Space–Time Mathematical Framework for Sedimentary Geology

Interpolating physical properties in the subsurface is a recurrent problem in geology. In sedimentary geology, the geometry of the layers is generally known with a precision much superior to that which one can reasonably expect for the properties. The geometry of the layers is affected by folding and faulting since the time of deposition, whereas the distribution of properties is, to a certain extent, determined at the time of deposition. As a consequence, it may be wise to model first the geometry of the layers and then, simplify the geologic equation by removing the influence of that geometry. Inspired from the work of H. E. Wheeler on Time-Stratigraphy, we define, mathematically, a new space where all horizons are horizontal planes and where faults, if any, have disappeared. We surmise that this new space, however approximative, is better to model physical properties of the subsurface whatever the subsequent interpolation method used. The proposed mathematical framework also provides solutions to complex problems such as determination of strains resulting from tectonic events and up-scaling of permeabilities on structured and unstructured 3D grids.     

Biochemie und Feinstruktur Fossiler Knochen aus Bituminösen Schichten

Zusammenfassung Eingangs wird kurz das Untersuchungsmaterial, seine stratigraphische Eingliederung und seine lokale Herkunft skizziert. Sämtliches Wirbelmaterial wurde aus bituminösen Schichten verschiedenen Alters entnommen. Bei der Bestimmung des Gehalts an organischer Substanz dor Wirbelknochen trennte ich zwischen ursprünglicher, d. h. knocheneigener organischer Substanz und aus dem Sediment eingewanderter organischer Substanz während der Einbettung der Knochen bzw. später.Chemismus und Feinstruktur der fossilen Wirbelknochen zeigen keine wesentlichen Unterschiede gegenüber den rezenten. Lediglich die Aminosäuren Histidin und Methionin fehlen unter denjenigen, die das rezente Kollagen enthält. Auf Grund ihres einerseits mengenmäßigen geringen Vorhandenseins im Kollagen und andererseits wesentlich unbeständigeren Charakters ist ihr Fehlen verständlich. Die röntgenographische Untersuchung der Knochen mit dem Zählrohrgoniometer und die polarisationsmikroskopische Betrachtung der Knochendünnschliffe zeigt, daß keine knochenfremden Mineralien in die Knochen eingewandert bzw. dort auskristallisiert sind. Elektronenmikroskopische Untersuchungen wurden gleichfalls an den Knochen durchgeführt. Die bisherigen vorläufigen Ergebnisse lassen noch nicht klar genug erkennen, ob die Veränderung der Knollagenstruktur auf das absolute geologische Alter der Knochen oder auf die nicht völlig identische Einbettung derselben in die bituminösen Schichten oder den Chemismus bzw. Bitumengehalt des Sediments zurückzuführen ist.Der unterschiedliche Feinbau der Wirbelknochen läßt eine verschieden starke Adsorptionsfähigkeit für Bitumen erkennen. Den höchsten Gehalt an Bitumen zeigt die Zone der inneren Generallamellen und das umgewandelte Gewebe der Chordascheide und des Chordagewebes bei den Ichthyosaurierwirbeln.

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The author analysed vertebrae taken from strata of different geological age. For some specified reasons only bones of bituminous layers have been analysed. These layers and the localities are: the bituminous schist of the Middle Alpine Trias (Anisian/Ladinian) of the Monte San Giorgio (Kanton Tessin, Switzerland), the Lias epsilon (Posidonomya Shales, Toarcium) of Holzmaden (Baden-Württemberg, Germany), and the bituminous swamps of Rancho La Brea (USA). It has turned out that under these special conditions of bedding the collagenous structure has been preserved to a great extent, and no migration of minerals out of the sediments into the bones has taken place. This could be proved by the use of an X-ray-counting goniometer (Zählrohrgoniometer).Comparing analyses of vertebrae taken from non-bituminous layers showed that in the those cases the collagenous structure had been destroyed, and thatThis means that the bitumen must have acted as a protecting film on the bones.

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Résumé Au départ seront brièvement esquissés le matériel de recherche, son enchaînement stratigraphique et son origine locale. L'ensemble du matériel vertébral a été retiré de couches bitumineuses d'âges différents. Par la détermination du contenu de la substance organique des vertèbres, j'ai séparé la substance primitive, c'est-à-dire organique propre aux os, du sédiment, de la substance organique implantée pendant le gisement des os ou après.Par rapport aux vertèbres actuelles, le chimisme et la configuration intime (constitution intime) des vertèbres fossiles n'offrent pas de différences essentielles. Simplement, parmi les acides aminés, l'histidine et la méthionine font défaut parmi ceux que contient le collagène récent. En raison de leur existence en faible quantité d'une part, et de leur caractère essentiellement labile d'autre part, leur absence est compréhensible.L'exploration radiographique des os au compteur goniomètrique et l'examen micropolarographique des coupes minces osseuses montrent qu'aucune substance minérale étrangère n'a été implantée dans les os, ou fixée. Des recherches au microscope électronique ont également été menées sur les os. Les résultats jusque là provisoires ne font pas encore assez clairement ressortir si la transformation de la structure du collagène est à rapporter à l'âge géologique absolu des os ou à leur localisation (Einbettung) non parfaitement identique dans les couches bitumineuses, ou encore au chimisme, disons plutôt au contenu bitumineux du sédiment.La constitution intime différente des vertèbres fait apparaître un potentiel d'adsorption variable pour les bitumes. C'est dans la zone des lamelles générales intérieures (inneren Generallamellen) et dans le tissu transformé (umgewandelte) de la gaine et des tissus chordaux des vertèbres d'Ichthyosaure que l'on trouve la plus grande teneur en bitumes.

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Estimation of the probability of success in petroleum exploration

A probabilistic model for oil exploration can be developed by assessing the conditional relationship between perceived geologic variables and the subsequent discovery of petroleum. Such a model includes two probabilistic components, the first reflecting the association between a geologic condition (structural closure, for example) and the occurrence of oil, and the second reflecting the uncertainty associated with the estimation of geologic variables in areas of limited control. Estimates of the conditional relationship between geologic variables and subsequent production can be found by analyzing the exploration history of a training area judged to be geologically similar to the exploration area. The geologic variables are assessed over the training area using an historical subset of the available data, whose density corresponds to the present control density in the exploration area. The success or failure of wells drilled in the training area subsequent to the time corresponding to the historical subset provides empirical estimates of the probability of success conditional upon geology. Uncertainty in perception of geological conditions may be estimated from the distribution of errors made in geologic assessment using the historical subset of control wells. These errors may be expressed as a linear function of distance from available control. Alternatively, the uncertainty may be found by calculating the semivariogram of the geologic variables used in the analysis: the two procedures will yield approximately equivalent results. The empirical probability functions may then be transferred to the exploration area and used to estimate the likelihood of success of specific exploration plays. These estimates will reflect both the conditional relationship between the geological variables used to guide exploration and the uncertainty resulting from lack of control. The technique is illustrated with case histories from the mid-Continent area of the U.S.A.This paper was presented at Symposium 116.3, Quantitative Strategy for Exploration, held as part of the 25th International Geological Congress, Sydney, Australia, August 1976.     

Prediction of volumes and risk in hydrocarbon exploration: a quantification of geology

 The prediction of the hydrocarbon potential of a specific trap or of a number of specific traps (venture), referred to herein as prospect appraisal, concerns a probabilistic exercise based on the quantification of geology in terms of structural closure, reservoir quality, hydrocarbon charge, and the retention potential of the seal. Its objectives include: (a) prediction of the hydrocarbon volumes that could be present in the trap from an analysis of its geologic attributes; (b) the amount of uncertainty introduced in the volumetric prediction by the uncertainties in the subsurface geology; (c) the risk that one or more of the essential attributes of the prospect are underdeveloped and recoverable reserves are absent. The uncertainty of the geologic input requires a probabilistic approach, for which the Monte Carlo procedure is well suited. Prospect appraisal forms the basis for decision-making in oil exploration and development and, therefore, should be reliable, consistent, and auditable. This requires the use of a consistent methodology, the development of reliable models to quantify the geologic processes involved, and the collection of comprehensive and relational databases for the many geologic variables. As a result of data availability, uncertainty and risk tend to increase strongly from mature, producing basins to areas of frontier exploration. This may complicate management of exploration portfolios. Received: 1 July 1996/Accepted: 25 November 1996     

Kriging with imprecise (fuzzy) variograms. I: Theory

Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The accuracy of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create good experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data.     

A review of conventional techniques for subsurface characterization of landslides

Naturally occurring landslides can be difficult to characterize and often exhibit anomalies in controlling geometry and consistency. The characterization of landslides in engineering geology practice is usually based on program of subsurface exploration; focused on identifying subsurface materials, structure and stratigraphy, hydrologic conditions, and appropriate strength parameters. On native slopes bereft of anthropogenic modification (excavation), geomorphic evidence of previous movement and its relative depth and scale are often discernible to the experienced eye. This paper seeks to describe the various techniques that have been successfully employed in site-specific subsurface investigations of prehistoric landslides. These include considerations of limiting geometry (for planning subsurface exploration and sampling), overcoming problems with site access, exploratory trenches, small diameter borings, downhole logging of large diameter borings, and geophysical techniques. These procedures can be combined to develop more realistic cross sections along the vector of maximum landslide movement, so the displaced mass can be realistically analyzed. The respective advantages and disadvantages of these techniques are discussed, with baseline references on subsurface exploration.     

Morphologie de la Méditerranée Occidentale

Résumé Partant de la grandiose conception d'Edouard Suess, la géologie de la Méditerranée a été divisée en quatre étages méditerranéens.Si le premier représente le début de la création d'une mer transgressive, le deuxième représente l'extension maximum de cette mer au delà de la chaîne alpine, puis il est suivi par une regression très générale. Au quatrième méditerranéen ou Pliocène, la mer pénètre dans toutes les vallées, dépressions du continent, réalisant la forme actuelle de cette mer où, depuis le Plaisancien se déposent les mêmes « argiles bleues » extraordinairement uniformes. Ces dépôts sont toujours très épais.Les unités morphologiques de la Méditerranée actuelle sont à peu près les mêmes que celles que les océanographes des Etats-Unis ont reconnu dans l'Atlantique: plaine littorale, plateau continental, pente continentale, plaine abyssale. Les sea-mounts ont même été reconnus en Tyrrhénienne et en Méditerranée Orientale. Les modifications du fond de la mer sont presque toujours dues au jeu des failles, soit d'effondrement comme en Tyrrhénienne, soit au contraire, de surrection, qui amènent à émerger d'anciens fonds de la mer.Les modifications corrélatives du fond de la mer, par abaissement et surtout par disjonction de la surface des continents, ont comme conséquences une regression depuis le Crétacé, entrecoupée de transgressions accompagnées d'épanchements de nature basaltique sur le fond de la mer. Ces mouvements se font de part et d'autre du pied de la Pente continentale qui est presque linéaire.A mon sens, les transformations de la Méditerranée se sont faites beaucoup plus autour des failles que par des plissements.

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Since the grand conception ofEdouard Suess, the geology of the Mediterranean has been divided into four Mediterranean stages.If the first stage represents the beginning of the creation of a transgressive sea, the second represents the maximum extension of this sea beyond the Alpine range, and is then followed by a general regression. At the fourth stage, Mediterranean or Pliocene, the sea imades all valleys, depressions of the adjoining continent, realizing the present form of this sea, where, since the Plaisancian, the same blue clays form thick deposits of extraordinarily uniform character.The morphologic units of the present Mediterranean are about the same as the cones that have been found in the Atlantic by the oceanographers of the United States: coastal plain, continental shelf, continental slope, abyssal plain. Even sea-mounts have been found in the Tyrrhenean sea and in the Eastern Mediterranean. The modifications of the bottom of the sea are mostly due to tectonics, either by lowering as in the Tyrrhenean sea, or, by rising, causing emergences.The correlative modifications of the sea-bottom, by subsidence and mostly by disjunction of the surface of the continents consequently display a regression since Cretaceous times, intersected by transgressions accompanied by submarin extrusions of a basaltic nature. Such movements occur at the foot of the (almost linear) continental slope.In my opinion, the transformations of the Mediterranean have occurred much more by faulting than by folding.

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Zusammenfassung Nach der grandiosen Konzeption von E.Suess ist die Geologie des Mittelmeeres in vier mediterrane Phasen gegliedert worden.Die erste Phase stellt den Beginn eines transgressiven Meeres dar, die zweite bezeichnet die maximale Ausdehnung dieses Meeres jenseits der Alpen, darauf folgt eine allgemeine Regression. Während der vierten Phase, dem Pliozän, dringt das Meer in alle Täler und Depressionen des Kontinents ein, wobei die heutige Form des Mittelmeeres entsteht, und mit dem Plaisancien kommt es zur Ablagerung der blauen Tone, die außerordentlich einheitlich und stets sehr mächtig sind. Die morphologischen Einheiten des heutigen Mittelmeeres sind etwa dieselben, wie sie die Ozeanographen der USA im Atlantik vorgefunden haben: Litoralebene, Kontinentalplateau, Kontinentalabhang, Tiefsee-Ebene. Die Seeberge (sea-mounts) wurden wiedererkannt im Tyrrhenischen Meer und im östlichen Mittelmeer. Die Veränderungen des Meeresgrundes sind fast immer auf die Wirkung von Verwerfungen zurückzuführen, wobei Senkung, wie im Tyrrhenischen Meer, stattfand oder aber Hebung zur Emersion des alten Meeresbodens führte. Die wechselseitigen Veränderungen des Meeresbodens durch Senkung und besonders durch Trennung der Kontinentoberflächen haben seit der Kreide eine Regression zur Folge, die von Transgressionen mit Basaltergüssen auf dem Meeresboden unterbrochen wurde. Diese Bewegungen fanden auf beiden Seiten am Fuße des Kontinentalabhanges statt, der fast linear ist.Nach meiner Meinung wurden die Umwandlungen des Mittelmeeres mehr durch Verwerfungen als durch Faltungen hervorgerufen.

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Zur Geochemie der Uranvererzungen in den Schweizer Alpen

Zusammenfassung Die im Verlaufe der letzten Jahre in den Schweizeralpen gefundenen Uranvorkommen sind auf einer geologischen Karte dargestellt. Das wichtigste Uranmineral ist Pechblende. Die mineralisierten Gesteine, wie Chlorit-Serizitschiefer und -Gneise und Serizit-Albitgneise zeigen wechselnd starke Metamorphose. An Proben von mehreren Tonnen sind Analysen ausgeführt und dabei die Gehalte von U, Th sowie von Metallen wie Cu, Pb und anderen begleitenden Spurenelementen ermittelt worden. Eine Kurvendarstellung und Tabellen enthalten die gefundenen Daten. In den metamorphen, mineralisierten Gesteinen ist der U-Gehalt immer deutlich höher als der Th-Gehalt.

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The various localities at which uranium was found in the Swiss Alps are noted in a geological map. Pitchblende is the most important uranium ore mineral to be found. The ore-containing rocks such as the chlorite- and sericite-schists and gneisses and the sericite-albite-gneisses are metamorphic to varying degrees. The uranium- and thorium-contents as well as the content of other metals such as Cu, Pb and of other accompanying trace-elements have been determined by means of various analytical methods from samples of several tons. The results are presented in tables and in a graph. It was found out that in mineralized, metamorphic rocks the uranium-content is substantially higher than that of thorium.

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Résumé Les gisements d'uranium des Alpes suisses trouvés au cours des dernières années sont indiqués sur une carte géologique. La pechblende est sans doute le minerai d'uranium le plus important. Les roches minéralisées telles que les schistes et les gneiss à chlorite et séricite et à séricite et albite sont plus ou moins métamorphisées. Différentes sortes d'analyses d'uranium, de thorium et de métaux tels que le Cu, Pb et d'autres éléments en trace ont été effectuées sur plusieurs tonnes d'échantillons. Les résultats obtenus sont représentés sous forme de tableaux et d'un graphique. Dans les roches métamorphiques et minéralisées la teneur en uranium est toujours nettement plus élevée que la teneur en thorium.

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Analysis of hydrologic relations between Eğirdir-Beyşehir-Suğla lakes system and adjacent basins by means of remote sensing techniques (southern Turkey)

The study area is situated within the complex structure and karst system of the western Taurids. Basinwide interpretation of the structural features, each of which has great importance, will enlighten many complicated hydrogeologic problems encountered in the area. Thus, considering the previous views on the structural geology of the area, an interpretation of the structural and tectonic features of the study area by means of satellite images was undertaken, and based on the data gained, new approaches were suggested to solve the hydrogeological problems. In particular, determination of the recharge-discharge mechanisms of the Olukköprü and Dumanli karst springs, which are the most important karst groundwater discharge points in the region, has been attempted. Within the framework of this study, a tectonic-lineament map of a large area covering Eirdir, Beyehir, and Sula lakes at the north and the basins to the south of these lakes was prepared.     

The anthracite smokers of eastern pennsylvania: PS2 (g)P_{S_2 (g)} -T stability diagram by TL analysis

Coal seams and culm banks associated with mine fires in the anthracite region of eastern Pennsylvania have been burning for decades. Many of the fires may have ignited by spontaneous combustion or by the burning of trash. Minerals associated with the combustion of anthracite form by the condensation of gas exhaled through surficial gas vents or anthracite smokers. A Pressure-Temperature (P-T) stability diagram is constructed for the condensation of orthorhombic sulfur from anthracite gas using Thermodynamic Loop Analysis (TL analysis). This method of analyzing chemical systems incorporates Kirchhoff's Law into a four step procedure structured around a closed thermodynamic cycle or thermodynamic loop. The four steps, referred to us The Four S S of Thermodynamic Loop Analysis, include: (1) Set Up—graphical characterization of the problem. (2) Sum—the application of thermodynamic principles. (3) Substitute—the use of materials data available from the literature, and (4) Solve—computation of one or more variables. The example presented demonstrates that thermodynamic loops can incorporate any number of polymorphic phase transformations. In addition, thermodynamic loop analysis is applicable to any geologic process involving the condensation of minerals from a gas. The stability diagram derived by TL analysis may have applicability in monitoring the release of sulfur gas into the atmosphere.     

Investigation into Factors Affecting Roadway Deformation in the Selby Coalfield

The introduction of roofbolting in the UK coal mining industry has been well documented and is an example of reinforcement design utilizing a design by measurement or observational approach. This has involved detailed monitoring of rock strata movements and rockbolt loads at a large number of sites. Analysis of roadway deformation monitoring information from across the Selby coalfield provided an ideal opportunity of assessing how geological and stress variations affect the stability of reinforced coal mine roadways. Statistical analysis of this data has confirmed the detrimental effects of maximum horizontal stress direction and relatively weak roof geology on the magnitude of roof deformation. Further analysis has led to the development of a roof lithology index for assessing the quality of the immediate roof geology and the use of geological hazard analysis for providing useful information for the development of a stability index for assessing support requirements of existing and future roadways. This investigation has also verified previous observations regarding mechanisms controlling roadway deformational behaviour and highlights the importance of the site-specific nature of reinforcement design.     

An example of cluster analysis applied to a large geologic data set: Aerial radiometric data from Copper Mountain, Wyoming

One objective of the aerial radiometric surveys flown as part of the U.S. Department of Energy's National Uranium Resource Evaluation (NURE) program was to ascertain the spatial distribution of near-surface radioelement abundances on a regional scale. Some method for identifying groups of observations with similar -ray spectral signatures and radioelement concentration values was therefore required. It is shown in this paper that cluster analysis can identify such groups with or without a priori knowledge of the geology of an area. An approach that combines principal components analysis with convergentk-means cluster analysis is used to classify 6991 observations (each observation comprising three radiometric variables) from the Precambrian rocks of the Copper Mountain, Wyoming area. This method is compared with a convergentk-means analysis that utilizes available geologic knowledge. Both methods identify four clusters. Three of the clusters represent background values for the Precambrian rocks of the area, and the fourth represents outliers (anomalously high²¹⁴Bi). A segmentation of the data corresponding to geologic reality as interpreted by other methods has been achieved by perceptive quantitative analysis of aerial radiometric data. The techniques employed are composites of classical clustering methods designed to handle the special problems presented by large data sets.     

Examining Fluvial Stratigraphic Architecture Using Ground‐Penetrating Radar at the Fanta Stream Fossil and Archaeological Site,Central Ethiopia

The Fanta Stream site is an archaeological and paleontological locality in Addis Ababa, Ethiopia. The site contains a rich assemblage of fossil mammals and Acheulean artifacts of approximately 600 ka located in a rare high‐altitude context. A ground‐penetrating radar (GPR) survey was conducted in order to provide three‐dimensional imaging of the subsurface, which the authors use to interpret the geometry and distribution of fossil‐containing stratigraphic units. Utilizing the stream's natural cut bank exposure, we calibrate GPR data to known geologic units through radar facies analysis. Shallow, high‐amplitude coherent reflection geometries are attributed to volcanic tuff deposits, as these units exhibit subparallel continuous reflections consistent with planar stratified sedimentary deposition. Deeper, discontinuous reflection packages are interpreted as conglomeritic, fossil‐containing deposits. The results of the GPR survey outline the location of the Fanta Stream's paleodepositional features as well as suggest the extent of fossiliferous stratigraphic units for use in future excavations.     

Groundwater development in Lemoa, Guatemala

In the rural Guatemalan Central Highlands, drinking water wells are a rare commodity due to lack of data regarding depth and sustainability of groundwater. At a study well in Lemoa, aquifer sustainability and other characteristics were estimated using hydrograph data and Theiss recovery method for pumping tests. These tests showed that while specific capacity remained fairly constant, transmissivity increased, indicating development of the well subsequent to installation of the study well. The time domain electromagnetic (TDEM) method was evaluated at the site as a prospective groundwater prospecting technique. Characterization of subsurface conditions using TDEM is feasible with local subsurface data for correlation; however, it is limited to delineating low electrical resistive zones without geologic data for correlation. Data showed that groundwater produced from volcanic alluvium at approximately 79 m in depth is sustainable at the study area at current use rates.     

Fission track study of uranium in two granites of central texas

The four primary modes of microscopic occurrence of uranium in the Katemcy and Streeter granites of central Texas as revealed by fission track mapping are: 1) in accessory minerals; 2) along grain boundaries; 3) in microfractures; and 4) in quartz and feldspars. Most of the uranium occuring in the first three modes, accounting for more than three-fourths of the total, appears to be readily mobilized during weathering.     

精细地质初议

通过对经济建设、资源勘探、环境保护和地学发展的需求分析,提出了进行精细地质研究的必要性,诠释了精细地质的概念及其技术体系。认为精细地质是以先进的技术方法和高灵敏度的测量仪器,对地质体进行精确细致的研究,形成先进、精确、实用的成果,达到提高地学科研与调查水平,高效服务经济建设的目的。精细地质的技术体系包括遥感、物探、化探、钻探、同位素测年、空间定位技术、计算机技术等,通过空中地表地下全方位立体化的综合调查,完成对研究对象的精细研究。通过物探、遥感、同位素测年、化探等核心技术在国内外精细地质研究中的发展应用状况分析,以遥感技术为例,阐述了进行精细地质调查研究的可能性,展望了精细地质在矿产资源勘探、地学研究、环境保护、国防建设、地质灾害调查等领域的应用前景。     

如何使用AutoGAD 2004编制图切剖面图

MAPGIS和AutoCAD 2004是地质勘查行业使用较为广泛的数字制图软件,二者各有优劣。本文介绍了一种在MAPGIS制作完成的地形地质图上,利用AutoCAD 2004制图程序完成图切剖面图编制的方法。     

Non-riemannian and fractal geometries of fracturing in geomaterials

The mechanism of earthquakes is presented by use of the elastic dislocation theory. With consideration of the continuous dislocation field, the general problem of medium deformation requires analysis based on non-Riemannian geometry with the concept of the continuum with a discontinuity (no-more continuum). Here we derive the equilibrium equation (Navier equation) for the continuous dislocation field by introducing the relation between the concepts of the continuous dislocation theory and non-Riemannian geometry. This equation is a generalization of the Laplace equation, which can describe fractal processes like diffusion limited aggregation (DLA) and dielectric breakdown (1313). Moreover, the kinematic compatibility equations derived from Navier equation are the Laplace equations and the solution of Navier equation can be put in terms of functions which satisfy the biharmonic equation, suggesting a close formal connection with fractal processes. Therefore, the relationship between the non-Riemannian geometry and the fractal geometry of fracturing (damage) in geomaterials as earthquakes can be understood by using the Navier equation. Moreover, the continuous dislocation theory can be applied to the problem of the earthquake formation with active folding related with faulting (active flexural-slip folding related to the continuous dislocation field).     

Directions and possibilities of mathematical geology

This paper considers the present state of mathematical geology. Three directions are recognized: applied, theoretical, and mathematical. Applied mathematical geology includes formal use of mathematics to solve problems and computer processing of data. Success is achieved by a correspondence of mathematical methods used to the nature of geological data. This correspondence can be demonstrated by purely mathematical means. Theoretical mathematical geology uses mathematics as a language of geology; however, a number of methodological problems must be solved: formalization of initial geological concepts and creation of a strict conceptual basis, substantiation of initial principles of mathematical simulation, creation of theoretical geological models, problems of elementary and coincidence in geology, and methodological substantiations of possibilities of any mathematical model to approximate geological models. The essense and significance of these problems are considered. The main task of mathematical geology is to prove its correspondence to the nature of the geological objects studied, geological data obtained, and geological problems solvable. Finally, the main problems of mathematical geology are not so much mathematical as geological and methodological.