Exact and asymptotic synthetic multiplet spectra on an ellipsoidal earth

Summary. Exact spectra of a normal mode multiplet _nS_l or _n T_l on a non-rotating ellipsoidal earth are composed of l + 1 lines. Asymptotically, in the limit of large l , such spectra appear, however, as a single line or peak broadened by attenuation alone. The location within the multiplet of this single peak depends only upon the angle of inclination of the source-receiver great circle path to the axis of ellipsoidal symmetry. The appearance of a single peak is produced by the cancellation of nearby singlets. To assess the utility of the single peak approximation, exact and asymptotic synthetic spectra have been compared directly for a number of multiplets and for a variety of source-receiver configurations. Except in the immediate vicinity of the source and its antipode, the approximation appears to be satisfactory on an ellipsoidal earth down to about l ∼ 10. Additional studies will be required to determine the limits of validity on a laterally heterogeneous earth.     

Exact synthetic seismograms for an inhomogeneity in a layered elastic half-space

Summary. The propagation of a pulsed elastic wave in the following geometry is considered. An elastic half-space has a surface layer of a different material and the layer furthermore contains a bounded 3-D inhomogeneity. The exciting source is an explosion, modelled as an isotropic pressure point source with Gaussian behaviour in time.
The time-harmonic problem is solved using the null field approach (the T matrix method), and a frequency integral then gives the time-domain response. The main tools of the null field approach are integral representations containing the free space Green's dyadic, expansions in plane and spherical vector wave functions, and transformations between plane and spherical vector wave functions. It should be noted that the null field approach gives the solution to the full elastodynamic equations with, in principle, an arbitrarily high accuracy. Thus no ray approximations or the like are used. The main numerical limitation is that only low and intermediate frequencies, in the sense that the diameter of the inhomogeneity can only be a few wavelengths, can be considered.
The numerical examples show synthetic seismograms consisting of data from 15 observation points at increasing distances from the source. The normal component of the velocity field is computed and the anomalous field due to the inhomogeneity is sometimes shown separately. The shape of the inhomogeneity, the location and depth of the source, and the material parameters are all varied to illustrate the relative importance of the various parameters. Several specific wave types can be identified in the seismograms: Rayleigh waves, direct and reflected P -waves, and head waves.     

A note on MESA and spectral analysis of the hundred-year geomagnetic data at Zo-se

Summary. In the maximum entropy spectrum analysis (MESA) of geomagnetic data, the required order can be estimated by the zero-frequency half-power width (ZHW) minimum method proposed in this paper. The spectra of the data for 1876–1975 at Zo-se showed a period of 40yr, in addition to the well-known periods. The amplitudes of the variations were estimated with parabolic-sinusoidal series fitting.     

A note on further refinements to a procedure for the extraction of carbonaceous fly-ash particles from sediments

This paper describes improvements to a previously published technique for the extraction of carbonaceous fly-ash particles from sediments. By using test-tubes in a water-bath rather than beakers on a hot-plate, the number of simultaneous preparations that can be done is increased and the length of time spent on the preparations and the amounts of hazardous chemicals used is reduced. As the digestion vessel remains the same throughout the procedure, potential loss of particles due to transfer of material between vessels is also minimised, whilst keeping sensitivity, accuracy and detection limit the same.     

A note on the Jewish population of the USSR from the 1989 census data

This note provides additional, more detailed information on the composition and spatial distribution of the Jewish population of the USSR in 1989. It supplements the author's previous study on the nationality distribution in the USSR.     

Voronoi tessellation on the ellipsoidal earth for vector data

Voronoi tessellation, and its dual the Delaunay triangulation, provide a cohesive framework for the study and interpretation of phenomena of geographical space in two and three dimensions. The planar and spherical solutions introduce errors in the positional accuracy of both Voronoi vertices and Voronoi edges due to errors in distance computations and the path connecting two locations with planar lines or great circle arcs instead of geodesics. For most geospatial applications the introduction of the above errors is insignificant or tolerable. However, for applications where the accuracy is of utmost importance, the ellipsoidal model of the Earth must be used. Characteristically, the introduction of any positional error in the delimitation of maritime zones and boundaries results in increased maritime space for one state at the expense of another. This is a situation that may, among others, have a serious impact on the financial activities and the relations of the states concerned. In the context of previous work on maritime delimitation we show that the Voronoi diagram constitutes the ideal solution for the development of an automated methodology addressing the problem in its entirety. Due to lack of a vector methodology for the generation of Voronoi diagram on the ellipsoid, the aforementioned solution was constrained by the accuracy of existing approaches. In order to fill this gap, in this paper we deal with the inherent attributes of the ellipsoidal model of the Earth, e.g. the fact that geodesics are open lines, and we elaborate on a methodology for the generation of the Voronoi diagram on the ellipsoid for a set of points in vector format. The resulting Voronoi diagram consists of vertices with positional accuracy that is only bounded by the user needs and edges that are comprised of geodesics densified with vertices equidistant to their generators. Finally, we present the implementation of the proposed algorithm in the Python programming language and the results of two case studies, one on the formation of closest service areas and one on maritime boundaries delimitation, with the positional accuracy set to 1 cm.     

Thermohaline structure inhomogeneity associated with polynia at the northern margin of Emery Ice-shelf

Based on the hydrographic data in austral summer during the 22nd Antarctic Expedition of China(2005/2006),some features can be found about the northern margin of Emery ice shelf as follows.The heat content in the surface layer(0-50 m) at the eastern end and the western end of the ice-shelf margin is much higher than that at the middle.The upper mixing-layer depth and the seasonal thermocline depth at the middle of the ice-shelf northern margin are much shallower than those at the both ends.However there is much less difference between the middle and the ends in the bottom layer.The remote sensing photos show that the inhomogeneity in the surface-layer water is closely related to the spatial distribution of the floes and polynia in the area.     

A note on lithospheric bending calculations

Summary. This paper derives exact solutions to the equations of static plane strain by means of propagator matrices for homogeneous, gravitating and non- gravitating elastic media. These solutions are immediately verifiable and are flexible under a variety of boundary conditions. Propagator matrices are eminently suitable for computer encoding and, through their multiplication, are applicable to depth-dependent structures. Attention is focused upon the bending of floating plates which are loaded to simulate the deflection of oceanic lithosphere in the vicinity of trenches. By comparing responses computed with and without body forces, I find that gravity does not meaningfully change deflection profiles; however, it can influence important aspects of the internal stress state. Gravitational stresses are proportional to the gradient of the vertical deformation and amount to about 10 per cent of the bending stresses in these models. Propagators which include gravity are used to investigate the effect of regional horizontal stresses upon bending plates. I conclude that applied compressive forces can transport the neutral surface through 10–20 km of depth without significantly deforming the plate profile or increasing the maximum internal stress by more than 30 percent. These calculations support the contention that variable compressive stresses resulting from interplate coupling could account for observed regional differences in neutral surface height. For elastic-plastic material, the fundamental equations of motion become non-linear; however, there appears to be no a priori objection to their linearization. I speculate that the propagator formalism, when applied in an iterative approach, could be a powerful method for computing the deformation of such media.     

A late quaternary ostracod record from the Tso Kar basin (North India) with a note on the distribution of recent species

The fossil ostracod associations from a radiocarbon dated sediment core (15.3–0 cal kyr) of the high altitude (4,527 m a.s.l.) hyperhaline Tso Kar lake in North India reveal changes in ostracod species abundances and composition. These document the process of lake formation and ongoing desiccation during the latest quaternary and broadly confirm the results of previous geochemical, geomorphological and pollen analysis. The most striking feature of the core record is a period of freshwater conditions between 9.0 and 6.5 cal kyr BP, as calculated by means of an ostracod-based conductivity transfer function. This early- to mid-Holocene interval of the core correlates with similar ostracod assemblages (Cytherissa lacustris—Candona candida—Eucypris afghanistanensis) of an outcrop section at the basin margin, about 98 m above the modern lake level and marks the highest lake level under the influence of an intensified Indian Summer Monsoon. After 6.5 cal kyr BP, Limnocythere inopinata is the sole representative of the ostracod fauna in the sediment core, which suggests rising salinity conditions most probably due to lake shallowing. From 3.2 cal kyr BP to present, the near absence of ostracods in the core Tk106 is most likely a consequence of salinisation of the lake towards the hyperhaline conditions that are realised at present. Although the modern morphology and physico-chemical properties of Tso Kar lake are in contrast to the past lake conditions, most of the ostracod species, except for Limnocythere mirabilis found in the sediment core, are also identified from surface sediment and outcrop samples. In contrast, Heterocypris salina and Eucypris dulcifons are widespread in the shallow surface waters with a total dissolved solids content ranging from 0.6 to 15.0 g L^?1, but are excluded from the core record and outcrop strata. At a basinal scale, the lake shrinkage and segregation into the Tso Kar and hydrologically open freshwater lake Startsapuk Tso have forced diversification of ostracod taxa, probably as an effect of the emergence of new ecological niches under enhanced “environmental pressure”.     

A note on the propagation of precursors in poroelastic media

Summary. In this note we discuss the behaviour of Green's functions for Biot's equation in the neighbourhood of the wavefronts which provide precursors. Uniform wavefront expansions are obtained which are valid for all possible values of the physical parameters. The results of this note complete the work of Burridge & Vargas.     

A note on the surface volume change of shallow earthquakes

Summary. This note presents an exact analytical formula for determining the magnitude of coseismic surface volume change (δ V ) of earthquake faults in a half-space. For a Poisson solid, the formula is remarkably simple; δ V = M _zz |8μ, where M _zz is one of the moment tensor elements of the source. Maximum δ V values derive from dip slip on faults plunging 45°. For these events, surface volume changes of 0.0001 and 4.3 km³ can be expected for magnitude 5 and 8 earthquakes respectively. All of the coseismic surface volume change is recovered in the interseismic period through relaxation of the Earth and rebound of the surface. A useful rule of thumb for estimating the magnitude of vertical rebound in 45° dip slip events is δ h _p=Δ s /24, where Δ s is the coseismic slip on the fault.     

A note on the lake level variations of Nam Co,south-central Tibetan Plateau from 2005 to 2019

Tibetan lake levels are sensitive to global change, and their variations have a large impact on the environment, local agriculture and animal husbandry practices. While many remote sensing data of Tibetan lake level changes have been reported, few are from in-situ measurements. This note presents the first in-situ lake level time series of the central Tibetan Plateau. Since 2005, daily lake level observations have been performed at Lake Nam Co, one of the largest on the Tibetan Plateau. The interannual lake level variations show an overall increasing trend from 2006 to 2014, a rapid decrease from 2014 to 2017, and a surge from 2017 to 2018. The annual average lake level of the hydrological year (May-April) rose 66 cm from 2006 to 2014, dropped 59 cm from 2014 to 2017, and increased 20 cm from 2017 to 2018, resulting in a net rise of 27 cm or an average rate of about 2 cm per year. Compared to the annual average lake level based on the calendar year, it is better to use the annual average lake level based on the hydrological year to determine the interannual lake level changes. As the lake level was stable in May, it is appropriate to compare May lake levels when examining interannual lake level changes with fewer data. Overall, remote sensing results agree well with the in-situ lake level observations; however, some significant deviations exist. In the comparable 2006-2009 period, the calendar-year average lake level observed in-situ rose by 10-11 cm per year, which is lower than the ICESat result of 18 cm per year.