Multiple volcano deformation sources in a post-rifting period: 1989–2005 behaviour of Krafla,Iceland constrained by levelling,tilt and GPS observations

The Krafla rifting episode, which occurred in North Iceland in 1975–1984, was followed by inflation of a shallow magma chamber until 1989. At that time, gradual subsidence began above the magma chamber and has continued to the present at a declining rate. Pressure decrease in a shallow magma chamber is not the only source of deformation at Krafla, as other deformation processes are driven by exploitation of two geothermal fields, together with plate spreading. In addition, deep-seated magma accumulation appears to take place, with its centre ∼ 10 km north of the Krafla caldera. The relative strength of these sources has varied with time. New results from a levelling survey and GPS measurements in 2005 allow an updated view on the deformation field. Deformation rates spanning 2000–2005 are the lowest recorded in the 30-year history of geodetic studies at the volcano. The inferred rate of 2000–2005 subsidence related to processes in the shallow magma chamber is less than 0.3 cm/yr whereas it was ∼ 5 cm/yr in 1989–1992. Currently, the highest rate of subsidence takes place in the Leirbotnar area, within the Krafla caldera, and appears to be a result of geothermal exploitation.     

Proglacial sediment trapping in recently formed Silt Lake,upper Lillooet Valley,Coast Mountains,British Columbia

The sedimentology of proglacial Silt Lake was assessed by lake sediment coring and monitoring of lacustrine processes during a late‐summer period of high glacier melt to characterize sediment delivery from the heavily glacierized catchment and investigate the sediment trapping dynamics of this upland lake. A complete varve chronology was established for a distal basin of the lake which was exposed by Lillooet Glacier retreat between 1947 and 1962. The varve record showed decreasing sedimentation rates in the basin while the glacier retreated, and as the lake became free of ice contact in the early 1970s. Although recession has continued over recent decades, and glacier proximity to the lake has, therefore, continued decreasing, lacustrine sedimentation rates are now accelerating due to changing basin morphometry caused by delta progradation. Over shorter time scales, lake sedimentation patterns respond to changing runoff conditions, including late‐summer glacier melt intensity, intra‐annual flooding events, diumal runoff fluctuations, and within‐lake turbidity currents. Turbidity currents included quasi‐regular flows during high diurnal discharges and an episodic flushing of temporarily stored sediment from the sandur or delta at a time of low stage. Suspended sediment yield to Silt Lake is estimated to exceed 10³ Mg km^?2 a^?1, a magnitude that surpasses previous local and regional yield estimates for the glacierized headwaters of the Lillooet River valley. Since Silt Lake currently traps a significant prooportion of that upland sediment supply, and the trapping efficiency of the basin has been variable at decadal time scales, the formation and continued development of Lilt Lake has likely had a significant influence on downstream sediment delivery. Lacustrine sediment‐based proxies of long‐term hydroclimatic variability being developed in glacially distal settings should include provisions for dynamic sediment trapping effects in upstream water bodies that often form in the active proglacial environment. Copyright © 2008 John Wiley & Sons, Ltd.     

Steady flow to a well near a stream with a leaky bed

We present an explicit analytic solution for steady, two-dimensional ground water flow to a well near a leaky streambed that penetrates the aquifer partially. Leakage from the stream is approximated as occurring along the centerline of the stream. The problem domain is infinite and pumping on one side of the stream induces flow on the other side. The solution includes the effects of uniform flow in the far field and a sloping hydraulic head in the stream. We use the solution to investigate the interaction between ground water and surface water in the stream, the effects of pumping on the opposite side of the stream, and the effects of the leaky streambed on the capture zone envelope of the well. We develop a relationship between parameters such that the pumping well will not capture water from the stream, or from the opposite side of the stream. When the discharge of the well is large enough to capture water from the stream, the shape of the capture zone envelope depends on flow conditions on the side of the stream opposite the well.     

Stability and Grid Dispersion of the P-SV 4th-Order Staggered-Grid Finite-Difference Schemes

Stability and grid dispersion in the P-SV 4th-order in space, 2nd-order in time, displacement-stress staggered-grid finite-difference scheme is investigated in the case of a homogeneous unbounded medium. All results, however, also apply to the velocity-stress and displacement- velocity-stress finite-difference schemes. Independent stability conditions for the P and S waves are obtained by exact separation of equations for the two types of waves. Since the S-wave group velocity can differ from the actual velocity as much as 5% for the sampling ratio 1/5, commonly used in numerical modelling, the sampling of the minimum S wavelength by 6 grid spacings (with the velocity difference not larger than 2.5%) is recommended. Grid dispersion is strongest for a wave propagating in a direction of a coordinate axis and weakest for a wave propagating along a plane diagonal. Grid dispersion in the 4 ^th -order scheme for the sampling ratios s = 1/5 and s = 1/6 is smaller than grid dispersion in the 2 ^nd -order scheme for s = 1/10 and s = 1/12, respectively.     

Mixed Integer-Real Valued Adjustment (IRA) Problems: GPS Initial Cycle Ambiguity Resolution by Means of the LLL Algorithm

In order to achieve to GPS solutions of first-order accuracy and integrity, carrier phase observations as well as pseudorange observations have to be adjusted with respect to a linear/linearized model. Here the problem of mixed integer-real valued parameter adjustment (IRA) is met. Indeed, integer cycle ambiguity unknowns have to be estimated and tested. At first we review the three concepts to deal with IRA: (i) DDD or triple difference observations are produced by a properly chosen difference operator and choice of basis, namely being free of integer-valued unknowns (ii) The real-valued unknown parameters are eliminated by a Gauss elimination step while the remaining integer-valued unknown parameters (initial cycle ambiguities) are determined by Quadratic Programming and (iii) a RA substitute model is firstly implemented (real-valued estimates of initial cycle ambiguities) and secondly a minimum distance map is designed which operates on the real-valued approximation of integers with respect to the integer data in a lattice. This is the place where the integer Gram-Schmidt orthogonalization by means of the LLL algorithm (modified LLL algorithm) is applied being illustrated by four examples. In particular, we prove that in general it is impossible to transform an oblique base of a lattice to an orthogonal base by Gram-Schmidt orthogonalization where its matrix enties are integer. The volume preserving Gram-Schmidt orthogonalization operator constraint to integer entries produces “almost orthogonal” bases which, in turn, can be used to produce the integer-valued unknown parameters (initial cycle ambiguities) from the LLL algorithm (modified LLL algorithm). Systematic errors generated by “almost orthogonal” lattice bases are quantified by A. K. Lenstra et al. (1982) as well as M. Pohst (1987). The solution point of Integer Least Squares generated by the LLL algorithm is = (L')⁻¹[L'◯] ∈ ℤ ^m where L is the lower triangular Gram-Schmidt matrix rounded to nearest integers, [L], and = [L'◯] are the nearest integers of L'◯, ◯ being the real valued approximation of z ∈ ℤ ^m , the m-dimensional lattice space Λ. Indeed due to “almost orthogonality” of the integer Gram-Schmidt procedure, the solution point is only suboptimal, only close to “least squares.” ? 2000 John Wiley & Sons, Inc.     

The Stokes and Vening-Meinesz functionals in a moving tangent space

The regularized solution of the external sphericalStokes boundary value problem as being used for computations of geoid undulations and deflections of the vertical is based upon theGreen functions S ₁(₀, ₀, , ) ofBox 0.1 (R = R ₀) andV ₁(₀, ₀, , ) ofBox 0.2 (R = R ₀) which depend on theevaluation point {₀, ₀} S _R0 ² and thesampling point {, } S _R0 ² ofgravity anomalies (, ) with respect to a normal gravitational field of typegm/R (free air anomaly). If the evaluation point is taken as the meta-north pole of theStokes reference sphere S _R0 ² , theStokes function, and theVening-Meinesz function, respectively, takes the formS() ofBox 0.1, andV ₂() ofBox 0.2, respectively, as soon as we introduce {meta-longitude (azimuth), meta-colatitude (spherical distance)}, namely {A, } ofBox 0.5. In order to deriveStokes functions andVening-Meinesz functions as well as their integrals, theStokes andVening-Meinesz functionals, in aconvolutive form we map the sampling point {, } onto the tangent plane T₀S _R0 ² at {₀, ₀} by means ofoblique map projections of type(i) equidistant (Riemann polar/normal coordinates),(ii) conformal and(iii) equiareal.Box 2.1.–2.4. andBox 3.1.– 3.4. are collections of the rigorously transformedconvolutive Stokes functions andStokes integrals andconvolutive Vening-Meinesz functions andVening-Meinesz integrals. The graphs of the correspondingStokes functions S ₂(),S ₃(r),,S ₆(r) as well as the correspondingStokes-Helmert functions H ₂(),H ₃(r),,H ₆(r) are given byFigure 4.1–4.5. In contrast, the graphs ofFigure 4.6–4.10 illustrate the correspondingVening-Meinesz functions V ₂(),V ₃(r),,V ₆(r) as well as the correspondingVening-Meinesz-Helmert functions Q ₂(),Q ₃(r),,Q ₆(r). The difference between theStokes functions / Vening-Meinesz functions andtheir first term (only used in the Flat Fourier Transforms of type FAST and FASZ), namelyS ₂() – (sin /2)^–1,S ₃(r) – (sinr/2R ₀)^–1,,S ₆(r) – 2R ₀/r andV ₂() + (cos /2)/2(sin² /2),V ₃(r) + (cosr/2R ₀)/2(sin² r/2R ₀),, illustrate the systematic errors in theflat Stokes function 2/ or flatVening-Meinesz function –2/². The newly derivedStokes functions S ₃(r),,S ₆(r) ofBox 2.1–2.3, ofStokes integrals ofBox 2.4, as well asVening-Meinesz functionsV ₃(r),,V ₆(r) ofBox 3.1–3.3, ofVening-Meinesz integrals ofBox 3.4 — all of convolutive type — pave the way for the rigorousFast Fourier Transform and the rigorousWavelet Transform of theStokes integral / theVening-Meinesz integral of type equidistant, conformal and equiareal.     

Temporal behavior of manganese and iron in a sandy coastal sediment exposed to water column anoxia

The influence of bottom water anoxia on manganese (Mn), iron (Fe), and sulfur (S) biogeochemistry was examined in defaunated sandy sediment from Kærby Fed, Denmark, under controlled laboratory incubations. The initial narrow peaks and steep gradients in solid Mn(IV) and Fe(III) as well as porewater Mn²⁺ and Fe²⁺ observed in the upper 2–5 cm of the sediment indicate rapid metal reduction-oxidation cycles under oxic conditions in the overlying water. The fe zones were generally displaced about 0.5 cm downward compared with the Mn zones due to differences in reactivity. Mn(IV) was reduced and gradually disappeared first (within 10 d) when the sediment was exposed to anoxia followed by reduction and disappearance of Fe(III) (day 7 to 18). The associated loss of Mn²⁺ to the overlying water was most rapid during the first 15 d, whereas the Fe²⁺ efflux initiated around day 10, and after a few days with modest rates the efflux peaked around day 20. A considerable portion of the total Mn (26%) and Fe (23%) inventory initially present in the sediment was lost by efflux after about 1 mo of anoxia. The ability of the sediment to retain upward diffusion of H₂S gradually disappeared in a temporal pattern closely related to the changes in pool size of the reactive Mn and Fe present. The total metal pool in Kærby Fed sediment prevented H₂S release to the overlying water for at least a month of anoxia. It is speculated that external supplies from the overlying water allows a rapid refuelling of surface Mn and Fe oxides in the field when oxic conditions returns between periods of anoxia.     

GPS Solutions: Closed Forms, Critical and Special Configurations of P4P

P4P is the pseudo-ranging 4-point problem as it appears as the basic configuration of satellite positioning with pseudo-ranges as observables. In order to determine the ground receiver/satellite receiver (LEO networks) position from four positions of satellite transmitters given, a system of four nonlinear (algebraic) equations has to be solved. The solution point is the intersection of four spherical cones if the ground receiver/satellite receiver clock bias is implemented as an unknown. Here we determine the critical configuration manifold (Determinantal Loci, Inverse Function Theorem, Jacobi map) where no solution of P4P exists. Four examples demonstrate the critical linear manifold. The algorithm GS solves in a closed form P4P in a manner similar to Groebner bases: The algebraic nonlinear observational equations are reduced in the forward step to one quadratic equation in the clock bias unknown. In the backward step two solutions of the position unknowns are generated in closed form. Prior information in P4P has to be implemented in order to decide which solution is acceptable. Finally, the main target of our contribution is formulated: Can we identify a special configuration of satellite transmitters and ground receiver/satellite receiver where the two solutions are reduced to one. A special geometric analysis of the discriminant solves this problem. ? 2002 Wiley Periodicals, Inc.     

Bayesian techniques for seismic hazard assessment using imprecise data

Some Bayesian methods of dealing with inaccurate or vague data are introduced in the framework of seismic hazard assessment. Inaccurate data affected by heterogeneous errors are modeled by a probability distribution instead of the usual value plus a random error representation; these data are generically called imprecise. The earthquake size and the number of events in a certain time are modeled as imprecise data. Imprecise data allow us to introduce into the estimation procedures the uncertainty inherent in the inaccuracy and heterogeneity of the measuring systems from which the data were obtained. The problem of estimating the parameter of a Poisson process is shown to be feasible by the use of Bayesian techniques and imprecise data. This background technique can be applied to a general problem of seismic hazard estimation. Initially, data in a regional earthquake catalog are assumed imprecise both in size and location (i.e errors in the epicenter or spreading over a given source). By means of scattered attenuation laws, the regional catalog can be translated into a so-called site catalog of imprecise events. The site catalog is then used to estimate return periods or occurrence probabilities, taking into account all sources of uncertainty. Special attention is paid to priors in the Bayesian estimation. They can be used to introduce additional information as well as scattered frequency-size laws for local events. A simple example is presented to illustrate the capabilities of this methodology.     

The application of cascading consequences for emergency management operations

How societies organize themselves to respond to cascading impacts exacerbated by climate change will help define the future of disaster planning, mitigation, response, and recovery. Current emergency management risk analyses focus on identifying a broad array of threats and hazards that may affect an area. However, there is limited attention and understanding of the totality of hazard impacts, the relationship of consequences across disasters, and the dangers of not addressing critical capabilities necessary to rapidly managing consequences—including the potential to create new incidents within incidents. Through a focused review of the related literature and guiding policy documents, this study aims to provide a cascading consequence-based framework that can support emergency managers in the analysis of their jurisdictional risks, development of emergency operations plans, and decision-making. Results include the identification of an alternative framework to identify cascading networks, the creation of a supplementary model for downstream risk assessment, and refined Threat and Hazard Identification and Risk Analysis (THIRA) outputs for improved grant allocation. The proposed framework has the potential to help organizations factor both conspicuous and downstream consequences into their Emergency Operations Plans in the planning and mitigations phases. This proposed refinement, which looks deeper into the progression of a disaster, has both national and international implications.