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E328: Theoretical and computational studies in full-waveform inversion (Lead Supervisor: David Al-Attar, Earth Sciences)

Supervisors: David Al-Attar (Earth Sciences) and Tarje Nissen-Meyer (University of Oxford)

Importance of the area of research:

Seismic tomography uses surface recordings of seismic waves to make quantitative inferences about the Earth's internal structure on exploration, regional, and global scales. Within the past decade or so, an approach to seismic tomography known as full-waveform inversion has become prominent. This method uses modern computational techniques to simulate the full physics of elastic wave propagation, while the inverse problem is solved in an iterative manner using adjoint methods coupled to gradient-based optimization. Full-waveform inversion is hugely promising as it generalises tomography to use any and all information within seismograms, and its application has already led to improved constraints on Earth structure. There remains, however, still much to be done from a methodological perspective. In particular, there exists no quantitative basis for optimising the choice of data nor type of measurements made, and satisfactory methods for uncertainty quantification in full-waveform tomography have yet to be developed. Such uncertainty estimates are clearly essential for the robust interpretation of seismic models, and for their use in the solution of Earth Science problems at all relevant scales.

Project summary:

This project will seek to improve the methodological basis for full-waveform inversion, with a particular emphasis on the quantification of resolution and uncertainty with the tomographic models obtained. At its outset, the main aims of the project will be to: (i) develop a computationally feasible approach for calculating the action of the linearised resolution operator within a non-linear iterative inversion, (ii) to investigate and develop quantitative methods for the design of optimal data measurements and misfit functions within full-waveform inversion, and (iii) develop computational efficient methods for exploring the structure of the non-linear null space in a tomographic problem, and in this manner begin to quantify the uncertainty within the solution.

What the student will do:

This is a project focused on computational and theoretical seismology, with the student being involved in the development and implementation of new computational methods for full-waveform inversion. This work will be done collaboratively with both supervisors and their research groups, along with a looser network of seismologists internationally. Initially, the focus of the project will be on simple “toy” tomographic problems where the student can readily learn to implement existing approaches for full-waveform inversion, and then begin to extend these methods to address questions related to resolution and uncertainty quantification. As the project progresses, this work will shift to full-scale tomographic problems, with the particular choice of application being determined by the student's interests. Computational work will be based on the use and extension of existing programs and libraries for elastic wave propagation and iterative optimisation.  

Please contact the lead supervisor directly for further information relating to what the successful applicant will be expected to do, training to be provided, and any specific educational background requirements.


Tromp et al. Seismic tomgraphy, adjoint methods, time reversal and banana-douhgnut kernels, 2005. Geophys. J. Int., 160, 195-216.

Nissen-Meyer, T, et al. 2014. AxiSEM: broadband 3-D seismic wavefields in axisymmetric media, Solid Earth, 5, 425-445, doi:10.5194/se-5-425-2014.

Colombi, Nissen-Meyer, Boschi, Giardini, 2014. Seismic waveform inversion for core–mantle boundary topography. Geophys. J. Int., doi: 10.1093/gji/ggu112.

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