Optimal Grid schemes for Full Waveform Inversion of Fractures (EPSRC DTP)


Dr Mark Hildyard and Dr Sofya Titarenko

Contact Dr Mark Hildyard (M.Hildyard@leeds.ac.uk) to discuss this project further informally.

Project description

Elastic wave interaction with individual and multiple fractures can be accurately modelled through numerical schemes. However, even for forward modelling alone this can require long runtimes. When we perform inversion we introduce an extra loop where these forward models are run iteratively until we converge to a possible solution.

Such inversions of simpler models (i.e. without fracturing) are currently extremely computationally challenging. We are developing methods for full waveform inversion (FWI) of fractures. For us to succeed in this goal we need to combine highly efficient grid schemes for wave propagation (comparable to those currently used in full waveform inversion) with efficient and sufficiently accurate representations of fracturing.

Combining these two needs is challenging. In our current inversion efforts we make use of a staggered grid scheme considered very efficient for the propagation of seismic waves. “Explicit” and “effective” representations of fracturing are implemented within this mesh.

The scheme has also been shown to be highly parallelisable on current multi-core CPU and GPU architectures readily exploiting efficiency gains from vectorisation and multiprocessing (Titarenko and Hildyard, 2016). However, the scheme is not ideal for fully general fracture zones.

This PhD will evaluate a variety of grid schemes with the aim of identifying the “optimal” grid schemes for this purpose. These would include existing grid schemes from literature (e.g. alternative staggered grids, hexahedral elements with hourglass control, tetrahedral elements) - provided these could be recast in a sufficiently computationally efficient way. Alternatively, completely novel schemes may be found.

Ultimately the decision on a scheme being optimal depends on it being (i) very efficient for modelling seismic waves; (ii) suitable for efficient and accurate explicit representation of fracturing; (iii) suitable for efficient and accurate effective representation of fracturing; (iv) suitable for fully exploiting parallelism offered through vectorisation and multiprocessing available on current multicore architectures (CPU and GPU).

This work has the potential to significantly influence future directions in full waveform inversion. FWI is currently a massive growth area within the geophysics industry particularly for exploration of resources. Including fracturing in this version is a major challenge but a goal which would create the capacity to interpret fault and fracture zones. Such fracture inversion is hugely desirable for other industries whether in subterranean excavations or in non-destructive testing in the built environment. Such inversion capability is also highly desirable for ultrasonic measurements in laboratory experiments.


You will: 1. develop your understanding of the physics and modelling of seismic wave interaction with fractures. 2. investigate and develop different numerical methods and grid schemes 3. develop different representations of fracturing for these schemes 4. develop understanding of and quantify the efficiency of these schemes 5. develop optimisations for modern processor architectures (CPU and GPU) 6. gain an appreciation for the full waveform inversion process and its potential in industry

Key benefits

This work is novel, with potential national and international impact, and topical, due to the current developments in full waveform inversion. Useful results will receive long-term academic and industry interest.

Entry requirements

Applications are invited from candidates with or expecting a minimum of a UK upper second class honours degree (2:1) or equivalent, and/or a Master's degree in the relevant subject area.

If English is not your first language, you must provide evidence that you meet the University’s minimum English Language requirements.

How to apply

Formal applications for research degree study should be made online through the university's website.

If you require any further information, please contact the Graduate School Office e: apply-phd@see.leeds.ac.uk, or t: +44 (0)113 343 1634.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.