Target-oriented least squares reverse time migration (TO-LSRTM) is a method designed for imaging below the complex overburden. It achieves this by bypassing the overburden and focusing wavefields over the region of interest. The critical aspect of this process lies in obtaining Marchenko double-focusing redatumed data. However, traditional Marchenko redatuming methods neglect the impact of anisotropy, leading to distortions in the travel times and amplitudes of redatumed data, thus affecting imaging accuracy. To overcome this problem, we develop a target-oriented vertical transverse isotropic least-squares reverse time migration (TO-VTI-LSRTM) method. This method uses the direct wave from the subsurface virtual source point obtained by the first-order VTI pseudo-acoustic equation as the initial condition to solve the Marchenko equation, so as to correct the velocity anisotropy in the process of redatuming, and the redatumed data is used as the virtual observed data for inversing the reflection coefficients of the subsurface local region. Numerical experiments validate the capabilities and advantages of the proposed method. Imaging results demonstrate that this approach effectively eliminates imaging artifacts caused by anisotropy and overburden internal multiple reflections, resulting in high-quality imaging results.

Marchenko imaging has the particular ability to generate the subsurface image free of spurious artifacts related to internal multiples. However, conventional Marchenko imaging (C-MI) is performed based on the assumption that the sources and receivers of the recorded seismic data are placed on a flat surface, which is restrictive and hard to satisfy in mountainous areas with rugged topography. The elevation-static correction (or time shift) is a usual solution to ensure this assumption holds. But it only works well if the surface consistency is satisfied. To alleviate the limitations of C-MI in processing seismic data acquired from mountainous areas with rugged topography, we present a technique for conducting Marchenko imaging from a floating datum. The proposed Topography-Marchenko imaging (T-MI) is achieved by estimating an initial down-going focusing function between a floating datum and a focal point in the subsurface. In this work, we use seismic data corrected to a floating datum rather than a final datum as input to the iterative Marchenko scheme to retrieve Green’s functions. The retrieved Marchenko Green’s functions are further used to generate the subsurface image. The T-MI method can effectively avoid imaging distortions caused by the elevation-static correction. The proposed T-MI method is validated through applications to a synthetic model with rugged topography and a land dataset acquired from a mountainous area in Northwest Sichuan, China.

The Marchenko method has received significant attention in geophysics due to its specific ability to retrieve the accurate Green's functions directly from data without a subsurface focal point to have an actual physical receiver located at it. However, its application capacity in anisotropic medium remains unexplored. Given the increasing complexity of exploration tasks, it has become imperative to investigate its feasibility of deploying the Marchenko method in anisotropic media. This study aims to assess the applicability of the Marchenko method in retrieving Green's functions in anisotropic medium with a synthetic dataset simulated over a tilted transversely isotropic (TTI) model. The Green's functions are retrieved based on the assumptions that the data are acquired from either an isotropic or TTI medium model. A comparison analysis reveals that the first arrivals obtained based on the TTI medium assumption provides more accurate travel times and amplitudes, resulting in a more accurate reconstruction of the Green's function. The study demonstrates that Marchenko method can be effectively applied in anisotropic medium.

Least-squares reverse time migration (LSRTM) is a migration method for retrieving subsurface reflectivity using linear inversion theory. Compared to traditional imaging methods, LSRTM offers higher resolution and amplitude preservation. However, the computational cost of LSRTM in the data-domain is high and inevitably leads to the creation of imaging artifacts due to internal multiples. In this study, we propose a target-oriented data-domain LSRTM based on the first-order velocity-stress equation and the Marchenko equation. By two steps of source redatuming and receiver redatuming, this method extrapolates the wavefield from the acquisition surface to beneath the complex overburden, eliminating the impact of multiple scattering within the overburden and achieving target-oriented imaging. Numerical result shows that this method effectively mitigates imaging artifacts caused by internal multiples within the overburden, thus enhancing imaging quality.

The least-squares reverse time migration (LSRTM) can obtain high resolution and true amplitude imaging results. However, LSRTM for full model domain data requires simulation throughout the entire model space, resulting in significant computational costs. In addition, the Born approximation, which is based on single scattering theory, can cause imaging artifacts by treating multiple reflections from the overburden as primary reflections. To address these issues, the Marchenko redatuming method can be used to separate the influence of the overburden. However, due to factors such as acquisition aperture, phase and amplitude errors can occur in far offset Marchenko redatumed data. Therefore, a prestack correlative LSRTM method based on Marchenko redatumed data is proposed for target-oriented imaging, which includes two key points. First, the method aims to reconstruct the data recorded from the surface onto the target datum using the Marchenko redatuming theory to obtain the response without the influence of overburden. Second, by constructing the prestack normalized zero-lag cross-correlation error function, the optimal reflection coefficient model is found for each shot's record, and the final imaging result is generated by stacking the optimal reflection coefficient model of all redatumed data, thereby alleviating the problem of the incoherent stacking at far offset in redatumed data, which reduces the imaging quality. Numerical examples demonstrate that the proposed method has higher computational efficiency and can provide imaging results with fewer artifacts.

Local full-waveform inversion (FWI) methods use redatumed seismic responses of virtual receivers within the subsurface to build the local objective function based on the convolution-type representation theorem. The Marchenko method is widely used to obtain the redatumed data. The method only requires a smoothed velocity model with correct kinematic characteristics of seismic responses for redatuming of the single-sided reflection data. However, the standard Marchenko method is insensitive to lateral propagation of the wavefield. By injecting the standard Marchenko redatumed wavefield along the boundary of the target, the local wavefield propagation modeling produces errors, which affects the accuracy of the local FWI. In this paper, a method to obtain more accurate Green’s functions is proposed by incorporating vertical seismic profile data (VSP) into the calculation process of the Marchenko source-receiver redatuming. This method allows one to obtain the accurate laterally propagating waveform, resulting in a significant improvement of lateral resolution. The proposed method is applied to a benchmark model dataset and compared with the local FWI based on standard Marchenko redatuming.

Spatial undersampling is a common problem in actual seismic data due to limitations in seismic survey environments, which can be satisfactorily solved by data regularization. The convolution-based deep-learning reconstruction methods require fewer assumptions than the conventional reconstruction methods (e.g., Curvelet-domain and F-X domain data regularization methods). However, the traditional convolution methods are not suitable for the large percentages of missing data. In this study, we propose an improved partial convolution-based (PConv-based) deep-learning network to reconstruct the missing data, which is evolved from the conventional convolution-based (CConv-based) method. The U-net is used as deep learning network to analyze both PConv-based method and CConv-based method. The PConv-based method adopts a hierarchical, regional-learning mechanism to dynamically update the constrained convolution results for the sample matrix. Hence, the problem of poor amplitude preservation in the data reconstruction has been addressed when multiple consecutive traces are missing. The influence of data loss ratio on reconstruction algorithm is also discussed in this study. The numerical test demonstrates that the trained network is able to process a sample dataset with 50% data lost and largely eliminate the noises in the frequency-wavenumber domain caused by the missing data. This proposed method is further evaluated by actual data, and the results are better than those obtained from the Curvelet-domain method. Moreover, the dataset reconstructed by the PConv-based deep-learning network has a great agreement with the original dataset in terms of amplitude.