Reflection and transmission of plane waves by a layer of compact inhomogeneities     

J. D. Achenbach  M. Kitahara  Y. Mikata  D. A. Sotiropoulos 《Pure and Applied Geophysics》1988,128(1-2):101-118

Reflection and transmission of elastic wave motion by a layer of compact inhomogeneities has been analyzed. For identical inhomogeneities whose geometrical centers are periodically spaced, the problem has been formulated and solved rigorously. The reflected and transmitted longitudinal and transverse wave motions have been expressed as superpositions of wavemodes, where each wavemode has its own cut-off frequency. At its cut-off frequency a mode converts from a standing into a propagating wavemode. The standing wavemodes decay exponentially with distance to the plane of the centers of the inhomogeneities. At small frequencies only the lowest order modes of longitudinal and transverse wave motion are propagating. Reflection and transmission coefficients have been defined in terms of the coefficients of the zeroth-order scattered wavemodes. These coefficients have been computed by a novel application of the Betti-Rayleigh reciprocal theorem. They are expressed as integrals over the surface of a single inhomogeneity, in terms of the displacements and tractions on the surface of the inhomogeneity. The system of singular integral equations for the surface fields has been solved numerically by the boundary integral equation method. Curves show the reflection and transmission coefficients for the reflected and transmitted longitudinal and transverse waves as functions of the frequency. Some results are also presented for planar distributions of cracks whose spacing and size are random variables. Finally, dispersion relations are discussed for solids which are completely filled with periodically spaced inhomogeneities.  相似文献   

Spatial and temporal distribution of Fe, Ni, Cu and Pb along 140°E in the Southern Ocean during austral summer 2001/02     

Xiaodong Lai  Kazuhiro Norisuye  Michi Mikata  Tomoharu Minami  Andrew R. Bowie  Yoshiki Sohrin   《Marine Chemistry》2008,111(3-4):171-183

The distribution of dissolved (D) and acid-dissolvable (AD) Fe, Ni, Cu and Pb in the upper water column (0–300 m depth) was determined in the Australian sector of the Southern Ocean (140°E meridian) during three cruises conducted between November 2001 and March 2002. For Ni and Cu, there was no significant difference in concentration between dissolved and acid-dissolvable species. DNi and DCu showed significant (P = 0.01) positive correlations with silicate, phosphate and nitrate, reflecting their strong nutrient-type behaviour. For Fe and Pb, the acid-dissolvable concentration mostly exceeded the dissolved concentration, reflecting the importance of labile particulate species for these elements. DPb decreased between January and February in the Polar Frontal Zone and in Antarctic continental shelf water. ADPb maxima occurred in the Antarctic Zone, resulting in a maximum AD/D ratio of 7. The mean DFe concentration in the surface mixed layer was 0.3 nM in the sub-Antarctic zone, 0.4 nM in the Polar Frontal Zone, 0.5 nM in the Antarctic Zone and increased southward beyond the Antarctic Divergence and towards the continent. DFe did not show a clear temporal change in its horizontal distribution, which was in contrast to the other nutrients and trace metals. ADFe substantially increased in Antarctic continental shelf water where the AD/D ratio reached 11. The following conclusions can be drawn from these data. (1) Ni and Cu exist exclusively as dissolved species and their distributions are mainly controlled by their biogeochemical cycling, similar to those of the major nutrients. (2) Pb is dominated by particulate species. The distribution of DPb is temporally and spatially variable due to a sporadic source and strong scavenging. (3) DFe is rather a minor fraction of total Fe in Antarctic continental shelf water where shelf sediments and Antarctic sea-ice appear to be strong sources for Fe. There is substantial temporal variation in the supply of Fe to the upper water column. DFe in the mixed layer of the open Southern Ocean is maintained at low concentrations throughout summer due to uptake by phytoplankton and scavenging.  相似文献