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Bayesian Machine Learning and Sampling Methods for Geophysical Inversion using Large Scale Seismic and Reservoir Simulations, NERC GW4+ DTP PhD studentship for 2023 Entry. PhD in Earth and Environment Science

   College of Life and Environmental Sciences

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  Dr S Das, Dr M Eyre  No more applications being accepted  Competition Funded PhD Project (Students Worldwide)

About the Project

About the Partnership

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.

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.

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.

For further information and to submit an application please visit -

Funding Notes

A stipend for 3.5 years (currently £17,668 p.a. for 2022-23) 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.


[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.
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