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.

I. Introduction

Directional resistivity logging while drilling (LWD) service has been widely used in the oil and gas exploration. A few year ago, a new generation of ultra-deep resistivity tools came into the market. This type of tools share the common concept of multi-spacing, multi-frequencies, and multi-components as shown in Fig. 1. The tilted antennas provide the sensitivity to the formation boundaries, resistivity, and anisotropy. In the recent years, the ultra-deep tools extend the depth-of-investigation (DoI) to over 100 feet from the wellbore by using lower frequency and longer transmitter-receiver spacing [1]. The consequence brings much more details of geological features into the detection scope and makes the mapping of entire reservoir possible.