Edge-elements formulation of 3d csem in geophysics: a parallel approach
- Autores: Octavio Castillo Reyes
- Directores de la Tesis: José María Cela Espin (dir. tes.), Josep de la Puente Álvarez (codir. tes.)
- Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2017
- Idioma: español
- Tribunal Calificador de la Tesis: Alejandro Marcuello Pascual (presid.), Mariano Vazquez (secret.), Julien Diaz (voc.)
- Programa de doctorado: Programa de Doctorado en Arquitectura de Computadores por la Universidad Politécnica de Catalunya
- Materias:
- Enlaces
- Tesis en acceso abierto en: TDX
- Resumen
Electromagnetic methods (EM) are an invaluable research tool in geophysics whose relevance has increased rapidly in recent years due to its wide industrial adoption. In particular, the forward modelling of three-dimensional marine controlled-source electromagnetics (3D CSEM FM) has become an important technique for reducing ambiguities in the interpretation of geophysical datasets through mapping conductivity variations in the subsurface. As a consequence, the 3D CSEM FM has application in many areas such as hydrocarbon/mineral exploration, reservoir monitoring, CO2 storage characterization, geothermal reservoir imaging and many others due to there quantities often displaying conductivity contrasts with respect to their surrounding sediments. However, the 3D CSEM FM at real scale implies a numerical challenge that requires an important computational effort, often too high for modest multicore computing architectures, especially if it fuels an inversion process.
On the other hand, although the HPC code development is dominated by compiled languages, the popularity of high-level languages for scientific computations has increased considerably. Among all of them, Python is probably the language that has shown more interest, mainly because of flexibility and its simple and clean syntax. However, its use for HPC geophysical applications is still limited, which suggests a path for research, development and improvement. Therefore, this thesis reports the attempts at designing and implementing a methodology that has not been systematically applied for solving 3D CSEM FM with an HPC application baked upon Python. The net contribution of this effort is the development and documentation of a new open-source modelling code for 3D CSEM FM in geophysics, namely, the Parallel Edge-based Tool for Geophysical Electromagnetic Modelling (PETGEM). The importance of having this modelling tools lies in the fact that they provide synthetic results that can be compared with real data which has a practical use both in the industry and academia. Still, available 3D CSEM FM codes are usually written in low-level languages whose implemented methods are often innaccessible to the scientific community since they are commercial.
PETGEM is written mostly in Python and relies on mpi4py and petsc4py packages for parallel computations. Other scientific Python packages used include Numpy andScipy. This code is designed to cope with the main challenges encountered within the numerical simulation of the problem under consideration: tackle realistic problems with accuracy, efficiency and flexibility. It uses the Nédélec Edge Finite Element Method (EFEM) as discretisation technique because its divergence-free basis is very well suited for solving Maxwell¿s equations. Furthermore, it supports completely unstructured tetrahedral meshes which allows the representation of complex geometries and local refinement, positively impacting the accuracy of the solution. The parallel implementation of the code using shared/distributed-memory architectures is investigated and described throughout this document.
In addition, the thesis deals with the numerical and physical challenges of the 3D CSEM FM problem. Through this work, frequency-domain Maxwell¿s equations have been discretised using EFEM and validated by comparison with analytical solutions and published data, proving that modelling results are highly accurate. Moreover, this work discusses an automatic mesh adaptation strategy and the convergence rate of the iterative solvers that are widely used in the literature for solving the EM problem is presented.
In summary, this thesis shows that it is possible to integrate Python and HPC for the solution of 3D CSEM FM at large scale in an effective way. The new modelling tool is easy to use and the adopted algorithms are not only accurate and efficient but also have the possibility to easily add or remove components without having to rewrite large sections of the code.
