Statistics for Modeling Heavy Tailed Distributions in Geology: Part II. Applications     

Jef Caers  Jan Beirlant  Marc A. Maes 《Mathematical Geology》1999,31(4):411-434

In this paper, we present three diverse types of applications of extreme value statistics in geology, namely: earthquakes magnitudes, diamond values, and impact crater size distribution on terrestrial planets. Each of these applications has a different perspective toward tail modeling, yet many of these phenomena exhibit heavy or long tails which can be modeled by power laws. It is shown that the estimation of important tail characteristics, such as the extreme value index, is directly linked to the interpretation of the underlying geological process. Only the most extreme data are useful for studying such phenomena, so thresholds must be selected above which the data become power laws. In the case of earthquake magnitudes, we investigate the use of extreme value statistics in predicting large events on the global scale and for shallow intracontinental earthquakes in Asia. Large differences are found between estimates obtained from extreme value statistics and the usually applied standard statistical techniques. In the case of diamond deposits, we investigate the impact of the most precious stones in the global valuation of primary deposits. It is shown that in the case of Pareto-type behavior, the expected value of few extreme stones in the entire deposit has considerable influence on the global valuation. In the case of impact crater distributions, we study the difference between craters distributions on Earth and Mars and distributions occurring on other planets or satellites within the solar system. A striking result is that all planets display the same distributional tail except for Earth and Mars. In a concluding account, we demonstrate the apparent loghyperbolic variation in all of the above-mentioned examples.  相似文献   

中国北方更新世极端冷期冬季风的快速变化   总被引：5，自引：3，他引：2  

鹿化煜  周杰  刘晓东  安芷生 《中国沙漠》2000,20(2):192-196

对黄土高原中部洛川和西峰黄土堆积的“上、下粉砂层”进行了间隔 5～ 6 cm的详细采样 ,测量了 80 0多个样品的粒度分布和磁化率值 ,根据沉积速率模式建立了一个相对独立的、较精确的时间标尺。结果表明 ,中国北方更新世极端冷期的黄土堆积记录了东亚冬季风频繁的和较大幅度的千年尺度变化。冬季风加强事件一般持续约1.8～ 2 .4ka。亚轨道时间尺度冬季风变化的可能原因是 ,在极端冷期赤道和极地气温差增大 ,纬向西风环流加强引起的大气环流和蒙古高亚不稳定 ,从而引起东亚冬季风千年尺度变化。在极端冷期降雨量和平均温度低于某个阈值的时候 ,虽然夏季风强度存在变化 ,但不足以影响磁铁矿和磁赤铁矿的形成 ,所以那时磁化率的变化不能很好地记录夏季风气候变化。  相似文献   

Sediment budget and tectonic evolution of the Meuse catchment in the Ardennes and the Roer Valley Rift System     

R. T. Van Balen  R. F. Houtgast  F. M. Van der Wateren  J. Vandenberghe  P. W. Bogaart 《Global and Planetary Change》2000,27(1-4)

The Meuse river system is located in the northeastern part of the Paris Basin, the Ardennes, and the Roer Valley Rift System (RVRS). The Meuse river system developed during the uplift of the Ardennes since the Eocene and it was affected by renewed rifting of the RVRS starting in the Late Oligocene. In response to the uplift of the Ardennes, the river system incised and a terrace sequence developed during the Plio–Pleistocene. The sediments generated by erosion in the catchment were transported into the RVRS and further to the north, into the Zuiderzee Basin and the North Sea Basin. Using a digital terrain model, the amount of eroded rock volume versus time for the Meuse catchment has been computed using the Paleogene and older planation surfaces and the fluvial terraces. Comparison of the amount of eroded material with the volume of sediment preserved in the RVRS for the early Middle Pleistocene shows that about 17.5% of the sediment volume transported into the RVRS remained there, the rest being transported further into the Zuiderzee Basin and the North Sea Basin. The Quaternary tectonic uplift of the Ardennes inferred from the incision history of the Meuse river system is characterized by a long-term uplift, on which a Middle Pleistocene acceleration is superimposed. The accelerated uplift is contemporaneous with an uplift event in the RVRS and in the neighbouring Eifel area, and with the onset of the youngest phase of volcanism in the Eifel area. The areal distribution of this uplift is characterized by a dome shape centered around the Eifel area.  相似文献   

Cokriging for multivariate Hilbert space valued random fields: application to multi-fidelity computer code emulation     

Ognjen?GrujicEmail authorView author&#;s OrcID profile  Alessandra?Menafoglio  Guang?Yang  Jef?Caers 《Stochastic Environmental Research and Risk Assessment (SERRA)》2018,32(7):1955-1971

In this paper we propose Universal trace co-kriging, a novel methodology for interpolation of multivariate Hilbert space valued functional data. Such data commonly arises in multi-fidelity numerical modeling of the subsurface and it is a part of many modern uncertainty quantification studies. Besides theoretical developments we also present methodological evaluation and comparisons with the recently published projection based approach by Bohorquez et al. (Stoch Environ Res Risk Assess 31(1):53–70, 2016.  https://doi.org/10.1007/s00477-016-1266-y). Our evaluations and analyses were performed on synthetic (oil reservoir) and real field (uranium contamination) subsurface uncertainty quantification case studies. Monte Carlo analyses were conducted to draw important conclusions and to provide practical guidelines for all future practitioners.  相似文献   

Bootstrap confidence intervals for reservoir model selection techniques     

Céline Scheidt  Jef Caers 《Computational Geosciences》2010,14(2):369-382

Stochastic spatial simulation allows generation of multiple realizations of spatial variables. Due to the computational time required for evaluating the transfer function, uncertainty quantification of these multiple realizations often requires a selection of a small subset of realization. However, by selecting only a few realizations, one may risk biasing the P10, P50, and P90 estimates as compared to the original multiple realizations. The objective of this study is to develop a methodology to quantify confidence intervals for the estimated P10, P50, and P90 quantiles when only a few models are retained for response evaluation. We use the parametric bootstrap technique, which evaluates the variability of the statistics obtained from uncertainty quantification and constructs confidence intervals. Using this technique, we compare the confidence intervals when using two selection methods: the traditional ranking technique and the distance-based kernel clustering technique (DKM). The DKM has been recently developed and has been shown to be effective in quantifying uncertainty. The methodology is demonstrated using two examples. The first example is a synthetic example, which uses bi-normal variables and serves to demonstrate the technique. The second example is from an oil field in West Africa where the uncertain variable is the cumulative oil production coming from 20 wells. The results show that, for the same number of transfer function evaluations, the DKM method has equal or smaller error and confidence interval compared to ranking.  相似文献   

Modelling the Effect of Tree Foliage on Sprayer Airflow in Orchards   总被引：1，自引：0，他引：1  

Ayenew Melese Endalew  Christof Debaer  Nick Rutten  Jef Vercammen  Mulugeta Admasu Delele  Herman Ramon  Bart M. Nicolaï  Pieter Verboven 《Boundary-Layer Meteorology》2011,138(1):139-162

The effect of tree foliage on sprayer airflow through pear trees in a fruit orchard was studied and modelled in detail. A new three-dimensional (3-D) computational fluid dynamics model that integrates the 3-D canopy architecture with a local closure model to simulate the effect of the stem and branches and leaves of trees separately on airflow was developed. The model was validated with field observations made in an experimental orchard (pcfruit, Sint-Truiden, Belgium) in spring and summer 2008 and was used to investigate the airflow from three air-assisted orchard sprayers (Condor V, Duoprop and AirJet quatt). Velocity magnitudes were measured before and behind leafless and fully-leafed pear canopies across the row while the operating sprayers are passing along the row, and were compared with the simulations. The simulation results predicted the measured values well with all the local relative errors within 20%. The effect of foliar density on airflow from the three air assisted sprayers was manifested by changing the magnitude and direction of the sprayers’ air velocity behind the canopy, especially at the denser regions of the canopy and by changing the pattern of velocity decay horizontally along the jet. The developed methodology will also allow a thorough investigation of atmospheric airflow in canopy structures.  相似文献   

A multi-resolution workflow to generate high-resolution models constrained to dynamic data   总被引：2，自引：0，他引：2  

Céline Scheidt  Jef Caers  Yuguang Chen  Louis J. Durlofsky 《Computational Geosciences》2011,15(3):545-563

Distance-based stochastic techniques have recently emerged in the context of ensemble modeling, in particular for history matching, model selection and uncertainty quantification. Starting with an initial ensemble of realizations, a distance between any two models is defined. This distance is defined such that the objective of the study is incorporated into the geological modeling process, thereby potentially enhancing the efficacy of the overall workflow. If the intent is to create new models that are constrained to dynamic data (history matching), the calculation of the distance requires flow simulation for each model in the initial ensemble. This can be very time consuming, especially for high-resolution models. In this paper, we present a multi-resolution framework for ensemble modeling. A distance-based procedure is employed, with emphasis on the rapid construction of multiple models that have improved dynamic data conditioning. Our intent is to construct new high-resolution models constrained to dynamic data, while performing most of the flow simulations only on upscaled models. An error modeling procedure is introduced into the distance calculations to account for potential errors in the upscaling. Based on a few fine-scale flow simulations, the upscaling error is estimated for each model using a clustering technique. We demonstrate the efficiency of the method on two examples, one where the upscaling error is small, and another where the upscaling error is significant. Results show that the error modeling procedure can accurately capture the error in upscaling, and can thus reproduce the fine-scale flow behavior from coarse-scale simulations with sufficient accuracy (in terms of uncertainty predictions). As a consequence, an ensemble of high-resolution models, which are constrained to dynamic data, can be obtained, but with a minimum of flow simulations at the fine scale.  相似文献   

Conditioning Facies Simulations with Connectivity Data   总被引：3，自引：3，他引：0  

Philippe Renard  Julien Straubhaar  Jef Caers  Grégoire Mariethoz 《Mathematical Geosciences》2011,43(8):879-903

When characterizing and simulating underground reservoirs for flow simulations, one of the key characteristics that needs to be reproduced accurately is its connectivity. More precisely, field observations frequently allow the identification of specific points in space that are connected. For example, in hydrogeology, tracer tests are frequently conducted that show which springs are connected to which sink-hole. Similarly well tests often allow connectivity information in a petroleum reservoir to be provided.  相似文献   

The Last Permafrost Maximum (LPM) map of the Northern Hemisphere: permafrost extent and mean annual air temperatures, 25–17 ka BP     

Jef Vandenberghe  Hugh M. French  Aldar Gorbunov  Sergei Marchenko  Andrey A. Velichko  Huijun Jin  Zhijiu Cui  Tingjun Zhang  Xudong Wan 《Boreas: An International Journal of Quaternary Research》2014,43(3):652-666

This paper accompanies a map that shows the extent of permafrost in the Northern Hemisphere between 25 and 17 thousand years ago. The map is based upon existing archival data, common throughout the Northern Hemisphere, that include ice‐wedge pseudomorphs, sand wedges and large cryoturbations. Where possible, a distinction is made between areas with continuous permafrost and areas where permafrost is either spatially discontinuous or sporadic. The associated mean annual palaeo‐temperatures that are inferred on the basis of present‐day analogues increase understanding of the possible changes in permafrost extent that might accompany current global warming trends. Areas with relict permafrost and areas that were formerly exposed due to lower sea level (submarine permafrost) are also mapped. Mapping is mostly limited to lowland regions (areas approximately <1000 m a.s.l.). Striking features that appear from the map are (i) the narrow permafrost zone in North America, which contrasts with the broader LPM permafrost zone in Eurasia (that may be related to different snow thickness or vegetation cover), (ii) the zonal extent of former LPM permafrost (that may reflect sea‐ice distribution), which contrasts with the present‐day pattern of permafrost extent (especially in Eurasia) and (iii) the relatively narrow zones of LPM discontinuous permafrost (that may indicate strong temperature gradients).  相似文献   

The extent of permafrost in China during the local Last Glacial Maximum (LLGM)   总被引：2，自引：0，他引：2  

Liang Zhao  Huijun Jin  Chuanchuan Li  Zhijiu Cui  Xiaoli Chang  Sergey S. Marchenko  Jef Vandenberghe  Tingjun Zhang  Dongliang Luo  Dongxin Guo  Gengnian Liu  Chaolu Yi 《Boreas: An International Journal of Quaternary Research》2014,43(3):688-698

Recent investigations into relict periglacial phenomena in northern and western China and on the Qinghai–Tibet Plateau provide information for delineating the extent of permafrost in China during the Late Pleistocene. Polygonal and wedge‐shaped structures indicate that, during the local Last Glacial Maximum (LLGM, between ～35 and 10.5 ka BP), the southern limit of latitudinal permafrost in northern China advanced southward at least to ～38–40°N in the east and to ～37–39°N in the west. This represents an advance of about 5–10° of latitude beyond present‐day permafrost limits. The lower limits of elevationally controlled permafrost on the Qinghai–Tibet Plateau and its peripheries were about 1000 m lower: this permafrost was largely continuous during the LLGM. This suggests a cooling of between 4 and 10°C, or more. This paper discusses the extent of permafrost during the LLGM and presents maps that have been constructed on the basis of extensive and integrative analysis of all reliable and pertinent data. The results indicate that the extent of LLGM permafrost in China was between ～3.8 and 4.3×10⁶ km². This is 80 to 100% more than that of ～2.15×10⁶ km² in the 1970s, and 120 to ～150% more than that of ～1.75×10⁶ km² today.  相似文献