Inversion of EM data is a critical and challenging problem in geosciences. Generally it is addressed initially as an unconstrained optimization problem and a penalty function is minimized iteratively by successively updating a conductivity model. Model updates are based on comparison of observed and forward-modeled data and on a priori information included in the penalty function. On the other hand, some research has also been done to deal with the Partial Differential Equation (PDE) constrained optimization problem directly. Using this strategy, the fields remain as part of the objective function and the PDE equations are added as constraints, giving as inversion parameters: the EM fields, the conductivity model and a set of Lagrange multipliers. The inexact all-at-once methodology has been used in previous works for the 3-D EM inversion showing that the solution can be reached faster than in traditional unconstrained approaches. In this paper, we present our development of a formulation and a code for the 2.5-D CSEM inverse problem using a Partial Differential Equation (PDE) constrained optimization. The code uses a finite element forward modeling algorithm and solves the constrained optimization through a Sequential Quadratic Problem.


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