Mathematical Geosciences最新文献

The purpose of mineral prospectivity mapping (MPM) is to discover unknown mineral deposits by means of fusing multisource prospecting information. In recent years, with rapid advancements in artificial intelligence, deep learning algorithms (DLAs) as a groundbreaking technique have exhibited outstanding capabilities in geoscience. However, conventional DLAs for MPM face certain challenges in feature extraction and the fusion of multimodal prospecting data. Moreover, opaque DLAs lead to an insufficient understanding of the predictive results by experts. In this study, a dual-branch convolutional neural network (DBCNN) and its post hoc interpretability were jointly constructed to map gold prospectivity in western Henan Province of China. In particular, channel and spatial attention modules were integrated into two branches to complement the respective advantages of multichannel and high spatial prospecting data for MPM. The Shapley additive explanations (SHAP) framework was then adopted to explain the predictive results by exploring the feature contributions. The comparative experiments illustrated that DBCNN can enhance feature representation and fusion abilities to improve the performance of MPM compared to conventional DLAs. The high-probability areas delineated by the DBCNN model exhibited close spatial relevance with known gold deposits, and the SHAP further confirmed the reliability of the predictive result obtained by the DBCNN model, thereby guiding future gold exploration in this study area.

The atmospheric (textrm{CO}_{2}) level, global average temperature, and sea level, which are three key metrics characterizing Earth’s surface environments, underwent a series of significant changes over geologic time. Here, I investigate the variation rates of these three variables during the Phanerozoic Eon and show that they systematically exhibit scale-independent behaviors. I then derive a general mathematical form of these scale-independent patterns based on geosystem-specific assumptions and basic physical principles. From the perspective of statistical mechanics, these scale-independent behaviors appearing in the planetary-scale geological system imply that the internal dynamics and interactions of different components in the Earth system have significantly influenced its evolution and stability, which sheds light on Earth’s sustainability and habitability.

Landslides pose a significant risk to human life and property, making landslide susceptibility mapping (LSM) a crucial component of landslide risk assessment. However, spatial correlations among mapping units are often neglected in statistical or machine learning models proposed for LSM. This study proposes KNN-GCN, a deep learning model for slope-unit-based LSM based on a graph convolutional network (GCN) and the K-nearest neighbor (KNN) algorithm. The model was experimentally applied to the Lueyang region and validated through the following steps. Firstly, we collected data for 15 landslide causal factors and from landslide inventories and established a slope unit map (SUM) through slope unit division. Next, we performed a multicollinearity analysis of landslide causal factors and divided the training and test sets at a 7:3 ratio. We then constructed a GCN model based on a slope unit graph (SUG) generated from the SUM using the KNN algorithm. The proposed KNN-GCN model was tuned using a grid search with fivefold cross-validation on the training set, and then trained and validated on training and test sets separately. Finally, the performance of the KNN-GCN model was compared with that of six other models which were categorized into two groups: CG#1 was the traditional KNN, support vector regression (SVC), and automated machine learning (AutoML), and CG#2 included KNN-G, SVC-G and AutoML-G with additional spatial information. Our results demonstrate that the proposed model achieves superior performance (area under the curve [AUC] = 0.8351) and generates the most comprehensible susceptibility map with distinct boundaries between different susceptibility levels. Notably, while the proposed KNN-GCN model displays exceptional performance in slope-unit-based LSM, its implementation requires high-level computing resources, and it is not recommended for small datasets.

In recent decades, extreme precipitation events have increased in frequency and intensity in Greece and across regions of the Mediterranean, with significant environmental and socioeconomic impacts. Therefore, extensive statistical analysis of the extreme rainfall characteristics on a dense temporal scale is crucial for areas with important economic activity. For this reason, this paper uses the daily precipitation measurements of four meteorological stations in a mining area of northeastern Chalkidiki peninsula from 2006 to 2021. Three statistical approaches were carried out to develop the best-fitting probability distribution for annual extreme precipitation conditions, using the maximum likelihood method for parameter estimation: the block maxima of the generalized extreme value (GEV) distribution and the peak over threshold of the generalized Pareto distribution (GPD) based on extreme value theory (EVT), and the gamma distribution. Based upon this fitting distribution procedure, return periods for the extreme precipitation values were calculated. Results indicate that EVT distributions satisfactorily fit extreme precipitation, with GPD being the most appropriate, and lead to similar conclusions regarding extreme events.

Abstract

Effective geochemical anomaly identification is crucial in mineral exploration. Recent trends have favored deep learning (DL) to decipher geochemical survey data. Yet purely data-driven DL algorithms often lack logical explanations and geological consistency, occasionally clashing with known geological insights and complicating model interpretation. A deep understanding of the geological processes forming the target mineral deposit is vital for accurate anomaly detection. Here, we introduce an adversarial autoencoder (AAE) network that integrates prior geological knowledge to identify geochemical anomalies linked to tungsten mineralization in southern Jiangxi Province, China. Considering the geochemical patterns linked to tungsten mineralization, Yanshanian granites and faults were strategically chosen as ore-controlling factors. The methodology employed multifractal singularity analysis to quantitatively measure the correlations between these ore-controlling factors and known tungsten deposits, aiming to establish an ore-forming regularity. This regularity serves as a priori distribution to control the encoder network's latent vector, refining the model's output. A comparison of detected geochemical anomalies under different constraints (AAE, Granite_AAE, Fault_AAE, and Fault_Granite_AAE) revealed that AAE models incorporating prior geological information consistently outperformed unconstrained models in terms of anomaly detection. Integrating geological expertise with DL, our study overcomes the challenges of models relying purely on data or theory, offering a promising approach to geochemical exploration.

Covariance functions are the core of spatial statistics, stochastic processes, machine learning, and many other theoretical and applied disciplines. The properties of the covariance function at small and large distances determine the geometric attributes of the associated Gaussian random field. Covariance functions that allow one to specify both local and global properties are certainly in demand. This paper provides a method for finding new classes of covariance functions having such properties. We refer to these models as hybrid, as they are obtained as scale mixtures of piecewise covariance kernels against measures that are also defined as piecewise linear combinations of parametric families of measures. To illustrate our methodology, we provide new families of covariance functions that are proved to be richer than other well-known families proposed in earlier literature. More precisely, we derive a hybrid Cauchy–Matérn model, which allows us to index both long memory and mean square differentiability of the random field, and a hybrid hole-effect–Matérn model which is capable of attaining negative values (hole effect) while preserving the local attributes of the traditional Matérn model. Our findings are illustrated through numerical studies with both simulated and real data.

Trace element fingerprints preserved in zircons offer clues to their origin and crystallization conditions. Numerous geochemical indicators have been established to evaluate the source rock characteristics from a geochemical perspective; however, multivariate trace element data have not been sufficiently investigated statistically. As substantial amounts of zircon data from a wide range of rock types have become accessible over the past few decades, it is now essential to reassess the utility of trace elements in discriminating source rock types. We employed a new zircon trace element dataset and established classification models to distinguish eight types of source rocks: igneous (acidic, intermediate, basic, kimberlite, carbonatite, and nepheline syenite), metamorphic, and hydrothermal. Whereas a conventional decision tree analysis was unable to correctly classify the new dataset, the random forest and support vector machine algorithms achieved high-precision classifications (> 80% precision, recall, and F1 score). This work confirms that trace element composition is a helpful tool for province studies and mineral exploration using detrital zircons. However, the compiled dataset with many missing values leaves room for improving the models. Trace elements, such as P and Sc, which cannot be measured by quadrupole inductively coupled plasma mass spectrometry, are vital for more accurate classification.

Abstract

The knowledge of fracture properties and its geometrical patterns is often required for the analysis of mechanical and flow properties in fractured reservoirs, as fracture characterization plays a critical role in the optimization of hydrocarbon production or estimation of storage capacity of subsurface reservoirs. A stochastic method based on a Markov chain Monte Carlo (MCMC) algorithm is proposed to estimate fracture properties using a rock physics model for fractured rocks. Two implementations are presented: a Metropolis algorithm based on a Gaussian prior distribution and an extended Metropolis algorithm with an informative prior obtained from multiple-point statistics simulations. The results are compared to a Bayesian analytical approach where the solution is based on a linearized approximation of the rock physics model. The novelty of the proposed approach is the use of a training image, that is, a conceptual geological model, to account for the spatial distribution of the fractures. Two fracture properties are considered, namely fracture density and aspect ratio, and the spatial distribution and geometrical characteristics of fractures are also investigated to understand the connectivity patterns that control fluid flow. The MCMC approach with a training image is more computationally demanding but provides geometrical models of the spatial distribution of fractures. The inversion results show that the prediction accuracy of fracture density and aspect ratio obtained by the MCMC methods is similar to the one obtained with the analytical approach, and that the MCMC methods provide a reliable assessment of the posterior uncertainty as well.

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.