Minimum relative entropy and probabilistic inversion in groundwater hydrology   总被引：3，自引：0，他引：3  

Allan D. Woodbury  Tadeusz J. Ulrych 《Stochastic Environmental Research and Risk Assessment (SERRA)》1998,12(5):317-358

The similarity between maximum entropy (MaxEnt) and minimum relative entropy (MRE) allows recent advances in probabilistic inversion to obviate some of the shortcomings in the former method. The purpose of this paper is to review and extend the theory and practice of minimum relative entropy. In this regard, we illustrate important philosophies on inversion and the similarly and differences between maximum entropy, minimum relative entropy, classical smallest model (SVD) and Bayesian solutions for inverse problems. MaxEnt is applicable when we are determining a function that can be regarded as a probability distribution. The approach can be extended to the case of the general linear problem and is interpreted as the model which fits all the constraints and is the one model which has the greatest multiplicity or “spreadout” that can be realized in the greatest number of ways. The MRE solution to the inverse problem differs from the maximum entropy viewpoint as noted above. The relative entropy formulation provides the advantage of allowing for non-positive models, a prior bias in the estimated pdf and `hard' bounds if desired. We outline how MRE can be used as a measure of resolution in linear inversion and show that MRE provides us with a method to explore the limits of model space. The Bayesian methodology readily lends itself to the problem of updating prior probabilities based on uncertain field measurements, and whose truth follows from the theorems of total and compound probabilities. In the Bayesian approach information is complete and Bayes' theorem gives a unique posterior pdf. In comparing the results of the classical, MaxEnt, MRE and Bayesian approaches we notice that the approaches produce different results. In␣comparing MaxEnt with MRE for Jayne's die problem we see excellent comparisons between the results. We compare MaxEnt, smallest model and MRE approaches for the density distribution of an equivalent spherically-symmetric earth and for the contaminant plume-source problem. Theoretical comparisons between MRE and Bayesian solutions for the case of the linear model and Gaussian priors may show different results. The Bayesian expected-value solution approaches that of MRE and that of the smallest model as the prior distribution becomes uniform, but the Bayesian maximum aposteriori (MAP) solution may not exist for an underdetermined case with a uniform prior.  相似文献   

Sompi, Pisarenko and the extended information criterion     

Tadeusz J. Ulrych  Mauricio D. Sacchi 《Geophysical Journal International》1995,122(3):719-724

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Comment on 'Simultaneous time-domain deconvolution with application to the computation of receiver functions' by H. Gurrola, G. E. Baker and J. B. Minster     

Mauricio D. Sacchi  Tadeusz J. Ulrych 《Geophysical Journal International》1996,127(1):253-254

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Contamination of tsunami sediments in a coastal zone inundated by the 26 December 2004 tsunami in Thailand     

Witold Szczuciński  Przemysław Niedzielski  Grzegorz Rachlewicz  Tadeusz Sobczyński  Anetta Zioła  Artur Kowalski  Stanisław Lorenc  Jerzy Siepak 《Environmental Geology》2005,49(2):321-331

Tsunami sediments deposited in a coastal zone of Thailand by the 26 December 2004 tsunami wave were sampled within 50 days after the event. All surface and ground waters in tsunami- inundated zone revealed significant salinity at that time. The tsunami sediments, composed mainly of fine to medium sand, contain significantly elevated contents of salts (Na⁺, K⁺, Ca⁺², Mg⁺², Cl and SO ₄ ⁻² ) in water-soluble fraction, and of Cd, Cu, Zn, Pb in the bioavailable fraction and As in the exchangeable fraction in relation to the reference sample. The origin of contaminants is marine, as well as litho- and anthropogenic. The salts and Pb, Zn and Cu reveal high correlation to each other and to the mean grain size (pore size and porosity). Serious environmental hazard exists in that region because, due to gentle morphology, there is a risk of migration of the contaminants into ground waters and food chain.  相似文献   

A new determination of recent vertical movements of the Earth's crust in Poland     

Tadeusz Wyrzykowski 《Journal of Geodynamics》1987,8(2-4)

A new determination of recent vertical movements of the Earth's crust in Poland is described in this paper. It resulted from the joint adjustment of the network of repeated levelling in 7 countries of Eastern and Central Europe. The author presents the characteristics of the levelling data sets used (measurements made in 1953–1957 and 1974–1979), results of the repeated levelling, the method of determination of the recent crustal movements and of the preparation of the map at a scale of 1:2.500.000 presenting these movements for the area of the whole country. The results of the determination of the Earth's crustal movements are discussed, and causes of the prevailing appearance of sinking movements are suggested. Differences between the values of vertical movements of the Earth's crust obtained during various determinations are presented, as well as the maximum mean error of the difference between new and old determinations. The conformity of these determinations is assessed.  相似文献   

Carbon and oxygen isotopic composition and foraminifers of condensed basal Zechstein (Upper Permian) strata in western Poland: environmental and stratigraphic implications     

Tadeusz Marek Peryt  Stanis&#x;aw Ha&#x;as  Danuta Peryt 《Geological Journal》2015,50(4):446-464

The basinal facies of the Lopingian Zechstein Limestone in SW Poland consists of thin (often less than 1 m thick) limestones and/or dolomites, often containing the Kupferschiefer (few tens of centimetres thick) at their base, and local thick (up to 90 m) reefal carbonates. The δ¹³C curve of these basal Zechstein deposits strongly suggests that even when the Kupferschiefer is lacking, the thin (condensed) sequences record the entire interval of the Zechstein prior to the onset of evaporite deposition, in contrast to the thick reef sequences which lack the characteristic δ¹³C curve for the lowermost part of the Zechstein. The calcite samples show considerable ranges of δ¹⁸O values. If the maximum δ¹⁸O values are considered to be the closest to the pristine original ones and if δ¹⁸O_water value = 0 is assumed, then the calculated range of palaeotemperatures for the Kupferschiefer and Zechstein Limestone calcite ranges from 19 to 34 °C. The faunal restriction, common dwarf foraminifers and the predominance of lagenids in the foraminiferal assemblage indicate continual dysaerobic conditions and possibly elevated salinity of seawater during deposition of thin basinal Zechstein Limestone deposits. The mixing of shallow and deeper waters in the stratified Zechstein Basin caused by upwelling could result in prolific carbonate precipitation in reefs located at the slope of the marginal carbonate platform of the Zechstein Limestone and in isolated reefs related to palaeohighs within the basin; however, there is no isotopic record of eventual upwelling. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献