Estimation of Probabilities of Three Kinds of Petrologic Hypotheses with Bayes Theorem

Physical-chemical explanations of the causes of variations in rock suites are evaluated by comparing predicted to measured compositions. Consistent data turn an explanation into a viable hypothesis. Predicted and measured values seldom are equal, creating problems of defining consistency and quantifying confidence in the hypthesis. Bayes theorem leads to methods for testing alternative hypotheses. Information available prior to data collection provides estimates of prior probabilities for competing hypotheses. After consideration of new data, Bayes theorem updates the probabilities for the hypotheses being correct, returning posterior probabilities. Bayes factors, B, are a means of expressing Bayes theorem if there are two hypotheses, H ₀ and H ₁. For fixed values of the prior probabilities, B > 1 implies an increased posterior probability for H ₀ over its prior probability, whereas B < 1 implies an increased posterior probability for H ₁ over its prior probability. Three common problems are: (1) comparing variances in sets of data with known analytical uncertainties, (2) comparing mean values of two datasets with known analytical uncertainties, and (3) determining whether a data point falls on a predicted trend. The probability is better than 0.9934 that lava flows of the 1968 eruption of Kilauea Volcano, Hawaii, are from a single magma batch. The probability is 0.99 that lava flows from two outcrops near Mount Edziza, British Columbia, are from different magma batches, suggesting that the two outcrops can be the same age only by an unlikely coincidence. Bayes factors for hypotheses relating lava flows from Volcano Mountain, Yukon Territory, by crystal fractionation support the hypothesis for one flow but the factor for another flow is so small it practically guarantees the fractionation hypothesis is wrong. Probabilities for petrologic hypotheses cannot become large with a single line of evidence; several data points or datasets are required for high probabilities.     

再论《统计假设检验在地学应用中的两种“错误”》

本文首先指出实际工作中使用统计假设检验方法常出现的问题,具体介绍了假设检验方法,并分析两种错误之间的关系。最后,提出当对原假设了解不充分,不能肯定原假设出现的可能性大时,可采用贝叶斯方法进行检验。     

Phase‐shifts in shear stress as an explanation for the maintenance of pool–riffle sequences

The stability of the pool–rif?e sequence is one of the most fundamental features of alluvial streams. For several decades, the process of velocity, or shear stress, reversal has been proposed as an explanation for an increase in the amplitude of pool–rif?e sequence bars during high ?ows, offsetting gradual scour of rif?es and deposition in pools during low ?ows. Despite several attempts, reversal has rarely been recorded in ?eld measurements. We propose that, instead of being reversed, maxima and minima in shear stress are phase‐shifted with respect to the pool–rif?e sequence bedform pro?le, so that maximum shear stress occurs upstream of rif?e crests at high ?ow, and downstream at low ?ow. Such phase‐shifts produce gradients of shear stress that explain rif?e deposition, and pool scour, at high ?ow, in accord with sediment continuity. The proposal is supported by results of a one‐dimensional hydraulic model applied to the surveyed bathymetry of a pool–rif?e sequence in a straight reach of a gravel‐bed river. In the sequence studied, the upstream phase‐shift in shear stress at high ?ow was associated with variations in channel width, with width minima occurring upstream of rif?e crests, approximately coincident with shear stress maxima, and width maxima occurring downstream of rif?e crests. Assuming that the width variation is itself the result of ?ow de?ection by rif?e crests at low ?ow, and associated bank‐toe scour downstream, low and high ?ow can be seen to have complementary roles in maintaining alluvial pool–rif?e sequences. Copyright © 2004 John Wiley & Sons, Ltd.     

Experimental research on critical point hy- pothesis

Introduction Earthquake is a kind of severe natural disaster. In order to predict earthquake effectively, thegeoscientists at home and abroad have carried out a great deal of studies on seismicity. For exam-ple,Willis, (1924) and Tocher (1959) made some early investigations on seismicity before largeearthquake. Chinese geoscientists performed even more studies in this field (CHEN, et al, 1981;HUANG, FENG, 1981; LIU, 1982; LU, 1985; LU, et al, 2001; MA, et al, 1982; MEI, 1960; …     

Assessing the temporal variance of evapotranspiration considering climate and catchment storage factors

Understanding the temporal variance of evapotranspiration (ET) at the catchment scale remains a challenging task, because ET variance results from the complex interactions among climate, soil, vegetation, groundwater and human activities. This study extends the framework for ET variance analysis of Koster and Suarez (1999) by incorporating the water balance and the Budyko hypothesis. ET variance is decomposed into the variance/covariance of precipitation, potential ET, and catchment storage change. The contributions to ET variance from those components are quantified by long-term climate conditions (i.e., precipitation and potential ET) and catchment properties through the Budyko equation. It is found that climate determines ET variance under cool-wet, hot-dry and hot-wet conditions; while both catchment storage change and climate together control ET variance under cool-dry conditions. Thus the major factors of ET variance can be categorized based on the conditions of climate and catchment storage change. To demonstrate the analysis, both the inter- and intra-annul ET variances are assessed in the Murray-Darling Basin, and it is found that the framework corrects the over-estimation of ET variance in the arid basin. This study provides an extended theoretical framework to assess ET temporal variance under the impacts from both climate and storage change at the catchment scale.     

空间大地测量GPS揭示的汾渭盆地及其邻域现今地壳应变场变化特征

利用汾渭盆地及其邻域2001—2007年与2009—2011年高精度GPS监测资料,基于区域构造特点,采用块体运动应变模型结合数理统计假设检验法,建立了区域合理的地壳运动应变模型,基于此定量研究了区域现今地壳应变场及其变化特征,特别是2008年汶川强震对汾渭盆地区域变形特征的作用影响,同时从盆地整体上分析了盆地内多发的地裂缝灾害与区域整体构造变形特征之间的内在关系.研究结果表明:经统计检验判断,选择合理的区域地壳运动应变模型,对获取真实反映区域实际构造变形特性的应变参数具有重要的作用;2008年汶川强震对青藏东边缘地块及渭河盆地西侧局部地区应变场造成一定的影响,但是震后上述区域并没有出现显著的应变积累而是呈现出应变量值较震前减小的特征,分析其原因可能是因为此区域并不是强震造成的库仑应力显著增加区,在震后2009—2011年时间段内处于构造应力场的松弛调整期;汶川强震没有显著改变研究域现今整体的构造变形背景特征,区域地壳构造活动特征仍具有较好的继承性;基于研究域构造块体具有各向同性连续弹性变形的前提,初步推断整个汾渭盆地内多发的地裂缝灾害可能是区域NW—SE向拉张应力场作用下的地表破裂响应.     

基于广义位势理论的类剑桥模型

广义位势理论直接从数学原理出发建立本构模型,避开了传统塑性理论中塑性势函数等复杂概念,为研究岩土本构模型提供了新的思路。基于广义位势理论中土的应力空间多重势面模型,对剑桥模型“能量方程假设”的数学原理进行分析,从数学角度上建立了一个改进的剑桥模型（即类剑桥模型）,而修正剑桥模型等可作为其特例。利用不同应力路径下的试验数据对其合理性进行验证,并与剑桥模型进行对比分析。结果表明：类剑桥模型的参数确定方便、自由,计算结果与试验较一致,甚至优于修正剑桥模型;类剑桥模型所采用的数学原理更明确,且避免了确定塑性势函数和能量方程的困难及其所带来的误差,是一个具有较好实用价值的模型。     

Glacial-Interglacial Atmospheric CO2 Change—The Glacial Burial Hypothesis

Organic carbon buried under the great ice sheets of the Northern Hemisphere is suggested to be the missing link in the atmospheric CO2 change over the glacial-interglacial cycles. At glaciation, the advancement of continental ice sheets buries vegetation and soil carbon accumulated during warmer pe-riods. At deglaciation, this burial carbon is released back into the atmosphere. In a simulation over two glacial-interglacial cycles using a synchronously coupled atmosphere-land-ocean carbon model forced by reconstructed climate change, it is found that there is a 547-Gt terrestrial carbon release from glacial maximum to interglacial, resulting in a 60-Gt (about 30-ppmv) increase in the atmospheric CO2, with the remainder absorbed by the ocean in a scenario in which ocean acts as a passive buffer. This is in contrast to previous estimates of a land uptake at deglaciation. This carbon source originates from glacial burial,continental shelf, and other land areas in response to changes in ice cover, sea level, and climate. The input of light isotope enriched terrestrial carbon causes atmospheric δ^13C to drop by about 0.3‰ at deglaciation,followed by a rapid rise towards a high interglacial value in response to oceanic warming and regrowth on land. Together with other ocean based mechanisms such as change in ocean temperature, the glacial burial hypothesis may offer a full explanation of the observed 80-100-ppmv atmospheric CO2 change.     

异常形变检测方法探讨

在讨讼以往方法的基础上,将拟准检定法拓展用于发现异常形变。该方法直接以真误差为研究对象,避免了其他方法以最二乘残差及其函数为研究对象的缺点。最后通过一个算例,简单介绍了拟准检定法检测异常形变的实施过程。     

行星反照率的取值和假设的讨论

首先分析了Wang的有关行星反照率假设的错误之处,而后分别对Budyko、North的行星反照率假设提出修改方案,最后提出了有关行星反照率的非线性分段、反馈假设: