ALBERT

Notes: Germination of annual pasture species was studied under controlled-environment conditions in south-western Australia at temperatures in the range from 4°C to 35°C. Subterranean clover (Trifolium subterraneum) and Wimmera ryegrass (Lolium rigidum) had a germination of 90% between 12°C and 29°C, whereas capeweed (Arctotheca calendula) had a high germination percentage in a much narrower temperature range with an optimum of 25°C. Growth of subterranean clover, capeweed and Wimmera ryegrass between 28 and 49 days after sowing (DAS) was also studied at two photon flux densities, 13 and 30 mol m−2 d−1, and at diel temperatures in the range from 15/10°C to 33/28°C. Pasture species grown at a density of 1000 plants m−2 accumulated at least twice the amount of shoot dry matter when subjected to temperatures of 21/16°C and 27/22°C, compared with a lower temperature of 15/10°C and a higher temperature of 33/28°C. Except at the highest temperature and at high photon flux density, capeweed had lower green area indices (GAI) than the other two species at 28 DAS. Crop growth rates between 28 and 49 DAS were higher in Wimmera ryegrass than in the other two species, whereas subterranean clover had a lower relative growth rate than the other two species at all temperatures and both photon flux densities. Subterranean clover and capeweed intercepted a greater proportion of the incident radiation compared with Wimmera ryegrass. The values of radiation interception and GAI were used to estimate the number of DAS to reach 75% radiation interception [f(0·75)]. The number of days to reach f(0·75) decreased with increasing temperature from 15/10°C to reach a minimum at 27/22°C. The time taken to achieve f(0·75) was always shorter by about 10 d when the photon flux density was 30 mol m−2 d−1 in the autumn compared with 13 mol m−2 d−1 in the winter. These results are discussed in relation to the early growth of annual pasture in the field.

Notes: Abstract The present paper describes the effects of growth of roots of wheat (Triticum aestivum cv. Gamenya) in hypoxic nutrient solutions on acrenchyma formation and O2 movement from shoots to roots. Two types of roots were investigated: (1) seminal roots of 4–7-d-old seedlings, and (2) seminal and nodal roots of 10–28-d-old plants. Gas-filled porosity of seminal and nodal roots increased from 3 to 12% and from 5–7 to 11–15%, respectively, when the roots emerged in stagnant or N2-flushed solutions (0.003 mol m −3 O2) compared with growth in continuously acrated solutions (0.26 mol m −3 O2). However, neither root type increased in porosity when they were longer than 100–200 mm at the start of the exposure to these stagnant or N2-flushed treatments. A vernier microscope and cylindrical platinum-electrode were used to examine the relationship between root extension and transport of O2 from shoots to roots via the gas spaces. Measurements were made when the roots were in an anoxic medium and were dependent solely on O2 supplied from the shoots. For seminal roots of 5–7-d-old seedlings raised in stagnant solutions (90–100 mm), internal O2 transport was sufficient to support a rate of root elongation in the O2-free medium of between 0.03 and 0.17 mm h−1. When the O2 pressure around the shoots was increased from 20 to 100 kPa O2, the O2 concentrations at the walls of the expanding zone (2–7 mm from the tip) of these roots increased from 0.006 mol m−3 to between 0.04 and 0.26 mol m−3, and the rate of root extension increased five-fold. Oxygen transport to roots grown continuously in acrated solutions was considerably less than for roots raised in stagnant solutions; this difference was greater for seminal than for nodal roots. When the acrated seminal roots were longer than 100 mm and transferred to an O2-free root medium, O2 concentration became zero at the root tip causing elongation to cease. After 24 h of anoxia, none of these roots were able to resume elongation following a return to acrated solutions.

Notes: Abstract Wheat, Triticum aestivum cv. Gamenya, seedlings were grown for 4d in acrated 0.5 mol m−3 CaSO4 solution. A cylindrical platinum-electrode and vernier microscope were used to examine the effects of the colcoptile sheath on O2 transport from shoots to seminal roots via the internal gas-space system, and on the clongation of the root tip. By removing the colcoptile sheath, O2 concentrations at the root tip in an O2-free medium at 5°C increased from 0.017 to 0.17 mol m−3 O2 when 100 kPa O2 was around the shoots. When the shoots were in air, the separation of the colcoptile sheath from the primary leaf caused the rate of root clongation in the anoxic medium to increase by two fold.

Notes: Abstract. Seedlings of Zea mays L. were grown in the dark at 27°C. Four-day-old seedlings were then exposed for 3 days to solutions equilibrated with gas mixtures to give O2 concentrations between 0.02 and 0.25 mol m−3. Root growth was impaired just as severely at 0.06 as 0.02 mol O2 m−3 while growth at 0.16 mol O2 m−3 was about the same as in solutions in equilibrium with air (0.25 mol O2 m−3).Growth of young seedlings at low O2 concentrations was inhibited to the same extent in nutrient solution and 0.5 ml m−3 CaCl2, showing that the adverse effect of O2 deficits on growth was not due to less uptake of inorganic nutrients. Furthermore, at low O2 concentrations neither exposure of the shoots to a relative humidity of 100% (26.0 g H2O m−3) nor excision of the entire shoot enhanced root growth relative to that in plants with shoots at a relative humidity of 50% (13.0 g H2O m−3). Therefore, for these seedlings growing in the dark, impairment of root growth at low O2 concentrations was not a consequence of water deficits in the shoot or of other shoot-root interactions.Total soluble sugars and amino acid concentrations were generally greater at low (0.02–0.06 mol O2m−3) than at high O2 concentrations (0.16–0.25 mol O2 m −3). This applied specifically to the root apices (0–2 mm) and expanding (2–15 mm) tissue except in some experiments where sugar concentrations in expanding tissue were slightly greater at high than at low O2 concentrations.Critical O2 pressures for respiration of excised root segments were approximately 0.117 and 0.065 mol O2 m−3 in the expanding and expanded zones of the roots, respectively. In contrast, the critical O2 pressure exceeded 0.20 mol O2 m−3 in the apex, suggesting that O2 supply for metabolic processes is most likely to be sub-optimal in this zone. Our results show clearly that the adverse effects of low O2 concentrations are unlikely to be a consequence of substrate shortage for either respiration or synthesis of macromolecules; low rates of ATP regeneration in growing root tissues are the logical cause for impaired growth in young seedlings while they are being sustained by seed reserves.

Notes: We point out that while the equations of seismic ray geometrical spreading given recently by Norris do differ as stated from equations given by Červeny, it does not imply that the latter equations are wrong. The two sets of equations differ only in form and in a way which, in part at least, can be ascribed to different choices of Hamiltonian by the two authors. Quantitatively, though, the two sets of equations are entirely equivalent. We also present some numerical results of ray tracing in anisotropic models simulating a continential rift, a spreading ridge and a subduction zone. These three structures span a range of geological mechanisms for seismic anisotropy. Though definitive conclusions cannot be easily drawn when there is both anisotropy and inhomogeneity, the results do indicate the magnitude of ray path, travel-time and amplitude variations to be expected for P-waves when anisotropy is introduced.

Notes: Maslov ray summation is ‘less local’ than ordinary ray theory, because the receiver waveform depends on non-Fermat or neighbouring rays and more information about the wavefront than just local Gaussian curvature. In this way, the Maslov solution is able to remain valid at caustics, where geometrical rays and corresponding stationary points of the Maslov phase coalesce. the wavefront information is expressed via the Legendre transformation, whereby the physical wavefront is represented as the envelope of a family of tangent ‘planes’ (Snell fronts). the actual form of the Snell fronts (true planes, sections of curves or surfaces, etc.) depends on the spatial coordinates used. Given a selection for the Snell fronts and Maslov phase, one can substitute the Maslov integral solution directly into the wave equation and obtain a transport equation for the Maslov amplitude. This direct substitution is analogous to that used in ordinary ray theory and avoids pseudo-differential operators.Sometimes the relative curvature of the physical wavefront and a tangential Snell front is zero. the envelope-forming process breaks down, because the local correspondence between the physical front and the Snell fronts is not one to one and invertible. This situation corresponds to a so-called ‘pseudo-caustic’ (slowness-domain caustic or telescopic point) in the Maslov solution. Pseudo-caustics are not real. A particular ray from the source may touch a pseudo-caustic at some time in one coordinate system, but in another system this ray will not have a pseudo-caustic (at the same time and place). It is easy to design a change of coordinates (e.g. from cartesian to curvilinear or polar) to deform a single-valued traveltime function appropriately, but a multi-valued or folded wavefront, as at a physical or real caustic, is less simple. Catastrophe theory is concerned with putting multi-valued functions into ‘normal forms’ which do not have psuedo-caustics. the manifold here is ‘Lagrangian’ and V. I. Arnold showed that a special type of deformation or ‘canonical transformation’ must be used. A ‘Lagrangian equivalence’ consists of a deformation of the ‘base’ (x-space) and/or the addition of a function on the base. the latter simply means factoring out an appropriate reference phase before Legendre transformation and we have found that this simple step is often sufficient for removing pseudo-caustics. It requires no new numerical work, only an inspection or understanding of the ray-tracing results at hand.We present some body-wave computations using the reference-phase technique for models with real caustics in 2-D and for a single-valued wavefront in 3-D. We point out that a Lagrangian equivalence may be used to turn a maximum of the Maslov phase function into a minimum. This has no effect on the frequency-domain solution, but may affect the causality of the computed waveform when the Chapman method is used to obtain the time-domain response. Causality is a property which one may need to impose explicitly. Only the non-delta or one-sided function part of the response (waveform tail) is affected by this consideration.Although zeroth-order Maslov theory correctly describes the severe waveform is clear from Secdistortion due to wavefront catastrophes, it may not adequately model the more subtle effects of smooth wavefront bending. Zeroth-order Maslov theory contains some but not all of the first-order (ω−1) terms of ordinary asymptotic ray theory. First-order Maslov theory is needed for complete consistency up to ω−1. Experimentation will several different zeroth-order Maslov representations is a simple, rapid way to ascertain the potential importance of thse more subtle waveform effects. If the waveform tails are too strong, the assumption that the Maslov (and ray theory) amplitude function can be expanded in powers of ω− may break down. Numerical integration of a wave equation is then necessary.

Notes: Traveltimes and amplitudes for P-waves from a 500 km-deep source in the Kuril subduction zone have been synthesized by ray tracing in smooth 3-D models that allow general anisotropy and inhomogeneity. the aim is to compare the effects of proposed anisotropy in or near slabs with those of lateral heterogeneity alone. to concentrate on these effects, the source position, slab thickness (90 km), dip (63°) and velocity anomaly (5 per cent) are held constant. Results are presented for isotropic models with slab penetration to 670km and 1000 km. Anisotropic models with 670 km-deep slabs have anisotropy within the slab (Anderson 1987) and in a 10° wedge above the slab (Ribe 1989a; McKenzie 1979). the resulting wavefront topology is never as simple as that in a laterally homogeneous reference Earth and there is strong model dependence of shadow zones, caustics and areas of multipathing.Rays are traced through slab models defined by 3-D cubic-spline interpolation of up to 21 elastic constants. Outside the slab region, 1-D ray tracing through PREM and spherical trigonometry are used to complete the ray path. the results illustrate the importance of using both traveltime and amplitude information when interpreting slab structure from teleseismic data. Some anisotropic slab models have been found which produce large (〉2 s) traveltime residuals that are similar in many parts of the world to those for the deep isotropic model, but the amplitude patterns are substantially different. the model with a deep isotropic slab produces a narrow band of large traveltime residuals (3 s) and high amplitudes in a region across northern Canada. This feature is due to the focusing of rays that have travelled down the high-velocity core of the deep slab. Regions where ray theory fails (i.e. caustics) are obvious through multipathing and amplitude singularities. Hilbert-transforms and Airy-type decay caustics should be observed in many places if the models presented are good representations of the Earth. Multipathing in along-strike regions is a pervasive feature of the models considered and the degree of such multipathing is highly dependent on the nature of the slab-boundary velocity gradients. the model with anisotropy above the slab produces multipathing (traveltime triplication) in the down-dip region (i.e. a narrow region through Europe). Identifying such non-linear or ‘catastrophic’ features in teleseismic data is potentially more diagnostic than linearized interpretations (automated inversion). Overall, the results show that a range of conservative models representing a range of structural theories can encompass a wide range of wavefront consequences.Drs M. Weber and V. Červený are thanked for helpful reviews of the manuscript. Advice and reprints from Dr K. Fujita are appreciated and Dr D. L. Anderson is thanked for suggesting the anisotropic slab model with no isotropic velocity anomaly. the authors acknowledge the support of NSERC (Canada) through Operating Grant number A1465. J-M.K. is supported by an Amoco Postgraduate Scholarship and an Ontario Graduate Scholarship.

Notes: When a P-wave is incident on an isotropic-anisotropic boundary, the reflected S conversion will generally contain some transverse (SH) component. Numerical results show that the magnitude of this SH component is strongly related to the transmitted qP-wave and the form of the P-wave anisotropy (degree and orientation) in the lower medium, rather than the jump in shear wave velocities over the interface. Varying Poisson's ratio in the incident medium changes the amplitude of the reflected SV component, as one would expect, but has minimal effect on the reflected SH signal. Therefore, it is possible to obtain reflected S-waves that are almost purely transverse, even though the source is compressional and the medium of propagation is isotropic. This study of these indirect effects of anisotropy was prompted by anomalous transverse signals in a refraction data set, which is included for comparison.

Notes: Lighthill and others have expressed the ray-theory limit of Green's function for a point source in a homogeneous anisotropic medium in terms of the slowness-surface Gaussian curvature. Using this form we are able to match with ray theory for inhomogeneous media so that the final solution does not depend on arbitrarily chosen ‘ray coordinates’ or ‘ray parameters’ (e.g. take-off angles at the source). The reciprocity property is clearly displayed by this ‘ray-coordinate-free’ solution. The matching can be performed straightforwardly using global Cartesian coordinates. However, the ‘ray-centred’ coordinate system (not to be confused with ‘ray coordinates’) is useful in analysing diffraction problems because it involves 2 times 2 matrices not 3 times 3 matrices. We explore ray-centred coordinates in anisotropic media and show how the usual six characteristic equations for three dimensions can be reduced to four, which in turn can be derived from a new Hamiltonian. The corresponding form of the ray-theory Green's function is obtained. This form is applied in a companion paper.

Notes: An S-wavefront from an isotropic region is expected to separate into two fronts when it passes into a gradually more anisotropic region. Standard ray expansions may be used to continue the waves in the anisotropic region when these two S-wavefronts have separated sufficiently. However, just inside the anisotropic region the two S-waves interfere with an effect that is stronger than the usual ω-1 corrections of the ray method. A waveform distortion can occur and this should be considered when modelling S-waves in, e.g., subduction zones with regions of isotropy grading into regions of anisotropy.The interference is studied here by local analysis of an integral equation obtained by the Green's function method. It is found that if the elasticity and its first two derivatives are continuous at the isotropy/anisotropy border, then zeroth-order ray theory may still be used to continue the incident wave into the anisotropic region. The incident displacement is simply resolved into two definite directions at the point where the anisotropy begins. These two directions are the limits of the unique eigenvectors on the anisotropic rays as the point of isotropy (onset of splitting) is approached. If the nth derivative of the elasticity is discontinuous at the isotropy/anisotropy border, then the scattering integral which describes the interference makes a correction to ray theory which is O(ω-1/n+1) in magnitude. Hence, the interference effect is stronger when the emergence of anisotropy is more gradual.Although the corrections are given by simple expressions, it is not reasonable to specify numerical velocity models up to such high-order derivatives. For a smooth interpolation scheme, such as cubic splines, it is more practical to monitor the splitting rays obtained by ray tracing and to use the best-fitting ‘equivalent’ high-order discontinuity. This will lead to an estimate of the importance of the correction terms. An example is given for a subduction zone model involving olivine alignment in the mantle-wedge above the slab.