The ongoing transformation of the energy industry is responding to multiple factors, including growing energy demand with population growth, the growth of unconventional and renewable energy resources, hybrid energy systems and the mitigation of influences on climate change. Beyond widespread and fast-moving digital transitions, the industry is adopting new operational practices and rapidly translating technologies from other industries to meet energy needs. In this context, the convergence of emerging technologies with mathematical geoscience has opened new research avenues, not only for the energy industry but for many areas of natural resource and environmental management. This evolution is hybridizing skill sets used by geoscientists, creating new partnerships and changing organizations. New paradigms are strengthening industry adoption of technologies and research advances related to mathematical geoscience

Digital revolution has caused unimaginable impact on human life. Big data and data discovery have not only encouraged and stimulated rapid increase of data generation and capability of data handling, but also enforced all other fields of science meeting the trend of digital revolution and accelerating the advance of science and technology as well as new model of industrialization. There is no doubt that big data and data analytical technologies including artificial intelligence and machine learning will bring new way of conducting research. For example, with the current computing power and cloud environment data analysis may no longer constraint to data sample and local optimization. The simple explicit “cause – result” relation may not need to be the hypothesis for research. Recently a new initiative of Deep-time Digital Earth (DDE) was proposed by several Adhering National Members and International Associations Affiliated Members of the International Union of Geological Sciences (IUGS). DDE program has been approved by IUGS EC as the first IUGS Recognized Big Science Program. The primary goal of the Deep-time Digital Earth project is to develop an open platform facilitating efficiency and effectiveness of utilization of varieties of digital earth data with proper temporal and spatial reference according to paleogeology and paleogeography rather than to today’s geology and geography. The Deep-time Digital Earth is an international consortium that aims to develop a platform of connected geoscience informatics efforts that link Earth’s spheres (hydrosphere, geosphere, atmosphere, biosphere) in geological history. The Deep-time Digital Earth will provide digital earth with 4D (Deep space, Deep ocean, Deep earth and Deep-time as well as Deep-time Digital Data Discovery) representing complete evolution of earth from past to present and towards the future. It opens great opportunities for scientists from the whole world to conduct transdisciplinary research and international collaboration.

Statistical data analysis should always be done with care if outliers are present in the data, since they have the potential to spoil the analysis. However, usually it is not clear if multivariate data contain outliers, and in particular, if such outliers would affect the statistical method to be used. Diagnostic plots of the results from the analysis will only reveal outliers if the method itself is robust against the outliers. Moreover, the impact of outliers depends on the statistical model being used. Identifying outliers in compositional data is even more tricky because their values are unusual not in the absolute but in a relative sense. With the log-ratio approach for compositional data analysis, outliers could even be artificially created by including variables with extremely low and unreliable values - a frequent practical issue. We will discuss these problems and provide more detailed insight, propose some possible approaches to cope with these issues, and illustrate them at real data, mainly from the field of geochemistry.

Models are abstractions of reality. The modeler’s job is to keep the model as simple as possible, so the results can be understood, without making them too simplistic. Drawing on work from my career as an Earth historian, I provide examples of where simple models were appropriately used to provide insights on long-term earth evolution, and complicated models were used to investigate Earth system biogeochemical interactions. I also provide examples where complicated models were used to address simple problems, and simplistic models were used to study complex problems, both somewhat unsuccessfully or unnecessarily. On balance, models have kept me from saying stupid things, at least most of the time (I think).

The analysis of complex data distributed over large or highly textured regions poses new challenges for spatial statistics. Object Oriented Spatial Statistics (O2S2) is a recent system of ideas and methods that allows to analyze high dimensional and complex data when their spatial dependence is an important issue. We present the key concepts of O2S2, as a general approach to analyze and predict georeferenced complex data, interpreted as objects in appropriate mathematical spaces. Examples of object data include functional data, distributional data or tensors. We discuss the extension of key geostatistical concepts (e.g., stationarity) and methods (e.g., Kriging) to the context of O2S2, and discuss recent extensions of these methods that permit the the analysis of object data distributed over complex regions. Here, we shall ground our developments on computational intensive methods, based on random domain decompositions of the study domain. The presented models and methods will be illustrated through real environmental case studies. (joint work with P. Secchi)

Problems with compositional data, like spurious correlation and negative bias, are well known in the Geosciences. Not so well known is the fact that the same problems appear when dealing with regionalized compositions. These problems are illustrated, and a solution is presented that is based on the principle of working in coordinates using isometric logratio representations. The proposed approach offers not only a tool for standard geostatistical studies, but also a way of modelling crossvariograms based on the matrix valued variation variogram. Moreover, it allows to overcome usual inconsistencies with indicator kriging through simplicial indicator kriging. One concern about the proposed solutions is that available compositional methods lead to a representation of results in proportions, while often practical applications require results in the original units-non-closed forms. In order to solve such a problem, specific tools to recover original units have been studied. In summary, the main aspects related to the modelling and analysis of regionalized compositions have found satisfactory solutions.

Karstic aquifers are characterized by the presence of rare but highly permeable karstic conduits embedded in a carbonate matrix of lower permeability. This highly heterogeneous structure results from the dissolution of the matrix by acidic water and a self-reinforcing process. Karst aquifers can present very fast flow and contaminant transfer in the conduits. Consequently, these aquifers are often highly vulnerable to groundwater pollution and extremely sensitive to climate fluctuations. In recent years, significant progresses have been made to model karstic reservoirs. In this presentation, we will discuss several of these modeling aspects, including techniques that can be used to simulate the geometry of karstic networks (often only partially known), flow and transport simulation methods, but also the speleogenesis processes and in particular the role of ocean tides in the case of coastal aquifers.

Mineral exploration according to methods of mathematical geosciences generally includes mineralization related geo-information extraction and integration. In this talk, singularity-based algorithms and applied research are discussed for geological feature recognition and mineral potential mapping by the processing of geophysical, geochemical and geological data with the use of novel GIS and computer-based techniques. Singularity theory initially proposed in former studies by Dr. Qiuming Cheng several years ago is helpful for identifying target areas in mineral exploration and the study of regional geochemical pollution patterns. The frequently applied square window-based methods are limited to investigate anisotropy of mineralization related anomalies. This study further developed the analytical algorithm of singularity theory, and proposed “Geological Window”-based singularity algorithms. Compared with other singularity estimation methods, the new technique objectively identifies anisotropic geochemical features and investigates the non-linear geochemical behaviors. Geographic regression analysis (GWR) model well practiced in social science was mainly utilized to characterized spatial non-stationary relations among social factors, e.g., between housing price and density of population, education level, traffic facility, etc. GWR model is currently applied to depict non-stationary influences of tectono-magmatic processes on ore material accumulation in spatial scenario. Examining spatial distributions of regression coefficients, it can be inferred that mineralization at different locations was caused by interactivities of multiple geo-processes to different degrees. This applied research which helps to improve understanding of local metallogeny can be a useful reference to future regression analysis on geological issues.