Parallel tempered trans-dimensional Bayesian inference for the inversion of ultra-deep directional logging-while-drilling resistivity measurements

• Published in: Journal of petroleum science & engineering Vol. 188; no. C
• Main Authors: Shen, Qiuyang, Chen, Jiefu, Wu, Xuqing, Han, Zhu, Huang, Yueqin
• Format: Journal Article
• Language: English
• Published: United States Elsevier 18.01.2020
• Subjects: Bayesian inference; logging while drilling; pParallel tempering; statistical inversion; trans-dimensional MCMC; ultra-deep resistivity
• ISSN: 0920-4105

As one of the most important downhole technology, directional Electromagnetic (EM) logging-while-drilling (LWD) has been developing over the decades. The new generation of resistivity logging service expands the depth of investigation (DoI) to over 100 ft from the wellbore. As a result, more geological features are within the scope of the logging tool, which increases the complexity of logging measurements dramatically. Reservoir imaging relies on the inversion of the logging measurements, whereas most conventional inversion approaches depend on the deterministic optimization which oftentimes suffers from local minima. Many efforts were focused on the improvement of data processing workflow by using prior knowledge of the formation structure to constrain the optimizer from stepping into local minima although the prior can be inaccurate. As such, to reduce the negative impact of inaccurate prior assumptions, we propose to infer the model parameters via the trans-dimensional Markov chain Monte Carlo (tMCMC) method. Governed by the Bayesian theorem, the trans-dimensional inference addresses the complexity of the model by allowing the number of layers of the target model to be a free parameter. Driven by the measurements, the joint posterior distribution of model parameters is sampled accordingly, which provides a probability solution of a potential answer. Bayesian sampling is computationally expensive with a slow convergence rate. In this paper, we propose a meta-technique called parallel tempering (PT) combining with tMCMC to improve the sampling performance. PT is also known as replica Bayesian sampling where multiple Markov chains are constructed to explore the posterior distribution simultaneously with periodic information exchange between chains. Verified by our experiments, combining tMCMC and PT builds an efficient and reliable framework for interpreting ultra-deep LWD resistivity measurements. The inversion results from a series of benchmark models demonstrate that the proposed data-driven framework is robust and can be used to infer a reservoir-scale earth model.