A MULTIPLICATIVE REGULARIZED GAUSS-NEWTON ALGORITHM AND ITS APPLICATION TO THE JOINT INVERSION OF INDUCTION LOGGING AND NEAR-BOREHOLE PRESSURE MEASUREMENTS

Abstract

Due to the ill-posed nature of nonlinear inverse problems of borehole geophysics, a parameterization approach is necessary when the available measurement data are limited and measurements are only carried out from sparse transmitter-receiver positions (limited data diversity). A potential remedy is the joint inversion of multi- physics measurements. A parametric inversion approach has desirable attributes for multi-physics measurements with difierent resolutions. It provides a ∞exible framework to put the sensitivities of multi- physics multi-resolution measurements on equal footing. In addition, the number of unknown model parameters to be inverted is rendered tractable with parameterization. Consequently, a Gauss-Newton based inversion algorithm taking advantage of the Hessian information can be advantageously employed over inversion approaches that rely only on gradient information. We describe a new dual-physics parametric joint-inversion algorithm to estimate near-borehole ∞uid permeability and porosity distributions of rock formations from ∞uid-∞ow and electromagnetic measurements. In order to accommodate the cases in which the measurements are redundant or lack sensitivity with respect