THE EXPANSION METHOD: IMPLICATIONS FOR GEOGRAPHIC RESEARCH*

Geographic phenomena and our models of them are closely linked to the spatial-temporal contexts in which they are observed. The expansion method is a procedure that incorporates contextual effects into mathematical models. More importantly, it is the basis for a movement by some geographers away from the classical spatial science paradigm. The evolving paradigm associated with the expansion method represents a reformulation of the way in which geographers think about and use models, and is consistent with a more realistic perspective on the nature of geographic inquiry.     

Evolution of grains in a turbulent solar nebula

In accretion disk models of the solar nebula, turbulence is driven by convective instability. This mechanism requires high opacity, which must be provided by solid grains. Evolution of the grain size distribution in a turbulent disk is computed numerically, using realistic collisional outcomes and strengths of grain aggregates, rather than an arbitrary “sticking efficiency.” The presence of turbulence greatly increases the rate of grain collisions; the coagulation rate is initially much greater than in a nonturbulent disk. Aggregates quickly reach sizes ～0.1–1 cm, but erosion and breakup in collisions prevent growth of larger bodies for plausible aggregate impact strengths. These aggregates are too small to settle to the plane of the disk, and planetesimal formation is impossible as long as the turbulence persists. However, the opacity of the disk is reduced by aggregate formation; some combinations of opacity law and surface density produce an optically thin disk, cutting off turbulent convection. The disk may experience alternating periods of turbulence and quiescence, as grains are depleted by coagulation and replenished by infall from the presolar cloud. Planetesimals can form only during the quiescent intervals; it is argued that such episodes were rare during the lifetime of the accretion disk.     

Seismic body waves in anisotropic media: propagation through a layer

Summary. The square-root energy ratios and pulse shapes are presented for P, SV and SH waves transmitted through a layer of orthorhombic olivine between two isotropic half-spaces. Off incident planes of symmetry, incident P waves generate two small amplitude SH waves (one from each interface), whose amplitudes decrease slowly with increasing period. Incident SV (or SH ) waves can generate large amplitude SH (or SV ) waves which decrease rapidly with increasing period. For incident S waves, many pulses not present in isotropic models are generated, often of large relative amplitude, with many of the transmitted S pulses showing evidence of double arrivals, either in the form of S-wave splitting, or a modification of the shape of the input waveform.     

How fast do Galilean satellites spin?

Each of the Galilean satellites, as well as most other satellites whose initial rotations have been substantially altered by tidal dissipation, has been widely assumed to rotate synchronously with its orbital mean motion. Such rotation would require a small permanent asymmetry in the mass distribution in order to overcome the small mean tidal torque. Since Io and Europa may be substantially fluid, they may not have the strenght to support the required permanent asymmetry. Thus, each may rotate at the unknown but slightly nonsynchronous rate that corresponds to zero mean tidal torque. This behaviour may be observable by Galileo spacecraft imaging. It may help explain the longitudinal variation of volcanism on Io and the cracking of Europa's crust.     

Wax esters and triacylglycerols in sinking particulate matter in the Peru upwelling area (15°S, 75°W)

The flux and composition of wax esters and triacylglycerols were measured in particulate matter collected by free-drifting sediment traps in the Peru upwelling area. The purpose was to assess diurnal variations in sources and vertical transport of these lipids. Traps were deployed for periods of 8–12 h during both day and night at the base of the euphotic zone (10–14m) and at about 50m. Although the flux of total particulate organic carbon varied 4×, the flux of wax esters varied by 84× and triacylglycerols by 30×. POC, wax esters, and triacylglycerols also showed different temporal patterns. The highest wax ester flux was measured in shallow traps at night and is attributed to increased inputs from zooplankton which feed near the surface at night. Triacylglycerol flux was high in both shallow and deep nocturnal traps, consistent with inputs of both phytoplankton and zooplankton lipids. The composition of these lipids was also quite variable and attests to the complex nature of the lipid sources.     

Shear-wave polarizations near the North Anatolian Fault – I. Evidence for anisotropy-induced shear-wave splitting

Summary. The Turkish Dilatancy Projects (TDP1 in 1979 and TDP2 in 1980) recorded small earthquakes near the North Anatolian Fault with closely-spaced networks of three-component seismometers in order to investigate the possibility of diagnosing dilatancy from its effects of shear-wave propagation. This paper examines the polarizations of shear wavetrains recorded in the shear-wave window immediately above the earthquake foci. Abrupt changes in the orientation and/or ellipticity of the shear-wave polarizations are almost always observed during the first few cycles following the initial shear-wave arrival on each seismogram. The horizontal projections of the polarizations of the first shear-wave arrivals at any given station show nearly parallel alignments with approximately the same orientations at each of the recording sites (with one exception). It is difficult to explain this uniform alignment over a wide area in terms of scattering at the irregular surface topography or by earthquake focal mechanisms. We demonstrate that the shear-wave splitting is likely to be the result of anisotropy in the region above the earthquake foci, which could produce polarizations displaying the observed alignments. The temporal change of the azimuth of alignment, observed at one locality between 1979 and 1980, may be due to the release of a local stress anomaly by a very near earthquake.