# Browsing by Subject "Velocity estimation"

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Item Multiazimuth velocity analysis using velocity-independent seismic imaging(2011-05) Burnett, William Andrew, 1983-; Fomel, Sergey B.; Stoffa, Paul L., 1948-Show more Multiazimuth seismic data contains information about how the Earth’s seismic response changes with azimuthal direction. Directional-dependence of the seismic response can be caused by anisotropy or heterogeneity, associated with subsurface features such as fractures, stresses, or structure. Characterizing azimuthal variations is done through velocity analysis, which provides a link between an acquired data set and its image, as well as between the image and subsurface geology. At the stage which conventional velocity analysis is applied, it is difficult to distinguish the geologic cause of observed azimuthal velocity variations. The inability to distinguish the similar effects of anisotropy and heterogeneity leads to positioning errors in the final image and velocity estimates. Regardless of the cause, azimuthally variable velocities require at least three parameters to characterize, as opposed to the conventional single-parameter isotropic velocity. The semblance scan is the conventional tool for seismic velocity analysis, but it was designed for the isotropic case. For multiple parameters, the semblance scan becomes computationally impractical. In order to help address the xiissues of geologic ambiguity and computational efficiency, I develop three methods for multiazimuth seismic velocity analysis based on “velocity-independent” imaging techniques. I call this approach, velocity analysis by velocity-independent imaging, where I reverse the conventional order of velocity estimation followed by image estimation. All three methods measure time-domain effective-velocity parameters. The first method, 3D azimuthally anisotropic velocity-independent NMO, replaces the explicit measurement of velocity with local slope detection. The second method, time-warping, uses local slope information to predict traveltime surfaces without any moveout assumption beforehand, and then fit them with a multiparameter velocity model. The third method, azimuthal velocity continuation, uses diffraction image focusing as a velocity analysis criterion, thereby performing imaging and velocity analysis simultaneously. The first two methods are superior to the semblance scan in terms of computational efficiency and their ability to handle multi-parameter models. The third method is similar to a single multi-parameter semblance scan in computational cost, but it helps handle the ambiguity between structural heterogeneity and anisotropy, which leads to better positioned images and velocity estimates.Show more Item Seismic imaging and velocity model building with the linearized eikonal equation and upwind finite-differences(2014-05) Li, Siwei, 1987-; Fomel, Sergey B.Show more Ray theory plays an important role in seismic imaging and velocity model building. Although rays are the high-frequency asymptotic solutions of the wave equation and therefore do not usually capture all details of the wave physics, they provide a convenient and effective tool for a wide range of geophysical applications. Especially, ray theory gives rise to traveltimes. Even though wave-based methods for imaging and model building had attracted significant attentions in recent years, traveltime-based methods are still indispensable and should be further developed for improved accuracy and efficiency. Moreover, there are possibilities for new ray theoretical methods that might address the difficulties faced by conventional traveltime-based approaches. My thesis consists of mainly four parts. In the first part, starting from the linearized eikonal equation, I derive and implement a set of linear operators by upwind finite differences. These operators are not only consistent with fast-marching eikonal solver that I use for traveltime computation but also computationally efficient. They are fundamental elements in the numerical implementations of my other works. Next, I investigate feasibility of using the double-square-root eikonal equation for near surface first-break traveltime tomography. Compared with traditional eikonal-based approach, where the gradient in its adjoint-state tomography neglects information along the shot dimension, my method handles all shots together. I show that the double-square-root eikonal equation can be solved efficiently by a causal discretization scheme. The associated adjoint-state tomography is then realized by linearization and upwind finite-differences. My implementation does not need adjoint state as an intermediate parameter for the gradient and therefore the overall cost for one linearization update is relatively inexpensive. Numerical examples demonstrate stable and fast convergence of the proposed method. Then, I develop a strategy for compressing traveltime tables in Kirchhoff depth migration. The method is based on differentiating the eikonal equation in the source position, which can be easily implemented along with the fast-marching method. The resulting eikonal-based traveltime source-derivative relies on solving a version of the linearized eikonal equation, which is carried out by the upwind finite-differences operator. The source-derivative enables an accurate Hermite interpolation. I also show how the method can be straightforwardly integrated in anti-aliasing and Kirchhoff redatuming. Finally, I revisit the classical problem of time-to-depth conversion. In the presence of lateral velocity variations, the conversion requires recovering geometrical spreading of the image rays. I recast the governing ill-posed problem in an optimization framework and solve it iteratively. Several upwind finite-differences linear operators are combined to implement the algorithm. The major advantage of my optimization-based time-to-depth conversion is its numerical stability. Synthetic and field data examples demonstrate practical applicability of the new approach.Show more