  In this paper we study a history matching approach that consists of finding
stable approximations to the problem of minimizing the weighted least-squares
functional that penalizes the misfit between the reservoir model predictions
$G(u)$ and noisy observations $y^{\eta}$. In other words, we are interested in
computing $u^{\eta}\equiv \arg\min_{u\in X}\frac{1}{2}\vert\vert
\Gamma^{-1/2}(y-G(u))\vert\vert_{Y}^{2} $ where $\Gamma$ is the measurements
error covariance, $Y$ is the observation space and $X$ is a set of admissible
parameters. This is an ill-posed nonlinear inverse problem that we address by
means of the regularizing Levenberg-Marquardt scheme developed in
\cite{Hanke,Hanke2}. Under certain conditions on $G$, the theory of
\cite{Hanke,Hanke2} ensures convergence of the scheme to stable approximations
to the inverse problem. We propose an implementation of the regularizing
Levenberg-Marquardt scheme that enforces prior knowledge of the geologic
properties. In particular, the prior mean $\overline{u}$ is incorporated in the
initial guess of the algorithm and the prior error covariance $C$ is enforced
through the definition of the parameter space $X$. Our main goal is to
numerically show that the proposed implementation of the regularizing
Levenberg-Marquardt scheme of Hanke is a robust method capable of providing
accurate estimates of the geologic properties for small noise measurements. The
performance for recovering the true permeability with the regularizing
Levenberg-Marquardt scheme is compared against the more standard techniques for
history matching proposed in \cite{Li,Tavakoli,svdRML,Oliver}. Our numerical
experiments suggest that the history matching approach based on iterative
regularization is robust and could potentially be used to improve further on
various methodologies already proposed as effective tools for history matching
in petroleum reservoirs
