By solving a linear inverse problem, least-squares migration (LSM) can provide higher-precision images of complex subsurface structures than traditional adjoint-operator-based migration. LSM can be conducted in the data domain and the image domain (IDLSM). IDLSM in acoustic media has been extensively studied, commonly using single-parameter point-spread function (PSF) deconvolution. For high-accuracy imaging of complex media, we develop an image-domain elastic least-squares imaging method using multiparameter PSF deconvolution for vertically transversely isotropic (VTI) media. The multiparameter PSFs, including P-P, P-S, S-P, and S-S components, are calculated on a sparse grid using elastic VTI wave equation Born modeling and migration. The traditional migration result is then decomposed into individual local results, each corresponding to the size of a single PSF, through unit partitioning. Finally, a set of filters is derived from four elastic VTI PSF components to approximate the Hessian inverse, which are subsequently assembled to reconstruct an entire deconvolved image. The numerical experiments confirm that our method can significantly decrease multiparameter crosstalk artifacts and improve spatial resolution and amplitude fidelity.

Kirchhoff beam migration (KBM) is a ray-based seismic imaging method, which can handle multi-arrivals caused by model complexity. Apart from its high imaging precision, it also retains the merits of Kirchhoff migration, such as efficiency, stability, and flexibility. However, two issues should be taken into consideration when this method is expanded to the complicated surface conditions: first, the computational accuracy deficiency of the original local plane-wave decomposition method cannot suit for low signal-to-noise ratio seismic data; second, as the rays traveling, the beam width increases rapidly, which cannot guarantee the computational accuracy of the corresponding grid points’ attribute information. In addition, the insufficient coverage of the beam in the shallow part of the model might affect the imaging quality of this region. Kirchhoff dynamic focused beam migration based on compressed sensing is proposed to resolve these two problems. For the first problem, the local plane-wave decomposition method based on compressed sensing is introduced into KBM to enhance its computational accuracy. To solve the second problem, this paper adopts the dynamic focused beam to replace the original simplified Gaussian beam in the migration method, control the divergence of beam, and increase the coverage of beam in the shallow part of the model. Both Marmousi model and Canadian Foothills model are employed in this paper to test the new migration imaging method.

High-resolution and amplitude-preserved imaging is crucial for mapping impedance interfaces and identifying hydrocarbon reservoirs in subsurface. Although elastic reversetime migration (RTM) is capable for imaging complicated structures, it actually is the adjoint of seismic forward modeling and produces unsatisfactory images with irregular acquisition system and uneven illumination. To address this issue, we develop an elastic image-domain least-squares migration (LSM) method based on the point-spread function (PSF) deconvolution. Instead of choosing P- and S-wave velocities as the reflectivities in conventional elastic LSM, we define the density perturbation as the reflectivity model. Full-wavefield elastic modeling and PS-separation-based RTM are then applied to compute PSFs. This framework does not involve the crosstalk issue because only two types of PSFs, that corresponds to the diagonal elements of the Hessian matrix, are generated. Then, the two kinds of PSFs are respectively used for local image deconvolution for PP and PS images to correct Hessian blurring effect, in which the unit partitioning with multi-dimensional Gaussian functions is adopted to generate optimal local windows. Numerical experiments demonstrate the feasibility of the proposed method and the potential to enhances image resolution and amplitude fidelity.

In order to overcome the shortcomings of serious arc drawing and low computational efficiency in the crosswell seismic migration method and the problems of the inaccurate velocity model and sparse distribution of reflection points in the traditional stack imaging method, the article proposes an inverse Fresnel beam XSP-CDP stack imaging method based on first-arrival wave velocity tomography combined with the characteristics of crosswell seismic wave field. Firstly, an accurate crosswell velocity model is established by the first-arrival wave tomography inversion method based on the characteristics of high energy and easy pick-up of the first-arrival wave in crosswell seismic. Secondly, the velocity model is optimized, and the energy contribution weights of effective rays to the receiver point are calculated through the crosswell seismic Fresnel beam wave field forward numerical simulation method. Then, the reflected wave field is dynamically migrated to the reflection points within the first Fresnel zone according to the weight function, and the intensive common reflection point (CRP) gather after normal moveout (NMO) correction is generated. Finally, an appropriate bin is selected for stacking. In this article, the inverse Fresnel beam method is used to decompose the single-channel seismic wave field into the effective reflection points in the Fresnel zone, which makes the fold of the reflection point more uniform and improves the imaging accuracy. The model test and actual data processing results proved the validity and robustness of this method.

The vertical seismic profiling (VSP) Gaussian beam migration is a seismic imaging method with both computational efficiency and imaging precision. It can get high-resolution structural features near the well. However, the VSP migration based on primary reflection imaging is limited by the observation system, which makes it unable to image for the shallow structure at far offset. The free-surface multiples in VSP can expand the illumination range for far offset effectively. Therefore, Gaussian beam migration (GBM) for free-surface multiples imaging in VSP is proposed. Firstly, based on the ground Gaussian beam pre-stack depth migration, the method for decomposing the plane wave is improved and adapted into VSP geometry. We decompose the seismic records received by the well into plane waves in different directions according to different window centers and image the plane wave of each direction independently. Secondly, through the mirror image of both the velocity model and VSP receivers, the VSP free-surface multiples are converted into VSP primary reflections which are involved in the VSP Gaussian beam migration method, and thus, the method of the primaries is used to image the free-surface multiples. Finally, the effectiveness and robustness of the proposed method are verified by the theoretical model and practical data.