Efficient Bayesian inversion of borehole geophysical measurements with a gradient‐based Markov chain Monte Carlo method

Well logs are geophysical measurements of rock properties acquired continuously along a borehole. Because the physics underlying their operation, borehole logging instruments perform local spatial averages in vicinity borehole, yielding well that often affected by tool design, layer boundaries, environmental conditions and mud-filtrate invasion. Such effects ubiquitous can lead to errors petrophysical–property estimations from if not accounted for interpretation. Separate well-log inversion mitigates matching with numerical simulations. The latter simulations rely on specific assumptions about relative geometry rocks penetrated well. For vertical wells penetrating horizontal layers, it is common assume piecewise-constant we collectively refer as earth model; some these have direct relationship (e.g. resistivity, gamma ray, density acoustic slowness). Well-log traditionally approached deterministic methods such Levenberg–Marquardt algorithm minimize differences between simulations, without accounting measurement noise model uncertainty. Bayesian inversion, other hand, yields posterior probability distribution estimated intrinsically quantifies However, usually involves implementation Markov chain Monte Carlo sampling, which requires prohibitive number forward therefore suitable rapid petrophysical and/or elastic mechanical evaluations rocks. We introduce an efficient method using gradient-based method. Gradient-based group relatively new algorithms combine gradient updates Hessian-based sampling. draws samples efficiently information guide towards high-probability regions Hessian approximate locally. verify synthetic logs, including density, neutron porosity, photoelectric factor compressional/shear-wave slowness. Results show decreases computational cost more than 90% compared conventional Next, applied field example Central North Sea, where interpretation yield shale concentration, sandstone porosity water saturation up 19.2%, 14.9% 48.8%, respectively. products satisfactorily reproduce available only modest increase approaches.