A Multiplicative Regularized Gauss-newton Algorithm and Its Application to the Joint Inversion of Induction Logging and Near- Borehole Pressure Measurements

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 multiphysics measurements. A parametric inversion approach has desirable attributes for multi-physics measurements with different resolutions. It provides a flexible framework to put the sensitivities of multiphysics 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 fluid permeability and porosity distributions of rock formations from fluid-flow and electromagnetic measurements. In order to accommodate the cases in which the measurements are redundant or lack sensitivity with respect Received 5 September 2010, Accepted 8 March 2011, Scheduled 25 March 2011 Corresponding author: Faruk Omer Alpak ([email protected]). † Currently with Shell International E&P Inc., USA.