Regularized pilot points method for the characterization of heterogeneity

• Autores: Rubén Alcolea Rodríguez
• Directores de la Tesis: Jesús Carrera Ramírez (dir. tes.), Agustín Medina Sierra (dir. tes.)
• Lectura: En la Universitat Politècnica de Catalunya (UPC) ( España ) en 2006
• Idioma: español
• Tribunal Calificador de la Tesis: Ghislain De Marsily (presid.), Xavier Sánchez Vila (secret.), Francisco Javier Elorza Tenreiro (voc.), Alberto Guadagnini (voc.), José Jaime Gómez Hernández (voc.)
• Materias:
  • Matemáticas
    • Probabilidad
      • Plausibilidad
  • Ciencias de la tierra y del espacio
    • Ciencias de la atmósfera
      • Simulación numérica
    • Geología
      • Hidrogeología
    • Hidrología
      • Aguas subterráneas
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• Resumen

  • Geostatistical inversion represents a powerful tool to characterize heterogeneity, The pilot points method (PPM) is arguably the most flexible among the inverse approaches. However, the PPM suffers from instability. A tactic to combat instability consists of adding a regularization term to the objective function. Surprisingly, this option had not been applied to the PPM in a consistent manner. This dissertation aims at filling this gap. A modification of the PPM (termed 'regularized pilot points method', RPPM) is presented. The main novelty consists of the addition of a plausibility term, which quantifies the departure of model parameters from their prior estimates. This term improves the identification of heterogeneity and the stability of the problem. This thesis consists of four self-contained papers.

    The RPPM is presented in the first paper and its performance is explored on a synthetic example. The method aims at obtaining the conditional estimation of transmissivity from direct measurements of this property and of dependent variables. Emphasis is placed on assessing the weighting of the plausibility term, which quantifies the importance of the prior information of parameters in the calibration. Results show that neglecting plausibility (standard option in the context of PPM) leads to the best fit of dependent variables, but to an unstable identification of model parameters. On the contrary, giving too much importance to plausibility biases the solution towards the prior information. The necessary optimal weighting of the plausibility term is done in the statistical framework of maximum likelihood estimation. This results in statistical consistency, increased stability and enhanced resolution. The added stability allows the use of as many pilot points as computationally feasible (what contradicts the traditional use of the PPM).

    These results are extended to the case of seeking stochastic simulations conditioned to direct measurements and dependent vari