2024-03-19T05:32:54Zhttps://www.tdx.cat/oai/requestoai:www.tdx.cat:10803/4006162017-09-27T05:45:09Zcom_10803_1col_10803_146183
nam a 5i 4500
Geofísica
Geophysics
Anàlisi numèrica
Análisis numérico
Numerical analysis
Two-dimensional modeling and inversion of the controlled-source electromagnetic and magnetotelluric methods using finite elements and full-space PDE-constrained optimization strategies
[Barcelona] :
Universitat de Barcelona,
2017
Accés lliure
http://hdl.handle.net/10803/400616
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Galiana Blanch, Savitri,
autor
1 recurs en línia (265 pàgines)
Tesi
Doctorat
Universitat de Barcelona. Facultat de Geologia
2016
Universitat de Barcelona. Facultat de Geologia
Tesis i dissertacions electròniques
Garcia, Xavier,
supervisor acadèmic
Queralt, Pilar,,
supervisor acadèmic
TDX
The controlled-source electromagnetics (CSEM) and magnetotellurics (MT) methods are common geophysical tools for imaging the Earth's electrical interior. To appreciate measured data, both methods require forward and inverse modeling of the subsurface with the ultimate goal of finding a feasible model for which the simulated data reasonably fits the observations. The goodness of this fit depends on the error in the measured data, on the numerical error and on the degree of approximation inferred by numerical modeling. Therefore, active research focuses on new methods for modeling and inversion to improve accuracy and reliability for increasingly complex scenarios. In a first step, physical factors such as anisotropy, topography and realistic sources must be taking into account. Second, numerical methods need to be assessed in terms of solution accuracy, time efficiency and memory demand. The finite elements (FE) methods offer much flexibility in model geometry and contain quality control mechanisms for the solution, as shape function order and adaptive mesh refinement. Most emerging modeling programs are based on FE, however, inversion programs are generally based on finite differences (FD) or integral equation (IE) methods. On the other hand, inverse modeling is usually based on gradient methods and formulated in the reduced-space, where the electrical conductivity is the only optimization variable. Originally, the inverse problem is stated for the EM fields and the conductivity parameter (in the full-space), and constrained by governing partial differential equations (PDEs). The reduced-space strategy eliminates the field variables by applying equality constraints and solves then, the unconstrained problem. A common drawback of this is the repeated costly computation of the forward solution. Solving the PDE-constrained optimization problem directly, in the full-space, has the advantage that it is only necessary to exactly solve the PDEs at the end of the optimization, but it comes at the cost of a larger number of variables.
This thesis develops a robust and versatile adaptive unstructured mesh FE program to model the total field for two-dimensional (2-D) anisotropic CSEM and MT data, allowing for arbitrarily oriented, three-dimensional (3-D) sources, for which a two-and-a-half-dimensional (2.5-D) approximation is employed. The formulations of the problems in a FE framework are derived for isotropic and anisotropic subsurface conductivity structures. The accuracy of the solution is controlled and improved by a goal-oriented adaptive mesh refinement algorithm. Exhaustive numerical experiments validate the adaptive FE program for both CSEM and MT methods and on land and marine environments. The influence of the model dimensions, mesh design and order of shape functions on the solution accuracy is studied and notably, an outperformance of quadratic shape functions is found (compared to linear and cubic). Several examples demonstrate the effect of complex scenarios on EM data. In particular, we study the distortion caused by: the bathymetry, the orientation and geometry of the sources and the anisotropy, considering vertical and dipping cases. All examples showcase the importance of adequate consideration of these very common physical features of real world data. Further, a formulation for the 2.5-D CSEM inversion as a PDE-constrained optimization in full-space is derived within a FE framework following two strategies: discretize-optimize and optimize-discretize. The discretize-optimize formulation is implemented using a general purpose optimization algorithm. Two examples, a canonical reservoir model and a more realistic marine model with topography, demonstrate the performance of this inversion scheme, recovering in both cases the model’s main structures within an acceptable data misfit. Finally, the optimize-discretize formulation is derived in a FE framework, as a first step towards a development of an inversion scheme using adaptive FE meshes.
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