Project description
Permeability, a key control on fluid flow, is central to applications such as energy production, geothermal systems, and carbon storage. Because it is difficult to measure directly at depth, indirect methods are required.
Seismic waves provide such an indirect probe. As they propagate through fluid-saturated rocks, they lose energy (attenuation) and undergo waveform distortion due to frequency-dependent wave speeds (dispersion). These effects are inherently linked and contain information about the physical properties of the medium.
In porous media, attenuation and dispersion arise from wave-induced fluid flow. Pressure gradients at the wavelength scale generate relative motion between the solid frame and pore fluid, as described by Biot’s theory of poroelasticity (Biot, 1962). The resulting wave behaviour depends on parameters such as permeability, fluid viscosity, and elastic moduli.
At smaller scales, additional mechanisms such as squirt flow—fluid movement within pores and cracks—can significantly enhance attenuation, particularly at higher frequencies (Jakobsen et al., 2003). These effects depend strongly on pore geometry and connectivity.
Together, these mechanisms suggest that attenuation may contain information about permeability. This motivates the key question: to what extent can permeability be estimated from wave data?
Such questions are typically addressed using inverse methods, where model parameters are adjusted to match observed data. In practice, this often involves simplified models and robust global optimization techniques, such as simulated annealing (Sen and Stoffa, 2013).
This project investigates how permeability influences attenuation and waveform behaviour, and how these effects can be exploited for parameter estimation in controlled settings.
SCOPE AND APPROACH
The project focuses on physical understanding and parameter estimation in simplified models.
You will first study how key parameters, such as permeability and fluid viscosity, affect wave propagation, with particular emphasis on attenuation, waveform distortion, and the slow P-wave. This will be done through systematic sensitivity analyses in homogeneous and simple layered media.
You will then explore parameter estimation in low-dimensional settings, aiming to identify which parameters can realistically be constrained from wave data. The emphasis will be on simple and robust methods, including grid search, misfit analysis, and global optimization techniques such as simulated annealing (Sen and Stoffa, 2013).
The work builds on an existing frequency-domain solver for the Biot equations (Jakobsen et al., 2025). Time-domain responses are obtained through reconstruction and used for interpretation. Depending on your interests, the project may be extended to more complex settings, such as layered or anisotropic media.
WORK TASKS
Typical tasks include:
* Simulating wave propagation in poroelastic media
* Performing sensitivity studies of key parameters
* Analysing attenuation as a function of frequency
* Investigating how permeability affects waveform behaviour
* Implementing simple parameter estimation methods
* Testing inversion in low-dimensional parameter spaces
LEARNING OUTCOMES
You will gain experience with:
* Wave propagation in porous media (Biot theory)
* Sensitivity analysis and parameter estimation
* Inverse problems in simplified settings
* Numerical modelling of physical systems
* Scientific computing and data fitting
* Optimization methods, including global search techniques
These skills are highly transferable to careers in geophysics, energy, environmental modelling, and computational
science.
WHY THIS PROJECT?
This project combines physics, computation, and applications:
* Exposure to wave-based modelling methods relevant to industry
* Development of computational and modelling skills
* Insight into how inverse problems are solved in practice
* Connection between theoretical concepts and geoscience applications
It provides a realistic introduction to wave-based parameter estimation without requiring large-scale industrial inversion methods.
The project is suitable for master’s students in Geophysics or applied physics. Basic knowledge of mathematics and programming is helpful, but motivation and interest in modelling, wave phenomena, and computational methods are most important.
RELEVANCE
Estimating permeability remains a central challenge in reservoir characterization. While seismic data are widely
available, extracting fluid-related properties from such data is difficult.
This project explores how attenuation—linked to fluid flow in porous media—may provide useful information about permeability. These mechanisms are often even more pronounced at ultrasonic frequencies, offering a link between field-scale observations and laboratory experiments.
The project is connected to ongoing research and is co-supervised by Equinor, ensuring relevance to both academic and industrial applications.
REFERENCES
- Biot, M. A. (1962). Mechanics of deformation and acoustic propagation in porous media. Journal of Applied Physics, 33(4), 1482–1498.
- Carcione, J. M. (2022). Wave Fields in Real Media (4th ed.). Elsevier. Jakobsen, M., Johansen, T. A., & McCann, C. (2003). The acoustic signature of fluid flow in complex porous media.
- Journal of Applied Geophysics, 54(3–4), 219–246. Jakobsen, M., Stokke, J. S., Kumar, K., & Radu, A. F. (2025). Frequency Domain Biot–Allard Equations for Isotropic and Anisotropic Poroelastic Media: Two-field formulations and iterative splitting. Research Square.
- Jakobsen, M., & Carcione, J. M. (2026). Verification of reciprocity in anisotropic poroelastic wave simulation using symmetric Strang splitting. SEG Expanded Abstracts.
- Sen, M. K., & Stoffa, P. L. (2013). Global Optimization Methods in Geophysical Inversion. Cambridge University Press.