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Full-waveform inversion (FWI) is among the most effective methods of velocity modelling in seismic exploration. However, because of the strong nonlinearity of the FWI, if the velocity in the target geobody is not sharply different from that in its surroundings, the total variation (TV) of the model will not be sufficiently sparse. To alleviate this issue, we propose a novel TV-regularised FWI method that can consider the sparsity of the high-order regularisation operator and consequently improve the stability of the inversion process and produce more focused model boundaries. We use a split-Bregman algorithm to solve the inversion optimisation problem while building the TV-regularised objective function. We show that stable model updates can be obtained by this algorithm, which proved to be effective and reliable in the numerical tests. These tests also show that the proposed method converges faster, can model the velocity domain better than conventional methods and can effectively identify layer boundaries with a weak velocity contrast. We conclude that the novel FWI method based on high-order TV regularisation is robust and accurate.

Ray-based tomography in the imaging domain, implemented with seismic migration, is currently widely used in industrial applications. However, conventional ray-based tomography has some inherent problems, such as shadow area, multi-path problem and so on, which limit the inversion accuracy. To alleviate these problems, we proposed Gaussian beam velocity tomography (GBT) based on azimuth-opening angle domain common imaging gathers (ADCIGs). According to the first-order Born and Rytov approximations, we derived a linear relationship between travel-time perturbation and velocity perturbation in the imaging domain, by which we construct the explicit expression of the sensitivity kernel function and use a Gaussian beam operator to compute the kernel. Furthermore, by introducing the preconditioned model regularization, a method of GBT under the constraint of a structure-guided filter is derived. Iterative applications of migration and tomography, both based on a Gaussian beam propagator, embody the idea of integrating velocity inversion and imaging. Numerical tests on both synthetic data and field data demonstrate that Gaussian beam propagator-based travel-time tomography in the imaging domain is effective.

The ray-tracing technique under the high-frequency assumption has been widely used in seismic wave propagation and migration. However, the practical use of conventional ray tracing is limited in complicated media especially when seismic data are band limited. Besides, the ray-tracing method also suffers from shadow zones in complex media. To alleviate these problems, we have developed a band-limited beam propagator and we apply it in seismic wave propagation and migration, which is flexible to implement and can be friendly to extract angle gathers. To derive the band-limited beam propagator, the band-limited ray-tracing method is adopted to compute the central ray of the beam. These rays in the first Fresnel zone are weighted to obtain the band-limited ray based on the assumption of a local plane wave. Then, the band-limited ray is extended to the band-limited beam propagator using the paraxial approximation. Because the beam propagator has a certain beam width perpendicular to the central ray, it has better illumination than the conventional ray-tracing method, and it could partially alleviate the problem of shadow zones. Finally, we use the band-limited beam propagator to develop a band-limited beam migration and analyze the angle gathers in complicated areas. Numerical examples on synthetic models indicate that the proposed band-limited beam propagator outperforms the conventional ray method in terms of illumination. Its applications in migration determine that it could enhance the imaging quality and produce better angle gathers in a complex area.

Kirchhoff integral migration is widely used in 3-D data processing. However, it is assumed that the acquisition geometry is regular. In fact, the acquisition geometry is, in most cases, irregular. Therefore, Kirchhoff integral migration formula will give wrong imaging amplitude. The distorted amplitude may mislead the AVO analysis and confuse the interpretation. In order to reduce the footprint caused by the irregular acquisition, a topologic transformation is introduced implicitly to change the irregular acquisition into a regular one by adjusting the weighting function of Kirchhoff pre-stack migration formula. Numerical Examples demonstrate that the approach is simple and effective for reducing the acquisition footprint.

Common-image gathers indexed by opening angle and azimuth at imaging points in 3D situations are the key inputs for amplitude-variation-with-angle and velocity analysis by tomography. The Gaussian beam depth migration, propagating each ray by a Gaussian beam form and summing the contributions from all the individual beams to produce the wavefield, can overcome the multipath problem, image steep reflectors and, even more important, provide a convenient and efficient strategy to extract azimuth?opening angle domain common-image gathers (ADCIGs) in 3D seismic imaging. We present a method for computing azimuth and opening angle at imaging points to output 3D ADCIGs by computing the source and receiver wavefield direction vectors which are restricted in the effective region of the corresponding Gaussian beams. In this paper, the basic principle of Gaussian beam migration (GBM) is briefly introduced; the technology and strategy to yield ADCIGs by GBM are analyzed. Numerical tests and field data application demonstrate that the azimuth?opening angle domain imaging method in 3D Gaussian beam depth migration is effective.