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.     

Anhydrite pseudomorphs and the origin of stratiform Cu–Co ores in the Katangan Copperbelt (Democratic Republic of Congo)

The stratiform Cu–Co ore mineralisation in the Katangan Copperbelt consists of dispersed sulphides and sulphides in nodules and lenses, which are often pseudomorphs after evaporites. Two types of pseudomorphs can be distinguished in the nodules and lenses. In type 1 examples, dolomite precipitated first and was subsequently replaced by Cu–Co sulphides and authigenic quartz, whereas in type 2 examples, authigenic quartz and Cu–Co sulphides precipitated prior to dolomite and are coarse-grained. The sulphur isotopic composition of the copper–cobalt sulphides in the type 1 pseudomorphs is between −10.3 and 3.1‰ relative to the Vienna Canyon Diablo Troilite, indicating that the sulphide component was derived from bacterial sulphate reduction (BSR). The generation of during this process caused the precipitation and replacement of anhydrite by dolomite. A second product of BSR is the generation of H₂S, resulting in the precipitation of Cu–Co sulphides from the mineralising fluids. Initial sulphide precipitation occurred along the rim of the pseudomorphs and continued towards the core. Precipitation of authigenic quartz was most likely induced by a pH decrease during sulphide precipitation. Fluid inclusion data from quartz indicate the presence of a high-salinity (8–18 eq. wt.% NaCl) fluid, possibly derived from evaporated seawater which migrated through the deep subsurface. ⁸⁷Sr/⁸⁶Sr ratios of dolomite in type 1 nodules range between 0.71012 and 0.73576, significantly more radiogenic than the strontium isotopic composition of Neoproterozoic marine carbonates (⁸⁷Sr/⁸⁶Sr = 0.7056–0.7087). This suggests intense interaction with siliciclastic sedimentary rocks and/or the granitic basement. The low carbon isotopic composition of the dolomite in the pseudomorphs (−7.02 and −9.93‰ relative to the Vienna Pee Dee Belemnite, V-PDB) compared to the host rock dolomite (−4.90 and +1.31‰ V-PDB) resulted from the oxidation of organic matter during BSR.     

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.     

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.     

Trace elements in groundwater as indicators of anthropogenic impact

The distribution of several minor and trace elements mainly in fresh (dominating TDS 160–400 mg/l) groundwater of Latvia have been investigated by the Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) technique. An evaluation of results of about 700 analyses leads to the conclusion that concentrations of these elements is influenced by: pH–Eh conditions, groundwater residence time and diffuse contamination, whereas the role of water-bearing sediments is of secondary importance. Most trace elements are characterised by low mobility under alkaline and reducing conditions; concentrations in confined aquifers are much smaller than the Maximum Permissible Values for drinking water. The strongest anomalies of REE, Al and P were found in shallow groundwater around the former agrochemical storehouses.     

Magma Ascent and Crustal Accretion at Ultraslow-Spreading Ridges: Constraints from Plagioclase Ultraphyric Basalts from the Arctic Mid-Ocean Ridge

Plagioclase ultraphyric basalts (PUBs) with up to 54% plagioclasephenocrysts were dredged in the rift valley and adjacent flanksof the ultraslow-spreading Mohns and Knipovich ridges. The PUBsshow large variations in crystal morphologies and zoning. Thelarge variations suggest that single basalt samples containa mixture of plagioclase crystals that aggregated at differentlevels in the magma conduits. Resorbed crystals and repeatedreverse zones suggest that the magma reservoirs were replenishedand heated several times. Thin concentric zones with melt inclusions,and sharp reductions in the anorthite content of 3–7%,are common between the reverse zones. These zones, and skeletalcrystals with distinctly lower anorthite contents than massivecrystals, are interpreted to be the result of rapid crystalliztionduring strong undercooling. The changes between short periodsof cooling and longer periods with reheating are explained bymultiple advances of crystal-rich magma into cool regions followedby longer periods of gradual magma inflow and temperature increase.The porphyritic basalts are characterizd by more depleted andmore fractionated compositions than the aphyric basalts, withlower (La/Sm)_N, K₂O and Mg-numbers. This relationship, and theobservation that PUBs are sampled only close to segment centresalong these ridges, suggests that the PUBs formed by higherdegrees of melting and evolved in more long-lived magma reservoirs.We propose that the zoning patterns of plagioclase crystalsand crystal morphologies of these PUBs reflect the developmentand flow of magma through a stacked sill complex-like conduitsystem, whereas the aphyric equivalents represent later flowof magma through the conduit. The formation of voluminous higher-degreemelts may trigger the development of the magma conduits andexplain the generally depleted compositions of PUB magmas. KEY WORDS: basalt; mineral chemistry; MORB; magma mixing; magma chamber; major element