FAST BAYESIAN INVERSION METHOD FOR THE GENERALIZED PETROPHYSICAL AND COMPOSITIONAL INTERPRETATION OF MULTIPLE WELL LOGS WITH UNCERTAINTY QUANTIFICATION

摘要

Borehole measurements (resistivity, nuclear properties, and acoustic slowness) are affected by several factors specific to the design of logging instruments. These effects can be corrected using fast numerical simulations of well logs and inversion algorithms, thereby improving the estimation of mineral/fluid concentrations. Gradient-based inversion yields acceptable results; however, the calculation of derivatives is difficult without explicit information of the tool/instrument properties. Bayesian methods can also be useful, but they are computationally expensive, requiring ～10,000 times of simulations, which translates into hours if not days of CPU time.We develop an efficient Bayesian method for generalized well-log inversion (petrophysical and compositional). First, we estimate layer-by-layer properties combining a quasi-Newton method with Markov chain Monte Carlo (QNMCMC) sampling. Derivatives are approximated by the difference between the target field log and its numerical simulation. Next, uncertainty of inversion results is determined using Gaussian distributions. Estimated layer-by-layer properties and their uncertainties are used to estimate compositional properties using MCMC sampling accelerated by a surrogate model constructed with radial basis functions (RBF).We verify the applicability of the proposed method with both synthetic and field data. Results from the synthetic example indicate that the proposed method is reliable and efficient under extreme conditions (large property contrasts and thin layers). The application to field measurements yields 75% of core data within the 95% credible interval of interpreted results. Comparison to traditional random-walk MCMC (RWMCMC) indicates that the computational time for separate and joint inversion is reduced by a factor of 30 and 100, respectively.In addition to its speed, robustness, and reliability, the Bayesian inversion method provides great flexibility to include user-defined correlations among solid components and mineral groups. It can also perform rock-class-dependent detection based on Gaussian Mixture Models (GMM) with minimum user intervention, thereby successfully competing with commercial solvers.