An introduction to Maslov's asymptotic method

Summary. Familiar concepts such as asymptotic ray theory and geometrical spreading are now recognized as an asymptotic form of a more general asymptotic solution to the non-separable wave equation. In seismology, the name Maslov asymptotic theory has been attached to this solution. In its simplest form, it may be thought of as a justification of disc-ray theory and it can be reduced to the WKBJ seismogram. It is a uniformly valid asymptotic solution, though. The method involves properties of the wavefronts and ray paths of the wave equation which have been established for over a century. The integral operators which build on these properties have been investigated only comparatively recently. These operators are introduced very simply by appealing to the asymptotic Fourier transform of Ziolkowski & Deschamps. This leads quite naturally to the result that phase functions in different domains of the spatial Fourier transform are related by a Legendre transformation. The amplitude transformation can also be inferred by this method. Liouville's theorem (the incompressibility of a phase space of position and slowness) ensures that it is always possible to obtain a uniformly asymptotic solution. This theorem can be derived by methods familiar to seismologists and which do not rely on the traditional formalism of classical mechanics. It can also be derived from the sympletic property of the equations of geometrical spreading and canonical transformations in general. The symplectic property plays a central role in the theory of high-frequency beams in inhomogeneous media.     

Shear-wave polarizations on a curved wavefront at an isotropic free surface

Summary. We present polarization diagrams of the particle motions at the free surface of an isotropic half-space generated by incident shear waves from a local buried point source. The reflectivity technique is used to calculate synthetic seismograms from which the particle motions are plotted. The particle motions are examined over a range of epicentral distances in a uniform isotropic half-space for different source frequencies and polarization angles, and for different Poisson's ratios. The particle motions due to a curved wavefront possess different characteristics from those generated by plane wavefronts at corresponding incidence angles. A curved wavefront generates a local SP -phase: a P -headwave which propagates along the free surface, and arrives shortly before the direct S -wave. These two arrivals give rise to cruciform particle motions in the sagittal and horizontal planes, which could be misinterpreted as anisotropy-induced shear-wave splitting. An examination of the particle motion in the transverse plane, mutually orthogonal to the sagittal and horizontal planes, can be used to discriminate between isotropic and anisotropic interpretations. The amplitude of the SP -phase is enhanced when it propagates in a low-velocity surface layer overlying the source layer, and may then become the dominant phase on radial-component seismograms. The presence of even a single surface layer may introduce considerable complexity into the seismogram, and we examine the effects of layer thickness, velocity contrast, and source depth on the corresponding polarization diagrams. Reliable information on the source and propagation path characteristics of shear waves from a buried local point source can only be obtained from free-surface records if they are recorded within a very limited epicentral distance range.     

Decomposition of Hudson estuary macrophytes: Photosynthetic pigment transformations and decay constants

Plant pigment decay constants were determined for four macrophytes collected from the Hudson Estuary.Typha angustifolia andScirpus fluviatilis were used as representatives of emergent aquatic vegetation (EAV), andPotamogeton sp. andVallisneria americana were used to represent submerged aquatic vegetation (SAV). Litter bags were maintained in an environmental chamber in the dark for 104 d. The fastest rate of total mass loss was in the SAVV. americana and slowest in the EAVT. angustifolia. Changes in carotenoid and chloropigment concentration resulting from microbial and meiofaunal heterotrophy in each of the macrophytes were quantified using reverse-phase, high-performance liquid chromatography (RP-HPLC) techniques. Chlorophyllc and the carotenoid, fucoxanthin, provided useful biomarkers in determining the presence of epiphytic diatom growth, which only occurred on the SAV. The highest concentrations of phaeophorbidea, commonly used as an indication of metazoan grazing, were found in the SAVV. americana. Low concentrations of phaeophorbidea in the SAVPotamogeton sp. indicate inefficient use of this SAV by meiofaunal grazers. Lutein decayed slower than all other carotenoids in both EAV and SAV. Microcosm studies such as this are necessary to further understand the mechanisms and kinetics of photosynthetic pigment transformations in natural systems.     

Supercritical gas sorption on moist coals

The effect of moisture on the CO₂ and CH₄ sorption capacity of three bituminous coals from Australia and China was investigated at 55 °C and at pressures up to 20 MPa. A gravimetric apparatus was used to measure the gas adsorption isotherms of coal with moisture contents ranging from 0 to about 8%. A modified Dubinin–Radushkevich (DR) adsorption model was found to fit the experimental data under all conditions. Moisture adsorption isotherms of these coals were measured at 21 °C. The Guggenheim–Anderson–de Boer (GAB) model was capable of accurately representing the moisture isotherms over the full range of relative pressures.Moist coal had a significantly lower maximum sorption capacity for both CO₂ and CH₄ than dry coal. However, the extent to which the capacity was reduced was dependent upon the rank of the coal. Higher rank coals were less affected by the presence of moisture than low rank coals. All coals exhibited a certain moisture content beyond which further moisture did not affect the sorption capacity. This limiting moisture content was dependent on the rank of the coal and the sorbate gas and, for these coals, corresponded approximately to the equilibrium moisture content that would be attained by exposing the coal to about 40–80% relative humidity. The experimental results indicate that the loss of sorption capacity by the coal in the presence of water can be simply explained by volumetric displacement of the CO₂ and CH₄ by the water. Below the limiting moisture content, the CO₂ sorption capacity reduced by about 7.3 kg t^− 1 for each 1% increase in moisture. For CH₄, sorption capacity was reduced by about 1.8 kg t^− 1 for each 1% increase in moisture.The heat of sorption calculated from the DR model decreased slightly on addition of moisture. One explanation is that water is preferentially attracted to high energy adsorption sites (that have high energy by virtue of their electrostatic nature), expelling CO₂ and CH₄ molecules.     

Plesiosaurs

Plesiosaurs are an unusual and intriguing group of extinct aquatic reptiles ( Fig. 1 ). They are sauropterygians, a group known from an array of semi‐aquatic forms during the Triassic period: placodonts, pachypleurosaurs and nothosaurs. The first plesiosaurs are known from the very latest Triassic, but by the Early Jurassic plesiosaurs were cosmopolitan in distribution and lasted successfully to the latest Cretaceous, when they became victims of the K‐T extinction event. Plesiosaurs were predominantly marine organisms, although their fossils are not uncommon in brackish or even fresh water deposits. We know that all plesiosaurs were carnivorous; many of them were top predators in their respective ecosystems. But with no living descendants (or analogues) plesiosaurs are mysterious fossil organisms—as we will see, many questions regarding their biology remain unanswered or contentious. However, plesiosaurs are currently undergoing renewed scientific attention.

Figure 1 Open in figure viewer PowerPoint The beautifully preserved skeleton of the plesiosaur Rhomaleosaurus victor seen in ventral view, from the Lower Jurassic (Toarcian) of Holzmaden, Germany (total length 3.44 m). Redrawn from Fraas (1910).     

Helium isotopes in ferromanganese crusts from the central Pacific Ocean

Helium isotopes have been measured in samples of two ferromanganese crusts (VA13/2 and CD29-2) from the central Pacific Ocean. With the exception of the deepest part of crust CD29-2 the data can be explained by a mixture of implanted solar- and galactic cosmic ray-produced (GCR) He, in extraterrestrial grains, and radiogenic He in wind-borne continental dust grains. ⁴He concentrations are invariant and require retention of less than 12% of the in situ He produced since crust formation. Loss has occurred by recoil and diffusion. High ⁴He in CD29-2 samples older than 42 Ma are correlated with phosphatization and can be explained by retention of up to 12% of the in situ-produced ⁴He. ³He/⁴He of VA13/2 samples varies from 18.5 to 1852 R_a due almost entirely to variation in the extraterrestrial He contribution. The highest ³He/⁴He is comparable to the highest values measured in interplanetary dust particles (IDPs) and micrometeorites (MMs). Helium concentrations are orders of magnitude lower than in oceanic sediments reflecting the low trapping efficiency for in-falling terrestrial and extraterrestrial grains of Fe-Mn crusts. The extraterrestrial ³He concentration of the crusts rules out whole, undegassed 4-40 μm diameter IDPs as the host. Instead it requires that the extraterrestrial He inventory is carried by numerous particles with significantly lower He concentrations, and occasional high concentration GCR-He-bearing particles.