Stacking and migration in an/isotropic media

Abstract

Traveltimes and amplitudes of elastic waves are the foundation of the seismic world. Our ultimate goal, detailed knowledge of the structure and material parameters of the subsurface, can only be obtained from the measurement of the time a wave needs to travel from one place to another, as well as the amplitude changes the wave undergoes while propagating through Earth.

In a typical seismic experiment, a wave is excited by a source. Depending on the subsurface properties, the wave is reflected, refracted, and diffracted at interfaces and through changes in the velocity distribution, before it is registered by a network of receivers. The raw output from the experiment then needs to be pre-processed and sorted into common midpoint (CMP) gathers, which are subsequently stacked into simulated zero-offset sections. These provide images of the subsurface; however, the images are distorted because the "positions" of reflectors and diffractors are given not at depth but in time, and furthermore, their lateral positions do not coincide with their real locations.

Therefore, the data need to be "migrated", i.e., the reflectors and diffractors are moved to their correct position and, finally, given at depth. In order to migrate the data, a velocity model is required. Since the trajectory for the previously carried out stack is determined by a velocity parameter, it is possible to use this parameter for the migration. The stacking velocity is not the "real" medium velocity that we are interested in, but it can be used to obtain a less distorted subsurface image that is, however, still a time domain image.

Considerably more effort is required to obtain a depth-migrated image. Here, the "true" velocity model is needed, and traveltimes are computed by numerical means, e.g., ray tracing. Usually, the initial model has to be refined through several migration steps, each of which is followed by a velocity analysis and update.

Finally, once a velocity model has been determined that is consistent with the data, a true-amplitude migration can be performed. Only with this method, it is possible to gain not only information about the structure and velocities, but also the reflection strengths. The latter can be very important for reservoir characterisation or a means to constrain shear velocities if only a PP survey was carried out.

Stacking and migration are powerful methods. It is not surprising that they are also very costly in terms of computer time and storage. Therefore, a lot of work has been invested in developing efficient strategies. More sophisticated stacking methods have been introduced as well as techniques to reduce the computational effort in migration, particularly of the true-amplitude type. In this thesis, I catalogue the main results of my work over the past fifteen years.

The thesis is structured into three parts. Beginning with the introduction of a hyperbolic traveltime interpolation method that is valid for media of arbitrary heterogeneity, anisotropy, and wavetype, I set a foundation for the subsequent chapters. The interpolation method is closely-related to multiparameter stacking formulations, which I investigate before introducing a new, non-hyperbolic operator, the i-CRS that is applicable to heterogeneous and anisotropic media and leads to better results than the classic stacking methods.

In the second part, I dedicate a chapter to the determination of geometrical spreading, a measure for seismic amplitudes. I suggest a method to obtain the spreading directly from traveltime information. As for the traveltimes in the first part, the spreading computation can be carried out in all types of media, including anisotropy. Since the geometrical spreading is a key ingredient for true-amplitude migration, I have developed a migration method that requires only traveltimes on coarse grids for the computation of all auxiliary quantities needed for the migration. This traveltime-based strategy has significant advantages over conventional migration methods, in particular if anisotropy has to be considered.

I demonstrate the superiority of the new stacking and migration methods with numerous meaningful examples, beginning with simple generic isotropic and anisotropic models in order to evaluate the accuracy. Application to complex media and field data shows that the new migration technique leads to equivalent results as obtained by standard methods, but with highly-increased efficiency and significantly lower demands on the input velocity model. This is especially true if seismic anisotropy has to be considered. The new stacking operator results in a highly-improved image in comparison to classic stacks. The reflector continuity and, particularly, the resolution of small structures like diffractors are significantly enhanced if the new i-CRS operator is applied.

Finally, a third part supplies an appendix with useful background information that would have been out of proportion in the main text.