer crosstalk artifacts. A drawback of this approach, though, was that the polarity reversal of the separated S-wave could cause destructive interference in the converted-wave image after stacking over multiple shots. Unlike the conventional decomposition method, the elastic wavefields can also be decomposed in the vector domain using the decoupled elastic wave equation, which preserves the amplitude and phase information of the original elastic wavefields. We have developed an inner-product imaging condition to match the vector-separated P- and S-wave modes to obtain scalar reflectivity images of the subsurface. Moreover, an auxiliary P-wave stress image can supplement the elastic imaging. Using synthetic examples with a layered model, the Marmousi 2 model, and a fault model, we determined that the inner-product imaging condition has prominent advantages over the other two imaging conditions and generates images with preserved amplitude and phase attributes.

The advanced seismic imaging technology is reverse-time migration (RTM), which generates Earth's structural image by cross-correlating the forward-propagated source wavefield and the back-propagated receiver wavefield. Both these wavefields conventionally are assumed to be acoustic waves. When applying this RTM technology to seismic elastic waves, which are the multi-component rather than the single-component data, the cross-correlation procedure will generate a crosstalk effect between different wave modes. Therefore, prior to RTM imaging, both the source and receiver wavefields need to be decomposed into the pure P-wave mode and the pure S-wave mode. This paper envisages the advanced features of a vector-wavefield decomposition method that presents either the P- or the S-wave mode as a vector wavefield. This vector-wavefield decomposition method is based on a group of decoupled wave equations. The two separated vector wavefields preserve the true amplitude and phase information. Then, the associated RTM imaging condition is an inner-product of these two vector wavefields, rather than the cross correlation that is applicable to two scalar wavefields. The conventional elastic RTM approach uses the Helmholtz decomposition method to derive P- and S-waves and then implements cross correlation to produce the image. In comparison to this conventional combination, this paper demonstrates that the elastic RTM method using a combination of the vector-wavefield decomposition and the inner-product imaging condition is capable of producing seismic images with correct amplitudes and phases of various reflection modes.

The natural damping effect of the Earth typically results in significant distortion of seismic waveforms, which greatly diminishes the precise of subsequent processes such as parameter inversion, migration imaging, and reservoir description. Compensating for this attenuation is crucial to achieving precise underground parameter measurements. While inversion or imaging techniques that rely on wave path compensation have the potential to address attenuation effects better, they encounter challenges, including heightened demands for input models, rapidly escalating algorithm intricacy, and computational burdens. Consequently, developing novel attenuation compensation methods that balance computational efficiency and accuracy is important in enhancing the precision of exploring complex reservoirs. This study utilizes a groundbreaking convolutional neural network, which integrates an attention mechanism and residual learning. This network establishes an inherent link between attenuated seismic data and their non-attenuated counterparts, effectively accomplishing data-driven compensation for seismic data attenuation. The more advanced acoustic (non-attenuated) full waveform inversion or reverse time migration framework is directly applied to enhance the modeling or imaging of attenuated seismic data with improved accuracy and efficiency. Simulation data and actual test results confirm that the suggested Q-compensation approach successfully enhances the amplitude of deep structural reflection signals, rectifies phase distortion induced by attenuation, and widens the seismic frequency range. This mitigates issues like the cycle-skipping problem associated with low-frequency absence in traditional FWI and the numerical instability and increased computational complexity found in attenuation compensation FWI. Furthermore, the imaging profile’s resolution is further heightened due to the effective attenuation correction and enhancement of high-frequency components.

Deep-image prior (DIP) is a novel approach to solving ill-posed inverse problems whose solution is parameterized with an untrained deep neural network and cascaded with the forward modeling operator. A key component to the success of such a method is represented by the choice of the network architecture, which must act as a natural prior to the inverse problem at hand and provide a strong inductive bias toward the desired solution. Inspired by the close link between neural networks and iterative algorithms in classical optimization, we apply an unrolled version of the gradient descent (GD) algorithm as our DIP network architecture, denoted as the deep-unrolling (DU) architecture. Each layer of the unrolled network is comprised of two parts: the first part corresponds to the GD step of the data-fidelity term, whereas the second part, formed by a six-layer convolutional neural network (CNN), plays the role of a regularizer in the associated objective function. The developed DU architecture is applied to the problem of image-domain least-squares migration (IDLSM) to invert migrated seismic images for their underlying reflectivity and is denoted as DU-IDLSM. As such, the DU architecture parameterizes the reflectivity, and the input of each layer of the unrolled network is the reflectivity at the previous layer. Similar to the classical DIP approach, the parameters of the DU architecture are optimized in an unsupervised fashion by minimizing the data misfit function itself. Through experiments with a part of the Sigsbee2A model and a marine field data set, we test the effectiveness of the DU-IDLSM approach and highlight two key benefits. First, the DU architecture can effectively regularize the inversion process, resulting in reflectivity estimates with fewer artifacts and higher image resolution than those produced by conventional IDLSM approaches. Second, we indicate that by including dropout layers in the CNN architecture, DU-IDLSM can produce a qualitative measure of the uncertainty associated with the least-squares migration process.

Attenuation and the occurrence of missing traces are prevalent challenges in field seismic data, significantly affecting subsequent processing and imaging. While numerous studies have been conducted to address these issues, both traditional methods and deep learning approaches often treat seismic data reconstruction and attenuation compensation as distinct problems. This fragmented approach may neglect the potential correlation and shared characteristics between compensation and reconstruction. Consequently, this article presents a novel nonlinear activation-free network (NAFNet) (CSNAF-Net3+) specifically designed to simultaneously conduct seismic data reconstruction and attenuation compensation. The proposed network integrates U-Net3+, NAFNet, and convolutional block attention module (CBAM) methodologies, leveraging the automatic feature learning and end-to-end processing capabilities inherent in deep learning. This integration significantly enhances performance in both reconstruction and compensation tasks. Numerical simulation and field data tests demonstrate that CSNAF-Net3+ exhibits exceptional efficacy in addressing issues related to missing traces, attenuation, and noise. Notably, it achieves substantial improvements in reconstructing and compensating for extensive gaps within continuously missing traces. Moreover, we further introduce a more accurate and robust compensation method based on a multi-Q value model training framework. This strategy possesses significant potential to improve the network’s adaptability for field seismic data.