FORWARD MODELING IN THE FREQUENCY-SPACE DOMAIN*

Forward modeling of zero-offset data is performed in the frequency-space domain using a one-way extrapolation equation. The use of the frequency domain offers several advantages over conventional time domain methods. The greatest advantage of the frequency domain is that all time derivatives are evaluated exactly by a simple multiplication. Synthetic zero-offset sections are computed with a high degree of accuracy for arbitrary velocity and reflectivity structures. Examples are shown for realistic complicated models and compared with results from physical modeling.     

Comment on the group velocity of surface waves on the plasma sheet boundary

In the recent estimation by Maltsev and Lyatsky (1984) of the group velocity of surface waves on the inner boundary of the plasma sheet, the effect of the curvature of the field lines of the ambient magnetic field of the Earth on the spectrum has been assessed. The authors have not accounted for the fact, however, that the group velocity of the compressional surface magnetohydrodynamic waves itself is nonzero transverse to the magnetic field—a characteristic which has been omitted in the spectrum of Chen and Hasegawa (1974), being used by Maltsev and Lyatsky.This characteristic of compressional surface MHD waves is inherent for the spectrum $\text{ω = (}\text{k}{}_6\text{k}\text{)V}{}_{\mathrm{A}}\text{(k}{}^2{}_6\text{+ 2k}{}^2{}_{\mathrm{\perp }}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, obtained by Nenovski (1978) in the cold plasma limit V_A ? V_S(V_A is Alfvén velocity, and V_S, sound velocity). A comment has been made on the restrictions, proceeding from the approximation, used by Maltsev and Lyatsky. The estimation of the velocities for movements of auroral riometer absorption bays have been reviewed.     

The Early Pleistocene Praetiglian and Ludhamian pollen stages in the North Sea Basin and their relationship to the marine isotope record

In this paper, the currently accepted correlation of the Early Pleistocene Ludhamian stage of England with the Tiglian‐A sub‐stage of the Netherlands is challenged. Recent investigations of Early Pleistocene marine North Sea deposits from a borehole near Noordwijk (the Netherlands) yielded evidence from molluscs, dinoflagellate cysts and sporomorphs for an alternation of warm‐temperate and arctic intervals within the Praetiglian and Tiglian stages. Marine equivalents of the terrestrial‐based pollen sub‐stages Tiglian A and B have been recognised in the upper part of the sequence. A Praetiglian age can be assigned to the lower part of the sequence on the basis of mollusc analysis. Within the Praetiglian, an alternation of warm and cold phases has been recognised from both the dinoflagellate cyst and molluscan records. Three cold phases within the Praetiglian are tentatively correlated with marine isotope stages (MIS) 96–100. The molluscan assemblages provide evidence for climate forcing of the sea level: highest sea levels are reached in the warm‐temperate intervals. Within the Praetiglian, an interval with an acme zone of the dinoflagellate cyst Impagidinium multiplexum, is correlated with the Ludhamian and tentatively linked to MIS 97 and/or MIS 96. The cold molluscan assemblages from the Noordwijk borehole include an acme zone of Megayoldia thraciaeformis, the first and only occurrence of this North Pacific bivalve in the North Sea Basin. Copyright © 2006 John Wiley & Sons, Ltd.     

Design of stable drainage networks in upland forestry plantations

Erosion of man-made, forestry drainage channels occurs when the plough cuts through the surface peat layer into the underlying erodible mineral soil. A procedure is developed, based on hydraulic considerations, which will allow the drainage engineer to design stable drainage networks in upland forestry plantations. An example design chart is given for an erodible sandy loam type soil.     

A new stereo‐analytical method for determination of removal blocks in discontinuous rock masses

The paper provides a new stereo‐analytical method, which is a combination of the stereographic method and analytical methods, to separate finite removable blocks from the infinite and tapered blocks in discontinuous rock masses. The methodology has applicability to both convex and concave blocks. Application of the methodology is illustrated through examples. Addition of this method to the existing block theory procedures available in the literature improves the capability of block theory in solving practical problems in rock engineering. Copyright © 2003 John Wiley & Sons, Ltd.     

Predicting the polarization of the microwave background from the WMAP temperature maps

In this paper, we study how to predict the polarization of the Cosmic Microwave Background (CMB) using knowledge of only the temperature (intensity) and the cross-correlation between temperature and polarization. We derive a “Wiener prediction” method and apply it to the Wilkinson Microwave Anisotropy Probe (WMAP) all-sky CMB temperature maps and to the MAXIMA field.     

A micromechanical finite element model for linear and damage‐coupled viscoelastic behaviour of asphalt mixture

This study presents a finite element (FE) micromechanical modelling approach for the simulation of linear and damage‐coupled viscoelastic behaviour of asphalt mixture. Asphalt mixture is a composite material of graded aggregates bound with mastic (asphalt and fine aggregates). The microstructural model of asphalt mixture incorporates an equivalent lattice network structure whereby intergranular load transfer is simulated through an effective asphalt mastic zone. The finite element model integrates the ABAQUS user material subroutine with continuum elements for the effective asphalt mastic and rigid body elements for each aggregate. A unified approach is proposed using Schapery non‐linear viscoelastic model for the rate‐independent and rate‐dependent damage behaviour. A finite element incremental algorithm with a recursive relationship for three‐dimensional (3D) linear and damage‐coupled viscoelastic behaviour is developed. This algorithm is used in a 3D user‐defined material model for the asphalt mastic to predict global linear and damage‐coupled viscoelastic behaviour of asphalt mixture. For linear viscoelastic study, the creep stiffnesses of mastic and asphalt mixture at different temperatures are measured in laboratory. A regression‐fitting method is employed to calibrate generalized Maxwell models with Prony series and generate master stiffness curves for mastic and asphalt mixture. A computational model is developed with image analysis of sectioned surface of a test specimen. The viscoelastic prediction of mixture creep stiffness with the calibrated mastic material parameters is compared with mixture master stiffness curve over a reduced time period. In regard to damage‐coupled viscoelastic behaviour, cyclic loading responses of linear and rate‐independent damage‐coupled viscoelastic materials are compared. Effects of particular microstructure parameters on the rate‐independent damage‐coupled viscoelastic behaviour are also investigated with finite element simulations of asphalt numerical samples. Further study describes loading rate effects on the asphalt viscoelastic properties and rate‐dependent damage behaviour. Copyright © 2006 John Wiley & Sons, Ltd.