Parallel multiple-chain DRAM MCMC for large-scale geosteering inversion and uncertainty quantification

Geosteering is the proactive control of a wellbore placement based on the downhole measurements, aiming at maximizing economic production from the well. The recent development of azimuthal resistivity logging-while-drilling (LWD) tools have a much larger depth of detection, thus sets higher demands for geosteering inversion as more unknown parameters need to be taken into account in the earth model to be inverted. For complicated non-linear problems, traditional deterministic inversion methods are more likely to be trapped near local optima. In general, Markov chain Monte Carlo (MCMC) inversion methods are more capable of finding the global optimal solution and providing additional uncertainty analyses by sampling from the target distribution. However, MCMC methods usually have the problem of slow convergence. Even though optimization methods like delayed rejection (DR) and adaptive Metropolis (AM) were proposed to speed up the convergence, using MCMC methods to solve geosteering inversion problems may still incur unacceptable time cost. To reduce the sampling cost of MCMC methods, we use parallel multiple-chain DRAM MCMC methods to solve geosteering inverse problems and estimate the corresponding uncertainty. A clustering method, density-based spatial clustering of applications with noise (DBSCAN), is applied to select the best solution among many results. The simulation results show that running many relatively short MCMC chains for one problem can obtain a similar result as running a long single chain. Besides, avoiding communications between multiple Markov chains during the sampling process yields almost linear scalability.