Traditional viscoacoustic migration methods effectively compensate for amplitude loss and phase distortion caused by viscous attenuation. However, these methods predominantly focus on achieving accurate structural imaging. Preserving relative-amplitude information in migrated images is crucial for accurately restoring medium properties while imaging geometric structures under viscous attenuation conditions. In this paper, we present an efficient and stable method for viscoacoustic true-amplitude Gaussian beam migration in the common-offset domain, specifically designed to tackle this challenge. Our approach utilizes the multiparameter viscoacoustic Born scattering mechanism to recover the velocity and quality factorQ. The incorporation ofQinto the migration process is achieved by definingQ-related complex-valued traveltime to compensate for attenuation effects. We illustrate the forward single scattering integral for the central beam component of the viscoacoustic common-offset scattered pressure wavefield, using attenuation-compensated Gaussian-beam expansions of the viscoacoustic Green’s function. This description, along with the estimation of the kernel of the single-scattering Hessian operator, enables us to develop a viscoacoustic Gaussian-beam pseudoinverse migration operator for common-offset data. This operator includes a Beylkin determinant and an invertible normal matrix associated with a causality term. Employing this derived pseudoinverse operator enhances subsurface structure imaging accuracy and preserves amplitude response information of material parameters throughout the viscoacoustic migration process. Numerical experiments and field data tests demonstrate that, with the proposed attenuation compensation method, it is possible to align the estimated parameters with their true values, yielding more accurate imaging and parameter estimations in viscoacoustic media compared to the traditional acoustic approach without attenuation compensation.

Seismic imaging from sparsely acquired data faces challenges such as low image quality, discontinuities, and migration swing artifacts. Existing convolutional neural network (CNN)-based methods struggle with complex feature distributions and cannot effectively assess uncertainty, making it hard to evaluate the reliability of their processed results. To address these issues, we propose a new method using a generative diffusion model (GDM). Here, in the training phase, we use the imaging results from sparse data as conditional input, combined with noisy versions of dense data imaging results, for the network to predict the added noise. After training, the network can predict the imaging results for test images from sparse data acquisition, using the generative process with conditional control. This GDM not only improves image quality and removes artifacts caused by sparse data but also naturally evaluates uncertainty by leveraging the probabilistic nature of the GDM. To overcome the decline in generation quality and the memory burden of large-scale images, we develop a patch fusion strategy that effectively addresses these issues. Synthetic and field data examples demonstrate that our method significantly enhances imaging quality and provides effective uncertainty quantification.

Multi-component elastic Gaussian-beam migration is relatively accurate, efficient, and flexible. However, a large amount of land seismic data is recorded by single-component geophones, which means that only vertical ground motions can be measured. In this case, the multi-component elastic Gaussian-beam migration cannot be applied. Conventionally, the vertical component is simply interpreted as the PP component and migrated using an acoustic migration method. But in fact, the vertical component also records the shear wave information. To perform elastic migration using only vertical-component data (in cases where multi-component data are not available), we propose a single-component elastic Gaussian-beam migration method for PP and PS imaging. Based on the Kirchhoff–Helmholtz integral, we give an effective formula for downward extrapolation of multi-mode waves. Using our method, different wave modes are separated during migration by applying a decomposition vector to single-component data without prior data separation, resulting in better elimination of crosstalk artifacts and lower processing cost. Numerical experiments on 3D land seismic data and 2D VSP data are provided to demonstrate the performance of the method. Results show that PS-wave imaging is also feasible when we only have vertical component data.

The ocean bottom node (OBN) seismic acquisition system is designed to gather high-fidelity, wide-azimuth, and long-offset four-component (4C) data, which includes shear waves and enables the use of the elastic assumption in imaging and inversion. However, deploying geophysical instruments on the seafloor is difficult and costly, leading to the usual adoption of sparse node spacing. This can, however, lead to poor illumination and imaging challenges, especially in the shallow subsurface near the seafloor. To address these issues in the context of 4C elastic imaging, we propose a deep learning-based method using a multi-scale convolutional neural network (Ms-CNN) to improve the imaging quality of OBN surveys with sparse data acquisition. As an alternative to interpolating the sparse seismic data in the data domain, which can be a challenging task due to the limitations attributed to sampling theorem and the often larger amounts of data compared to the image, we train an Ms-CNN in a supervised fashion to map from sparse data images of PP and PS sections produced by 4C Gaussian beam migration to the equivalent dense data images, allowing for the direct processing of sparse data to improve imaging quality. Here, we combine the mean absolute error and multiscale structure similarity index measure in the loss function to optimize the network’s training process, and to help improve the performance. The effectiveness of the method is demonstrated through experiments on synthetic and field data, resulting in improved event continuity and reduced noise in migration results from sparse OBN acquisitions.

Amplitude-preserving migration is very important for reservoir characterization, which can faithfully provide information on the strength of the reflectors. However, conventional migration algorithms do not compensate for variable illumination effects and can hardly obtain true amplitudes of medium parameter. Least-squares migration (LSM) is an effective method to address this issue. Unfortunately, there is a key problem with LSM methods: most LSM methods only consider illumination compensation but not consider the accuracy of migration velocity model. The accuracy of the migration velocity model directly affects the quality of migrated images. Moreover, changes in velocity are more indicative of reservoir properties than reflectivity. Therefore, it is necessary to incorporate velocity estimation into migration imaging to realize joint inversions. Based on these facts, we present an iterative reweighted LSM method by approximating the local Hessian using point spread functions. Then, we related the LSM results to the scattering potential, simultaneously achieving velocity update with illumination compensation. Based on the gradually changing characteristics of rock properties, we adopted a sparse derivative constraint rather than requiring the result to be sparse. Consequently, this processing caused the results to contain broader bandwidths, giving the image a more continuous and textured appearance. Next, we evaluated the proposed method using the Marmousi2 model. The results had a higher resolution and a more reliable amplitude than the initial migration images. Hence, we efficaciously completed the velocity model update, with our method achieving encouraging results under both relatively accurate migration velocity and highly smoothed migration velocity model tests.

The extension of Gaussian-beam migration (GBM) from isotropic media to anisotropic media is a straightforward process that involves adapting the existing framework to incorporate anisotropic effects. However, the true challenge for GBM lies in simultaneously performing geometric structure imaging and accurately restoring medium properties in the presence of anisotropy. In this paper, we propose a novel approach for true-amplitude GBM in acoustic transversely isotropic (TI) media with a vertical axis of symmetry (VTI). The recovered parameters include the NMO velocity parameter vn, the anelliptic parameter η, and Thomsen’s parameter δ. We employ Gaussian-beam expansions for the acoustic VTI Greens function to represent the forward single scattering integral for a single-beam-center component of the common-offset scattered pressure wavefield. Based on this representation and estimation of the kernel of the single-scattering Hessian operator, we construct an acoustic VTI Gaussian-beam pseudoinverse operator. This operator includes a Beylkin determinant and a normal matrix integral over the local dip vectors chosen from the local slant stacks of the common-offset data. By utilizing this derived pseudoinverse operator, we are able to improve the accuracy of subsurface structure imaging and preserve the amplitude response information of material parameters during the acoustic VTI migration process. We apply the present approach to synthetic data examples and demonstrate its effectiveness in terms of imaging accuracy and amplitude fidelity.

Elastic least-squares migration (ELSM) has the potential to produce high-resolution images. It can be implemented in either data-domain or image-domain but is much faster in the image domain. A critical step of image-domain ELSM is the calculation of the Hessian. However, it is impractical to directly calculate the Hessian due to its high storage and costs. In this letter, the Hessian is efficiently constructed with elastic point spread functions (PSFs) calculated by a combination of multicomponent Gaussian beam Born modeling (of scattering points with elastic parameters perturbation) and elastic Gaussian beam migration. Based on this, we propose a fast image-domain ELSM method. A hyper-Laplacian priori regularization is used to produce sparse solutions. We evaluate the proposed method with the Marmousi2 model, and the results demonstrate the capability of the method to image complex structures with improved resolution relative to the initial migrated image.