Institute of Geophysics and Tectonics (IGT) PhD Projects

Novel representations of explicit angled fractures for investigating seismic wave behaviour in fractured media

Supervisors: Dr Mark Hildyard, Dr Sebastion Rost and Professor Graham Stuart

The study of fractured media remains of fundamental importance to a broad range of research areas in earth science - whether to understand structure of the upper crust, fault zones, near-field earthquake data, or for locating and understanding the detailed structure of fracture zones for industry purposes such as quantifying oil reserves or evaluating potential for nuclear waste leakage. Traditional inversions of velocity structure simply do not go far enough to satisfy these needs. Instead we need to interpret true fracture sizes, fracture density, fracture spacing, fluid content, and actual fracture positions. This requires new technologies in forward modelling, and this project aims to enhance the numerical capability to accurately model full dynamic interaction of seismic waves with fractures. Hildyard (2007) achieved considerable success in modelling detailed wave behaviour due to large numbers of fractures using explicit representations of fractures. Critical limitations however were its confinement to orthogonal, grid-aligned fractures. This project will therefore investigate a range of numerical options for implementing generalised fracturing, including equivalent materials, grid mapping of orthogonal explicit fractures, and novel grid designs. The methods will be evaluated by testing their accuracy at representing real experimental data, and on their efficiency and usefulness for representing sufficiently large numbers of fractures with a wide range of fracture scales. A genuine breakthrough will be of much wider impact, influencing capabilities for research in the fields of geophysics, rock mechanics, and geomechanics, and enabling investigations of questions of both scientific and industrial interest.

A key aspect of this project will be discovering methods which can be implemented within the staggered grid finite difference method used for elastodynamic wave propagation. Figure 1 illustrates a unit cell within the staggered grid where different components of the stress tensor and velocity vector are solved for at distributed positions in space. The result is an efficient and accurate method which is very widely used in seismological applications. Hildyard and Young (2002) show a method for implementing accurate orthogonally aligned explicit fractures within this grid.

However Hildyard (2007), also identifies some of the complexities of extending the method to more generalised fracturing. Broadly speaking, the options seem to be to consider grid mappings, to explore novel grids with coincident grid components, to couple different grids, or to explore implementations of effective media.