Wavefield tomography using image-warping

Abstract

The main objective of this thesis is to study new methods for estimating the macro velocity model, which controls the wave kinematics, in the context of reflection seismology. Migration velocity analysis evaluates the quality of the velocity model used for imaging seismic data by comparing images of the subsurface structures as a function of extension parameters, such as offset, reflection angle, or shot-index. The angle domain has proved to be a suitable domain for velocity analysis because of its robustness against the noise introduced by the migration operator and against the ambiguities due to complex wave propagation in the subsurface. Nonetheless, angle gathers require an extra computational effort especially in full azimuth 3D scenarios. On the other hand, most migration algorithms naturally process the reflection data and output images in the shot-domain, which is usually regarded as a poor option for velocity analysis. The ability to extract reliable information about the velocity model from single-experiment images has value not only for the construction of macro velocity models for imaging but also for the regularization of high-resolution data-fitting techniques in a way that is compliant with the physics of wave propagation. In this thesis, I investigate how to make shot-domain velocity analysis algorithms more robust by exploiting the coherency of the structural features in the migrated domain and using the concept of image-warping. I link the difference between two migrated images with the concept of image-warping and show that with image-warping, one can obtain an approximation of the image difference that is less sensitive to the distance between the shot points. I use the image-warping approximation of the standard image difference as the input of a linearized inversion scheme to reconstruct the velocity anomaly in the migration model. The linearized inversion is based on one-way migration algorithms and relies on a series of assumptions about the strength of the perturbation in the wavefields and in the model. In order to remove these assumptions, I use the insight gained about the relationship between the orientation of the structural features in the image and the warping vector field to design an optimization problem that does not involve any up-front linearization of the propagation operator. Using adjoint-state techniques, I was able to compute the gradient of the objective function and thus implement a two-way wavefield tomography scheme. The basic building block of my tomography algorithm is the measure of the apparent displacement between two nearby shot gathers along the normal direction to the imaged reflector. Because no stacking of partial images is needed to obtain the measure of velocity error, my approach is intrinsically shot-based. This feature of the error measure and inversion scheme allows one to reconstruct errors in the migration velocity from a minimum number of experiments. I show how this approach can reconstruct, using a single experiment, the anomaly in a hydrocarbon reservoir that undergoes depletion because of production. The measure of local apparent displacements with penalized local correlations proves to be effective in scenarios where the geometry of the reflectors is simple and the orientation of the structural features can be unambiguously computed. Moreover, penalized local correlations are particularly sensitive to the shot distance for shallow interfaces and may suffer from crosstalk due to other reflectors falling in the same correlation window. Following these considerations and using the relationship between image difference and image-warping, I show that image-warping can be used to modify the expression of the adjoint sources for standard differential semblance optimization to make the method robust against cycle skipping in the image domain even with strong errors in the velocity model.