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Optimal Grid schemes for Full Waveform Inversion of Fractures

  • Full or part time
    Dr M Hildyard
    Dr Sofya Titarenko
  • Application Deadline
    Thursday, January 31, 2019
  • Funded PhD Project (UK Students Only)
    Funded PhD Project (UK Students Only)

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
Potential for high impact outcome
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.
The postgraduate researcher will work under the supervision of Dr Mark Hildyard and Dr Sofya Titarenko. The project provides a high level of specialist scientific training in: (i) Numerical modelling, particularly seismic wave modelling and interaction with fractures; (ii) Inversion techniques; (iii) Use of cutting-edge supercomputers. Supervision will involve regular supervisor meetings and interaction with researchers on related projects. The successful applicant will be actively encouraged to attend and present work at conferences and to publish papers. The successful applicant will have access to a broad spectrum of training workshops put on by the Faculty from training in numerical modelling, through to managing your degree or preparing for your viva (

Funding Notes

3.5 years, subject to satisfactory progress, to include tuition fees (£4,400 for 2018/19), tax-free stipend (£14,777 for 2018/19), and research training and support grant. Eligibility is UK and those EU normally resident in the UK for at least 3 years immediately preceding the commencement of the PhD.


• Bentham, H.L.M., Morgan, J.V., and Angus, D.A. (2018) Investigating the use of 3-D full-waveform inversion to characterize the host rock at a geological disposal site, Geophysical Journal International, Vol. 215, Issue 3, Dec 2018, pp2035-2046,
• Hildyard, M.W., (2007). Manuel Rocha Medal recipient: Wave interaction with underground openings in fractured rock, Rock Mechanics and Rock Engineering, Vol. 40, pp 531-561.
• Titarenko, S,, and Hildyard, M.W. (2017). “Hybrid multicore/vectorisation technique applied to the elastic wave equation on a staggered grid.” Computer Physics Communications 216 (2017), pp 53-62.

How good is research at University of Leeds in Earth Systems and Environmental Sciences?

FTE Category A staff submitted: 79.20

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