Project description
This project is based on the concept of real media (Carcione, 2022), where realistic geological features are incorporated into physically consistent wave propagation models. In this context, fracture-induced anisotropy provides a well-defined and practically important framework for studying seismic responses in reservoirs.
The project emphasizes the combined use of accurate numerical methods and rock-physics-based parameterization. In particular, anisotropic effective medium properties will be derived from rock physics models developed by Jakobsen et al. (2003), providing a direct link between microstructure and seismic observables. Related work on waveform inversion in fracture-induced anisotropic media has been carried out in earlier studies (Erstad, 2020).
OBJECTIVES
The main objective is to investigate how fracture-induced anisotropy influences seismic wave propagation and observable seismic signatures. This includes: (1) Study seismic wave propagation in anisotropic media representing fractured reservoirs. (2) Analyze azimuthal and amplitude variations caused by aligned fractures. (3) Compare different numerical methods for wave propagation in fractured anisotropic media. (4) Understand the relationship between fracture properties and seismic response.
METHODOLOGY
The project involves numerical simulation of seismic wave propagation in anisotropic media with a primary focus on the pseudo-spectral method. This method offers high accuracy for solving the elastic wave equation and is well suited for modeling wave propagation in complex media (Carcione et al., 2002; Igel, 2017)
To assess its performance and practical applicability, the pseudo-spectral method will be systematically compared with a finite-difference time-domain (FDTD) method implemented on a staggered grid (Igel, 2017). The comparison will focus on accuracy, numerical dispersion, computational efficiency, and stability in anisotropic media.
Fractured rocks will be represented using anisotropic effective medium models. The elastic stiffness parameters defining the anisotropy will be estimated using rock-physics models developed by Jakobsen et al. (2003). These models relate fracture properties such as density, orientation, and compliance to macroscopic elastic behavior.
The focus will be on elastic wave propagation, allowing a clear and robust analysis of fracture-induced anisotropy without the added complexity of full viscoelastic modeling. The analysis will include wavefront propagation and travel times, amplitude variations with offset and azimuth (AVO/AVAz), and polarization effects.
WORK TASKS
(1) Implement or utilize a pseudo-spectral method for elastic wave propagation. (2) Implement or utilize a finitedifference time-domain method on a staggered grid. (3) Perform a systematic comparison of the two methods in isotropic and anisotropic media. (4) Construct anisotropic models of fractured reservoirs using effective medium parameters derived from Jakobsen-type rock physics models. (5) Simulate wave propagation and analyze azimuthal variations in amplitudes and travel times. (6) Compare numerical results with theoretical predictions for anisotropic media. (7) Interpret results in terms of fracture properties and seismic signatures.
OPTIONAL EXTENSIONS
- Introduction of simple attenuation models Investigation of fluid effects on seismic attenuation and dispersion.
- Coupling between anisotropy and attenuation in fractured media.
INDUSTRY RELEVANCE
Fracture-induced anisotropy plays a key role in AVO and AVAz analysis, fracture characterization in hydrocarbon reservoirs, and monitoring of fractured and unconventional reservoirs. The collaboration with Equinor ensures relevance to real industrial challenges in seismic interpretation and reservoir characterization.
EXPECTED OUTCOMES
- Insight into seismic wave propagation in anisotropic media
- Experience with advanced numerical modeling methods
- Understanding of the link between rock physics and seismic observables
- The scope can be adapted to the student’s background and interests.
The project is suitable for students interested in numerical modeling and programming in MATLAB or Python.
REFERENCES
- Carcione, J. M. (2022). Wave Fields in Real Media. Elsevier.
- Carcione, J. M., Herman, G. C., & ten Kroode, A. P. E. (2002). Seismic modeling. Geophysics, 67(4), 1304–1325.
- Erstad, J. H. (2020). Elastic Full-Waveform Inversion in the Presence of Fracture-Induced Anisotropy. MSc Thesis, University of Bergen
- Jakobsen, M., Johansen, T. A., & McCann, C. (2003). The acoustic signature of fluid flow in complex porous media. Journal of Applied Geophysics.
- Igel, H. (2016/2017). Computational Seismology: A Practical Introduction. Oxford University Press.