Density measurements are generally affected by the presence of mudcake against the formation. In order to correct for such environmental effects, a density device comprises several detectors having different depths of investigation. Algorithms in current use combine the different sensor measurements in order to derive corrected formation density as a function of the detector count rates. In this paper, we discuss a measurement analysis technique based on physical response models of the sensors. These models predict the tool response as a function of various physical and geometrical parameters affecting the measurement. Given a set of measurements with different depths of investigation, the inversion of the response equations using iterative techniques will allow the computation of formation parameters free of mudcake effects. The use of a forward model-based inversion brings the following advantages compared to previous analysis techniques; optimal estimation, error characterization and solution control. The first part of the paper details how the parametric forward model is established and calibrated, using reference experimental data and a priori knowledge of the physics of Compton scattering and of the photoelectric effect. In the second part, the inversion algorithm based on the minimization of a cost function is presented. The minimization technique, the computation of errors in formation parameters, and the constraints and control of the solution are discussed and illustrated by several examples.

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