Handbook of Mathematical Geosciences

This Open Access handbook published at the IAMG's 50th anniversary, presents a compilation of invited path-breaking research contributions by award-winning geoscientists who have been instrumental in shaping the IAMG. It contains 45 chapters that are categorized broadly into five parts (i) theory, (ii) general applications, (iii) exploration and resource estimation, (iv) reviews, and (v) reminiscences covering related topics like mathematical geosciences, mathematical morphology, geostatistics, fractals and multifractals, spatial statistics, multipoint geostatistics, compositional data analysis, informatics, geocomputation, numerical methods, and chaos theory in the geosciences

Book of Abstracts

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Statistical and deep learning methods for geoscience problems

Machine learning is the new frontier for technology development in geosciences and has developed extremely fast in the past decade. With the increased compute power provided by distributed computing and Graphics Processing Units (GPUs) and their exploitation provided by machine learning (ML) frameworks such as Keras, Pytorch, and Tensorflow, ML algorithms can now solve complex scientific problems. Although powerful, ML algorithms need to be applied to suitable problems conditioned for optimal results. For this reason ML algorithms require not only a deep understanding of the problem but also of the algorithm’s ability. In this dissertation, I show that Simple statistical techniques can often outperform ML-based models if applied correctly. In this dissertation, I show the success of deep learning in addressing two difficult problems. In the first application I use deep learning to auto-detect the leaks in a carbon capture project using pressure field data acquired from the DOE Cranfield site in Mississippi. I use the history of pressure, rates, and cumulative injection volumes to detect leaks as pressure anomaly. I use a different deep learning workflow to forecast high-energy electrons in Earth’s outer radiation belt using in situ measurements of different space weather parameters such as solar wind density and pressure. I focus on predicting electron fluxes of 2 MeV and higher energy and introduce the ensemble of deep learning models to further improve the results as compared to using a single deep learning architecture. I also show an example where a carefully constructed statistical approach, guided by the human interpreter, outperforms deep learning algorithms implemented by others. Here, the goal is to correlate multiple well logs across a survey area in order to map not only the thickness, but also to characterize the behavior of stacked gamma ray parasequence sets. Using tools including maximum likelihood estimation (MLE) and dynamic time warping (DTW) provides a means of generating quantitative maps of upward fining and upward coarsening across the oil field. The ultimate goal is to link such extensive well control with the spectral attribute signature of 3D seismic data volumes to provide a detailed maps of not only the depositional history, but also insight into lateral and vertical variation of mineralogy important to the effective completion of shale resource plays

Summaries of FY 1996 geosciences research

The Geosciences Research Program is directed by the Department of Energy`s (DOE`s) Office of Energy Research (OER) through its Office of Basic Energy Sciences (OBES). Activities in the Geosciences Research Program are directed toward building the long-term fundamental knowledge base necessary to provide for energy technologies of the future. Future energy technologies and their individual roles in satisfying the nations energy needs cannot be easily predicted. It is clear, however, that these future energy technologies will involve consumption of energy and mineral resources and generation of technological wastes. The earth is a source for energy and mineral resources and is also the host for wastes generated by technological enterprise. Viable energy technologies for the future must contribute to a national energy enterprise that is efficient, economical, and environmentally sound. The Geosciences Research Program emphasizes research leading to fundamental knowledge of the processes that transport, modify, concentrate, and emplace (1) the energy and mineral resources of the earth and (2) the energy by-products of man

Abstracts of manuscripts submitted in 1993 for publication

This volume contains the abstracts of manuscripts submitted for publication during calendar year 1993 by the staff and students of the Woods Hole Oceanographic Institution. We identify the journal of those manuscripts which are in press or have been published. The volume is intended to be informative, but not a bibliography. The abstracts are listed by title in the Table of Contents and ar grouped into one of our five departents, Marine Policy Center, Coastal Research Center, or the student category. An author index is presented in the back to facilitate locating specific papers

Mathematical Methods, Modelling and Applications

This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods

Impact of Etna’s volcanic emission on major ions and trace elements composition of the atmospheric deposition

Mt. Etna, on the eastern coast of Sicily (Italy), is one of the most active volcanoes on the planet and it is widely recognized as a big source of volcanic gases (e.g., CO2 and SO2), halogens, and a lot of trace elements, to the atmosphere in the Mediterranean region. Especially during eruptive periods, Etna’s emissions can be dispersed over long distances and cover wide areas. A group of trace elements has been recently brought to attention for their possible environmental and human health impacts, the Technology-critical elements. The current knowledge about their geochemical cycles is still scarce, nevertheless, recent studies (Brugnone et al., 2020) evidenced a contribution from the volcanic activity for some of them (Te, Tl, and REE). In 2021, in the framework of the research project “Pianeta Dinamico”, by INGV, a network of 10 bulk collectors was implemented to collect, monthly, atmospheric deposition samples. Four of these collectors are located on the flanks of Mt. Etna, other two are in the urban area of Catania and three are in the industrial area of Priolo, all most of the time downwind of the main craters. The last one, close to Cesarò (Nebrodi Regional Park), represents the regional background. The research aims to produce a database on major ions and trace element compositions of the bulk deposition and here we report the values of the main physical-chemical parameters and the deposition fluxes of major ions and trace elements from the first year of research. The pH ranged from 3.1 to 7.7, with a mean value of 5.6, in samples from the Etna area, while it ranged between 5.2 and 7.6, with a mean value of 6.4, in samples from the other study areas. The EC showed values ranging from 5 to 1032 μS cm-1, with a mean value of 65 μS cm-1. The most abundant ions were Cl- and SO42- for anions, Na+ and Ca+ for cations, whose mean deposition fluxes, considering all sampling sites, were 16.6, 6.8, 8.4, and 6.0 mg m-2 d, respectively. The highest deposition fluxes of volcanic refractory elements, such as Al, Fe, and Ti, were measured in the Etna’s sites, with mean values of 948, 464, and 34.3 μg m-2 d-1, respectively, higher than those detected in the other sampling sites, further away from the volcanic source (26.2, 12.4, 0.5 μg m-2 d-1, respectively). The same trend was also observed for volatile elements of prevailing volcanic origin, such as Tl (0.49 μg m-2 d-1), Te (0.07 μg m-2 d-1), As (0.95 μg m-2 d-1), Se (1.92 μg m-2 d-1), and Cd (0.39 μg m-2 d-1). Our preliminary results show that, close to a volcanic area, volcanic emissions must be considered among the major contributors of ions and trace elements to the atmosphere. Their deposition may significantly impact the pedosphere, hydrosphere, and biosphere and directly or indirectly human health

Impact of geogenic degassing on C-isotopic composition of dissolved carbon in karst systems of Greece

The Earth C-cycle is complex, where endogenic and exogenic sources are interconnected, operating in a multiple spatial and temporal scale (Lee et al., 2019). Non-volcanic CO2 degassing from active tectonic structures is one of the less defined components of this cycle (Frondini et al., 2019). Carbon mass-balance (Chiodini et al., 2000) is a useful tool to quantify the geogenic carbon output from regional karst hydrosystems. This approach has been demonstrated for central Italy and may be valid also for Greece, due to the similar geodynamic settings. Deep degassing in Greece has been ascertained mainly at hydrothermal and volcanic areas, but the impact of geogenic CO2 released by active tectonic areas has not yet been quantified. The main aim of this research is to investigate the possible deep degassing through the big karst aquifers of Greece. Since 2016, 156 karst springs were sampled along most of the Greek territory. To discriminate the sources of carbon, the analysis of the isotopic composition of carbon was carried out. δ13CTDIC values vary from -16.61 to -0.91‰ and can be subdivided into two groups characterized by (a) low δ13CTDIC, and (b) intermediate to high δ13CTDIC with a threshold value of -6.55‰. The composition of the first group can be related to the mixing of organic-derived CO2 and the dissolution of marine carbonates. Springs of the second group, mostly located close to Quaternary volcanic areas, are linked to possible carbon input from deep sources

EVOLUTION OF THE SUBCONTINENTAL LITHOSPHERE DURING MESOZOIC TETHYAN RIFTING: CONSTRAINTS FROM THE EXTERNAL LIGURIAN MANTLE SECTION (NORTHERN APENNINE, ITALY)

Our study is focussed on mantle bodies from the External Ligurian ophiolites, within the Monte Gavi and Monte Sant'Agostino areas. Here, two distinct pyroxenite-bearing mantle sections were recognized, mainly based on their plagioclase-facies evolution. The Monte Gavi mantle section is nearly undeformed and records reactive melt infiltration under plagioclase-facies conditions. This process involved both peridotites (clinopyroxene-poor lherzolites) and enclosed spinel pyroxenite layers, and occurred at 0.7–0.8 GPa. In the Monte Gavi peridotites and pyroxenites, the spinel-facies clinopyroxene was replaced by Ca-rich plagioclase and new orthopyroxene, typically associated with secondary clinopyroxene. The reactive melt migration caused increase of TiO2 contents in relict clinopyroxene and spinel, with the latter also recording a Cr2O3 increase. In the Monte Gavi peridotites and pyroxenites, geothermometers based on slowly diffusing elements (REE and Y) record high temperature conditions (1200-1250 °C) related to the melt infiltration event, followed by subsolidus cooling until ca. 900°C. The Monte Sant'Agostino mantle section is characterized by widespread ductile shearing with no evidence of melt infiltration. The deformation recorded by the Monte Sant'Agostino peridotites (clinopyroxene-rich lherzolites) occurred at 750–800 °C and 0.3–0.6 GPa, leading to protomylonitic to ultramylonitic textures with extreme grain size reduction (10–50 μm). Compared to the peridotites, the enclosed pyroxenite layers gave higher temperature-pressure estimates for the plagioclase-facies re-equilibration (870–930 °C and 0.8–0.9 GPa). We propose that the earlier plagioclase crystallization in the pyroxenites enhanced strain localization and formation of mylonite shear zones in the entire mantle section. We subdivide the subcontinental mantle section from the External Ligurian ophiolites into three distinct domains, developed in response to the rifting evolution that ultimately formed a Middle Jurassic ocean-continent transition: (1) a spinel tectonite domain, characterized by subsolidus static formation of plagioclase, i.e. the Suvero mantle section (Hidas et al., 2020), (2) a plagioclase mylonite domain experiencing melt-absent deformation and (3) a nearly undeformed domain that underwent reactive melt infiltration under plagioclase-facies conditions, exemplified by the the Monte Sant'Agostino and the Monte Gavi mantle sections, respectively. We relate mantle domains (1) and (2) to a rifting-driven uplift in the late Triassic accommodated by large-scale shear zones consisting of anhydrous plagioclase mylonites. Hidas K., Borghini G., Tommasi A., Zanetti A. & Rampone E. 2021. Interplay between melt infiltration and deformation in the deep lithospheric mantle (External Liguride ophiolite, North Italy). Lithos 380-381, 105855