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

被引:1
|
作者
Deng, Tianqi [1 ]
Ambia, Joaquin [1 ]
Torres-Verdin, Carlos [1 ]
机构
[1] Univ Texas, Hildebrand Dept Petr & Geosyst Engn, Austin, TX 78712 USA
关键词
borehole geophysics; interpretation; inversion; modelling; petrophysics; MUD-FILTRATE INVASION; PETROPHYSICAL INTERPRETATION; SENSITIVITY FUNCTIONS; NUCLEAR MEASUREMENTS; SONIC MEASUREMENTS; RAPID SIMULATION; RESISTIVITY; MCMC;
D O I
10.1111/1365-2478.13311
中图分类号
P3 [地球物理学]; P59 [地球化学];
学科分类号
0708 ; 070902 ;
摘要
Well logs are geophysical measurements of rock properties acquired continuously along a borehole. Because of the physics underlying their operation, borehole logging instruments perform local spatial averages of rock properties in the vicinity of the borehole, yielding well logs that are often affected by tool design, layer boundaries, borehole environmental conditions and mud-filtrate invasion. Such environmental effects are ubiquitous and can lead to errors in petrophysical-property estimations from well logs if not accounted for in the interpretation. Separate well-log inversion mitigates environmental effects by matching well logs with their numerical simulations. The latter simulations rely on specific assumptions about the relative geometry of the borehole and the rocks penetrated by the well. For vertical wells penetrating horizontal layers, it is common to assume piecewise-constant layer properties that we collectively refer to as the earth model; some of these properties have a direct relationship to well logs (e.g. resistivity, gamma ray, density and acoustic slowness). Well-log inversion is traditionally approached with deterministic methods such as the Levenberg-Marquardt algorithm to minimize the differences between well logs and their numerical simulations, often without accounting for the relationship between measurement noise and model uncertainty. Bayesian inversion, on the other hand, yields the posterior probability distribution of estimated properties and intrinsically quantifies their uncertainty. However, Bayesian Well-log inversion usually involves the implementation of Markov chain Monte Carlo sampling, which requires a prohibitive number of forward simulations and is therefore not suitable for rapid petrophysical and/or elastic and mechanical evaluations of rocks. We introduce an efficient Bayesian Well-log inversion method using a gradient-based Markov chain Monte Carlo method. Gradient-based Markov chain Monte Carlo is a group of relatively new Markov chain Monte Carlo algorithms that combine gradient updates with Hessian-based sampling. gradient-based Markov chain Monte Carlo draws samples efficiently from the posterior probability distribution using the gradient information to guide samples towards high-probability regions and the Hessian to approximate the posterior probability distribution locally. We verify the gradient-based Markov chain Monte Carlo inversion method with the inversion of synthetic well logs, including gamma ray, resistivity, density, neutron porosity, photoelectric factor and compressional/shear-wave slowness. Results show that gradient-based Markov chain Monte Carlo decreases the computational cost by more than 90% compared to conventional Markov chain Monte Carlo sampling. Next, gradient-based Markov chain Monte Carlo inversion is applied to a field example from the Central North Sea, where conventional interpretation methods yield shale concentration, sandstone porosity and water saturation with errors up to 19.2%, 14.9% and 48.8%, respectively. Gradient-based Markov chain Monte Carlo inversion products satisfactorily reproduce the available measurements with only a modest increase in computational cost compared to deterministic inversion approaches.
引用
收藏
页码:471 / 494
页数:24
相关论文
共 50 条
  • [1] Geostatistical approach to bayesian inversion of geophysical data: Markov chain Monte Carlo method
    Oh, SH
    Kwon, BD
    [J]. EARTH PLANETS AND SPACE, 2001, 53 (08): : 777 - 791
  • [2] Geostatistical approach to bayesian inversion of geophysical data: Markov chain Monte Carlo method
    Seok-Hoon Oh
    Byung-Doo Kwon
    [J]. Earth, Planets and Space, 2001, 53 : 777 - 791
  • [3] Gradient-based Adaptive Markov Chain Monte Carlo
    Titsias, Michalis K.
    Dellaportas, Petros
    [J]. ADVANCES IN NEURAL INFORMATION PROCESSING SYSTEMS 32 (NIPS 2019), 2019, 32
  • [4] A gradient-based Markov chain Monte Carlo method for full-waveform inversion and uncertainty analysis
    Zhao, Zeyu
    Sen, Mrinal K.
    [J]. GEOPHYSICS, 2021, 86 (01) : R15 - R30
  • [5] Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem
    Malinverno, A
    [J]. GEOPHYSICAL JOURNAL INTERNATIONAL, 2002, 151 (03) : 675 - 688
  • [6] Gradient-Based Markov Chain Monte Carlo for MIMO Detection
    Zhou, Xingyu
    Liang, Le
    Zhang, Jing
    Wen, Chao-Kai
    Jin, Shi
    [J]. IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, 2024, 23 (07) : 7566 - 7581
  • [7] Gradient-Based Sequential Markov Chain Monte Carlo for Multitarget Tracking With Correlated Measurements
    Lamberti, Roland
    Septier, Francois
    Salman, Naveed
    Mihaylova, Lyudmila
    [J]. IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS, 2018, 4 (03): : 510 - 518
  • [8] Gradient-Based Markov Chain Monte Carlo for Bayesian Inference With Non-differentiable Priors
    Goldman, Jacob Vorstrup
    Sell, Torben
    Singh, Sumeetpal Sidhu
    [J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2022, 117 (540) : 2182 - 2193
  • [9] A Gradient-Based Blocking Markov Chain Monte Carlo Method for Stochastic Inverse Modeling
    Fu, Jianlin
    Gomez-Hernandez, J. Jaime
    Du, Song
    [J]. GEOSTATISTICS VALENCIA 2016, 2017, 19 : 777 - 788
  • [10] MIMO Detection Using Gradient-Based Markov Chain Monte Carlo Methods
    Zhou, Xingyu
    Liang, Le
    Zhang, Jing
    Wen, Chao-Kai
    Jin, Shi
    [J]. IEEE CONFERENCE ON GLOBAL COMMUNICATIONS, GLOBECOM, 2023, : 5683 - 5688