Shibo Xu

Perturbation‐based moveout approximations in anisotropic media

ABSTRACT The moveout approximations play an important role in seismic data processing. The standard hyperbolic moveout approximation is based on an elliptical background model with two velocities: vertical and normal moveout. We propose a new set of moveout approximations based on a perturbation series in terms of anellipticity parameters using the alternative elliptical background model defined by vertical and horizontal velocities. We start with a transversely isotropic medium with a vertical symmetry axis. Then, we extend this approach to a homogeneous orthorhombic medium. To define the perturbation coefficients for a new background, we solve the eikonal equation with horizontal velocities in transversely isotropic medium with a vertical symmetry axis and orthorhombic media. To stabilise the perturbation series and improve the accuracy, the Shanks transform is applied for all the cases. We select different parameterisations for both velocities and anellipticity parameters for an orthorhombic model. From the comparison in traveltime error, the new moveout approximations result in better accuracy comparing with the standard perturbation‐based methods and other approximations.

Generalized non-hyperbolic approximation for qP-wave relative geometrical spreading in a layered transversely isotropic medium with a vertical symmetry axis: Generalized non-hyperbolic approximation

Compensation for geometrical spreading along the ray-path is important in amplitude variation with offset analysis especially for not strongly attenuative media since it contributes to the seismic amplitude preservation. The P-wave geometrical spreading factor is described by a non-hyperbolic moveout approximation using the traveltime parameters that can be estimated from the velocity analysis. We extend the P-wave relative geometrical spreading approximation from the rational form to the generalized non-hyperbolic form in a transversely isotropic medium with a vertical symmetry axis. The acoustic approximation is used to reduce the number of parameters. The proposed generalized non-hyperbolic approximation is developed with parameters defined by two rays: vertical and a reference rays. For numerical examples, we consider two choices for parameter selection by using two specific orientations for reference ray. We observe from the numerical tests that the proposed generalized non-hyperbolic approximation gives more accurate results in both homogeneous and multi-layered models than the rational counterpart.

Preserved travel-time smoothing in orthorhombic media

ABSTRACT Certain degree of smoothness of velocity models is required for most ray‐based migration and tomography. Applying conventional smoothing in model parameters results in offset‐dependent travel‐time errors for reflected events, which can be large even for small contrasts in model parameters between the layers. This causes the shift in both the depth and residual moveout of the migrated images. To overcome this problem in transversely isotropic medium with a vertical symmetry axis, the preserved travel‐time smoothing method was proposed earlier. We extend this method for orthorhombic media with and without azimuthal variation between the layers. We illustrate this method for a single interface between two orthorhombic layers and show that the smoothing‐driven errors in travel time are very small for practical application.

Estimation of the Anisotropy Parameters from Imaging Moveout of Diving Wave in a Factorized VTI Medium

The importance of diving waves is being realized since they provide long model wavelength information, which can be utilized to invert the reflection wave information in a full waveform inversion (FWI). The factorized model is defined as a combination of vertical heterogeneity and constant anisotropy, and we define the closed form description of the diving wave traveltime. We propose analytical approximation for residual imaging moveout of diving waves in a factorized anisotropic medium. By using the classical semblance analysis, we estimate the optimal anisotropic parameters that can be later used for FWI initial model building.