Mathematical Geosciences最新文献

Abstract

We introduce a new methodology for inference of fluid composition from measurements of mineralogical or chemical compositions, expanding upon the use of reactive transport models to understand hydrothermal alteration processes. The reactive transport models are used to impute a latent variable explanatory mechanism in the formation of hydrothermal alteration zones and mineral deposits. An expectation maximisation algorithm is then employed to solve the joint problem of identifying alteration zones in the measured data and estimating the fluid composition, based on the fit between the mineral abundances in the measured and predicted alteration zones. Using the hydrothermal alteration of granite as a test case (greisenisation), a range of synthetic tests is presented to illustrate how the methodology enables objective inference of the mineralising fluid. For field data from the East Kemptville tin deposit in Nova Scotia, the technique generates inferences for the fluid composition which compare favourably with previous independent estimates, demonstrating the feasibility of the proposed calibration methodology.

Because it is generally impossible to completely characterize the uncertainty in complex model variables after assimilation of data, it is common to approximate the uncertainty by sampling from approximations of the posterior distribution for model variables. When minimization methods are used for the sampling, the weights on each of the samples depend on the magnitude of the data mismatch at the critical points and on the Jacobian of the transformation from the prior density to the sample proposal density. For standard iterative ensemble smoothers, the Jacobian is identical for all samples, and the weights depend only on the data mismatch. In this paper, a hybrid data assimilation method is proposed which makes it possible for each ensemble member to have a distinct Jacobian and for the approximation to the posterior density to be multimodal. For the proposed hybrid iterative ensemble smoother, it is necessary that a part of the mapping from the prior Gaussian random variable to the data be analytic. Examples might include analytic transformation from a latent Gaussian random variable to permeability followed by a black-box transformation from permeability to state variables in porous media flow, or a Gaussian hierarchical model for variables followed by a similar black-box transformation from permeability to state variables. In this paper, the application of weighting to both hybrid and standard iterative ensemble smoothers is investigated using a two-dimensional, two-phase flow problem in porous media with various degrees of nonlinearity. As expected, the weights in a standard iterative ensemble smoother become degenerate for problems with large amounts of data. In the examples, however, the weights for the hybrid iterative ensemble smoother were useful for improving forecast reliability.

Kriging is the most widely used spatial interpolation method in geostatistics. For many environmental applications, kriging may have to satisfy the stationarity and isotropy hypothesis, and new techniques using machine learning suffer from a lack of labeled data. In this paper, we propose the use of deep image prior, which is a U-net-like deep neural network designed for image reconstruction, to perform spatial interpolation and conditional map generation without any prior learning. This approach allows us to overcome the assumptions for kriging as well as the lack of labeled data when proposing uncertainty and probability above a certain threshold. The proposed method is based on a convolutional neural network that generates a map from random values by minimizing the difference between the output map and the observed values. With this new method of spatial interpolation, we generate n maps to obtain a map of uncertainty and a map of probability of exceeding the threshold. Experiments demonstrate the relevance of the proposed methods for spatial interpolation on both the well-known digital elevation model data and the more challenging case of pollution mapping. The results obtained with the three datasets demonstrate competitive performance compared with state-of-the-art methods.

Tight sandstone reservoirs have low porosity, low permeability, and a complex pore structure. The seepage from tight sandstones is a key factor in evaluating the oil and gas accumulation in these reservoirs. Therefore, reservoir permeability prediction has become the focus of researchers. Using nuclear magnetic resonance (NMR), high-pressure mercury injection, scanning electron microscopy, and other experimental methods, scholars have established various permeability prediction models, which have obvious advantages and disadvantages. However, there is less research conducted on predicting the permeability of tight sandstone reservoirs according to their single-peak NMR T₂ distribution. Based on NMR experiments and the bimodal Gaussian density formula, this study identified the criteria for determining the types of reservoir pore structures with single-peak NMR T₂ distribution and established the parameters (η₁ and η₂) that can be used in the evaluation of reservoir pore structure. A novel model for predicting the permeability of tight sandstone reservoirs was established using η₁ and η₂. The results of the prediction model proposed in this study were found to be superior to the results of eight permeability prediction models established by other scholars in the studied case of the Huangliu Formation. However, permeability prediction models established using the NMR experimental results of different sources were found to be ineffective. Additionally, the new model is suitable for use with sandstone reservoirs with both single-peak and double-peak NMR T₂ distributions in the studied case of the Yanchang Formation. Logging curves can be used to predict η₁ and η₂, and the permeability of a single well of a tight sandstone reservoir. The study findings would be useful for predicting tight sandstone reservoir permeability.

Groundwater resources in Mediterranean coastal aquifers are under several threats including saltwater intrusion. This situation is exacerbated by the absence of sustainable management plans for groundwater resources. Management and monitoring of groundwater systems require an integrated approach and the joint interpretation of any available information. This work investigates how uncertainty can be integrated within the geo-modelling workflow when creating numerical three-dimensional aquifer models with electrical resistivity borehole logs, geostatistical simulation and Bayesian model averaging. Multiple geological scenarios of electrical resistivity are created with geostatistical simulation by removing one borehole at a time from the set of available boreholes. To account for the spatial uncertainty simultaneously reflected by the multiple geostatistical scenarios, Bayesian model averaging is used to combine the probability distribution functions of each scenario into a global one, thus providing more credible uncertainty intervals. The proposed methodology is applied to a water-stressed groundwater system located in Crete that is threatened by saltwater intrusion. The results obtained agree with the general knowledge of this complex environment and enable sustainable groundwater management policies to be devised considering optimistic and pessimistic scenarios.

A geophysical Bayesian inversion problem may target the posterior distribution of geological or hydrogeological parameters given geophysical data. To account for the scatter in the petrophysical relationship linking the target parameters to the geophysical properties, this study treats the intermediate geophysical properties as latent (unobservable) variables. To perform inversion in such a latent variable model, the intractable likelihood function of the (hydro)geological parameters given the geophysical data needs to be estimated. This can be achieved by approximation with a Gaussian probability density function based on local linearization of the geophysical forward operator, thereby, accounting for the noise in the petrophysical relationship by a corresponding addition to the data covariance matrix. The new approximate method is compared against the general correlated pseudo-marginal method, which estimates the likelihood by Monte Carlo averaging over samples of the latent variable. First, the performances of the two methods are tested on a synthetic test example, in which a multivariate Gaussian porosity field is inferred using crosshole ground-penetrating radar first-arrival travel times. For this example with rather small petrophysical uncertainty, the two methods provide near-identical estimates, while an inversion that ignores petrophysical uncertainty leads to biased estimates. The results of a sensitivity analysis are then used to suggest that the linearized Gaussian approach, while attractive due to its relative computational speed, suffers from a decreasing accuracy with increasing scatter in the petrophysical relationship. The computationally more expensive correlated pseudo-marginal method performs very well even for settings with high petrophysical uncertainty.

The linear calibration model is a powerful statistical tool that can be utilized to predict an unknown response variable, Y, through observations of a proxy or predictor variable, X. Since calibration involves estimation of regression model parameters on the basis of a limited amount of noisy data, an unbiased calibration slope estimation is of utmost importance. This can be achieved by means of state-of-the-art, data-driven statistical techniques. The present paper shows that weighted least-squares for both variables estimation (WLSXY) is able to deliver unbiased slope estimations under heteroscedasticity. In the case of homoscedasticity, besides WLSXY, ordinary least-squares (OLS) estimation with bias correction (OLSBC) also performs well. For achieving unbiasedness, it is further necessary to take the correct regression direction (i.e., of Y on X) into account. The present paper introduces a pairwise moving block bootstrap resampling approach for obtaining accurate estimation confidence intervals (CIs) under real-world climate conditions (i.e., non-Gaussian distributional shapes and autocorrelations in the noise components). A Monte Carlo simulation experiment confirms the feasibility and validity of this approach. The parameter estimates and bootstrap replications serve to predict the response with CIs. The methodological approach to unbiased calibration is illustrated for a paired time series dataset of sea-surface temperature and coral oxygen isotopic composition. Fortran software with implementation of OLSBC and WLSXY accompanies this paper.

A thorough understanding of the interplay between polarization mechanisms is pivotal for the interpretation of electrical measurements, since sub-megahertz electrical measurements in sedimentary rocks are dominated by interfacial polarization mechanisms. Nonetheless, rock-physics models oversimplify pore-network geometry and the interaction of electric double layers relating to adjacent grains. Numerical algorithms present the best possible framework in which to characterize the electrical response of sedimentary rocks, avoiding the constraints intrinsic to rock-physics models. Recently, an algorithm was introduced that can simulate the interactions of electric fields with the ions in solution. The sub-kilohertz permittivity enhancement in sedimentary rocks is dominated by Stern-layer polarization, but a model for the polarization mechanism associated with the Stern layer has not been developed. Hence, the aim of this paper is to develop and test a numerical simulation framework to quantify the influence of Stern- and diffuse-layer polarization, temperature, ion concentration, and pore-network geometry on multi-frequency complex electrical measurements. The algorithm numerically solves the Poisson–Nernst–Planck equations in the time domain and a mineral-dependent electrochemical adsorption/desorption equilibrium model to determine surface charge distribution. Then, the numerical simulator is utilized to perform a sensitivity analysis to quantify the influence of electrolyte and interfacial properties on the permittivity of pore-scale samples at different frequencies.

Machine learning (ML)-based landslide susceptibility mapping (LSM) has achieved substantial success in landslide risk management applications. However, the complexity of classically trained ML is often beyond nonexperts. With the rapid growth of practical applications, an “off-the-shelf” ML technique that can be easily used by nonexperts is highly relevant. In the present study, a new paradigm for an end-to-end ML modeling was adopted for LSM in the Three Gorges Reservoir area (TGRA) using automated machine learning (AutoML) as the backend model support for the paradigm. A well-defined database consisting of data from 290 landslides and 11 conditioning factors was collected for implementing AutoML and compared with classically trained ML approaches. The stacked ensemble model from AutoML achieved the best performance (0.954), surpassing the support vector machine with artificial bee colony optimization (ABC-SVM, 0.931), gray wolf optimization (GWO-SVM, 0.925), particle swarm optimization (PSO-SVM, 0.925), water cycle algorithm (WCA-SVM, 0.925), grid search (GS-SVM, 0.920), multilayer perceptron (MLP, 0.908), classification and regression tree (CART, 0.891), K-nearest neighbor (KNN, 0.898), and random forest (RF, 0.909) in terms of the area under the receiver operating characteristic curve (AUC). Notable improvements of up to 11% in AUC demonstrate that the AutoML approach succeeded in LSM and could be used to select the best model with minimal effort or intervention from the user. Moreover, a simple model that has been customarily ignored by practitioners and researchers has been identified with performance satisfying practical requirements. The experimental results indicate that AutoML provides an attractive alternative to manual ML practice, especially for practitioners with little expert knowledge in ML, by delivering a high-performance off-the-shelf solution for ML model development for LSM.