Anisotropic Modelling and Full Waveform Inversion

Project description
Motivation (background):
Anisotropy is an important concept in geosciences. Many important minerals and rocks, including sedimentary rocks such as clay and shale, are anisotropic, and in some cases the anisotropy is quite strong. Morever, the anisotropic properties concerns a number of physical quantities related to rocks, including the elastic parameters, electrical conductivity and permeability. Another feature related to anisotropy is that materials may be isotropic on a certain length scale, but anisotropic on another length scale. A good example of this is a rock which consists of many thin layers. Thus both this type of anisotropy as well as the intrinsic anisotropy mentioned before are of importance in exploration and CO2 monitoring. The goal of this project is to develop a new method to determine elastic anisotropic properties.

Hypothesis (scientific problem):
Processing of seismic waves typically is done by assuming that the waves propagate through an acoustic or elastic isotropic medium. In this case the processing very roughly consists of four processing steps: 1. pre-processing, 2. multiple attenuation, 3. velocity analysis and 4. imaging. The complexity and computational expense of these steps roughly increases with each step. The last two steps, velocity analysis and imaging can be iterated and also combined with full waveform inversion (FWI). FWI increases the resolution but also the complexity and computation time. Moreover, the velocity analysis in practice already yields an anisotropic rather than an acoustic/isotropic velocity model. Therefore, in theory, both the background model as well as the inverted model need to be anisotropic in practice.

Test (work):
A crucial component of both imaging and FWI is the underlying forward modeling method. In acoustic and elastic isotropic media this may be either a fully numerical method (in practice finite difference modeling is the most popular of such methods) or ray tracing (which is approximate, but considerably faster than finite difference modeling, and quite accurate at high frequencies). The difference in computation speed increases significantly in anisotropic media. Therefore, in this thesis the focus will be on using (an)isotropic ray tracing through the background model. This will then also enable the efficient computation of waveforms using the elastic ray-Born approximation with an anisotropic perturbation. Various representations and types of anisotropy will be investigated in this project. Finally, the computation of elastic ray-Born synthetics will enable the testing of anisotropic imaging and FWI, on models that specifically, are of interest for CO2 monitoring.

Proposed course plan during the master's degree (60 ECTS):
GEOV276 (10sp)
GEOV274 (10sp)
MAT212 (10sp)
GEOV300 (5sp)
Z-GEOV (Kiel course) (5sp)
GEOV375 (10sp)
GEOV352 (5sp)
AG335 (10sp)