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.     

岩体三维节点偶对分析及其应用

本文讨论了节点偶对分析的三维扩展。节点偶对分析是针对摩擦滑动节理单元的约束边界进行的序列矢量判定。在三维节理单元的分析中,几何约束和相应的力学判据极为复杂,采用节点偶对等效结合力方法才能迎刃而解。文中对三维转向节理模型的分析得到合理的结果,它表明本文所提出的方法可成功地应用于节理岩体的有限元分析。     

地壳演化与成矿作用——以川滇地洼系“四层楼”铜矿床序列为例

提出川滇地洼系“四层楼”铜矿床序列的形成与陆壳演化的成生联系,是与本区陆壳由前地槽—地槽—地台—地洼演化各阶段与之相匹配的成矿作用的产物.与此同时,并总结了本区“四层楼”铜矿床序列的成矿作用具有明显的继承性、新生性、旋回性及层控性四大特点和多因复成矿床的成矿模式.     

Alluvial architecture of the Holocene Rhine–Meuse delta (the Netherlands)

Ancient fluvial successions often act as hydrocarbon reservoirs. Sub‐surface data on the alluvial architecture of fluvial successions are often incomplete and modelling is performed to reconstruct the stratigraphy. However, all alluvial architecture models suffer from the scarcity of field data to test and calibrate them. The purposes of this study were to quantify the alluvial architecture of the Holocene Rhine–Meuse delta (the Netherlands) and to determine spatio‐temporal trends in the architecture. Five north–south orientated cross‐sections, perpendicular to the general flow direction, were compiled for the fluvial‐dominated part of the delta. These sections were used to calculate the width/thickness ratios of fluvial sandbodies (SBW/SBT) and the proportions of channel‐belt deposits (CDP), clastic overbank deposits (ODP) and organic material (OP) in the succession. Furthermore, the connectedness ratio (CR) between channel belts was calculated for each cross‐section. Distinct spatial and temporal trends in the alluvial architecture were found. SBW/SBT ratios decrease by a factor of ca 4 in a downstream direction. CDP decreases from ca 0·7 (upstream) to ca 0·3 (downstream). OP increases from less than 0·05 in the upstream part of the delta to more than 0·25 in the downstream delta. ODP is approximately constant (0·4). CR is ca 0·25 upstream, which is approximately two times larger than in the downstream part of the delta. Furthermore, CDP in the downstream Rhine–Meuse delta increases after 3000 cal yr BP. These trends are attributed to variations in available accommodation space, floodplain geometry and channel‐belt size. For instance, channel belts tend to narrow in a downstream direction, which reduces SBW/SBT, CDP and CR. Tectonics cause local deviations in the general architectural trends. In addition, the positive correlation between avulsion frequency and the ratio of local to regional aggradation rate probably influenced alluvial architecture in the Rhine–Meuse delta. The Rhine–Meuse data set can be a great resource when developing more sophisticated models for alluvial architecture simulation, which eventually could lead to better characterizations of hydrocarbon reservoirs. To aid such usage of the Rhine–Meuse data set, constraints for relevant parameters are provided at the end of the paper.     

A seismic source zone model for the seismic hazard assessment of the Italian territory

We designed a new seismic source model for Italy to be used as an input for country-wide probabilistic seismic hazard assessment (PSHA) in the frame of the compilation of a new national reference map.

We started off by reviewing existing models available for Italy and for other European countries, then discussed the main open issues in the current practice of seismogenic zoning.

The new model, termed ZS9, is largely based on data collected in the past 10 years, including historical earthquakes and instrumental seismicity, active faults and their seismogenic potential, and seismotectonic evidence from recent earthquakes. This information allowed us to propose new interpretations for poorly understood areas where the new data are in conflict with assumptions made in designing the previous and widely used model ZS4.

ZS9 is made out of 36 zones where earthquakes with M_w > = 5 are expected. It also assumes that earthquakes with M_w up to 5 may occur anywhere outside the seismogenic zones, although the associated probability is rather low. Special care was taken to ensure that each zone sampled a large enough number of earthquakes so that we could compute reliable earthquake production rates.

Although it was drawn following criteria that are standard practice in PSHA, ZS9 is also innovative in that every zone is characterised also by its mean seismogenic depth (the depth of the crustal volume that will presumably release future earthquakes) and predominant focal mechanism (their most likely rupture mechanism). These properties were determined using instrumental data, and only in a limited number of cases we resorted to geologic constraints and expert judgment to cope with lack of data or conflicting indications. These attributes allow ZS9 to be used with more accurate regionalized depth-dependent attenuation relations, and are ultimately expected to increase significantly the reliability of seismic hazard estimates.     

Origin and mechanisms of K–Si-metasomatism of ca. 3.4–3.3 Ga volcaniclastic deposits and implications for Archean seawater evolution: Examples from cherts of Kittys Gap (Pilbara craton, Australia) and Msauli (Barberton Greenstone Belt, South Africa)

The effects of K–Si-metasomatism during the formation of Early Archean replacement cherts have been quantified in this study by the investigation of two well-known stratigraphic sections: the Msauli chert (MC, Barberton greenstone belt, South Africa) and the Kittys Gap chert (KGC, Pilbara craton, Western Australia). The KGCs have a dacitic precursor similar to Duffer Formation dacites (Pilbara craton), while the MCs are derived from Al-depleted komatiites similar to those from the Weltevreden Formation (Barberton greenstone belt). Mass balance calculations reveal that the volcaniclastic deposits had initial porosities of up to 85 vol.% for the KGC and of 65 vol.% for the MC. Secondary porosities (27 vol.%: MC, 8 vol.%: KGC) produced during K-metasomatism are proportional to the dissolution of Fe, Ca, Mg-rich glass and precursor minerals. Komatiites have a higher chemical exchange potential than dacites, each gram releasing 1.2 mmol Fe²⁺, 2.8 mmol Mg²⁺, 1.4 mmol Ca²⁺ and 1.1 mmol Na⁺ to seawater, together with 4.4 mmol O²⁻. K-metasomatism of 1 g of komatiite further implies an uptake of 0.67 mmol of K⁺ and 2.7 mmol of H⁺. The highest silica uptake is achieved for the KGC (82 mmol/g of precursor). This silica enrichment most likely operated in the water column and at the sediment–water interface by sorption mechanisms on the surface of detrital particles and particulate organic matter, as a result of seawater silica-saturation. Acidic conditions (pH 5.5–6.5) and hot temperatures (>70 °C) favored the formation of K-rich phyllosilicates by interaction with seawater during the early diagenetic alteration of the volcaniclastic particles. The widespread occurrence of K–Si-metasomatism in volcanic and sedimentary rocks can be regarded as a general alteration process of the Early Archean seafloor, with a major influence on seawater composition. The highly K-selective metasomatism confirms previous studies suggesting that the Archean ocean was acidic and probably in equilibrium with a CO₂-rich atmosphere.     

江西浒坑钨矿含矿石英脉的地质特征及成矿构造演化

位于赣西武功山地区的江西浒坑钨矿是一个大型石英脉型钨矿床,与赣南典型的“五层楼”模式不同,矿脉主要集中在岩体内接触带。含矿石英脉除了普通的块状构造以外,还普遍存在条带状构造。详细的野外编录和镜下研究表明含矿块状石英脉在形成后遭受不同程度的韧性剪切,从而形成不同成分的分异条带。剪切带以出现新生的面理和线理（拉伸线理）为特征。岩石学研究表明条带状矿石属于糜棱岩,具有丰富的塑性变形显微构造特征。通过对含矿石英脉的构造解析,认为与岩浆岩有关的原生节理系统基本上是同时形成的,沿节理充填的石英脉经历了长期的、多期次的构造运动,从而形成了复杂的石英脉和矿石类型。建立了原生节理形成→石英充填→韧性剪切发生→二期石英充填→脆性碎裂的矿区构造演化序列。韧性剪切作用的动力学背景可能是受后期岩浆侵入的影响,最后的脆性破裂应与区域上存在南北向的压应力有关。     

Application of MODFLOW and geographic information system to groundwater flow simulation in North China Plain, China

MODFLOW is a groundwater modeling program. It can be compiled and remedied according to the practical applications. Because of its structure and fixed data format, MODFLOW can be integrated with Geographic Information Systems (GIS) technology for water resource management. The North China Plain (NCP), which is the politic, economic and cultural center of China, is facing with water resources shortage and water pollution. Groundwater is the main water resource for industrial, agricultural and domestic usage. It is necessary to evaluate the groundwater resources of the NCP as an entire aquifer system. With the development of computer and internet information technology it is also necessary to integrate the groundwater model with the GIS technology. Because the geological and hydrogeological data in the NCP was mainly in MAPGIS format, the powerful function of GIS of disposing of and analyzing spatial data and computer languages such as Visual C and Visual Basic were used to define the relationship between the original data and model data. After analyzing the geological and hydrogeological conditions of the NCP, the groundwater flow numerical simulation modeling was constructed with MODFLOW. On the basis of GIS, a dynamic evaluation system for groundwater resources under the internet circumstance was completed. During the process of constructing the groundwater model, a water budget was analyzed, which showed a negative budget in the NCP. The simulation period was from 1 January 2002 to 31 December 2003. During this period, the total recharge of the groundwater system was 49,374 × 10⁶ m³ and the total discharge was 56,530 × 10⁶ m³ the budget deficit was −7,156 × 10⁶ m³. In this integrated system, the original data including graphs and attribution data could be stored in the database. When the process of evaluating and predicting groundwater flow was started, these data were transformed into files that the core program of MODFLOW could read. The calculated water level and drawdown could be displayed and reviewed online.     

Recharge source and hydrogeochemical evolution of shallow groundwater in a complex alluvial fan system,southwest of North China Plain

Many cities around the world are developed at alluvial fans. With economic and industrial development and increase in population, quality and quantity of groundwater are often damaged by over-exploitation in these areas. In order to realistically assess these groundwater resources and their sustainability, it is vital to understand the recharge sources and hydrogeochemical evolution of groundwater in alluvial fans. In March 2006, groundwater and surface water were sampled for major element analysis and stable isotope (oxygen-18 and deuterium) compositions in Xinxiang, which is located at a complex alluvial fan system composed of a mountainous area, Taihang Mt. alluvial fan and Yellow River alluvial fan. In the Taihang mountainous area, the groundwater was recharged by precipitation and was characterized by Ca–HCO₃ type water with depleted δ¹⁸O and δD (mean value of −8.8‰ δ¹⁸O). Along the flow path from the mountainous area to Taihang Mt. alluvial fan, the groundwater became geochemically complex (Ca–Na–Mg–HCO₃–Cl–SO₄ type), and heavier δ¹⁸O and δD were observed (around −8‰ δ¹⁸O). Before the surface water with mean δ¹⁸O of −8.7‰ recharged to groundwater, it underwent isotopic enrichment in Taihang Mt. alluvial fan. Chemical mixture and ion exchange are expected to be responsible for the chemical evolution of groundwater in Yellow River alluvial fan. Transferred water from the Yellow River is the main source of the groundwater in the Yellow River alluvial fan in the south of the study area, and stable isotopic compositions of the groundwater (mean value of −8.8‰ δ¹⁸O) were similar to those of transferred water (−8.9‰), increasing from the southern boundary of the study area to the distal end of the fan. The groundwater underwent chemical evolution from Ca–HCO₃, Na–HCO₃, to Na–SO₄. A conceptual model, integrating stiff diagrams, is used to describe the spatial variation of recharge sources, chemical evolution, and groundwater flow paths in the complex alluvial fan aquifer system.