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.     

Overburden deformation associated with halokinesis in the Southern North Sea: implications for the origin of the Silverpit Crater

Gravitational collapse in response to the creation of salt swells and diapirs is a common phenomenon within regions such as the Southern North Sea. Although collapse faulting and slumping of linear salt swell flanks has previously been documented, the existence of concentric collapse structures surrounding diapirs and isolated salt lows is a recently recognised feature. 3-D seismic data from the Southern North Sea demonstrates that concentric collapse faulting around both diapirs and subcircular salt lows is common. The recognition of concentric collapse structures formed in response to salt withdrawal, and adjacent inflation, provides an alternative mechanism for the origin of the proposed Silverpit impact crater.     

Holocene sea-level changes along the North Carolina Coastline and their implications for glacial isostatic adjustment models

We have synthesized new and existing relative sea-level (RSL) data to produce a quality-controlled, spatially comprehensive database from the North Carolina coastline. The RSL database consists of 54 sea-level index points that are quantitatively related to an appropriate tide level and assigned an error estimate, and a further 33 limiting dates that confine the maximum and minimum elevations of RSL. The temporal distribution of the index points is very uneven with only five index points older than 4000 cal a BP, but the form of the Holocene sea-level trend is constrained by both terrestrial and marine limiting dates. The data illustrate RSL rapidly rising during the early and mid Holocene from an observed elevation of ?35.7 ± 1.1 m MSL at 11062–10576 cal a BP to ?4.2 m ± 0.4 m MSL at 4240–3592 cal a BP.We restricted comparisons between observations and predictions from the ICE-5G(VM2) with rotational feedback Glacial Isostatic Adjustment (GIA) model to the Late Holocene RSL (last 4000 cal a BP) because of the wealth of sea-level data during this time interval. The ICE-5G(VM2) model predicts significant spatial variations in RSL across North Carolina, thus we subdivided the observations into two regions. The model forecasts an increase in the rate of sea-level rise in Region 1 (Albemarle, Currituck, Roanoke, Croatan, and northern Pamlico sounds) compared to Region 2 (southern Pamlico, Core and Bogue sounds, and farther south to Wilmington). The observations show Late Holocene sea-level rising at 1.14 ± 0.03 mm year^?1 and 0.82 ± 0.02 mm year^?1 in Regions 1 and 2, respectively. The ICE-5G(VM2) predictions capture the general temporal trend of the observations, although there is an apparent misfit for index points older than 2000 cal a BP. It is presently unknown whether these misfits are caused by possible tectonic uplift associated with the mid-Carolina Platform High or a flaw in the GIA model. A comparison of local tide gauge data with the Late Holocene RSL trends from Regions 1 and 2 support the spatial variation in RSL across North Carolina, and imply an additional increase of mean sea level of greater than 2 mm year^?1 during the latter half of the 20th century; this is in general agreement with historical tide gauge and satellite altimetry data.     

Wisp motions in the Crab nebula

We present the results of a CCD monitoring campaign of the continuum emission from the central region of the Crab nebula, amounting to 17 epochs spread over 3.5 years. The data provide clear evidence that the brightest wisps move outward from the pulsar at mildly relativistic velocities. This motion, combined with the shape of the wisps, supports the idea that they arise at a standing shock in an equatorial wind. The deprojected velocity of the wisps in the equatorial plane is c/3. We see only small changes in the so-called ‘thin wisps’ which leads us to suggest that these wisps may be the result of a back-flow from the shock in a toroidal cavity around the pulsar.     

Spatial characteristics of ocean surface waves

The spatial variability of open ocean wave fields on scales of O (10km) is assessed from four different data sources: TerraSAR-X SAR imagery, four drifting SWIFT buoys, a moored waverider buoy, and WAVEWATCH III^? model runs. Two examples from the open north-east Pacific, comprising of a pure wind sea and a mixed sea with swell, are given. Wave parameters attained from observations have a natural variability, which decreases with increasing record length or acquisition area. The retrieval of dominant wave scales from point observations and model output are inherently different to dominant scales retrieved from spatial observations. This can lead to significant differences in the dominant steepness associated with a given wave field. These uncertainties have to be taken into account when models are assessed against observations or when new wave retrieval algorithms from spatial or temporal data are tested. However, there is evidence of abrupt changes in wave field characteristics that are larger than the expected methodological uncertainties.     

Converging P-T paths of Mesozoic HP-LT metamorphic units (Diego de Almagro Island, Southern Chile): evidence for juxtaposition during late shortening of an active continental margin

Summary On Diego de Almagro Island in Chilean Patagonia (51°30S), a convergent strike slip zone, the Seno Arcabuz shear zone, separates the Diego de Almagro Metamorphic Complex from very low grade metagreywackes in the east, which were intruded by Jurassic granitoids. The Diego de Almagro Metamorphic Complex is composed of a metapsammopelitic sequence containing blueschist intercalations in the west and (garnet) amphibolite lenses in the east. Peak metamorphic conditions (stage I) at 9.5–13.5kbar, 380–450°C in the blueschist and at 11.2–13.2, 460–565°C in the amphibolite indicate subduction and accretion at different positions within the deepest part of the accretionary wedge. A K–Ar age of 117±28Ma of amphibole approximately dates the peak of metamorphism in the amphibolite. The early retrograde stage of metamorphism occurred under static conditions and resulted in localized equilibration (stage II) at 6.3–9.6kbar, 320–385°C in the blueschist and 6.1–8.4kbar, 310–504°C in the amphibolite. Both P-T paths converge within a midcrustal level.In contrast, an orthogneiss of trondhjemitic composition occurring within the Seno Arcabuz shear zone is associated with a garnet mica-schist containing a high temperature/intermediate pressure assemblage formed at 4.9–6.5kbar, 580–690°C. A muscovite K–Ar age of 122.2±4.6Ma dates cooling after this event which is related to a concomitant magmatic arc. These rocks were overprinted by a mylonitic deformation, which is caused by convergent strike slip shearing and ends during formation of a retrograde phengite-chlorite-stilpnomelane assemblage at a minimum pressure of approximately 5.7kbar (at 300°C).Zircon fission track ages from rocks of the Seno Arcabuz shear zone are 64.9±2.7 and 64.9±2.7Ma; they record the end of shearing in the Seno Arcabuz shear zone that juxtaposed all rocks in the middle crust. Zircon fission track ages ranging from 78 to 105Ma in the South Patagonian batholith to the east indicate earlier cooling through 280°C. The rocks of the Diego de Almagro Metamorphic Complex were initially slowly exhumed and resided at a midcrustal level before being emplaced via shearing in the Seno Arcabuz shear zone. Apatite fission track ages (54±8Ma) from the Seno Arcabuz shear zone show that exhumation and cooling rates increased after this event. The incorporation of continental crust within the subduction system was a late process, which modified the Cretaceous accretionary wedge, resulting in considerable shortening of the convergent margin.     

Auld Reekie MIST

The magnetosphere, ionosphere and solar–terrestrial physics community gathered at the University of Edinburgh from 29 March – 1 April 2004, for a meeting including a day of joint sessions with UKSP. The four day programme reflected the breadth and depth of the science covered. Neil Arnold and Alan Thomson report; the UKSP meeting is covered in the following pages.     

Residual currents in juan de Fuca strait

Abstract

We examine the residual (non‐tidal) flow in Juan de Fuca Strait on the west coast of Canada using current and bottom pressure data collected on cross‐channel sections in the summers of 1975 and 1984. A positive estuarine circulation was evident in both sections but was better defined at the mid‐strait section than at the outer section near the mouth of the strait. Magnitudes of the volume transports in both the upper and lower layers of the channel ranged from ～ 0.25 X 10 m s at the mid‐strait section to ～ 0.15 X 10 m s～ at the outer section. The method of geostrophic levelling (Garrett and Pétrie, 1981; Pétrie et al, 1988) is used to determine the relationship between the daily averaged long‐strait velocity component and the cross‐strait pressure difference. A statistically significant relationship, consistent with a cross‐strait geostrophic balance, is obtained between the time series of shallow currents and shallow bottom pressures at the mid‐strait section. The deep currents and cross‐strait pressure differences were correlated at both sections but, because of the placement of the pressure gauges and/or ageostrophic effects such as bottom friction, were not related through a simple geostrophic balance. Cross‐spectral analysis and the calculation of the current amplitude ratios (square root of the energy ratio between the deep and shallow currents) are used to examine the baroclinicity of the flow as a function of frequency. Results suggest that flow variability in Juan de Fuca Strait is strongly baroclinic and has marked cross‐channel structure throughout the low‐frequency band.