The influence of elastic anisotropy on seismic wave propagation is often neglected for the sake of simplicity. However, ignoring anisotropy may lead to significant errors in the processing of seismic data and ultimately in a poor image of the subsurface. This is especially true in wide-aperture Vertical Seismic Profiles where waves travel both vertically and horizontally. Anisotropy has been neglected in wavefront construction methods of seismic ray-tracing until Gibson (2000), who showed they are powerful tools to simulate seismic wave propagation in three-dimensional anisotropic subsurface models. The code is currently under development using a C++ object oriented programming approach because it provides high flexibility in the design of new components and facilitates debugging and maintenance of a complex algorithm. So far, the code was used to simulate propagation in homogeneous or simple heterogeneous anisotropic velocity models mainly designed for testing purposes. In particular, it has never been applied to simulate a field dataset. We propose here an analytical method involving little algebra and that allows the design of realistic heterogeneous anisotropic models using the C++ object oriented programming approach. The new model class can model smooth multi-layered subsurface with gradients or models with many dip variations. It has been used to model first arrival times of a wide-aperture VSP dataset from the Gulf of Mexico to estimate the amount of anisotropy. The proposed velocity model is transversely isotropic. The anisotropy is constant throughout the model and is defined via Thomsen's parameters. Values in the final model are epsilon = 0.055 and delta = -0.115. The model is compatible with the a priori knowledge of the local geology and reduces the RMS average time difference between measured and computed travel times by 51% in comparison to the initial isotropic model. These values are realistic and are similar to other measurements of anisotropy in the Gulf of Mexico.

The influence of elastic anisotropy on seismic wave propagation is often neglected for the sake of simplicity. However, ignoring anisotropy may lead to significant errors in the processing of seismic data and ultimately in a poor image of the subsurface. This is especially true in wide-aperture Vertical Seismic Profiles where waves travel both vertically and horizontally. Anisotropy has been neglected in wavefront construction methods of seismic ray-tracing until Gibson (2000), who showed they are powerful tools to simulate seismic wave propagation in three-dimensional anisotropic subsurface models. The code is currently under development using a C++ object oriented programming approach because it provides high flexibility in the design of new components and facilitates debugging and maintenance of a complex algorithm. So far, the code was used to simulate propagation in homogeneous or simple heterogeneous anisotropic velocity models mainly designed for testing purposes. In particular, it has never been applied to simulate a field dataset. We propose here an analytical method involving little algebra and that allows the design of realistic heterogeneous anisotropic models using the C++ object oriented programming approach. The new model class can model smooth multi-layered subsurface with gradients or models with many dip variations. It has been used to model first arrival times of a wide-aperture VSP dataset from the Gulf of Mexico to estimate the amount of anisotropy. The proposed velocity model is transversely isotropic. The anisotropy is constant throughout the model and is defined via Thomsen's parameters. Values in the final model are epsilon = 0.055 and delta = -0.115. The model is compatible with the a priori knowledge of the local geology and reduces the RMS average time difference between measured and computed travel times by 51% in comparison to the initial isotropic model. These values are realistic and are similar to other measurements of anisotropy in the Gulf of Mexico.

Understanding and modeling seismic wave propagation is important in regional and exploration seismology. Ray tracing is a powerful and popular method for this purpose. Wavefront construction (WFC) method handles wavefronts instead of individual rays, thereby controlling proper ray density on the wavefront. By adaptively controlling rays over a wavefront, it efficiently models wave propagation. Algorithms for a quasi-P wave wavefront construction method and a new coordinate system used to generate wavefront construction mesh are proposed and tested for numerical properties and modeling capabilities. Traveltimes, amplitudes, and other parameters, which can be used for seismic imaging such as migrations and synthetic seismograms, are computed from the wavefront construction method. Modeling with wavefront construction code is applied to anisotropic media as well as isotropic media. Synthetic seismograms are computed using the wavefront construction method as a new way of generating synthetics. To incorporate layered velocity models, the model based interpolation (MBI) ray tracing method, which is designed to take advantage of the wavefront construction method as well as conventional ray tracing methods, is proposed and experimental codes are developed for it. Many wavefront construction codes are limited to smoothed velocity models for handling complicated problems in layered velocity models and the conventional ray tracing methods suffer from the inability to control ray density during wave propagation. By interpolating the wavefront near model boundaries, it is possible to handle the layered velocity model as well as overcome ray density control problems in conventional methods. The test results revealed this new method can be an effective modeling tool for accurate and effective computing.