2021-03 - PhD position: Advanced numerical schemes to understand SeismoElectric Effects and improve the characterization of geological reservoirs

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PhD position - Advanced numerical schemes to understand SeismoElectric Effects and improve the characterization of geological reservoirs

Scientific context

The SEE4GEO (Seismoelectric Effects for Geothermal Resources Assessment and Monitoring) project brings together an international team composed of researchers of Laurence Livermore National Laboratory (LLNL, USA), the University of Hawaï at Manoa (UHM, USA), NORCE (Norway), TLS Geothermics (France), and the Université de Pau et des Pays de l’Adour (UPPA, France). The objective of the project is to develop a subsurface imaging technique based on seismoelectric effects technique (SEE), which is a new and innovative approach for geothermal subsurface imaging and monitoring at reservoir scale. We will assess SEE in terms of data acquisition, cost and quality, and determine its capability in comparison with classical imaging and monitoring techniques, particularly decoupled seismic and electromagnetic methods. We will focus on developing new numerical tools for forward and inverse modeling, and inform on optimized field survey, data acquisition and processing for deployment in many other exploration projects in case of success.

In the framework of this project, UPPA proposes two PhD positions:

  • Numerical analysis: the PhD student will be involved in developing of a fast, true 3D numerical package, handling SEE imaging and subsurface properties characterization, including resistivity and permeability. Identified scientific and technical challenges will be related to the diffusive and attenuated nature of SEE signals. Numerically, this will imply extra care for stability of our algorithms for forward and inverse calculations.
  • Experimental analysis: the PhD student will be involved in developing laboratory experiments. The goal of the study will be defining the best experimental setup for detecting permeable zones in geothermal systems. It will be led with a geophysical approach, including theoretical and instrumental analyses.



Seismoelectric effects are a pore-scale phenomenon relying on electric charge separation created by streaming currents generated by pressure gradients, which occur when a seismic wave propagates (Pride, 1994). This defines seismic-to-electric conversion. The propagating seismic wave generates an electrical current, which in turn induces an electrical field. This electrical field is often referred to as a coseismic field, propagating with the seismic wave. When this coseismic field is disrupted by a heterogeneity (due to e.g. a mechanical, electrical, or pore-fluid contrast), an electric dipole is created, triggering an independently diffusing EM field that is instantaneously detectable and provides information at depth, and is referred to as the so-called interface response field. Although the signal-to-noise ratio of the converted seismic-to-electric signals can be challenging, SEE dataset can capture unique information on important geothermal reservoir properties and heterogeneities, such as resistivity, salinity, degree of saturation and viscosity (e.g., Smeulders et al., 2014), as opposed to purely seismic or purely electromagnetic records. Moreover, the SEE interface response fields created at changes in properties can detect thin layers and other fine-scaled structural features such as fractures beyond the seismic resolution (e.g., Grobbe and Slob, 2016).

The objective of the thesis is to design an imaging technique based on SEE and to develop an imaging software on top of our direct simulation tool. In Luo et al. (2009) and Zhu et al. (2009), the authors show how an impedance kernel based on seismic signal measurements, can be used to generate an image of the subsurface and help identify material discontinuities and salt dome boundaries. This first‐order, direct use of seismic Fréchet derivatives is closely related to the popular imaging principle introduced by Claerbout (1971) in exploration geophysics. However, thin fluid‐saturated layers or highly permeable fractures are difficult to detect using seismic imaging. Likewise, EM-based full waveform inversion is unable to infer high resolution structural features due to the low-frequencies required for geothermal reservoir scale imaging, and predominantly provides smooth, low-resolution images of subsurface fluid distribution.



The host team has developed a software able to model SEE in frequency domain, which allows for the consideration of a wide variety of parameters, and more importantly, to take full account of the seismoelectric effects. The mathematical model combines Biot’s and Maxwell’s equations following Pride’s theory (Pride 1994). It is discretized using Discontinuous Galerkin (DG), which have proven their efficiency to solve wave problems in complex media (Bonnasse-Gahot et al. 2018, Barucq et al. 2021). Besides being easy to implement in a massively parallel environment, they are h-p adaptive, which allows to reduce the computational costs while keeping a high level of accuracy. This is of great interest, particularly since the problem to be solved is multi-scale, combining electromagnetic and seismic wavelengths in the same simulation. This software will be the starting point of the software developments made during the thesis.

The first step will be to work on solving the forward problem with the aim of reducing the associated computational costs. This one uses computational resources that must be optimized before moving on to the resolution of the inverse problem in 3D. For that, we propose to investigate the following ideas:

  • The computational costs can be reduced by having a coarse mesh and it is well-known that large high-order cells perform better than small low order cells. However, the geometry of the geophysical domain along with the heterogeneities of the physical properties do not always allow to consider coarse elements. Regarding the heterogeneities, they can be considered with physical parameters varying as polynomials inside each cell. As far as the topography is concerned, hp adaptivity of DG discretizations is an interesting asset. As a first milestone of the workplan, all these approaches will be combined to guarantee to the forward problem both accuracy and rapidity of execution. This is mandatory for performing 3D inversions.
  • Domain decomposition is a key ingredient in the solution of large-scale wave problems in the frequency domain. In same time, domain decomposition is a natural candidate for solving wave problems with a very large number of sources that do not create disturbances on the whole domain but rather in a truncated domain defined by their propagation cone. Domain decomposition will be implemented by taking advantages of the DG framework that provides natural transmission conditions between subdomains.
  • The host team has developed a full waveform inversion (FWI) piece of software which is based on the adjoint method. Here, the question is to figure out if this piece of software can be extended to Pride equations in 3D. This development will benefit from the already installed framework for 3D elastic equations. This part of the workplan requires a lot of work that will be done in a team effort. A first step will be to carry out 2D imaging and inverse capability based upon adjoint method and assess the ability of the code to retrieve parameters of interest (e.g., permeability, resistivity, etc.) on synthetic cases. This study will help determine optimized monitoring configurations for SEE full waveform inversion. Then the possibility of having 3D versions will be addressed. This is a crucial question: FWI requires the solution of a huge linear system which might be prohibitive to conduct in 3D poroelastic media. Hence, it will be necessary to decide, by conducting some numerical experiments, if time-harmonic FWI can be used for 3D inversion or if a time-domain strategy should be preferred. This will be done in collaboration with LLNL.


  • Barucq, H., Diaz, J., Meyer, R. C., and Pham, H. Implementation of Hybridizable Discontinuous Galerkin method for time‐harmonic anisotropic poroelasticity in two dimensions. International Journal for Numerical Methods in Engineering, to appear (2021).
  • Bonnasse-Gahot, M., Calandra, H., Diaz, J., and Lanteri, S., (2018), “Hybridizable discontinuous Galerkin method for the 2D frequency-domain elastic wave equation, Geophysical Journal International, Volume 213, Issue 1, 637–659.
  • Grobbe, N. and Slob, E.C. (2016) “Seismo-electromagnetic thin-bed responses: Natural signal enhancements?”. Journal of Geophysical Research - Solid Earth, 121, 2460-2479.
  • Luo Y., Zhu, H., Nissen‐Meyer, T., Morency, C., and Tromp, J., (2009) “Seismic modeling and imaging based upon spectral‐element and adjoint methods.” The Leading Edge 28, 568.
  • Pride, S. R., (1994), “Governing equations for the coupled electromagnetics and acoustics of porous media.” Phys. Rev. B, 50, 15678–15696.
  • Smeulders, D.M.J., Grobbe, N., Heller, H.K.J., Schakel, M.D. (2014), “Seismoelectric conversion for the detection of porous medium interfaces between wetting and nonwetting fluids)”. Vadose Zone Journal, 13(5), 1-7.
  • Zhu, H., Luo, Y., Nissen‐Meyer, T., Morency, C., and Tromp, J., (2009) “Imaging and timelapse migration based upon adjoint methods.” Geophysics 74, WCA167‐WCA177.


Working conditions

Host Laboratory: Laboratory of Mathematics and their applications, Pau, France.

The LMAP is a joint research unit attached to UPPA and CNRS. He is a partner of Inria Bordeaux South-West through two joint teams Makutu and Cagire. It is a member of the Pluridisciplinary Institute for Applied Research in the Field of Petroleum Engineering (IPRA - FR CNRS 2952) and the Carnot-Isifor Institute.

The LMAP brings together the entire mathematical community of UPPA, 54 researchers and teacherresearchers,
at two sites: Pau and Anglet.

Its themes are mainly applied mathematics:

  • mathematical analysis: analysis of equations with deterministic or stochastic partial derivatives, optimization, dynamic systems, mathematical modeling,
  • in numerical analysis and simulation: discretization methods for EDPs, approximation, reverse problems, scientific calculation and high-performance computing,
  • probabilities and statistics: stochastic modeling, probabilistic analysis, statistical data processing, big data, artificial intelligence, semi-parametric and non-parametric inference. The areas of application mainly concern geo-resources, aerodynamics, environment, health, operational safety, optimization of structures.

Benefiting from a particularly favorable industrial fabric in the fields of petroleum engineering and aerodynamics, LMAP is developing a strong industrial partnership with both multinational companies and local SMEs.

The PhD student will join the Inria project team Makutu (20 people, 8 PhD students), whose research program is to develop numerical software packages for retrieving shapes and/or physical properties of complex media with a particular focus on the Earth and its natural reservoirs. One of the objectives is to couple seismic wave propagation with other physics to improve the knowledge of natural reservoirs whose complex definition requires using high-resolution imaging techniques.

The PhD student will benefit from the supervision/support of two members of Makutu: Hélène Barucq and Julien Diaz (Research directors at INRIA) experimental Geophysics group: and from the interaction with the experimental Geophysics group of LFCR (Laboratory of Complex Fluids and their Reservoirs,): Clarisse Bordes (Associate Professor), Daniel Brito (Professor).

Starting Date: October 1st, 2021

Duration: 3 years

Gross salary: 1 878 € / month (which includes extra gratification for teaching duties – 32h per year)



The candidate should be graduated in Applied Mathematics and should also have a strong predilection for software development.

Particular skills are sought in inverse problems, analysis of partial differential equations, seismic and signal processing, seismic/acoustic propagation, electromagnetism, parallel computing.

Programming skills: Fortran and/or C++, MPI, Openmp.

Fluency in English is mandatory. Basic French is necessary (free French courses are available).

Interest in teaching: the PhD student might be involved as teaching assistant in our bachelor and master programs (32h/year). Bachelor of Mathematics is taught in French. Part of master of Mathematics,

Modeling and Simulation is taught in English. The teaching assistant will have to manage exercises and practical sessions in general mathematics, basic computing, numerical analysis.



Requested documents:

  • CV
  • Cover letter presenting the motivation of the applicant
  • Master degree grade transcripts and ranking
  • Reference letter
  • Contact details of at least two people, from you work environment, who can be contacted for further reference

Selection process:

  • Establishment of the selection committee
  • Evaluation of the applicants' file
  • Interview with the selected candidates and ranking

Application files will be evaluated based on the following criteria:

  • Candidate's motivation, scientific maturity and curiosity
  • Candidate's knowledge in in mathematics and computing
  • Grades and ranking during your Master degree, steadiness in your academic background
  • English language proficiency
  • Oral and written communication skills
  • Candidate’s ability to present her/his work and results

All application files must be sent to Clarisse Bordes: helene.barucq @ inria.fr

Application deadline: June 1st 2021