Deep Learning Methods for Probabilistic Seismic Inversion and Interferometry. Mathematics NERC GW4+ DTP PhD Studentship. Ref: 3126

About the award

This project is one of a number that are in competition for funding from the NERC Great Western Four+ Doctoral Training Partnership (GW4+ DTP).  The GW4+ DTP consists of the Great Western Four alliance of the University of Bath, University of Bristol, Cardiff University and the University of Exeter plus six Research Organisation partners:  British Antarctic Survey, British Geological Survey, Centre for Ecology and Hydrology, the Met Office, the Natural History Museum and Plymouth Marine Laboratory.  The partnership aims to provide a broad training in earth and environmental sciences, designed to train tomorrow’s leaders in earth and environmental science. For further details about the programme please see

The Studentship will be awarded on the basis of merit and will commence in September 2018.  For eligible students the award will provide funding for a stipend which is currently £14,553 per annum (2017/2018), research costs and UK/EU tuition fees at Research Council UK rates for 42 months (3.5 years) for full-time students, pro rata for part-time students.

Location: University of Exeter, Penryn Campus, Penryn, Cornwall, TR10 9FE

Main Supervisor:  Dr. Saptarshi Das, (Department of Mathematics, University of Exeter)
Co-Supervisor: Dr. James Hickey, (Camborne School of Mines, University of Exeter)

Project Description:
In the present day’s practice in hydrocarbon exploration industries, given some array of seismic traces, determination of the subsurface and source properties are commonly known as the full-waveform inversion (FWI) and seismic source inversion respectively. Usually real seismic responses are buried under significant amount of ambient noise along with other difficulties in the inversion like limited number of surface receivers’ data etc. Both the FWI and source inversion are important aspects of reservoir or subsurface monitoring to understand the changing material properties and stress-fields of large-scale geological models. Such inverse problems in some typical Monte Carlo simulation framework, would need thousands of forward wave-propagation simulations on large heterogeneous geological models which takes significant computing time and resources. Storage, management and processing of such large volume of real and synthetic seismic data in a probabilistic inversion process is a great challenge to both industrial and academic researchers.


Image 1 (left): Image 2 (right):
Example of a 3D heterogeneous elastic geological model Synthetic seismograms for random seismic events in the subsurface


Project Aims and Methods:
This project will explore advanced statistical signal processing and machine learning approaches in particular deep-learning and Bayesian inference for parameter estimation and probabilistic inversion of large-scale geological models. The aim of this project is to reduce the computational time utilising the recent advancements in deep neural networks to approximate the physical data generation process i.e. the seismic wave simulation here. The concepts from seismic interferometry will be used for turning highly noisy traces into useful interpretable signals using various correlation-based methods. Quantification of the uncertainties in such inverse problems in terms of both seismic source properties and unknown elastic models (density, compressional and shear wave velocity) are a difficult industrial problem. The traditional inverse problems rely on the travel-time calculation between sources and receivers. However, uncertainties in the model can make these estimates highly erroneous and alternatively a full seismic-wave based inversion will be applied for improved imaging, although being computationally challenging. The project will also explore the effect of fusing 3-component geophone recordings apart from the pressure measurements by hydrophone in a marine environment. The traditional inversion or seismic imaging methods involve series of heuristic filtering steps that can be more optimally selected using a deep-learning based expert system.

The candidate will have a good undergraduate or master’s degree in any of the disciplines – Mathematics/Statistics, Computer Science, Physics, Engineering, Geology or Earth-sciences. Good analytical, computational skills and in particular, some prior experience in Matlab/Python/R programming is necessary. Some previous research experience in either data analytics, mathematical/statistical computing is also desirable. Any experience in high-performance computing will be highly advantageous for this project.

The student will get the required training to deliver the project and recommended to attend some of the Mathematics departmental modules like scientific computing, data analysis and machine learning and advanced statistical modelling etc. The student will exchange his research finding and methods to the peers and other researchers through regular presentations. The project is inter-disciplinary, so the student would get the opportunity to learn and discuss with other researchers both from Mathematics and Camborne School of Mines. It is expected that the student will also strengthen the existing collaboration of the first supervisor with the Oil and Gas industries.


Igel, Heiner. Computational seismology: a practical introduction. Oxford University Press, 2017.

Avseth, Per, Tapan Mukerji, and Gary Mavko. Quantitative seismic interpretation: Applying rock physics tools to reduce interpretation risk. Cambridge university press, 2010.

Schuster, Gerard Thomas. Seismic interferometry. Vol. 1. Cambridge: Cambridge University Press, 2009.

Schuster, Gerard T. Seismic inversion. Vol. 20. SEG Books, 2017.

Tarantola, Albert. Inverse problem theory and methods for model parameter estimation. Vol. 89. siam, 2005.

Caers, Jef. Modeling uncertainty in the earth sciences. John Wiley & Sons, 2011.

Menke, William. Geophysical data analysis: discrete inverse theory: MATLAB edition. Vol. 45. Academic press, 2012.

Sheriff, Robert E., and Lloyd P. Geldart. Exploration seismology. Cambridge university press, 1995.

Pyrcz, Michael J., and Clayton V. Deutsch. Geostatistical reservoir modeling. Oxford university press, 2014.

Das, Saptarshi, Xi Chen, and Michael P. Hobson. "Fast GPU-Based Seismogram Simulation from Microseismic Events in Marine Environments Using Heterogeneous Velocity Models." IEEE Transactions on Computational Imaging 3, no. 2 (2017): 316-329.

Araya-Polo, Mauricio, Joseph Jennings, Amir Adler, and Taylor Dahlke. "Deep-learning tomography." The Leading Edge 37, no. 1 (2018): 58-66.

Lewis, Winston, and Denes Vigh. "Deep learning prior models from seismic images for full-waveform inversion." In 2017 SEG International Exposition and Annual Meeting. Society of Exploration Geophysicists, 2017.

Yilmaz, Özdoğan. Seismic data analysis. Vol. 1. Tulsa: Society of Exploration Geophysicists, 2001.

Curtis, Andrew, Peter Gerstoft, Haruo Sato, Roel Snieder, and Kees Wapenaar. "Seismic interferometry—Turning noise into signal." The Leading Edge 25, no. 9 (2006): 1082-1092.

Virieux, J., A. Asnaashari, R. Brossier, L. Métivier, A. Ribodetti, W. Zhou, V. Grechka, and K. Wapenaar. "6. An introduction to full waveform inversion." Encyclopedia of Exploration Geophysics (2014): R1-1.


Entry requirements:       
Applicants should have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK.   Applicants with a Lower Second Class degree will be considered if they also have Master’s degree.  Applicants with a minimum of Upper Second Class degree and significant relevant non-academic experience are encouraged to apply.

All applicants would need to meet our English language requirements by the start of the  project

Applicants who are classed as International for tuition fee purposes are not eligible for funding.



Application deadline:8th May 2018
Value:£14,553 per annum for 2017-18
Duration of award:per year
Contact: PGR

How to apply

To apply for this funded studentship, please click and follow the 'Apply Now' button on this webpage.

During the application process you will be asked to upload several documents.  Please note our preferred format is PDF, each file named with your surname and the name of the document, eg. “Smith – CV.pdf”, “Smith – Cover Letter.pdf”, “Smith – Transcript.pdf”.

•       CV
•       Letter of application outlining your academic interests, prior research experience and reasons for wishing to
        undertake the project.
•       Transcript(s) giving full details of subjects studied and grades/marks obtained.  This should be an interim transcript
        if you are still studying.
•       If you are not a national of a majority English-speaking country you will need to submit evidence of your current
        proficiency in English.
You will be asked to name 2 referees as part of the application process however we will not contact these people until the shortlisting stage. Your referees should not be from the prospective supervisory team.

The closing date for applications is midnight on 8th May 2018.  Interviews will be held at the University of Exeter in the week commencing 21st May

If you have any general enquiries about the application process please email Project-specific queries should be directed to the supervisor.

During the application process, the University may need to make certain disclosures of your personal data to third parties to be able to administer your application, carry out interviews and select candidates.  These are not limited to, but may include disclosures to:
• the selection panel and/or management board or equivalent of the relevant programme, which is likely to include staff from one or more other HEIs;
• administrative staff at one or more other HEIs participating in the relevant programme.
Such disclosures will always be kept to the minimum amount of personal data required for the specific purpose. Your sensitive personal data (relating to disability and race/ethnicity) will not be disclosed without your explicit consent.