Range of validity of seismic ray and beam methods in general inhomogeneous media – I. General theory

Summary. The limitations of asymptotic wave theory and its geometrical manifestations are newly formalized and scrutinized. Necessary and sufficient conditions for the existence of acoustic and seismic rays and beams in general inhomogeneous media are expressed in terms of new physical parameters: the threshold frequency ω₀ associated with the P/S decoupling condition, the cut-off frequency ω_c associated with the radiation-zone condition, the total curvature of the wavefront and the Fresnel-zone radius.
The analysis is facilitated with the introduction of a new ancillary functional – the hypereikonal which is capable of representing ordinary as well as evanescent waves. The hypereikonal is the natural extension of the eikonal theory.
With the aid of the above new parameters, simple conditions are obtained for the decoupled far field, the decoupled near field, two point dynamic ray tracing, paraxial wavefields and Gaussian beams.     

The dust coma of periodic comet Churyumov-Gerasimenko (1982 VIII)

The dust coma of Comet P/Churyumov-Gerasimenko was monitored in the infrared (1–20 μm) from September 1982 to March 1983. Maximum dust production rate of ～2 × 10⁵ g/sec occured in December, 1 month postperihelion. The ratio of dust/gas production was higher than that in other short-period comets. No silicate feature was visible in the 8- to 13-μm spectrum on 23 October. The mean geometric albedo of the grains was ～0.04 at 1.25 μm and ～0.05 at 2.2 μm.     

An approximate method for evaluating the shear band thickness in saturated soils

A formula for the thickness of a shear band formed in saturated soils under a simple shear or a combined stress state has been proposed. It is shown that the shear band thickness is dependent on the pore pressure properties of the material and the dilatancy rate, but is independent of the details of the combined stress state. This is in accordance with some separate experimental observations. Copyright © 2004 John Wiley & Sons, Ltd.     

A WKBJ spectral method for computation of SV synthetic seismograms in a cylindrically symmetric medium

Summary. A method of synthetic seismogram computation for teleseismic SV -waves is developed in order to treat quantitatively SV -waves in problems of body wave source inversion and source—receiver structure studies. The method employs WKBJ theory for a generalized ray in a vertically inhomogeneous half-space and the propagator matrix technique for waves in near-surface homogeneous layers. Wavenumber integration is done along the real axis of the wavenumber plane and anelasticity is included by using complex velocity in all regions of the earth model. The near-surface source structure is taken into account in the computation for the case of the shallow source by allowing a point source to be located in the homogeneous layers. Source and receiver area structures are also allowed to differ. A general moment tensor point source is considered.     

Simulations of multimode bolometric interferometers

We describe a procedure for the numerical modelling of astronomical interferometers, with particular relevance to far-infrared and submillimetre wavelengths. The scheme is based on identifying a set of modes that carry power from the sky to the detector. The procedure is extremely general, and can be used to model scalar or vector fields, in any state of coherence and polarization, the only limitation being that the propagation of a coherent field through the system be described by an integral transform, a constraint that is in practise always met.
We present simulations of ideal, multimode two-dimensional interferometers, and show that the modal theory reproduces the correct behaviour of both Michelson and Fizeau interferometers. We calculate simulated visibility data for a multimode bolometric Michelson interferometer, with a synthesized source, and produce a dirty map, recovering the original source with the usual artefacts associated with interferometers.     

P‐wave transmission across fractures with nonlinear deformational behaviour

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.     

Thick and thin models of the evolution of carbon dioxide on Mars

We present results from a new simulation code that accounts for the evolution of the reservoirs of carbon dioxide on Mars, from its early years to the present. We establish a baseline model parameter set that produces results compatible with the present (i.e., Patm?6.5 mbar with permanent CO₂ ice cap) for a wide range of initial inventories. We find that the initial inventory of CO₂ broadly determines the evolutionary course of the reservoirs of CO₂. The reservoirs include the atmosphere, ice cap, adsorbed CO₂ in the regolith, and carbonate rocks. We track the evolution of the free inventory: the atmosphere, ice cap and regolith. Simulations begin at 4.53 Gyr before present with a rapid loss of free inventory to space in the early Noachian. Models that assume a relatively small initial inventory (?5 bar) have pronounced minima in the free inventory of CO₂ toward the end of the Noachian. Under baseline parameters, initial inventories below ∼4.5 bar result in a catastrophic loss of the free inventory to space. The current free inventory would be then determined by the balance between outgassing, sputtering losses and chemical weathering following the end of the late bombardment. We call these “thin” models. They generically predict small current free inventories in line with expectations of a small present CO₂ ice cap. For “thick” models, with initial inventories ?5 bar, a surplus of 300-700 mbar of free CO₂ remains during the late-Noachian. The histories of free inventory in time for thick models tend to converge within the last 3.5 Gyr toward a present with an ice cap plus atmospheric inventory of about 100 mbar. For thick models, the convergence is largely due to the effects of chemical weathering, which draws down higher free inventories more rapidly than the low. Thus, thick models have ?450 mbar carbonate reservoirs, while thin models have ?200 mbar. Though both thick and thin scenarios can reproduce the current atmospheric pressure, the thick models imply a relatively large current CO₂ ice cap and thin models, little or none. While the sublimation of a massive cap at a high obliquity would create a climate swing of greenhouse warming for thick models, under the thin model, mean temperatures and pressures would be essentially unaffected by increases in obliquity.     

The Cosmology of Extra Dimensions and Varying Fundamental Constants

I briefly present the Organizing Committee's and my own motivation for organizing this workshop, and I suggest a few key questions for which we will try to find possible answers in the coming days. This revised version was published online in July 2006 with corrections to the Cover Date.