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.     

Asymmetrically zoned reaction rims: assessment of grain boundary diffusivities and growth rates related to natural diffusion-controlled mineral reactions

This study explores garnet coronas around hedenbergite, which were formed by the reaction plagioclase + hedenbergite→garnet + quartz, to derive information about diffusion paths that allowed for material redistribution during reaction progress. Whereas quartz forms disconnected single grains along the garnet/hedenbergite boundaries, garnet forms ～20‐μm‐wide continuous polycrystalline rims along former plagioclase/hedenbergite phase boundaries. Individual garnet crystals are separated by low‐angle grain boundaries, which commonly form a direct link between the reaction interfaces of the plagioclase|garnet|hedenbergite succession. Compositional variations in garnet involve: (i) an overall asymmetric compositional zoning in Ca, Fe²⁺, Fe³⁺ and Al across the garnet layer; and (ii) micron‐scale compositional variations in the near‐grain boundary regions and along plagioclase/garnet phase boundaries. These compositional variations formed during garnet rim growth. Thereby, transfer of the chemical components occurred by a combination of fast‐path diffusion along grain boundaries within the garnet rim, slow diffusion through the interior of the garnet grains, and by fast diffusion along the garnet/plagioclase and the garnet/hedenbergite phase boundaries. Numerical simulation indicates that diffusion of Ca, Al and Fe²⁺ occurred about three to four, four and six to seven orders of magnitude faster along the grain boundaries than through the interior of the garnet grains. Fast‐path diffusion along grain boundaries contributed substantially to the bulk material transfer across the growing garnet rim. Despite the contribution of fast‐path diffusion, bulk diffusion through the garnet rim was too slow to allow for chemical equilibration of the phases involved in garnet rim formation even on a micrometre scale. Based on published garnet volume diffusion data the growth interval of a 20‐μm‐wide garnet rim is estimated at ～10³–10⁴ years at the inferred reaction conditions of 760 ± 50 °C at 7.6 kbar. Using the same parameterization of the growth law, 100‐μm‐ and 1‐mm‐thick garnet rims would grow within 10⁵–10⁶ and 10⁶–10⁷ years respectively.     

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.     

An experimental study of the grain-scale processes of peridotite melting: implications for major and trace element distribution during equilibrium and disequilibrium melting

The grain-scale processes of peridotite melting were examined at 1,340°C and 1.5 GPa using reaction couples formed by juxtaposing pre-synthesized clinopyroxenite against pre-synthesized orthopyroxenite or harzburgite in graphite and platinum-lined molybdenum capsules. Reaction between the clinopyroxene and orthopyroxene-rich aggregates produces a melt-enriched, orthopyroxene-free, olivine + clinopyroxene reactive boundary layer. Major and trace element abundance in clinopyroxene vary systematically across the reactive boundary layer with compositional trends similar to the published clinopyroxene core-to-rim compositional variations in the bulk lherzolite partial melting studies conducted at similar P–T conditions. The growth of the reactive boundary layer takes place at the expense of the orthopyroxenite or harzburgite and is consistent with grain-scale processes that involve dissolution, precipitation, reprecipitation, and diffusive exchange between the interstitial melt and surrounding crystals. An important consequence of dissolution–reprecipitation during crystal-melt interaction is the dramatic decrease in diffusive reequilibration time between coexisting minerals and melt. This effect is especially important for high charged, slow diffusing cations during peridotite melting and melt-rock reaction. Apparent clinopyroxene-melt partition coefficients for REE, Sr, Y, Ti, and Zr, measured from reprecipitated clinopyroxene and coexisting melt in the reactive boundary layer, approach their equilibrium values reported in the literature. Disequilibrium melting models based on volume diffusion in solid limited mechanism are likely to significantly underestimate the rates at which major and trace elements in residual minerals reequilibrate with their surrounding melt. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.