Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions

Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

doi:10.1103/physreve.94.033305

Cited by 14 publications

(16 citation statements)

References 32 publications

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“…When the number of observable data points (Nobs) decreases, the error on parameters estimated by the proposed methodology would increase, as suggested by previous studies on parameter estimation [57,58]. Although the effects of sparseness in the dataset on the estimation error were not…”

Section: Discussionmentioning

confidence: 74%

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

2018

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Water-rock interaction in surface and subsurface environments occurs in complex multicomponent systems and involves several reactions, including element transfer. Such kinetic information is obtained by fitting a forward model into the temporal evolution of solution chemistry or the spatial pattern recorded in the rock samples, although geochemical and petrological data are essentially sparse and noisy. Therefore, the optimization of kinetic parameters sometimes fails to converge toward the global minimum due to being trapped in a local minimum. In this study, we simultaneously present a novel framework to estimate multiple reaction-rate constants and the diffusivity of aqueous species from the mineral distribution pattern in a rock by using the reactive transport model coupled with the exchange Monte Carlo method. Our approach can estimate both the maximum likelihood and error of each parameter. We applied the method to the synthetic data, which were produced using a model for silica metasomatism and hydration in the olivine-quartz-H 2 O system. We tested the robustness and accuracy of our method over a wide range of noise intensities. This methodology can be widely applied to kinetic analyses of various kinds of water-rock interactions.2 of 15 happen simultaneously. Even for monomineralic systems, such as feldspar-water or olivine-water systems in batch experiments, coupled reactions could occur, marked by the dissolution of the primary mineral and the formation of a secondary mineral [9,[20][21][22][23]. Accordingly, an effective methodology is required to simultaneously estimate the reaction-rate constants of several minerals and/or diffusivity of elements from complex water-rock systems.However, multiple parameterizations from a coupled transport and reaction system, pertaining to the dissolution and precipitation of many minerals and the transport of aqueous species (ions and complexes), raise a difficult geochemical inverse problem due to computational difficulties. This is especially true when multiple parameters are to be estimated; estimation sometimes fails to converge to the global minima due to convergence to the local minima through error minimization [24,25]. Moreover, the data used for parameterization may be "noisy" due to analytical uncertainties, and therefore, the fitted parameters would also contain errors. Such errors on rate constants are typically ignored to avoid the complex computations required to handle error propagation. Therefore, it would be ideal to develop a versatile method that can extract multiple kinetic parameters and associated errors from noisy laboratory datasets without becoming trapped in local minima.In this study, we present a novel method to estimate not only multiple reaction-rate constants, but also the diffusivity of aqueous species using only the dataset of spatial mineral distribution, and by combining the reactive transport model and the exchange Monte Carlo (EMC) method [26][27][28]. The latter is well-known as an improvement on Markov chain Monte Carlo (MCMC) ...

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Section: Discussionmentioning

confidence: 74%

Multiple Kinetic Parameterization in a Reactive Transport Model Using the Exchange Monte Carlo Method

2018

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“…The SSM for history-tracking inversion can now be formulated using Eqs. (1), (4), and (5). Equations (1) and (4) correspond to system models describing the state vector x and reference position r t , respectively.…”

Section: A State-space Model For History-tracking Inversionmentioning

confidence: 99%

“…We use the above equations directly for the simulation operator h sim t that outputs the observation parameters y sim t based on the system parameters x t in the observation model [Eq. (5)].…”

Section: B Observation Modelmentioning

confidence: 99%

“…The likelihood function for the observation model [Eq. (5)] was then calculated using these mean and standard deviation values.…”

Section: B Estimation Of P-t -T Pathmentioning

confidence: 99%

“…DA is a probabilistic method that combines numerical simulations with observed data to forecast the future state of the system [1,2]. DA was developed for meteorology and oceanology, but has increasingly been applied in many natural science fields, including seismology, biology, chemistry, and materials science [3][4][5][6]. However, the conventional DA framework can only be directly applied to situations where time-series data are available.…”

Section: Introductionmentioning

confidence: 99%

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Recovering the past history of natural recording media by Bayesian inversion

et al. 2018

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Spatial growth patterns are natural recording media (NRMs) that preserve important historical information, which can be accessed and analyzed to reconstruct past environmental conditions and events. Here, we propose the Bayesian inversion method, which can reconstruct the evolution of target parameters from purely spatial data by extending data assimilation (DA), a method for integrating numerical simulations with time-series observations. Our method converts discrete spatial observation data to time-series data with the help of a law representing the NRM's time-evolution dynamics and Gaussian process regression, enabling us to directly compare the observations with a numerical simulation based on the DA framework. The method's effectiveness is demonstrated using a synthetic inversion problem, namely reconstructing the pressure-temperature-time (P-T-t) path of a metamorphic rock from chemical composition profiles of its zoned minerals. The proposed method is broadly applicable to a wide variety of NRMs.

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