A Special Issue: Geomathematics in practice: Case studies from earth- and environmental sciences – Proceedings of the Croatian-Hungarian Geomathematical Congress, Hungary 2015

1 Introduction

This volume is a proceeding of fascinating presentations given within the framework of 15^th Hungarian and 7^th Croatian and Hungarian Geomathematical Convent hosted by the city of Mórahalaom (Hungary) in May 2015. Geomathematical conferences in Hungary organized by the Geomathematical & Informatics Section of the Hungarian Geological Society (GIS-HGS; Fig. 1) have a long-standing history of 30 years, and since 2007 they have been jointly organized with the Geomathematical Section of Croatian Geological Society each summer. This year forty people attended the three day long meeting and had the opportunity to listen to 28 presentations and participate in a workshop.

Figure 1

New logo of the GIS-HGS (2015).

The year 2015 was special in many ways, a new directorate was elected to govern the Hungarian Geomathematical Section for the next three years. This gave the opportunity to express our gratitude to the last head, János Geiger, and secretary, József Kovács (Fig. 2) for their many years of hard work, enthusiasm and dedication in leading the Section. János Geiger was the head of the GIS-HGS between 2000 and 2015 and the secretary in period of 1985–1993, while József Kovács was the secretary of the GIS-HGS between 2004 and 2015.

Figure 2

Collage of the photographs taken at the 15^th Hungarian and 7^th Croatian and Hungarian Geomathematical Convent, 2015. Former head, János Geiger: third row, middle picture sitting in the middle and former secretary, József Kovács: third row leftmost picture with the microphone. Logos of the Hungarian Geological Society, the Department of Geology and Paleontology at the University of Szeged and the former logo of the GIS-HGS: last row, rightmost picture.

The 2015 Congress mainly focused on geomathematical models which can be considered as reflections of geological reality, or in certain cases science fiction. The conference hosted various topics in theoretical and practical sessions. Questions around the main topic were raised numerous times in the previous years, giving the idea to arrange the conference of 2015 around this particular obstacle.

Throughout the years a vast number of studies and papers have underlined the fact that mathematics has an often important role in earth sciences covering a wide spectrum of applied methods. Therefore, geomathematics has become one of the key sciences of studying the complex Earth system. Geomathematics is the discipline which aims to handle the qualitative and quantitative problems of the Earth’s systems using the tools of mathematics/statistics combined with the knowledge of earth sciences [1–4]. Wherever and whenever there are data and observations to be processed, i.e. the diverse scalar, vectorial, continuous or categorical, deterministic or probabilistic data we need mathematics [5].

One of the specific and most important task of geomathematics/geostatistics is to build a bridge between theoretical mathematics, its applied methods, along with the geotechnical applications, and the modelled geo-objects (earth, environments, reservoir, etc.). Often the real difficulty is that one may lose himself in model development trying to approximate reality as close as possible, arriving at a theoretical model which may “fall too far” from the actual heterogeneity of the pursued phenomenon.

In relation, mathematics is not just an applied science to obtain solutions, but it is applicable to translate the image of the real world to virtual models and vice versa [6]. This may take us back to rethink the original rules/theories and recalibrate the models in an iterative process, and if necessary develop new methods while not forgetting the back-transfer between the results derived from the modelled object and the real object either. As a last step, the mathematical model must be validated – based on actual measured data – because without it, it remains only science fiction [7].

2 Papers presented

The papers in this in this special issue of Open Geosciences were selected from within the framework of this conference with the hope of providing insights into-, and bridging the gap between mathematical and statistical practice among case studies from classical environmental applications of multivariate statistics [8, 9] through the solution of reservoir geological problems [10–14], to the application of methods that are new to this field of science [15] along with many other aspects of geology and environmental sciences. The issue consists of two main parts, the first part deals with studies mainly concerning petrology, while the second is related to urban/classical environmental problems, handled using geostatistics.

The issue is led by two papers dealing with the topics of basin analysis, petrophysical mapping and volume calculations. The first one is authored by Marko Cvetković, a study on a part of the Lonja Formation (Croatia) exploring its maturation and its expulsion of bacterial methane as a potential hydrocarbon source, and its reservoir rocks. His results indicated that selected member within the Lonja Formation has a large source rock potential for bacterial methane [10].

The following paper is more strictly concerned with the volume calculation topic; it is however, a purely methodological one written by Slavinić and Cvetković. As they state: “The volume calculation of geological structures is one of the primary goals of interest when dealing with the exploration or production of oil and gas in general” [11]. They therefore set themselves the task of comparing four different bulk volume calculation cases by standard numerical integration and cell based models. This, they achieved, though Simpson’s formula proved to be more precise but less practical regarding numerical integration approach [11].

Continuing in the field of petrology a new approach is introduced by Nemes from the MOL Plc., an integrated oil and gas company from Hungary. He presents a study concerning the relationship of initial water saturation profiles and capillarity in water-wet hydrocarbon reservoirs. The most significant benefit of this approach is that it combines the advantages of two widely used drainage capillary curve measurement methods, while being able to overcome their disadvantages, yielding a normalized, more realistic curve (or Look-up function) applicable in reservoir geological and engineering calculations [12].

In another quite theoretical contribution related to the MOL Plc. and discipline-vise to hydrology, Lux et al. were able to simplify the optimization of multi-lateral well patterns using unstructured grids, while keeping a similar effectiveness as the ones in literature [13].

The fifth paper is the last related to petrology, though already closer to sedimentology, traversing the first and second parts of the issue. In the past few decades process-sedimentology has become more-and-more important in the characterization of deep-water clastic depositional systems. In this way, the recognized faciological attributes can be associated with the depositional processes (e.g. deposits of slumps, sandy debris flows, turbidity currents etc). In the paper by Borka [14] this approach is presented through a case study of the Tercier deep-water sequence of the Pannonian-basin.

The last three papers in the issue focus on the use of geomathematical models in the area of handling urban/eco/paleo-environmental problems (case studies), giving an insight into the phenomenon that these models can indeed be considered the reflections of the geological/environmental reality.

The use of multivariate statistical methods in processing and evaluating engineering geological data has been outlined by Kovács et al. [8]. Five key engineering geological parameters were considered in their analyses, including the laboratory test results of #1260 core drillings obtained during the construction of metro line 4 in Budapest. The results suggest that there is a strong correlation between cohesion and compressive strength. The paper also emphasizes that the use of multivariate statistical methods allows the grouping of various sediments even when the data contains overlaps and has numerous uncertainties. Furthermore, the authors have also proven that the application of such methods for seemingly very scattered soil mechanical parameters is crucial in obtaining reliable engineering geological data for design.

The penultimate study moves away from geology towards the field of ecology/environmental science and gives another good example of the wide range of applicability of the geomathematical toolset represented in this issue. In the study of Dinka et al. [9] a selected parcel of the reed belt of the Hungarian part of Lake Fertő/Neusiedler See was examined, from the side of wastewater treatment, based on variables mainly related to the nutrient cycle of the system and the characteristics of the reed stand giving a breath of fresh air – literally – to the issue. Based on the results, authors provided further evidence that the nutrient retention capacity of the reed stand may be employed in the treatment of wastewater without endangering the natural assets of the lake.

The last contribution again reinforces the conviction that geostatistics is capable of making a connection between the world of numbers (theory) and reality. In their paper Topál et al. [15] present a comparison of numerous state-of-the-art breakpoint detection methods and apply them, utilizing knowledge gained on a paleoclimatological time series and capillary pressure curves – such as those Nemes [12] deals with – framing the issue. Such a comparison has not been published before, therefore, this is indeed another novelty in this issue of Open Geosciences.