INVERSE SOLUTIONS OF HANTUSH'S EQUATIONS FOR AXISYMMETRIC MOUNDING

Abstract. Hantush (1967) provided time-dependent equations for describing ground-water mounds resulting from axisymmetric recharge. Because these equations contain the well function, they cannot be solved explicitly for the several variables employed in terms of the known mound height. Newton's method provides a means to achieve solutions for specific yield, hydraulic conductivity, time, or radius. An additional routine is provided which searches for the second solution in the case in which the inverse solution for hydraulic conductivity is doublevalued. The iterations can be performed on an HP-41C handheld calculator with three memory modules. The code is provided and will run with or without the printer attached.     

Condensed water in tropical cyclone “Oliver”, 8 February 1993

On February 8, 1993, the NASA DC-8 aircraft profiled from 10,000 to 37,000 feet (3.1–11.3 km) pressure altitude in a stratified section of tropical cyclone “Oliver” over the Coral Sea northeast of Australia. Size, shape and phase of cloud and precipitation particles were measured with a 2-D Greyscale probe. Cloud/ precipitation particles changed from liquid to ice as soon as the freezing level was reached near 17,000 feet (5.2 km) pressure altitude. The cloud was completely glaciated at −5°C. There was no correlation between ice particle habit and ambient temperature. In the liquid phase, the precipitation-cloud drop concentration was 4.0 × 10³ m⁻³, the geometric mean diameter D_g=0.5−0.7 mm, and the liquid water content 0.7−1.9 g m⁻³. The largest particles anywhere in the cloud, dominated by fused dendrites at concentrations similar to that of raindrops (2.5 × 10³ m⁻³) but a higher condensed water content (5.4 g m⁻³ estimated) were found in the mixed phase; condensed water is removed very effectively from the mixed layer due to high settling velocities of the large mixed particles. The highest number concentration (4.9 × 10⁴ m⁻³), smallest size (D_g=0.3−0.4 mm), largest surface area (up to 2.6 × 10² cm² m⁻³ at 0.4−1.0 g m⁻³ of condensate) existed in the ice phase at the coldest temperature (−40°C) at 35,000 feet (10.7 km). Each cloud contained aerosol (haze particles) in addition to cloud particles. The aerosol total surface area exceeded that of the cirrus particles at the coldest temperature. Thus, aerosols must play a significant role in the upscattering of solar radiation. Light extinction (6.2 km⁻¹) and backscatter (0.8 sr⁻¹ km⁻¹) was highest in the coldest portion of the cirrus cloud at the highest altitude.     

Transport of water in frozen soil: I: Experimental determination of soil-water diffusivity under isothermal conditions

A new experimental method for measuring the soil-water diffusivity of frozen soil under isothermal conditions is introduced. The theoretical justification of the method is presented and the feasibility of the method is demonstrated by experiments conducted using marine deposited clay. The measured values of the soil-water diffusivity are found comparable to reported experimental data.     

Paleoceanography of surface waters in the Gulf of Mexico during the late Quaternary

Late Quaternary paleotemperatures and paleosalinities of surface waters of the Gulf of Mexico were estimated using a multivariate statistical analysis of census data of planktonic foraminifera. Two climatic extremes were selected for detailed basinwide study, the climatic optimum 125,000 yr ago and the glacial maximum 18,000 yr ago. In addition, patterns of climatic change were examined in seven piston cores from 127,000 yr ago to the present day. During the climatic optimum 125,000 yr ago temperature distributions in surface waters were similar to those of the present. The 22°C winter isotherm trended northeastward across the central basin and paleotemperatures decreased northward. Summer distributions were nearly homogeneous and ranged between 28° and 29°C. Winter salinities were 1‰ fresher than present values in the northmost Gulf and 0.4‰ fresher in the central basin. Summer salinities were similar during both times. In contrast, during the last glacial maximum temperatures were 1° to 2°C cooler in winter and 1°C cooler in summer, and isotherms formed a circular pattern in the Gulf during both seasons. Salinity was 0.3‰ fresher in winter than at present but 0.6‰ saltier in summer. Conditions deteriorated from the climatic optimum to the glacial maximum. In the Mexico Basin, winter temperatures were 2°C cooler from 75,000 to 45,000 yr ago (Y6 to Y3 Subzones), summer temperatures reached a minimum (3°C cooler) 32,000 yr ago (Y2–Y3 boundary), and seasonality reached minimal values (5°C) from 45,000 to 15,000 yr ago. All three parameters became similar in value to those in the Straits of Florida from 45,000 to 15,000 yr ago, suggesting that the exchange of surface waters was enhanced at this time between the two regions. Summer salinities remained similar to present conditions in the Mexico Basin, whereas, winter salinities increased 2‰ by 32,000 yr ago and then fell 0.5‰ until the glacial maximum ended. The Westerlies may have migrated southward over the Mexico Basin in winter from 32,000 to 15,000 yr ago.     

An 40Ar/39Ar study of a polymetamorphic complex in the Arunta Block,Central Australia

A polymetamorphic complex in the Arunta Block, Central Australia, which has undergone metasomatism involving introduction of Rb and loss of Sr has been investigated by ⁴⁰Ar/ ³⁹Ar step and total-degassing techniques in an attempt to date five metamorphic events (M1–M5) identified microstructurally. The complex isotopic data and apparent age spectra obtained have been interpreted in the light of constraints provided by an associated tectonometamorphic study, together with independent geochronological controls from the immediate study area and elsewhere in the Arunta Block. This has led to the delineation of ages of 1,780–1,820 M.y. for M1, 1,690–1,720 M.y. for M2, 1,450–1,500 M.y. for M3, 1,030–1,060 M.y. for M4 and 370–510 for M5. The polyphase M5 event is correlated with the Alice Springs Orogeny, previously accorded younger age limits of 330–370 M.y. The latter are interpreted to reflect closure of mica K/Ar systems as uplift continued subsequent to the close of the event, possibly culminating in minor high-level brittle deformation and the development of pseudotachylytes in the study area.Apparent age spectra recorded in this study do not all conform with generally accepted patterns of behaviour of mineral systems which have undergone polythermal histories. Two hornblendes have survived subsequent high temperature metasomatic reheating without loss of argon or resetting of their ages. Their resistance to argon loss may be attributable to low water contents, due to their growth under anhydrous granulite facies conditions, and may reflect a relationship between argon loss from hornblende and the water content of hornblende, which decreases with increasing metamorphic grade (Kostyuk and Sobolev 1969). Other samples display false plateaux in their apparent age spectra and in three cases the spectra are indistinguishable from those of undisturbed spectra.The age data recorded in this study suggest that during basement reactivation loss of argon is mainly confined to the vicinity of shear zones, implying that diffusion of argon from minerals in the deep crust may be dependent more on deformation than on reheating. However, thermal activity may also be associated with active shear zones, through the medium of superheated fluids streaming up the shear zones from below. The wide spread of K/Ar and ⁴⁰Ar/³⁹Ar ages (330–510 M.y.), recorded for the Alice Springs Orogeny in the Arunta basement, may reflect such controls.     

Plasma Beta above a Solar Active Region: Rethinking the Paradigm

In this paper, we present a model of the plasma beta above an active region and discuss its consequences in terms of coronal magnetic field modeling. The -plasma model is representative and derived from a collection of sources. The resulting variation with height in the solar atmosphere is used to emphasize that the assumption that the magnetic pressure dominates over the plasma pressure must be carefully employed when extrapolating the magnetic field. This paper points out (1) that the paradigm that the coronal magnetic field can be constructed from a force-free magnetic field must be used in the correct context, since the force-free region is sandwiched between two regions which have >1, (2) that the chromospheric Mgii–Civ magnetic measurements occur near the -minimum, and (3) that, moving from the photosphere upwards, can return to 1 at relatively low coronal heights, e.g., R1.2 R _s.     

∼3,850 Ma tonalites in the Nuuk region,Greenland: geochemistry and their reworking within an Eoarchaean gneiss complex

The Eoarchaean (>3,600 Ma) Itsaq Gneiss Complex of southern West Greenland is dominated by polyphase orthogneisses with a complex Archaean tectonothermal history. Some of the orthogneisses have c. 3,850 Ma zircons, and they vary from rare single phase metatonalites to more common complexly banded migmatites. This is due to heterogeneous strain, in situ anatexis and granitic veining superimposed during younger tectonothermal events. In the single-phase tonalites with c. 3,850 Ma zircon, oscillatory-zoned prismatic zircon is all 3,850 Ma old, but shows patchy ancient loss of radiogenic Pb. SHRIMP spot analyses and laser ablation ICP-MS depth profiling show that thin (usually < 10 μm) younger (3,660–3,590 Ma and Neoarchaean) shells of lower Th/U metamorphic zircon are present on these 3,850 Ma zircons. Several samples with this simple zircon population occur on islands near Akilia. In contrast, migmatites usually contain more complex zircon populations, with often more than one generation of igneous zircon present. Additional zircon dating of banded gneisses across the Complex shows that samples with c. 3,850 Ma igneous zircon are not just a phenomenon restricted to Akilia and adjacent islands. For example, migmatites from Itilleq (c. 65 km from Akilia) contain variable amounts of oscillatory-zoned 3,850 Ma and 3,650 Ma zircon, interpreted, respectively, as the rock age and the time of crustal melting under Eoarchaean metamorphism. With only 110–140 ppm Zr in the tonalites and likely magmatic temperatures of >850°C, zircon solubility–melt composition relationships show that they were only one-third saturated in zircon. Any zircon entrained in the precursor magmas would thus have been highly soluble. Combined with the cathodoluminesence imaging, this demonstrates that the c. 3,850 Ma oscillatory zoned zircon crystallised out of the melt and hence gives a magmatic age. Thus the rare well-preserved tonalites and palaeosome in migmatites testify that c. 3,850 Ma quartzo–feldspathic rocks are a widespread (but probably minor) component in the Itsaq Gneiss Complex. C. 3,850 Ma zircon with negative Eu anomalies (showing growth in felsic systems) also occurs as detrital grains in rare c. 3,800 Ma metaquartzites and as inherited grains in some 3,660 Ma granites (sensu stricto). These demonstrate that still more c. 3,850 Ma rocks were present, but were recycled into Eoarchaean sediments and crustally derived granites. The major and trace element characteristics (e.g. LREE enrichment, HREE depletion, low MgO) of the best-preserved c. 3,850 Ma rocks are typical of Archaean TTG suites, and thus argue for crust formation processes involving important contributions from melting of hydrated mafic crust to the earliest Archaean. Five c. 3,850 Ma tonalites were selected as the best preserved on the basis of field criteria and zircon petrology. Four of these samples have overlapping initial ɛ_Nd (3,850 Ma) values from +2.9 to +3.6± 0.5, with the fourth having a slightly lower value of +0.6. These data provide additional evidence for a markedly LREE-depleted early terrestrial mantle reservoir. The role of c. 3,850 Ma crust should be considered in interpreting isotope signatures of the younger (3,800–3,600 Ma) rocks of the Itsaq Gneiss Complex. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Determination of earthquake early warning parameters, τc and Pd, for southern California

We explore a practical approach to earthquake early warning in southern California by determining a ground-motion period parameter  τ _c   and a high-pass filtered displacement amplitude parameter Pd from the initial 3 s of the P waveforms recorded at the Southern California Seismic Network stations for earthquakes with M > 4.0. At a given site, we estimate the magnitude of an event from  τ _c   and the peak ground-motion velocity ( PGV ) from Pd . The incoming three-component signals are recursively converted to ground acceleration, velocity and displacement. The displacements are recursively filtered with a one-way Butterworth high-pass filter with a cut-off frequency of 0.075 Hz, and a P -wave trigger is constantly monitored. When a trigger occurs,  τ _c   and Pd are computed. We found the relationship between  τ _c   and magnitude ( M ) for southern California, and between Pd and PGV for both southern California and Taiwan. These two relationships can be used to detect the occurrence of a major earthquake and provide onsite warning in the area around the station where onset of strong ground motion is expected within seconds after the arrival of the P wave. When the station density is high, the methods can be applied to multistation data to increase the robustness of onsite early warning and to add the regional warning approach. In an ideal situation, such warnings would be available within 10 s of the origin time of a large earthquake whose subsequent ground motion may last for tens of seconds.     

Topographic monitoring of a middle estuary mudflat, Humber estuary, UK – Anthropogenic impacts and natural variation

Annual topographic surveys were carried out at the Saltend mudflat (Humber estuary, UK) between 1998 and 2006. These surveys formed part of an ongoing monitoring programme to examine the potential effects on the mudflat topography of the construction and operation of a waste water treatment works (WwTW) development by Yorkshire Water. Of particular concern was the potential disruption to the sedimentological regime within the special protection area (SPA) and candidate special area of conservation (cSAC) which could affect the invertebrate communities and ornithological functioning of the site. In addition to the development of the WwTW located to the extreme north-west of the site, a port extension removing 10 ha of the Saltend intertidal mudflat (outside the SPA but immediately south east of the WwTW) also occurred between 1999 and 2006. Minimal change was noted across the site following the construction and operation of the WwTW between 1998 and 2000. However, the construction of the bund in closer proximity to the SPA and cSAC masked any potential impact the WwTW could have had across the site after 2000. Profiles and contour mapping indicate that significant mudflat accretion occurred in the immediate area of the bund, with a general increase recorded across the western section of the site since 2000. In contrast the alternations to channel planform and subsequent rapid accretion of the mudflat to the east of the jetty, being a significant distance from the developments, are attributed to natural cyclical changes.