PhD Opportunity at Institute of Geophysics: Robust Optimization of Inverse Problems for Wave-based Seismic Imaging

Start date: 2023-10-01 End date: 2027-08-30

Deadline for submitting applications: June 15, 2023

We are looking for two highly motivated PhD students to join our computational imaging research teams at the Institute of Geophysics, Polish Academy of Sciences. The two PhD students will work on a project to develop robust optimization methods for full waveform inversion (FWI), with an emphasis on theory development and application on synthetic and real data. The project’s goals will be met through an interdisciplinary approach that includes computational geophysics, computational mathematics, nonlinear optimization, and HPC computing. Existing FWI methods, such as standard reduced-space FWI and extended FWI techniques based on model and source extension, will be examined.

The first project focuses on developing appropriate robust and efficient FWI methods. The student will collect existing methods developed under various names in various fields for FWI convexification. The methods based on source extension and model extension have recently demonstrated good potential for solving difficult FWI problems that could not be solved using traditional FWI methods. The student will examine the advantages and disadvantages of these two groups of methods, looking for methodological similarities and differences. The student will concentrate on establishing the theoretical link between his two groups of methods and comparing their performance on benchmark models. In this thesis, we will concentrate on developing a general method that possesses the robustness property of these methods.

The second project focuses on adapting the recently proposed multiplier waveform inversion (MWI) to elastic FWI and real-world applications. MWI uses the multiplier method, also known as the augmented Lagrangian method, to solve the FWI formulation. The focus here is on efficient construction of Lagrange multipliers rather than dealing with augmented wave equations and large Hessian matrices. Preliminary tests have yielded very interesting results in terms of increasing the convergence of FWI without dealing with complicated Hessian matrices, simply by gradient ascent update of the multiplier and gradient descent update of the model parameters. To better understand the algorithm’s behaviour, the student will concentrate on the physical interpretation of the multipliers. One of the main advantages of MWI over other extended FWI methods-based source extensions is that it is very efficient and suitable for time-domain applications because it does not require the use of Hessian matrices. This property enables us to scale it up to large-scale applications.

The students will be part of a solution-oriented dynamic international team and contribute to advancing the state-of-the-art in both theory and application of wave-based imaging and FWI.


  • Master degree in geophysics, applied mathematics, physics, or similar. It is allowed to submit applications by people who graduate from studies in the coming months and will submit the opinion of the master’s thesis supervisor.
  • Knowledge of research topics related to the propagation of seismic waves, seismic imaging and inversion methods, and seismic data processing.
  • Knowledge in the field of optimization methods and numerical analysis.
  • Very good programming skills in Matlab and one of languages Python, Fortran, C++.
  • Experience in HPC computing and clusters is very welcome.
  • Very good English speaking and writing skills enabling the presentation of results at international conferences, communication, reading and writing research papers in peer-reviewed journals.
  • Good interpersonal skills and the willingness to work in a multicultural team are expected.

Title of the NCN call: SONATA BIS-12

How to apply: To be employed, a candidate must participate in the Geoplanet Doctoral School of the Institute of Geophysics of the Polish Academy of Sciences. Required documents (phdstudies.php) should be sent in electronic form in one PDF file (by e-mail) only to the address:

Conditions of employment

Project scholarship: Approximately 3,690 PLN net per month for a period of 48 months

Employment: Specified period of 48 months

Working time: full time

Additional information:

The PhD student will join the group implementing the NCN project no. 2022/46/E/ST10/00266 titled “Robust Optimization of Inverse Problems for Wave-based Seismic Imaging”. The project is scheduled for 48 months. Beside doing research on the selected thesis topic, student must also participate in doctoral school courses, participate in research visits, report the research results in the related scientific conferences and write research articles

The thesis will be carried out under the supervision of: Professor Ali Gholami ( Institute of Geophysics of the Polish Academy of Sciences, ul. Księcia Janusza 64, 01-452 Warsaw.

The following documents are required in the recruitment procedure:

  1. The motion to enrol in the Doctoral School along with the consent for processing personal data for the recruitment purposes and the declaration about familiarizing with the present Regulations. The specimen of the motion is included in the Attachment 1 to the present Regulations.
  2. A copy of the diploma certifying the completion of studies or a certificate confirming the completion of studies. In the case when the candidate is not in the possession of the above mentioned documents, he/she is obliged to deliver them before the start of the education in the Doctoral School. The documents are not required from the person referred to in Article 186 paragraph 2 of the Law.
  3. The list of grades obtained during the first-cycle (B.A., B.Sc.) and second-cycle studies (M.A., M.Sc.) or the list of grades obtained during the long-cycle Master Degree studies.
  4. The curriculum vitae containing the course of the existing education and employment, the list of publications, information on the involvement in scientific activity (membership in student research groups, participation in scientific conferences, internships and trainings, obtained awards and distinctions).
  5. A letter of motivation containing a short description of interests and scientific achievements and the justification why the candidate intends to undertake the education in the Doctoral School.
  6. Certificates or other documents stating the level of command of English language if the candidate is in possession of such documents.
  7. At least one letter of recommendation from the current research supervisor, academic teacher or research worker describing the candidate and his/her scientific activity that has been carried out by him/her so far. The letter can be sent by the candidate or directly by the person who wrote the letter. It is also possible that the candidate indicates a person who is a research worker or an academic teacher and holds the scientific degree from whom the recruitment commission may independently obtain such an opinion. In such a case the recruitment commission asks for such an opinion within the term that allows for taking it into consideration during the recruitment time. The possible ways to deliver the letter are included in the recruitment announcement.