Adaptive Global Optimization of Real-Time Boundary Detection From the LWD Azimuthal Electromagnetic Measurements in Layered TI Formation With Arbitrarily Deviated Borehole

The article proposes an efficient global optimization of adaptive boundary detection from the logging while drilling (LWD) azimuthal electromagnetic (EM) measurements. The goal is to realize real-time geo-steering in 1-D layered transversely isotropic (TI) formation with an arbitrarily deviated borehole. The method includes apparent resistivity (APR) extraction and 0-D inversion, 1-D adaptive regularized iterative inversion, and global optimization. The APR extraction and 0-D inversion are used to quickly determine the initial horizontal and vertical resistivities of the bed where the tool is located. Subsequently, the 1-D regularized inversion is performed to achieve a local minimum solution near an arbitrarily given initial model. For solving the non-unique problem and acquiring the globally optimal solution, several different initial values are selected according to the possible range per model parameter to construct a serial of initial models. The OpenMP parallel technique is applied for simultaneous inversions at all initial models. Multiple inversion solutions may be obtained due to the non-uniqueness. The one with the minimal residual function in all inversion results will become the globally optimal solution. Furthermore, the tool response and its exact explicit Fréchet derivative with respect to each model parameter are analytically calculated, while an adaptive regularization factor ensures a gradual reduction of the objective function. The correction of field data is required to reduce the mandrel effect. The inversion results of synthetic and field data demonstrated that the proposed inversion algorithm efficiently provides the reliable bed boundaries and resistivities around the wellbore.