Geostatistical analysis of an experimental stratigraphy

[1] A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary basin dimensions where a natural log hydraulic conductivity (ln( K)) was assigned to each pixel on the basis of gray scale and conductivity end-members. The synthetic ln( K) map has mean, variance, and frequency distributions that are comparable to a natural alluvial fan deposit. A geostatistical analysis was conducted on selected regions of this map containing fluvial, fluvial/ floodplain, shoreline, turbidite, and deepwater sedimentary facies. Experimental ln(K) variograms were computed along the major and minor statistical axes and horizontal and vertical coordinate axes. Exponential and power law variogram models were fit to obtain an integral scale and Hausdorff measure, respectively. We conclude that the shape of the experimental variogram depends on the problem size in relation to the size of the local-scale heterogeneity. At a given problem scale, multilevel correlation structure is a result of constructing variogram with data pairs of mixed facies types. In multiscale sedimentary systems, stationary correlation structure may occur at separate scales, each corresponding to a particular hierarchy; the integral scale fitted thus becomes dependent on the problem size. The Hausdorff measure obtained has a range comparable to natural geological deposits. It increases from nonstratified to stratified deposits with an approximate cutoff of 0.15. It also increases as the number of facies incorporated in a problem increases. This implies that fractal characteristic of sedimentary rocks is both depositional process - dependent and problem-scale-dependent

Smart FRP Composite Sandwich Bridge Decks in Cold Regions

INE/AUTC 12.0

Multifractal Modeling of the US Treasury Term Structure and Fed Funds Rate

This paper identifies the Multifractal Models of Asset Return (MMARs) from the eight nodal term structure series of US Treasury rates as well as the Fed Funds rate and, after proper synthesis, simulates those MMARs. We show that there is an inverse persistence term structure in the sense that the short term interest rates show the highest persistence, while the long term rates are closer to the GBM's neutral persistence. The simulations of the identified MMAR are compared with the original empirical time series, but also with the simulated results from the corresponding Brownian Motion and GARCH processes. We find that the eight different maturity US Treasury and the Fed Funds rates are multifractal processes. Moreover, using wavelet scalograms, we demonstrate that the MMAR outperforms both the GBM and GARCH(1,1) in time-frequency comparisons, in particular in terms of scaling distribution preservation. Identified distributions of all simulated processes are compared with the empirical distributions in snapshot and over time-scale (frequency) analyses. The simulated MMAR can replicate all attributes of the empirical distributions, while the simulated GBM and GARCH(1,1) processes cannot preserve the thick-tails, high peaks and proper skewness. Nevertheless, the results are somewhat inconclusive when the MMAR is applied on the Fed Funds rate, which has globally a mildly anti-persistent and possibly chaotic diffusion process completely different from the other nodal term structure rates.MMAR, multifractal spectrum, long memory, scaling, term stucture, persistence, Brownian motion, GARCH, time-frequency analysis

Geostatistical analysis of an experimental stratigraphy

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95276/1/wrcr10212.pd

Spatiotemporal properties of multiscale two-dimensional ows

The extraordinary complexity of turbulence has motivated the study of some of its key features in flows with similar structure but simpler or even trivial dynamics. Recently, a novel class of such flows has been developed in the laboratory by applying multiscale electromagnetic forcing to a thin layer of conducting fluid. In spite of being stationary, planar, and laminar these flows have been shown to resemble turbulent ones in terms of energy spectra and particle dispersion. In this thesis, some extensions of these flows are investigated through simulations of a layer-averaged model carried out using a bespoke semi-Lagrangian spline code. The selected forcings generalise the experimental ones by allowing for various kinds of self-similarity and planetary motion of the multiple scales. The spatiotemporal structure of the forcings is largely reflected on the flows, since they mainly arise from a linear balance between forcing and bottom friction. The exponents of the approximate power laws found in the wavenumber spectra can thus be related to the scaling and geometrical forcing parameters. The Eulerian frequency spectra of the unsteady flows exhibit similar power laws originating from the sweeping of the multiple flow scales by the forcing motions. The disparity between fluid and sweeping velocities makes it possible to justify likewise the observed Lagrangian power laws, but precludes a proper analogy with turbulence. In the steady case, the absolute dispersion of tracer particles presents ballistic and diffusive stages, while relative dispersion shows a superquadratic intermediate stage dominated by separation bursts due to the various scales. In the unsteady case, the absence of trapping by fixed streamlines leads to appreciable enhancement of relative dispersion at low and moderate rotation frequency. However, the periodic reversals of the large scale give rise to subdiffusive absolute dispersion and severely impede relative dispersion at high frequency

Mathematical Methods, Modelling and Applications

This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods

Scaling, modeling, and interpolation of fluvially eroded topography

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2001.Includes bibliographical references (p. 192-202).by Jeffrey D. Niemann.Ph.D