Three Dimensional Elastic Full Waveform Inversion

Abstract

The full waveform inversion (FWI) method is a technique for estimating subsurface elastic parameters using inverse theory. FWI is formulated as an optimization problem that seeks to minimize the dissimilarities between field data and synthetic data. The prob- lem is solved by starting from an initial model which is then iteratively improved using linear approximations to the non-linear inverse problem. At the core of the method is the assumption that field data can be approximated by a numerical solution of the wave equation. The interaction between heterogeneous elastic media and the waves is complex and includes mode-conversions, pre- and post-critical reflections, transmissions, refrac- tions, multiple reflections and surface waves. The choice of the proper wave equation and physical model is thus important in order to accurately honor the complexity of the observed field data. In exploration geophysics, a classical assumption has been to consider the subsur- face as a two-dimensional acoustic medium. The aim of this thesis is to extend the FWI method to three dimensions using isotropic elastic wave theory, in addition to apply the method on time-lapse seismic data to reveal time-lapse changes directly in the elastic parameters. From a physical point of view, the elastic assumption is more correct as it includes, for example, important phenomena like shear waves, that are not predicted by the acoustic assumption, but that are often visible in seismic field data. Extending the FWI from two to three dimensions is complicated due to the increase in computer resources needed to solve the inverse problem. The content of the thesis is as follows: The inversion software that is developed is briefly described in the beginning of the text. A local migration regularization is in- troduced and tested in two dimensions using synthetic and field data. The purpose of the local migration regularization is to reduce time-lapse artifacts in the inverted elastic time-lapse parameters. A three dimensional wave field reconstruction method based on recording the particle velocity values at the boundaries is introduced and tested. This method greatly reduces the storage requirements in performing elastic FWI in three di- mensions. Different approaches for performing three-dimensional elastic time-lapse FWI method is then tested using synthetic multi-component ocean-bottom cable seismic data. The three dimensional elastic FWI method is then applied on field data from the Sleipner area in the North Sea. The first application demonstrates the use of the elastic FWI method to improve the elastic models of the subsurface prior the injection of the CO 2 . In the second application elastic FWI is used to reveal time-lapse changes in the subsur- face after ten years of CO 2 injection. The inverted elastic models are used to improve the seismic images and to understand the migration pathways of the injected gas in the subsurface.