Tilt effects on moment tensor inversion in the near field of active volcanoes

Dynamic tilts (rotational motion around horizontal axes) change the projection of local gravity onto the horizontal components of seismometers. This causes sensitivity of these components to tilt, especially at low frequencies. We analyse the consequences of this effect onto moment tensor inversion for very long period (vlp) events in the near field of active volcanoes on the basis of synthetic examples using the station distribution of a real deployed seismic network and the topography of Mt. Merapi volcano (Java, Indonesia). The examples show that for periods in the vlp range of 10-30 s tilt can have a strong effect on the moment tensor inversion, although its effect on the horizontal seismograms is significant only for few stations. We show that tilts can be accurately computed using the spectral element method and include them in the Green's functions. The (simulated) tilts might be largely influenced by strain-tilt coupling (stc). However, due to the frequency dependence of the tilt contribution to the horizontal seismograms, only the largest tilt signals affect the source inversion in the vlp frequency range. As these are less sensitive to stc than the weaker signals, the effect of stc can likely be neglected in this application. In the converse argument, this is not necessarily true for longer periods, where the horizontal seismograms are dominated by the tilt signal and rotational sensors would be necessary to account for it. As these are not yet commercially available, this study underlines the necessity for the development of such instrument

Horizontal rotation signals detected by "G-Pisa" ring laser for the Mw=9.0, March 2011, Japan earthquake

We report the observation of the ground rotation induced by the Mw=9.0, 11th of March 2011, Japan earthquake. The rotation measurements have been conducted with a ring laser gyroscope operating in a vertical plane, thus detecting rotations around the horizontal axis. Comparison of ground rotations with vertical accelerations from a co-located force-balance accelerometer shows excellent ring laser coupling at periods longer than 100s. Under the plane wave assumption, we derive a theoretical relationship between horizontal rotation and vertical acceleration for Rayleigh waves. Due to the oblique mounting of the gyroscope with respect to the wave direction-of-arrival, apparent velocities derived from the acceleration / rotation rate ratio are expected to be always larger than, or equal to the true wave propagation velocity. This hypothesis is confirmed through comparison with fundamental-mode, Rayleigh wave phase velocities predicted for a standard Earth model.Comment: Accepted for publication in Journal of Seismolog

Numerical modelling of climate change impacts on freshwater lenses on the North Sea Island of Borkum using hydrological and geophysical methods

A numerical, density dependent groundwater model is set up for the North Sea Island of Borkum to estimate climate change impacts on coastal aquifers and especially the situation of barrier islands in the Wadden Sea. The database includes information from boreholes, a seismic survey, a helicopter-borne electromagnetic (HEM) survey, monitoring of the freshwater-saltwater boundary by vertical electrode chains in two boreholes, measurements of groundwater table, pumping and slug tests, as well as water samples. Based on a statistical analysis of borehole columns, seismic sections and HEM, a hydrogeological model is set up. The groundwater model is developed using the finite-element programme FEFLOW. The density dependent groundwater model is calibrated on the basis of hydraulic, hydrological and geophysical data, in particular spatial HEM and local monitoring data. Verification runs with the calibrated model show good agreement between measured and computed hydraulic heads. A good agreement is also obtained between measured and computed density or total dissolved solids data for both the entire freshwater lens on a large scale and in the area of the well fields on a small scale. For simulating future changes in this coastal groundwater system until the end of the current century, we use the climate scenario A2, specified by the Intergovernmental Panel on Climate Change and, in particular, the data for the German North Sea coast. Simulation runs show proceeding salinisation with time beneath the well fields of the two waterworks Waterdelle and Ostland. The modelling study shows that the spreading of well fields is an appropriate protection measure against excessive salinisation of the water supply until the end of the current century

Bringing Order to Special Cases of Klee's Measure Problem

Klee's Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and k-Grounded (where the projection onto the first k dimensions is a Hypervolume instance). In this paper we bring some order to these special cases by providing reductions among them. In addition to the trivial inclusions, we establish Hypervolume as the easiest of these special cases, and show that the runtimes of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we show that any algorithm for one of the special cases with runtime T(n,d) implies an algorithm for the general case with runtime T(n,2d), yielding the first non-trivial relation between KMP and its special cases. This allows to transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)} algorithm exists for any of the special cases under reasonable complexity theoretic assumptions. Furthermore, assuming that there is no improved algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 - eps})) this reduction shows that there is no algorithm with runtime O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same assumption we show a tight lower bound for a recent algorithm for 2-Grounded [Yildiz,Suri'12].Comment: 17 page

Electron correlations for ground state properties of group IV semiconductors

Valence energies for crystalline C, Si, Ge, and Sn with diamond structure have been determined using an ab-initio approach based on information from cluster calculations. Correlation contributions, in particular, have been evaluated in the coupled electron pair approximation (CEPA), by means of increments obtained for localized bond orbitals and for pairs and triples of such bonds. Combining these results with corresponding Hartree-Fock (HF) data, we recover about 95 % of the experimental cohesive energies. Lattice constants are overestimated at the HF level by about 1.5 %; correlation effects reduce these deviations to values which are within the error bounds of this method. A similar behavior is found for the bulk modulus: the HF values which are significantly too high are reduced by correlation effects to about 97 % of the experimental values.Comment: 22 pages, latex, 2 figure

Influence of electron correlations on ground-state properties of III-V semiconductors

Lattice constants and bulk moduli of eleven cubic III-V semiconductors are calculated using an ab initio scheme. Correlation contributions of the valence electrons, in particular, are determined using increments for localized bonds and for pairs and triples of such bonds; individual increments, in turn, are evaluated using the coupled cluster approach with single and double excitations. Core-valence correlation is taken into account by means of a core polarization potential. Combining the results at the correlated level with corresponding Hartree-Fock data, we obtain lattice constants which agree with experiment within an average error of -0.2%; bulk moduli are accurate to +4%. We discuss in detail the influence of the various correlation contributions on lattice constants and bulk moduli.Comment: 4 pages, Latex, no figures, Phys. Rev. B, accepte

The geometry of nonlinear least squares with applications to sloppy models and optimization

Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem is then to find the point on the manifold closest to the data. We show that the model manifolds of a large class of models, known as sloppy models, have many universal features; they are characterized by a geometric series of widths, extrinsic curvatures, and parameter-effects curvatures. A number of common difficulties in optimizing least squares problems are due to this common structure. First, algorithms tend to run into the boundaries of the model manifold, causing parameters to diverge or become unphysical. We introduce the model graph as an extension of the model manifold to remedy this problem. We argue that appropriate priors can remove the boundaries and improve convergence rates. We show that typical fits will have many evaporated parameters. Second, bare model parameters are usually ill-suited to describing model behavior; cost contours in parameter space tend to form hierarchies of plateaus and canyons. Geometrically, we understand this inconvenient parametrization as an extremely skewed coordinate basis and show that it induces a large parameter-effects curvature on the manifold. Using coordinates based on geodesic motion, these narrow canyons are transformed in many cases into a single quadratic, isotropic basin. We interpret the modified Gauss-Newton and Levenberg-Marquardt fitting algorithms as an Euler approximation to geodesic motion in these natural coordinates on the model manifold and the model graph respectively. By adding a geodesic acceleration adjustment to these algorithms, we alleviate the difficulties from parameter-effects curvature, improving both efficiency and success rates at finding good fits.Comment: 40 pages, 29 Figure

Numerical modelling of climate change impacts on freshwater lenses on the North Sea Island of Borkum using hydrological and geophysical methods

A numerical, density dependent groundwater model is set up for the North Sea Island of Borkum to estimate climate change impacts on coastal aquifers and especially the situation of barrier islands in the Wadden Sea. The database includes information from boreholes, a seismic survey, a helicopter-borne electromagnetic (HEM) survey, monitoring of the freshwater-saltwater boundary by vertical electrode chains in two boreholes, measurements of groundwater table, pumping and slug tests, as well as water samples. Based on a statistical analysis of borehole columns, seismic sections and HEM, a hydrogeological model is set up. The groundwater model is developed using the finite-element programme FEFLOW. The density dependent groundwater model is calibrated on the basis of hydraulic, hydrological and geophysical data, in particular spatial HEM and local monitoring data. Verification runs with the calibrated model show good agreement between measured and computed hydraulic heads. A good agreement is also obtained between measured and computed density or total dissolved solids data for both the entire freshwater lens on a large scale and in the area of the well fields on a small scale. <br><br> For simulating future changes in this coastal groundwater system until the end of the current century, we use the climate scenario A2, specified by the Intergovernmental Panel on Climate Change and, in particular, the data for the German North Sea coast. Simulation runs show proceeding salinisation with time beneath the well fields of the two waterworks Waterdelle and Ostland. <br><br> The modelling study shows that the spreading of well fields is an appropriate protection measure against excessive salinisation of the water supply until the end of the current century