Fast Modeling and Practical Inversion of Laterolog-Type Downhole Resistivity Measurements

In this paper, we present a fast modeling and practical inversion scheme for the laterolog-type measurements that includes dual-laterolog and array laterolog methods. A modified domain decomposition finite-element method (DDFEM) is proposed to implement the fast modeling of the laterolog-type measurements in 2-D cylindrical coordinates. This method enables the simulation of the tool's responses at multiple measuring points along the well trajectory all at once, and thus accelerates the simulation process significantly. A Levenberg-Marquardt method is employed to derive the radial resistivity profile from the laterolog-type measurements. The kernel of the inversion is that the full 2-D response is separated into a fast-preliminary inversion process followed by a rigorous 2-D inversion. A 1-D radial response is used in the fast-preliminary inversion and the difference between the 1-D radial response and the strict 2-D response is attributed to the shoulder bed effects. The full 2-D inversion is only necessary at the end of the preliminary inversion process. Synthetic and field data are processed to illustrate the detailed implementations as well as the performance of the proposed method. Full 3-D modeling and inversion examples are also presented to show that the DDFEM method can be readily extended to 3-D. The resistivity anisotropy effects and invasion effects are also discussed.