Statistical Bayesian Inversion of Ultra-deep Electromagnetic LWD Data: Trans-dimensional Markov Chain Monte Carlo with Parallel Tempering

Solving the inversion of ultra-deep electromagnetic measurements is a challenging task in directional resistivity logging while drilling (LWD) service. The target is to reconstruct the subsurface formation structure around the borehole in the real-time drilling job. Due to the complexity of ultra-deep measurements, the inverse modeling is highly nonlinear and ill-posed. Hence, the conventional methods are insufficient to resolve this problem. In this paper, a statistical data-driven approach is proposed, which combines Bayesian inference and parallel tempering techniques.