Weak-contrast approximation of the elastic scattering matrix in anisotropic media

The plane-wave reflection and transmission coefficients at a plane interface between two anisotropic media constitute the elements of the elastic scattering matrix. For a 1-D anisotropic medium the eigenvector decomposition of the system matrix of the transformed elasto-dynamic equations is used to derive a general expression for the scattering matrix. Depending on the normalization of the eigenvectors, the expressions give scattering coefficients for amplitudes or for vertical energy flux.Computing the vertical slownesses and the corresponding polarizations, the eigenvector matrix and its inverse can be found. We give a simple formula for the inverse, regardless of the normalization of the eigenvectors. When the eigenvectors are normalized with respect to amplitudes of displacement (or velocity), the calculation of the scattering matrix for amplitudes is simplified.When the relative changes in all parameters are small, a weak-contrast approximation of the scattering matrix, based on the exactly determined polarization vectors in an average medium, is obtained. The same approximation is also derived directly from the transformed elasto-dynamic equations for a smooth vertically inhomogeneous medium, proving the consistency of the approximation.For monoclinic media, with the mirror symmetry plane parallel to the interface, the approximative scattering matrix is given in terms of analytic expressions for the non-normalized eigenvectors and vertical slownesses. For transversely isotropic media with a vertical axis of symmetry (VTI) and isotropic media, explicit solutions for the weak-contrast approximations of the scattering matrices have been obtained. The scattering matrix for amplitudes for isotropic media is well known. The scattering matrix for vertical energy flux may have applications in AVO analysis and inversion due to the reciprocity of the reflection coefficients for converted waves.Numerical examples for monoclinic and VTI media provide good agreement between the approximative and the exact reflection matrices. It is, however, expected that the approximations cannot be used when the symmetry properties of the two media are very different. This is because the approximation relies on a small relative contrast between the eigenvectors in the two media.Presented at the Workshop Meeting on Seismic Waves in Laterally Inhomogeneous Media, Castle of Trest, Czech Republic, May 22–27, 1995.     

Adaptive Multiscale Permeability Estimation

With multiscale permeability estimation one does not select parameterization prior to the estimation. Instead, one performs a hierarchical search for the right parameterization while solving a sequence of estimation problems with an increasing parameterization dimension. In some previous works on the subject, the same refinement is applied all over the porous medium. This may lead to over-parameterization, and subsequently, to unrealistic permeability estimates and excessive computational work. With adaptive multiscale permeability estimation, the new parameterization at an arbitrary stage in the estimation sequence is such that new degrees of freedom are not necessarily introduced all over the porous medium. The aim is to introduce new degrees of freedom only where it is warranted by the data. In this paper, we introduce a novel adaptive multiscale estimation. The approach is used to estimate absolute permeability from two-phase pressure data in several numerical examples.     

The Ensemble Kalman Filter: theoretical formulation and practical implementation

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.Responsible Editor: Jörg-Olaf Wolff     

Is pure groundwater safe to drink?: natural "contamination' of groundwater in Norway

The title of this article is designed to provoke. Naturally occurring parameters are, by definition, not contamination. Nevertheless, nature is not necessarily nice, and naturally occurring trace toxins can be every bit as undesirable as their counterparts derived from human pollution.     

High-Resolution Simulations of Nonhelical MHD Turbulence

According to the kinematic theory of nonhelical dynamo action, the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case, the magnetic energy peaks at the resistive scale. Using high resolution simulations (up to 1024³ meshpoints) with no large-scale imposed field, we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about five times larger than the forcing wavenumber. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of two to three. Both spectra are approximately parallel. The total energy spectrum seems to be close to k ^?3/2, but there is a strong bottleneck effect and we suggest that the asymptotic spectrum is instead k ^?5/3. This is supported by the value of the second-order structure function exponent that is found to be ζ₂ = 0.70, suggesting a k ^?1.70 spectrum. The third-order structure function scaling exponent is very close to unity,—in agreement with Goldreich–Sridhar theory. Adding an imposed field tends to suppress the small-scale magnetic field. We find that at large scales the magnetic energy spectrum then follows a k ^?1 slope. When the strength of the imposed field is of the same order as the dynamo generated field, we find almost equipartition between the magnetic and kinetic energy spectra.     

Amino acid diagenesis in the marine bivalve Arctica islandica Linné from northwest European sites: Only time and temperature?

Collections of the molluscan species Arctica islandica from seven sites in Norway, Scotland and the North Sea, ranging in age from recent to Early Pleistocene, have been sampled for amino acid analyses. The shells were sampled in profiles through the valves at different distances from the umbo. In the fossil material a general trend of increasing degree of isoleucine (lle) epimerisation and decreasing amino acid concentrations were found going from the inner part of the valve to the outer. Although less pronounced, there is a similar trend from the central part of the valve to the margin. As the concentration of alloisoleucine (alle) remains nearly constant, the observed changes in alle/lle ratios are a result of variations in the amount of isoleucine. The amino acid composition is fairly uniform in recent shells and the observed gradients are established in mid-Holocene samples. Therefore, it is suggested that the gradients are established during rapid early degradation of the protein, possibly due to microbiological activity. Differences in alle/lle ratios observed in molluscs from sites of the same age and same thermal history could be explained by differences in the exposure to amino-acid-consuming microorganisms during the very early stage of diagenesis.     

A precise multipass method for satellite Doppler positioning

A precise and efficient algorithm is developed for determining the locations of radio beacons (e.g. of the ARGOS or COSPAS/SARSAT type) based on Doppler shift measurements in overflying satellites. The method distinguishes itself through: (1) the use of a very compact analytic orbital theory valid for all eccentricities, (2) autonomous orbit improvement based on Doppler data for one or more local reference beacons accessible at a single LUT, (3) simultaneous orbit improvement and calculation of beacon coordinates for an arbitrary number of satellites, satellite passes, and beacons, and (4) very efficient semi-analytic matrix inversion by partitioning into global, semi-global, and local parameters.The algorithm has been implemented in a FORTRAN program which can be run on a PC. Error statistics are presented from applications of the program to a large number of actual Doppler curves obtained with the ARGOS and COSPAS/SARSAT systems.     

Evaluation of an ensemble of Arctic regional climate models: spatiotemporal fields during the SHEBA year

Simulations of eight different regional climate models (RCMs) have been performed for the period September 1997–September 1998, which coincides with the Surface Heat Budget of the Arctic Ocean (SHEBA) project period. Each of the models employed approximately the same domain covering the western Arctic, the same horizontal resolution of 50 km, and the same boundary forcing. The models differ in their vertical resolution as well as in the treatments of dynamics and physical parameterizations. Both the common features and differences of the simulated spatiotemporal patterns of geopotential, temperature, cloud cover, and long-/shortwave downward radiation between the individual model simulations are investigated. With this work, we quantify the scatter among the models and therefore the magnitude of disagreement and unreliability of current Arctic RCM simulations. Even with the relatively constrained experimental design we notice a considerable scatter among the different RCMs. We found the largest across-model scatter in the 2 m temperature over land, in the surface radiation fluxes, and in the cloud cover which implies a reduced confidence level for these variables. An erratum to this article can be found at