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Funding and scholarships for students

Award details

Bayesian Machine Learning and Sampling Methods for Geophysical Inversion using Large Scale Seismic and Reservoir Simulations, NERC GW4+ DTP PhD studentship for 2022 Entry, PhD in Mathematics Ref: 4257

About the award


Lead Supervisor

Dr Saptarshi Das, Department of Mathematics, University of Exeter, Penryn Campus, Cornwall

Additional Supervisors

Dr Xi Chen, Department of Computer Science, University of Bath

Location: Penryn Campus, University of Exeter, Penryn, Cornwall

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 five Research Organisation partners:  British Antarctic Survey, British Geological Survey, Centre for Ecology and Hydrology,  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

For eligible successful applicants, the studentships comprises:

  • An stipend for 3.5 years (currently £15,609 p.a. for 2021/22) in line with UK Research and Innovation rates
  • Payment of university tuition fees;
  • A research budget of £11,000 for an international conference, lab, field and research expenses;
  • A training budget of £3,250 for specialist training courses and expenses


Example of a 3D heterogeneous elastic geological model

Project details

Project Background

In earth science for hydrocarbon and mineral exploration, determining subsurface and source properties from seismic traces are challenging tasks, commonly known as the full-waveform inversion (FWI) and seismic source inversion, respectively. Often, seismic data are buried under significant amounts of ambient noise and combined with uncertainties in the geological model which complicates the inversion process. Both the FWI and source inversion are important aspects of subsurface monitoring to constrain changing material properties and evolving stress-fields of large geological models. Such inverse problems usually employ Monte Carlo simulation frameworks, requiring thousands of forward simulations on large complex geological models, which demand significant computing time and resource. This project will aim to accelerate this process using recent advances in Bayesian inference and machine learning, especially utilizing deep learning and deep Gaussian process models. Stress accumulation and fluid flow movement monitoring in reservoir needs complex geophysical and petrophysical simulations using known velocity models, permeability, permittivity etc. Efficient management and processing of such large volumes of synthetic seismic and petrophysical data in a probabilistic geophysical inversion, imaging process, history matching and uncertainty quantification is an open challenge, with outcomes that will benefit both industrial and academic research.


Synthetic seismograms for random microseismic events

Project Aims and Methods

This project will explore advanced signal/image processing, machine learning approaches, in particular, deep-learning and Bayesian inference for parameter/uncertainty estimation and probabilistic inversion of large-scale geological models fusing geophysical/seismic and petrophysical data. Here, the aim is to reduce computational time utilising the recent advancements in deep neural networks and deep Gaussian processes to approximate the physical data generation process, i.e. the seismic wave propagation and reservoir fluid flow simulations. The concepts from seismic interferometry will also be used for turning highly noisy traces into useful interpretable signals using various correlation-based methods. Quantification of the uncertainties in such geophysical inverse problems in terms of both seismic source properties and unknown elastic geological models (density, compressional and shear wave velocity) and petrophysical parameters like permeability, porosity etc. is a complex problem. Geophysical inverse problems rely on the travel-time calculation between sources and receivers. However, uncertainties in the velocity model can make these estimates highly erroneous. Alternatively, a full seismic wave based inversion can be attempted for improved imaging, albeit being computationally challenging. The project will also explore the inversion results of 3-component geophone recordings apart from pressure measurements by hydrophones in a marine environment. The traditional inversion or seismic imaging methods involve a series of heuristic filtering steps that can be more optimally selected using a deep machine learning based expert system.

Candidate requirements

The candidate will have a good master’s degree in any of the following disciplines – Mathematics/Statistics, Computer Science, Physics, Engineering, Geophysics 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 big data analytics, large scale scientific computing is also desirable. Prior experience on high-performance computing system especially on GPUs, clouds will be advantageous.

Project partners 

The student will be based in the University of Exeter, Penryn Campus and will also closely collaborate with the University of Bath. This will be in the form of sharing methods for analysing seismic and petrophysical datasets, estimating geological model parameters and uncertainties, communicating the research findings with the researchers in Bath, develop better understanding and interpretations of seismic, geophysical and petrophysical data analysis in a broader industrial/academic context, and writing collaborative publications.


The student will receive the required training to pursue fundamental and applied research in this project on geophysics, petrophysics, seismology and will have the opportunity to further develop Mathematical and computational skills. The student will exchange research findings and methods with their peers and other researchers through regular seminars and conference presentations. The project is inter-disciplinary in nature, so the student will have the opportunity to learn and discuss with other researchers both from mathematical and computational geoscience. It is expected that the student will also strengthen the existing collaborations of the supervisors with the Oil and Gas, Geoscience/mining industries, and other stakeholders. 

Background reading and references

[1] Tarantola, A., 2005. Inverse problem theory and methods for model parameter estimation (Vol. 89). SIAM.

[2] Das, S., Chen, X. and Hobson, M.P., 2017. Fast GPU-Based Seismogram Simulation from Microseismic Events in Marine Environments Using Heterogeneous Velocity Models. IEEE Transactions on Computational Imaging, 3(2), pp.316-329.

[3] Das, S., Chen, X., Hobson, M.P., Phadke, S., van Beest, B., Goudswaard, J. and Hohl, D., 2018. Surrogate regression modelling for fast seismogram generation and detection of microseismic events in heterogeneous velocity models. Geophysical Journal International, 215(2), pp.1257-1290.

[4] Das, S., Hobson, M.P., Feroz, F., Chen, X., Phadke, S., Goudswaard, J. and Hohl, D., 2021. Microseismic event detection in large heterogeneous velocity models using Bayesian multimodal nested sampling. Data-Centric Engineering, 2.

[5] Ramirez, B.A., Gelderblom, P.P., Eales, A.D., Chen, X., Hobson, M.P. and Esler, K., 2017, November. Sampling from the posterior in reservoir simulation. In Abu Dhabi International Petroleum Exhibition & Conference. OnePetro.

[6] Schuster, G.T., 2017. Seismic inversion. Society of Exploration Geophysicists.

[7] Araya-Polo, M., Jennings, J., Adler, A. and Dahlke, T., 2018. Deep-learning tomography. The Leading Edge, 37(1), pp.58-66.

[8] Yilmaz, Ö., 2001. Seismic data analysis (Vol. 1, pp. 74170-2740). Tulsa, OK: Society of Exploration Geophysicists.

[9] Schuster, G., 2009. Seismic interferometry. Cambridge University Press.

[10] Huang, L., Dong, X. and Clee, T.E., 2017. A scalable deep learning platform for identifying geologic features from seismic attributes. The Leading Edge, 36(3), pp.249-256.

[11] Wang, Z., Di, H., Shafiq, M.A., Alaudah, Y. and AlRegib, G., 2018. Successful leveraging of image processing and machine learning in seismic structural interpretation: A review. The Leading Edge, 37(6), pp.451-461.

[12] Xiong, W., Ji, X., Ma, Y., Wang, Y., BenHassan, N.M., Ali, M.N. and Luo, Y., 2018. Seismic fault detection with convolutional neural network. Geophysics, 83(5), pp.1-28.

[13] Bugge, A.J., Clark, S.R., Lie, J.E. and Faleide, J.I., 2018. A case study on semiautomatic seismic interpretation of unconformities and faults in the southwestern Barents Sea. Interpretation, 6(2), pp.SD29-SD40.

Useful links

For information relating to the research project please contact the lead Supervisor via


NERC GW4+ DTP studentships are open to UK and Irish nationals who, if successful in their applications, will receive a full studentship including payment of university tuition fees at the home fees rate.

A limited number of full studentships are also available to international students which are defined as EU (excluding Irish nationals), EEA, Swiss and all other non-UK nationals.  For further details please see the NERC GW4+ website.

Those not meeting the nationality and residency requirements to be treated as a ‘home’ student may apply for a limited number of full studentships for international students. Although international students are usually charged a higher tuition fee rate than ‘home’ students, those international students offered a NERC GW4+ Doctoral Training Partnership full studentship starting in 2022 will only be charged the ‘home’ tuition fee rate (which will be covered by the studentship). 

International applicants need to be aware that you will have to cover the cost of your student visa, healthcare surcharge and other costs of moving to the UK to do a PhD. More information on this is available from the universities you are applying to (contact details are provided in the project description that you are interested in.

The conditions for eligibility of home fees status are complex and you will need to seek advice if you have moved to or from the UK (or Republic of Ireland) within the past 3 years or have applied for settled status under the EU Settlement Scheme.



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


How to apply

In 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, please see the entry requirements for details.
  • Two references

Reference information
You will be asked to submit two references as part of the application process.  If you are not able to upload  your reference documents with your application please ensure you provide details of your referees.  If you provide contact details of referees only, we will not expect receipt of references until after the shortlisting stage. Your referees should not be from the prospective supervisory team.

If you are shortlisted for interview, please ensure that your two academic referees email their references to the, 7 days prior to the interview dates. Please note that we will not be contacting referees to request references, you must arrange for them to be submitted to us by the deadline.

References should be submitted by your referees to us directly in the form of a letter. Referees must email their references to us from their institutional email accounts. We cannot accept references from personal/private email accounts, unless it is a scanned document on institutional headed paper and signed by the referee.

All application documents must be submitted in English. Certified translated copies of academic qualifications must also be provided.

The closing date for applications is 1600 hours GMT Friday 10 January 2022. Interviews will be held between 28 February and 4 March 2022.  For more information about the NERC GW4+ DPT please visit

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

Data Sharing
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.


Application deadline:10th January 2022
Value:£15,609 per annum for 2021-2022
Duration of award:per year
Contact: PGR Enquiries