On the Elimination of Bias Averaging-Errors in Proxy Records

Knowledge of and insight into past environmental conditions can be obtained by processing and analyzing proxies. The proxies need to be processed as precisely and accurately as possible, otherwise the conclusion of the analysis will be biased. A calibration method which reduces bias errors in the proxy measurements due to averaging is presented. Sampling with nonzero sample sizes causes an averaging of the true proxy signal over the volume of the sample. The method is applied on a linear synthetic record which results in an optimal correction for frequency components ranging from the dc-frequency (DC) to one half of the sample frequency (f _s /2). Next, the method is tested on non-linear synthetic data where the signal is reconstructed reasonably well. Finally, the method is applied to a real vessel density record of R. mucronata from Makongeni, Kenya, and to a real delta deuterium record of ice core EDC from dome C, Antarctica. The method discussed in this paper is a valuable tool for the calibration of proxy measurements; it can be applied as a correction for low resolution measurements and expanded to other types of samples and proxies. Working with small sample sizes (high resolution) amounts to working near the detection limit, where the signal-to-noise-ratio is low. This correction method provides an alternative in which low resolution measurements can be upgraded to minimize the loss of information due to larger sample sizes.     

Grain-Size Control on Petrographic Composition of Sediments: Compositional Regression and Rounded Zeros

It is well-known that sediment composition strongly depends on grain size. A number of studies have tried to quantify this relationship focusing on the sand fraction, but only very limited data exists covering wider grain size ranges. Geologists have a clear conceptual model of the relation between grain size and sediment petrograpic composition, typically displayed in evolution diagrams. We chose a classical model covering grain sizes from fine gravel to clay, and distinguishing five types of grains (rock fragments, poly- and mono crystalline quartz, feldspar and mica/clay). A compositional linear process is fitted here to a digitized version of this model, by (i) applying classical regression to the set of all pairwise log-ratios of the 5-part composition against grain size, and (ii) looking for the compositions that best approximate the set of estimated parameters, one acting as slope and one as intercept. The method is useful even in the presence of several missing values. The linear fit suggests that the relative influence of the processes controlling the relationship between grain size and sediment composition is constant along most of the grain size spectrum.     

New U-Pb Geochronological Constraints on Formation and Evolution of the Susong Complex Zone in the Dabie Orogen

<正>Objective The Susong complex zone(SCZ)is a relatively lowgrade metamorphic unit mostly with an epidoteamphibolite facies,located in the southernmost part of the Dabie orogen.However,its rock compositions,ages,metamorphic processes and petrogenesis are still     

Kriging and Semivariogram Deconvolution in the Presence of Irregular Geographical Units

This paper presents a methodology to conduct geostatistical variography and interpolation on areal data measured over geographical units (or blocks) with different sizes and shapes, while accounting for heterogeneous weight or kernel functions within those units. The deconvolution method is iterative and seeks the point-support model that minimizes the difference between the theoretically regularized semivariogram model and the model fitted to areal data. This model is then used in area-to-point (ATP) kriging to map the spatial distribution of the attribute of interest within each geographical unit. The coherence constraint ensures that the weighted average of kriged estimates equals the areal datum.This approach is illustrated using health data (cancer rates aggregated at the county level) and population density surface as a kernel function. Simulations are conducted over two regions with contrasting county geographies: the state of Indiana and four states in the Western United States. In both regions, the deconvolution approach yields a point support semivariogram model that is reasonably close to the semivariogram of simulated point values. The use of this model in ATP kriging yields a more accurate prediction than a naïve point kriging of areal data that simply collapses each county into its geographic centroid. ATP kriging reduces the smoothing effect and is robust with respect to small differences in the point support semivariogram model. Important features of the point-support semivariogram, such as the nugget effect, can never be fully validated from areal data. The user may want to narrow down the set of solutions based on his knowledge of the phenomenon (e.g., set the nugget effect to zero). The approach presented avoids the visual bias associated with the interpretation of choropleth maps and should facilitate the analysis of relationships between variables measured over different spatial supports.     

Textures in deforming forsterite aggregates up to 8 GPa and 1673 K

We report results from axisymmetric deformation experiments carried out on forsterite aggregates in the deformation-DIA apparatus, at upper mantle pressures and temperatures (3.1–8.1 GPa, 1373–1673 K). We quantified the resulting lattice preferred orientations (LPO) and compare experimental observations with results from micromechanical modeling (viscoplastic second-order self-consistent model—SO). Up to 6 GPa (~185-km depth in the Earth), we observe a marked LPO consistent with a dominant slip in the (010) plane with one observation of a dominant [100] direction, suggesting that [100](010) slip system was strongly activated. At higher pressures (deeper depth), the LPO becomes less marked and more complex with no evidence of a dominant slip system, which we attribute to the activation of several concurrent slip systems. These results are consistent with the pressure-induced transition in the dominant slip system previously reported for olivine and forsterite. They are also consistent with the decrease in the seismic anisotropy amplitude observed in the Earth’s mantle at depth greater than ~200 km.     

The Tau Model for Data Redundancy and Information Combination in Earth Sciences: Theory and Application

Many decision-making processes in the Earth sciences require the combination of multiple data originating from diverse sources. These data are often indirect and uncertain, and their combination would call for a probabilistic approach. These data are also partially redundant with each other or with all others taken jointly. This overlap in information arises due to a variety of reasons—because the data arises from the same geology, because they originate from the same location or the same measurement device, etc. The proposed tau model combines partially redundant data, each taking the form of a prior probability for the event being assessed to occur given that single datum. The parameters of that tau model measure the additional contribution brought by any single datum over that of all previously considered data; they are data sequence-dependent and also data value-dependent. Data redundancy depends on the sequence in which the data is considered and also on the data values themselves. However, for a given sequence, averaging the tau model parameters over all possible data values leads to exact analytical expressions and corresponding approximations and inference avenues. Information on multiple-point connectivity of permeability arrives from core data, well-test data and seismic data which are defined over varying supports with complex redundancy between these information sources. In order to compute these tau weights for determining connectivity, one needs a model of data redundancy, here expressed as a vectorial training image (Ti) constructed using a prior conceptual knowledge of geology and the physics of data measurement. From such a vectorial Ti, the tau weights can be computed exactly. Neglecting data redundancy leads to an over-compounding of individual data information and the possible risk of making extreme decisions.     

Phreatic Surface in Island Aquifers with Regular Geometry and Time-Independent Recharge and Pumping

The equation of groundwater flow in marine island aquifers in which there is time-independent, spatially-variable recharge and pumping is solved in closed form for rectangular, circular, and elliptical island geometries. The solution of the groundwater flow equation is expressed in terms of the elevation of the phreatic surface within the flow domain. The depth of the seawater-freshwater interface below mean sea level follows from the Dupuit–Ghyben–Herzberg relation. The method of solution presented in this work relies on expanding the hydraulic head and forcing function (recharge and groundwater extraction) as Fourier series that transforms the two-dimensional Poisson-type flow equations into second-order ordinary differential equations solvable using classical theory. The important case of constant recharge (without groundwater extraction) leads to solutions in which the hydraulic head is expressible as the product of a flow factor equal to the squared root of the ratio of recharge over hydraulic conductivity times a geometric factor involving island shape parameters and flow boundary conditions. Estimability conditions for the hydraulic conductivity are derived for the cases of constant recharge and spatially variable recharge with pumping.     

Self-Similar and Self-Affine Properties of Two-Dimensional Fracture Patterns in Rocks

In this paper, we investigate the fractal properties of binary maps of rock fractures at different scales and different geological types, as well as different families of fracture patterns obtained from a two-dimensional Laplacian growth model (LGM). From these analyses we figure out which families of the LGM patterns match the structural properties of the fracture binary maps. The LGM is defined in terms of a nonlinear map that depends on two parameters, λ and \mathfraka\mathfrak{a}, that respectively define the area and shape of the elements of the aggregate that conforms the patterns. The fractal dimension and roughness exponent of the LGM patterns are found to depend on \mathfraka\mathfrak{a}, with 0 < \mathfrak a < 10<\mathfrak {a}<1. From a detailed statistical analysis of these patterns we found that the fractal dimensions of capacity, correlation and information decrease monotonically as \mathfraka\mathfrak{a} increases. We also found that the values of these three fractal dimensions tend to collapse on top of each other as \mathfraka\lessapprox1\mathfrak{a}\lessapprox1. Remarkably, the fractal properties of rock fractures in the scales from millimeters up to a few meters appear to be well represented by the fractal structure of the LGM families of patterns with \mathfraka=0.15\mathfrak{a}=0.15 and 0.30, while the fractal properties of rock fractures in the scale of kilometers seems to be well represented by the LGM family with \mathfraka=0.90\mathfrak{a}=0.90. In addition, the three fractal dimension values of fracture binary maps in the scales from millimeters up to meters were found to be different between them. Nonetheless, for fractures in the scale of kilometers, the values of the three fractal dimensions are very close to each other as an indication of self-similar behavior. Analysis of the corrections to the scaling of the roughness exponent, ζ, suggests that they are negligible for the LGM family of fracture patterns with \mathfraka=0.9\mathfrak{a}=0.9. This finding points to a self-affine structure for this family of patterns. In fact, the calculated roughness exponent results are in the range of values characteristic of rock fractures.     

The Use of Geographically Weighted Regression for Spatial Prediction: An Evaluation of Models Using Simulated Data Sets

Increasingly, the geographically weighted regression (GWR) model is being used for spatial prediction rather than for inference. Our study compares GWR as a predictor to (a) its global counterpart of multiple linear regression (MLR); (b) traditional geostatistical models such as ordinary kriging (OK) and universal kriging (UK), with MLR as a mean component; and (c) hybrids, where kriging models are specified with GWR as a mean component. For this purpose, we test the performance of each model on data simulated with differing levels of spatial heterogeneity (with respect to data relationships in the mean process) and spatial autocorrelation (in the residual process). Our results demonstrate that kriging (in a UK form) should be the preferred predictor, reflecting its optimal statistical properties. However the GWR-kriging hybrids perform with merit and, as such, a predictor of this form may provide a worthy alternative to UK for particular (non-stationary relationship) situations when UK models cannot be reliably calibrated. GWR predictors tend to perform more poorly than their more complex GWR-kriging counterparts, but both GWR-based models are useful in that they provide extra information on the spatial processes generating the data that are being predicted.     

Surge dynamics of disaster displaced populations in temporary urban shelters: future challenges and management issues

A tropical cyclone (TC) precipitation prediction scheme has been developed based on the physical quantities of the NCEP/NCAR reanalysis data as potential predictors and using fuzzy neural network (FNN) model. TC precipitation samples from 172 tropical cyclones (TCs) affecting Guangxi, China, spanning 1980–2015 are used for model development. The FNN model input is constructed from potential predictors by employing both a stepwise regression method (SRM) and a locally linear embedding (LLE) algorithm. The LLE algorithm is capable of finding meaningful low-dimensional architectures hidden in their nonlinear high-dimensional data space and separating the underlying factors. In this scheme, the newly developed model, which is termed the FNN–LLE model, is used for daily TC precipitation prediction from 20:00 (Beijing Time, or BT) of the previous day to 20:00 BT of the current day at 89 stations covering Guangxi, China. Using identical modeling samples and independent samples, predictions of the FNN–LLE model are compared with the widely used SRM and interpolation method using the fine-mesh data of the European Centre for Medium-Range Weather Forecasts (ECMWF) in terms of the performance of TC rainfall prediction at 89 stations in Guangxi. The root-mean-square error (RMSE), bias, and equitable threat score (ETS) results were employed to assess the predicted outcomes. Results show that the FNN–LLE model is superior to the interpolation method by ECMWF and SRM for TC precipitation prediction with RMSE values of 21.94, 24.07, and 25.22 in FNN–LLE model, interpolation method by ECMWF and SRM, respectively. Moreover, FNN–LLE model having average bias and ETS values close to 1.0 gave better predictions than did the interpolation method by ECMWF and SRM.     

Modelling Syntectonic Sedimentation: Combining a Discrete Element Model of Tectonic Deformation and a Process-based Sedimentary Model in 3D

This paper presents a new numerical program able to model syntectonic sedimentation. The new model combines a discrete element model of the tectonic deformation of a sedimentary cover and a process-based model of sedimentation in a single framework. The integration of these two methods allows us to include the simulation of both sedimentation and deformation processes in a single and more effective model. The paper describes briefly the antecedents of the program, Simsafadim-Clastic and a discrete element model, in order to introduce the methodology used to merge both programs to create the new code. To illustrate the operation and application of the program, analysis of the evolution of syntectonic geometries in an extensional environment and also associated with thrust fault propagation is undertaken. Using the new code, much more complex and realistic depositional structures can be simulated together with a more complex analysis of the evolution of the deformation within the sedimentary cover, which is seen to be affected by the presence of the new syntectonic sediments.     

Poloidal and Toroidal Field Modeling in Terms of Locally Supported Vector Wavelets

This paper deals with multiscale modeling of poloidal and toroidal fields such as geomagnetic field and currents. The wavelets are developed from scale-dependent regularizations of the Green function with respect to the Beltrami operator. They are constructed as to be locally compact, thus, allowing a locally reflected (zooming-in) reconstruction of the geomagnetic quantities. Finally, a reconstruction algorithm is indicated in form of a tree algorithm.