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.     

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.     

Flood hazard delineation combining geomorphological and hydrological methods: an example in the Northern Iberian Peninsula

Flood mapping requires the combination and integration of geomorphological and hydrological-hydraulic methods; however, despite this, there is very little scientific literature that compares and validates both methods. Two types of analysis are addressed in the present article. On the one hand, maps of flood plains have been elaborated using geomorphological evidence and historical flood data in the mountainous area of northwestern Spain, covering an area of more then 232 km² of floodplains. On the other hand, a hydrometeorological model has been developed (Clark semidistributed unit hydrograph) in the Sarria River basin (155 km², NW Spain). This basin is not gauged, hence the model was subjected to a goodness-of-fit test of its parameter (curve number) by means of Monte Carlo simulation. The peak flows obtained by means of the hydrological model were used for hydraulic modeling (one-phase, one-dimensional and steady flow) in a 4 km² urban stretch of the river bed. The delineation of surface areas affected by floods since 1918, as well as those analyzed subsequent to the geomorphological study, reveals a high degree of reliability in the delineation of the flooded areas with frequent recurrence intervals (<50 years). If we compare these flooded surface areas with the estimate obtained by the hydrological-hydraulic method we can see that the latter method overestimates the extent of the surface water by 144% for very frequent recurrence intervals (>10 years) and underestimates it as the recurrence interval increases, by up to 80% less floodplain for exceptional events (>500 years). Finally, a management map is put forth combining the most reliable results available by integrating both methods. Originally presented at the Sixth International Conference on Geomorphology.     

Numerical modeling of tide-surge interaction along Orissa coast of India

The Orissa coast of India is one of the most vulnerable regions of extreme sea levels associated with severe tropical cyclones. There was extensive loss of life and property due to the October 1999 super cyclone, which devastated large part of the Orissa coast. The shallow nature of the head bay, presence of a large number of deltas formed by major rivers of Orissa such as Mahanadi and Dhamra, and high tidal range are responsible for storm surge flooding in the region. Specifically, rising and falling tidal phases influence the height, duration, and arrival time of peak surge along the coast. The objective of the present study is to evaluate the tide-surge interaction during the 1999 Orissa cyclone by using nonlinear vertically integrated numerical models. The pure tidal solution for the head bay region of the Bay of Bengal provides the initial condition for the fine resolution nested grid Orissa model. However, the feedback from the Orissa model does not affect the head bay model as the study provides a one-way interaction. Numerical experiments are performed to study the tide-surge interaction by considering various relative phases of the tidal waves with the surge-wave produced by 1999 Orissa cyclone. The comparison, although utilizing only the limited estimates of tidal data, appears adequate to assert that the principal features are reproduced correctly.     

Influence of Structural Non-Stationarity of Surface Roughness on Morphological Characterization and Mechanical Deformation of Rock Joints

Summary Structural non-stationarity of surface roughness affects accurate morphological characterization as well as mechanical behaviour of rock joints at the laboratory scale using samples with a size below the stationarity threshold. In this paper, the effect of structural non-stationarity of surface roughness is investigated by studying the scale dependence of surface roughness and mechanical behaviour of rock joints. The results show that the structural non-stationarity mainly affects the accurate characterization of the surface roughness of the fracture samples. It also controls the amount and location of the contact areas during shear tests, which in turn affects the mechanical properties and asperity degradation of the samples. It is concluded that for accurate determination of the morphological and mechanical properties of rock joints at laboratory and field scales, samples with size equal to or larger than the stationarity threshold are required. Author’s address: Nader Fardin, Rock Mechanics Group, Department of Mining Engineering, Faculty of Engineering, University of Tehran, P.O. Box: 11365/4563, Tehran, Iran