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Bayesian Deep Learning and Sampling Methods for Probabilistic Seismic Inversion and Imaging. PhD in Mathematics studentship (NERC GW4+ DTP funded)

College of Engineering, Mathematics and Physical Sciences

Dr S Das , Dr James Hickey , Dr James Verdon Friday, January 08, 2021 Competition Funded PhD Project (Students Worldwide)

About the Project

In earth science 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 significantly accelerate this process using recent advances in Bayesian inference and deep learning. Efficient management and processing of such large volumes of real and synthetic seismic data in a probabilistic seismic inversion and imaging process is an open challenge, with outcomes that will benefit both industrial and academic research.

Project Aims and Methods:

This project will explore advanced signal/image processing and machine learning approaches, in particular, deep-learning and Bayesian inference for parameter/uncertainty estimation and probabilistic inversion of large-scale geological models. The aim is to reduce computational time utilising the recent advancements in deep neural networks to approximate the physical data generation process, i.e. the seismic wave propagation simulation. Concept 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 inverse problems in terms of both seismic source properties and unknown elastic geological models (density, compressional and shear wave velocity) 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 undergraduate and/or 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 either data analytics, mathematical/statistical computing is also desirable. Prior experience on high-performance computing especially on GPUs will be advantageous.

Collaborative Partner:

The student will be based in the University of Exeter, Penryn Campus and will also closely collaborate with the University of Bristol. This will be in the form of sharing seismic datasets, communicating the research findings with the researchers in Bristol, develop better understanding and interpretations of seismic data analysis in a broader industrial and academic context, and writing joint collaborative publications.


The student will receive the required training to pursue fundamental and applied research in this project on seismology and will have the opportunity to attend some of the departmental modules in Mathematics. 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 Mathematics and Geology. It is expected that the student will also strengthen the existing collaborations of the supervisors with the Oil and Gas, Geoscience and mining industries, and other stakeholders.

Useful links:

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

Prospective applicants:

For information about the application process please contact the Admissions team via .

Each research studentship project advertisement has an ‘Apply Now’ button linking to an application portal. Please note that applications received via other routes including a standard programme application route will not be considered for the studentship funding.

How to Apply:

The application deadline is Friday 8 January 2021 at 2359 GMT. Interviews will take place from 8th to 19th February 2021. For more information about the NERC GW4+ Doctoral Training Partnership please visit


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.

Funding Notes

NERC GW4+ funded studentship available for September 2021 entry. For eligible students, the studentship will provide funding of fees and a stipend which is currently £15,285 per annum for 2020-21.


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

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

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

7. Schuster, G., 2009. Seismic interferometry. Cambridge University Press.

8. 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.

9. 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.

10. 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.

11. 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.

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