Mathematical Geosciences最新文献

Probabilistic methods for geophysical inverse problems allow the use of arbitrarily complex prior information in principle. Geostatistical techniques, such as multiple-point statistics (MPS), for describing spatial correlation models and higher-order statistics have been proposed to achieve this inversion task, in which stochastic algorithms such as Markov chain Monte Carlo (McMC) are incorporated. However, stochastic sampling and optimization often require a large number of iterations, and thus geostatistical sampling of the prior model can become computationally demanding. To overcome this challenge, a deep learning model, namely conditional generative adversarial networks (CGANs), is proposed, which allows one to perform a random walk to sample the complex prior distribution. CGANs simulate conditional realizations conditioned to the available hard conditioning data, that is, direct measurements, while preserving the geometrical structure of the model parameters of interest and replicating the sequential Gibbs sampling algorithm. Despite the need for a training step, for a large number of simulations, CGANs are more efficient than traditional geostatistical simulation algorithms such as single normal equation simulation (SNESIM). The proposed methodology is used as part of the extended Metropolis algorithm to predict the distributions of categorical facies in two examples, a dune environment in the Gobi Desert and a channel system in an idealized subsurface reservoir, from indirect observational data such as acoustic impedance. The inversion results are compared to the extended Metropolis algorithm using standard MPS sampling.

Exponentially increasing amounts of copper mined over the last 120 years and Cu’s central place in modern society raise concerns about its long-term availability. Estimates of copper production from mines made here based on projected population (R² = 0.95) are lower than many previous studies. Projected world production of copper from mines in 2100 of 28.2 million tons Cu is approximately 34% more than 2021 production. Rough estimates of recycled Cu added to mine production are less than previous estimates of future consumed Cu. Although annual mined copper will peak in about 2086, production will continue in a gentle decline through 2100. Future availability of consumed copper is dependent on availability of mined copper plus recycled copper. Estimated total copper demand including new technologies is 33 million tons in 2040. Total expected copper from mines estimated here is 24 million tons in 2040, but with a recycling rate of 30%, required demand of 33 million tons would be satisfied. Per capita GDP effects on copper consumption require a logistic growth curve to model. In countries with high per capita GDP, per capita copper consumption is likely to reach saturation and stabilize or perhaps reduce demand for copper. Most countries will achieve high incomes at some point. If earlier studies of high-income copper consumption rates hold in the future, 10 kg per capita of copper for 10 billion people expected before 2100 leads to estimated total annual copper consumption of 100 million tons. This worst-case demand estimate greatly exceeds projected copper from mines and recycling and ignores increased demand due to electrification scenarios and declines in demand due to declining population by 2100 and possible dematerialization.

R-mode hierarchical clustering is a method for forming hierarchical groups of mutually exclusive subsets of variables. This R-mode cluster method identifies interrelationships between variables which are useful for variable selection and dimension reduction. Importantly, the method is based on metric elements defined on the sample space of variables. Consequently, hierarchical clustering of compositional parts should respect the particular geometry of the simplex. In this work, the connections between concepts such as distance, cluster representative, compositional biplot, and log-ratio basis are explored within the framework of the most popular R-mode agglomerative hierarchical clustering methods. The approach is illustrated in a paleoecological study to identify groups of species sharing similar behavior.