On matrix diffusion: formulations, solution methods and qualitative effects

 Matrix diffusion has become widely recognized as an important transport mechanism. Unfortunately, accounting for matrix diffusion complicates solute-transport simulations. This problem has led to simplified formulations, partly motivated by the solution method. As a result, some confusion has been generated about how to properly pose the problem. One of the objectives of this work is to find some unity among existing formulations and solution methods. In doing so, some asymptotic properties of matrix diffusion are derived. Specifically, early-time behavior (short tests) depends only on φ _m ² R _m D _m  / L _m ², whereas late-time behavior (long tracer tests) depends only on φ _m R _m , and not on matrix diffusion coefficient or block size and shape. The latter is always true for mean arrival time. These properties help in: (a) analyzing the qualitative behavior of matrix diffusion; (b) explaining one paradox of solute transport through fractured rocks (the apparent dependence of porosity on travel time); (c) discriminating between matrix diffusion and other problems (such as kinetic sorption or heterogeneity); and (d) describing identifiability problems and ways to overcome them. Received, October 1997 · Revised, November 1997 · Accepted, December 1997     

Source spectral phases of surface waves recovered from observed spectral amplitudes by using Hilbert transforms

Spectral phases of surface waves radiated at the seismic source are recovered by means of the Hilbert transform of spectral amplitudes. Through numerical simulations as well as the study of an earthquake with well known focal mechanism, it is shown that the recovered phases satisfy a criterion of coherency, so that they can be used in an inversion process for the retrieval of the seismic moment tensor.     

Generation of earth stratified models compatible with both ellipticity and phase velocity observations of Rayleigh waves

In the eigenvalue eigenvector decomposition used in inversion techniques, we can sometimes obtain eigenvalues close to zero. Related to these eigenvalues close to zero, a set of stratified earth models is generated. These are compatible with the theoretical observations according to a given model. The method is applied to ellipticities and phase velocities of Rayleigh waves, and supply proof of the advantage of working with both sets of data together.     

Thrusting of young lithosphere in subduction zones with special reference to structures in ophiolitic peridotites

Two contrasted types of structures have been recognized in peridotites from ophiolites and from the oceanic environment. The first one, typical of high-temperature/moderate-stress conditions, is observed in the upper part of ophiolitic peridotites and has been ascribed to plastic flow in an oceanic ridge environment. The second one, typical of moderate-temperature/high-stress conditions, is more specially dealt with here. It is printed in the peridotites above the basal metamorphic aureole found in many ophiolites. The strain increases downward over 1–2 km to produce peridotite mylonites at the contact with the metamorphic aureole. Similarities with rocks from trench and island arc environments suggest ascribing this deformation in ophiolites to a trench environment. We propose that shear fracturing in a young oceanic lithosphere is initiated by the compressive elastic stress in its lower part which is produced by bending of the subducted plate. An externally applied compressive stress is responsible for subsequent overthrusting of the fractured lithosphere. This interpretation is in good agreement with the available geophysical data on young subducted plates and with the physical data on ophiolitic peridotites.     

Zenisu Ridge: a deep intraoceanic thrust related to subduction, off southwest Japan

During the French-Japanese Kaiko project, Seabeam, seismic and submersible observations were made in the eastern part of the Nankai subduction zone, close to the area of collision between the Izu-Bonin island arc and the Japan margin. The most prominent feature is the Zenisu Ridge, an elongated relief of the Philippine Sea plate running parallel to the Trench. Magnetic anomalies indicate that the crust of the Zenisu Ridge is a part of the Shikoku oceanic basin formed in the Early Miocene, 23 Ma ago and presumably uplifted at a later stage. Structural analysis of seismic data and diving observations lead us to interpret the superficial structure as being due to compressive tectonics. Mapping the acoustic basement reveals that the southeastern flank of the ridge is bounded by a double thrust, both segments being of equal magnitude (vertical offset about 1 to 1.5 km). Geophysical data support the hypothesis of a main thrust cutting through most of the lithosphere and flattening at depth. The overall structure of the surrounding area reveals a compressive deformation zone widening toward the east, the magnitude of the compressive deformation decreasing westward as well as southward of the Zenisu Ridge.     

Geological study of sedimentary basins using SPOT data

This paper illustrates the benefits of DTMs created from SPOT images for the exploration of sedimentary basins. We chose an example located in the Ebro sedimentary basin in Spain, characterized by good outcropping conditions and slight deformations. The data used consist of a pair of SPOT panchromatic images and a SPOT XS image. The work consists of making up a 3D database, followed by interpretation of stereo pairs computed from orthoimages and the DTM. This interpretation is made on a stereoscopic desk and results in a digital file containing in the form of vectors all the observed faults and lithology. These vectors are then used to make calculations on the geometry of the objects they represent: we demonstrate that we can accurately measure layer directions and dips, sediment thicknesses and fault throws. Synthesis of perspective views made at the same time provide a good understanding of the structures and help to test their geometric consistency. Thus knowledge about relief given by DTMs helps to interpret remote detection images in 3D space, and particularly to accurately quantify the results of this interpretation.     

A modeling-based analysis of processes driving wave-dominated inlets

Among the different types of tidal inlets, wave-dominated inlets have been subjected to few quantitative studies, so that the physical processes controlling their dynamics are not fully understood. This study presents the application of a coastal area morphodynamic modeling system to a wave-dominated inlet (Óbidos Inlet, western coast of Portugal), in order to investigate the physical processes responsible for channel development during fair weather conditions and shoaling during periods of larger waves. The modeling system was able to reproduce reasonably well morphological changes at the Óbidos Inlet and subsequent tidal amplitude evolutions inside the lagoon over a period which includes 3 months of fair weather conditions, followed by 2 months representative of winter conditions. The inlet development during fair weather conditions was attributed to the strong ebb-dominance of the main channel without waves, enhanced by the combination of shallow channels and a meso-tidal range. The inlet infilling during the maritime winter was attributed to three main wave-induced mechanisms: (1) the onshore component of wave radiation stresse gradients, which is not fully compensated by the wave-induced setup in front of the inlet; (2) the acceleration and convergence of longshore transport toward the inlet, due to the presence of a strong lateral gradient in free surface elevation on both sides of the inlet, and, to a smaller extent, to wave refraction around the ebb-delta; and (3) the increase in mean water level inside the lagoon, which reduces tidal asymmetry and subsequent ebb-dominance.     

Numerical modelling of dynamic consolidation on granular soils

The application of Pastor–Zienkiewicz constitutive model for sands to dynamic consolidation problems is presented in this paper. This model is implemented in a coupled code formulated in terms of displacements for both solid and fluid phases (u?w formulation), which is firstly compared with u?p_w formulation for some simple examples. Its range of validity, previously established for elastic problems and harmonic loading, is explored. Once the suitability of the u?w formulation has been ascertained for this kind of dynamic problems in soils, one‐ and two‐dimensional (plane strain) dynamic consolidation numerical examples are provided, aiming to give some light into the physics of this ground improvement technique. A ‘wave of dryness’, observed at the soil surface during the impact in field cases, is numerically reproduced and justified. Some hints on the influence of the loading zone size are also given. Copyright © 2007 John Wiley & Sons, Ltd.