Review of resource analysis and related studies: Working group,Mathematical Geology,freie Universität Berlin

The working group Mathematical Geology of the Freie Universität Berlin was formed in 1971. We review quantitative methods used by the working group since 1983 to treat mineral exploration problems. The methods applied vary from elementary statistical analysis of multivariate exploration data to optimal strategies for selecting favorable targets, and from multiobjective decision-making for additional drill hole locations to expert systems in exploration.The methods applied are directly related to the level of information at each stage of the exploration process. Special emphasis was placed on the relationship between and evaluation of subjective and objective data. Case studies illustrating the various methods are presented for different kinds of mineral deposits and exploration environments.     

Age,origin and climatic controls on vegetated linear dunes in the northwestern Negev Desert (Israel)

The stabilized northwestern (NW) Negev vegetated linear dunes (VLD) of Israel extend over 1300 km² and form the eastern end of the Northern Sinai – NW Negev Erg. This study aimed at identifying primary and subsequent dune incursions and episodes of dune elongation by investigating dune geomorphology, stratigraphy and optically stimulated luminescence (OSL) dating. Thirty-five dune and interdune exposed and drilled section were studied and sampled for sedimentological analyses and OSL dating, enabling spatial and temporal elucidation of the NW Negev dunefield evolution.In a global perspective the NW Negev dunefield is relatively young. Though sporadic sand deposition has occurred during the past 100 ka, dunes began to accumulate over large portions of the dunefield area only at ～23 ka. Three main chronostratigraphic units, corresponding to three (OSL) age clusters, were found throughout most of the dunefield, indicating three main dune mobilizations: late to post last glacial maximum (LGM) at 18–11.5 ka, late Holocene (2–0.8 ka), and modern (150–8 years). The post-LGM phase is the most extensive and it defined the current dunefield boundaries. It involved several episodes of dune incursions and damming of drainage systems. Dune advancement often occurred in rapid pulses and the orientation of VLD long axes indicates similar long-term wind directions. The late Holocene episode included partial incursion of new sand, reworking of Late Pleistocene dunes as well as limited redeposition. The modern sand movement only reactivated older dunes and did not lengthen VLDs.This aeolian record fits well with other regional aeolian sections. We suggest that sand supply and storage in Sinai was initiated by the Late Pleistocene exposure of the Nile Delta sands. Late Pleistocene winds, substantially stronger than those usually prevailing since the onset of the Holocene, are suggested to have transported the dune sands across Sinai and into the northwestern Negev.Our results demonstrate the sensitivity of vegetated linear dunes located along the (northern) fringe of the sub-tropical desert belt to climate change (i.e. wind) and sediment supply.     

Estimating ground water recharge using flow models of perched karstic aquifers

The fraction of rain that is annually recharged to ground water is a function of the transient quantities of precipitation (wet vs. dry years) as well as other meteorological and geologic factors, and thus it is very difficult to estimate. In this study, we have used long records (20 to 30 years) of precipitation and spring discharge to reconstruct the transient character of yearly recharge. These data sets were used to calibrate numerical ground water flow models on the less than 3 km(2) scale for four separate perched karstic aquifers in the Judean and Samarian Mountains of Israel. The stratification and karstic character of the local carbonate rock aquifers cause ground water to flow through discrete dissolution channels and to discharge at isolated springs. An innovative, dual-porosity approach was used where a finite-difference solution simulates flow in the rock matrix, while the karstic channels are simulated using computationally simple drains. Perched conditions are also simulated innovatively using MODFLOW by treating the bottom unsaturated layer as if it is saturated, but by assuming zero pressure head throughout the "unsaturated" layer. Best fitting between measured and computed spring hydrograph data has allowed us to develop a set of empirical functions relating measured precipitation to recharge to the aquifer. The generic methodology presented gives insight into the suspected changes in aquifer recharge rates between particularly wet or dry years.     

Considered parameters in a least squares adjustment process

Least squares adjustment processes occasionally utilize constants with a known degree of uncertainty. If the covariance matrix of the adjusted parameters is estimated without considering those uncertainties the resulting estimate is invariably too optimistic. A method is proposed by which without altering the values of the adjusted parameters their a posteriori (after the adjustment) covariance matrix can be improved by the inclusion of the effect of uncertainties in the constants.     

Late Holocene climates of the Near East deduced from Dead Sea level variations and modern regional winter rainfall

The Dead Sea is a terminal lake of one of the largest hydrological systems in the Levant and may thus be viewed as a large rain gauge for the region. Variations of its level are indicative of the climate variations in the region. Here, we present the decadal- to centennial-resolution Holocene lake-level curve of the Dead Sea. Then we determine the regional hydroclimatology that affected level variations. To achieve this goal we compare modern natural lake-level variations and instrumental rainfall records and quantify the hydrology relative to lake-level rise, fall, or stability. To quantify that relationship under natural conditions, rainfall data pre-dating the artificial Dead Sea level drop since the 1960s are used. In this respect, Jerusalem station offers the longest uninterrupted pre-1960s rainfall record and Jerusalem rains serve as an adequate proxy for the Dead Sea headwaters rainfall. Principal component analysis indicates that temporal variations of annual precipitation in all stations in Israel north of the current 200 mm yr⁻¹ average isohyet during 1940–1990 are largely synchronous and in phase (70% of the total variance explained by PC1). This station also represents well northern Jordan and the area all the way to Beirut, Lebanon, especially during extreme drought and wet spells. We (a) determine the modern, and propose the past regional hydrology and Eastern Mediterranean (EM) climatology that affected the severity and length of droughts/wet spells associated with multiyear episodes of Dead Sea level falls/rises and (b) determine that EM cyclone tracks were different in average number and latitude in wet and dry years in Jerusalem. The mean composite sea level pressure and 500-mb height anomalies indicate that the potential causes for wet and dry episodes span the entire EM and are rooted in the larger-scale northern hemisphere atmospheric circulation. We also identified remarkably close association (within radiocarbon resolution) between climatic changes in the Levant, reflected by level changes, and culture shifts in this region.     

How Fast the Nucleus of Comet Hale–Bopp was Rotating?

At the First International Conference on Comet Hale–Bopp(Canaries, 1998) many astronomers agreed with the value of theperiod of axial rotation of its nucleus, which was obtained byobservers by a comparison of the two sequential patterns of thedust arcs. It was noted that the pattern had been repeated each∼12 hours. The value 11.35^h was taken as the periodof axial rotation. However, alternative periods of 4 and 8 days havealso been suggested. The possible reasons for thisdiscrepancy are discussed. It is shown that a short period could be obtained by a misidentification of the same arc on twosequential images and, as a result, an overestimate of theradial velocity of dust in the arcs. To obtain the half day period one must take the projected velocity of the arc ∼ 1.6 km/s,which exceeds the H₂O gas expansion velocity. If one takes a lower expansion velocity a longer period would be obtained.