Rough surface backscatter and statistics via extended parabolic integral equation

This paper extends the parabolic integral equation method, which is very effective for forward scattering from rough surfaces, to include backscatter. This is done by applying left-right splitting to a modified two-way governing integral operator, to express the solution as a series of Volterra operators; this series describes successively higher-order surface interactions between forward and backward going components, and allows highly efficient numerical evaluation. This and equivalent methods such as ordered multiple interactions have been developed for the full Helmholtz integral equations, but not previously applied to the parabolic Green's function. In addition, the form of this Green's function allows the mean field and autocorrelation to be found analytically to second order in surface height. These may be regarded as backscatter corrections to the standard parabolic integral equation method

Visualisation and Grid applications of electromagnetic scattering from aircraft

Proceedings of the 2003 UK e-Science All Hands Meeting, 31st August - 3rd September, Nottingham UKElectromagnetic scattering behaviour plays a central role in the design of aircraft and other complex structures. This paper describes progress on visualisation tools in this area and on initial development of a web portal to enable scientists at remote locations to collaborate

Solution of the inverse-scattering problem for grazing incidence upon a rough surface

The inverse-scattering problem for a scalar wave field incident at grazing angles upon a one-dimensional moderately rough surface is considered. The problem is solved directly by treating the scattering integral as an integral equation in the unknown field derivative at the surface and coupling this to a simple equation relating the derivative to the surface itself. An algorithm is described for the solution of this system, and results in which complicated rough surfaces are accurately reconstructed are presented

Moments of wave scattering by a rough surface,"

This paper gives the first two moments of a wave field scattered by grazing incidence on a moderately rough surface. The expressions are derived for normally distributed surfaces with arbitrary spectrum, and are valid at depths that are large compared with the surface height. It is demonstrated that the first moment has a weak dependence on the surface fluctuation spectrum. The first moment is compared with Monte Carlo simulations, and gives close agreement. It is also shown that for a given degree of surface roughness the first moment retains the fiat-surface reflection property of being determined by the distance from an "image source," i.e., the sum of the depths of source and receiver

Rough surface reconstruction at grazing angles by an iterated marching method.

An iterated marching method is presented for the reconstruction of rough perfectly reflecting one-dimensional (1D) surfaces from scattered data arising from a scalar wave at grazing incidence. This is based on coupled integral equations adapted from an earlier approach using the parabolic equation, relating the scattered field at a plane to the unknown surface. Taking the flat surface as an initial guess, these are solved here using at most three iterations. The method is applied to scattered field data generated from the full Helmholtz equations. This approach improves stability and self-consistency. The reconstructed surface profiles are found to be in good agreement with the exact forms. The sensitivity with respect to random noise is also investigated, and the algorithm is found to exhibit a type of self-regularization

Continental bedrock and riverine fluxes of strontium and neodymium isotopes to the oceans

Author Posting. © American Geophysical Union, 2010. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 11 (2010): Q03016, doi:10.1029/2009GC002869.Realistic models of past climate and ocean chemistry depend on reconstructions of the Earth's surface environments in the geologic past. Among the critical parameters is the geologic makeup of continental drainage. Here we show, for the present, that the isotope composition of dissolved strontium in rivers increases linearly with the age of bedrock in drainage basins, with the notable exception of the drainage area of Arabia, India, and Southeast Asia that is affected by unusually radiogenic dissolved Sr from the Himalaya. We also demonstrate that the neodymium isotope compositions of suspended matter in rivers as well as clastic sediments deposited along the ocean margins decrease linearly with the bedrock ages of river drainage basins and large-scale continental drainage regions, as determined from digital geologic maps. These correlations are used to calculate the present-day input of dissolved Sr (4.7 × 1010 mol yr−1, 87Sr/86Sr of ∼0.7111) and particulate Nd isotopes (ɛNd of approximately −7.3 ± 2.2) to the oceans. The fact that the regionally averaged ɛNd of the global detrital input to the global coastal ocean is identical to globally averaged seawater (ɛNd of −7.2 ± 0.5) lends credence to the importance of “boundary exchange” for the Nd isotope composition of water masses. Regional biases in source areas of detrital matter and runoff are reflected by the observation that the average age of global bedrock, weighted according to the riverine suspended sediment flux, is significantly younger (∼336 Myr) than the age of global bedrock weighted according to water discharge (394 Myr), which is younger than the average bedrock age of the nonglaciated, exorheic portions of the continents (453 Myr). The observation that the bedrock age weighted according to Sr flux is younger (339 Myr) than that weighted according to water flux reflects the disproportionate contribution from young sedimentary and volcanic rocks to the dissolved Sr load. Neither the isotope composition of the dissolved nor the particulate continental inputs to the ocean provide unbiased perspectives of the lithologic makeup of the Earth's surface. Temporal changes in bedrock geology as well as the shifting focal points of physical erosion and water discharge will undoubtedly have exerted strong controls on temporal and spatial changes in the isotope chemistry of past global runoff and thus seawater.NSF grants EAR‐ 0125873, EAR‐0519387, and OCE‐0851015 to B.P.‐E. and a CNRS‐funded “poste rouge” position for B.P.‐E. at the Observatoire Midi‐Pyrénées in Toulouse supported this work

Corridor Gothic

This article investigates the role of the corridor in Gothic fiction and horror film from the late eighteenth century to the present day. It seeks to establish this transitional space as a crucial locus, by tracing the rise of the corridor as a distinct mode of architectural distribution in domestic and public buildings since the eighteenth century. The article tracks pivotal appearances of the corridor in fiction and film, and in the final phase argues that it has become associated with a specific emotional tenor, less to do with amplified fear and horror and more with emotions of Angst or dread

Random scattering by rough surfaces with spatially varying impedance

A method is given for evaluating electromagnetic scattering by an irregular surface with spatially-varying impedance. This uses an operator expansion with respect to impedance variation and allows examination of its effects and the resulting modification of the field scattered by the rough surface. For a fixed rough surface and randomly varying impedance, expressions are derived for the scattered field itself, and for the coherent field with respect to impedance variation for both flat and rough surfaces in the form of effective impedance conditions