A lateral model parameter correlation procedure for one-dimensional inverse modelling

We present a new, fast and versatile method, the lateral parameter correlation method, of invoking lateral smoothness in model sections of one-dimensional (1D) models. Modern, continuous electrical and electromagnetic methods are capable of recording very large data sets and except for a few cases, standard inversion methodology still relies on 1D models. In environments where the lateral rate of change of resistivity is small, 1D inversion can be justified but model sections of concatenated 1D models do not necessarily display the expected lateral smoothness.
The lateral parameter correlation method has three steps. First, all sounding data are inverted individually. Next, a laterally smooth version of each model parameter, one at a time, is found by solving a simple constrained inversion problem. Identity is postulated between the uncorrelated and correlated parameters and the equations are solved including a model covariance matrix. As a last step, all sounding data are inverted again to produce models that better fit the data, now subject to constraints by including the correlated parameter values as a priori values. Because the method separates the inversion from the correlation it is much faster than methods where the inversion and correlation are solved simultaneously, typically with a factor of 200–500.
Theoretical examples show that the method produces laterally smooth model sections where the main influence comes from the well-determined parameters in such a way that problems with equivalence and poor resolution are alleviated. A field example is presented, demonstrating the improved resolution obtained with the lateral parameter correlation method. The method is very flexible and is capable of coupling models from inversion of different data types and information from boreholes.     

On the Motion of Trapped Particles in the Vicinity of Corotation Centers

In the present paper we analyse the motion of a massless particle during the capture process in an exterior mean-motion resonance under the effects of an external dissipative force. In particular, we study the orbital evolution from its initial approach to the commensurability up to the final nesting place in the periodic orbit around the equilibrium solution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Estimation of a non-stationary prior covariance from seismic data

Non-stationarity in statistical properties of the subsurface is often ignored. In a classical linear Bayesian inversion setting of seismic data, the prior distribution of physical parameters is often assumed to be stationary. Here we propose a new method of handling non-stationarity in the variance of physical parameters in seismic data. We propose to infer the model variance prior to inversion using maximum likelihood estimators in a sliding window approach. A traditional, and a localized shrinkage estimator is defined for inferring the prior model variance. The estimators are assessed in a synthetic base case with heterogeneous variance of the acoustic impedance in a zero-offset seismic cross section. Subsequently, this data is inverted for acoustic impedance using a non-stationary model set up with the inferred variances. Results indicate that prediction as well as posterior resolution is greatly improved using the non-stationary model compared with a common prior model with stationary variance. The localized shrinkage predictor is shown to be slightly more robust than the traditional estimator in terms of amplitude differences in the variance of acoustic impedance and size of local neighbourhood. Finally, we apply the methodology to a real data set from the North Sea basin. Inversion results show a more realistic posterior model than using a conventional approach with stationary variance.     

Assessment of climate change and associated impact on selected sectors in Poland

The present paper offers a brief assessment of climate change and associated impact in Poland, based on selected results of the Polish–Norwegian CHASE-PL project. Impacts are examined in selected sectors, such as water resources, natural hazard risk reduction, environment, agriculture and health. Results of change detection in long time series of observed climate and climate impact variables in Poland are presented. Also, projections of climate variability and change are provided for time horizons of 2021–2050 and 2071–2100 for two emission scenarios, RCP4.5 and RCP8.5 in comparison with control period, 1971–2000. Based on climate projections, examination of future impacts on sectors is also carried out. Selected uncertainty issues relevant to observations, understanding and projections are tackled as well.     

A secondary resonance in Mercury’s rotation

The resonant rotation of Mercury can be modelised by a kernel model on which we can add perturbations. Our kernel model is a two-degree of freedom one written in Hamiltonian formalism. For this kernel, we consider that Mercury is solid and rotates on a Keplerian orbit. By introducing the perturbations due to the other planets of the Solar System, it appears that, in a particular case, our slow degree of freedom may enter into a 1:1 resonance with the Great Inequality of Jupiter and Saturn. Actually, as the moments of inertia of Mercury are still poorly known, this phenomenon cannot be excluded.     

Limits on the X-ray and optical luminosity of the progenitor of the Type Ia supernova 2007sr

We present Hubble Space Telescope ( HST )/Wide Field Planetary Camera 2 (WFPC2), Galaxy Evolution Explorer ( GALEX ) and Chandra observations of the position of the Type Ia supernova 2007sr in the Antennae galaxy, taken before the explosion. No source is found in any of the observations, allowing us to put interesting constraints on the progenitor luminosity. In total there is about 450 ks of Chandra data, spread over seven different observations. Limiting magnitudes of far-ultraviolet (FUV) (23.7 AB mag), near-ultraviolet (NUV) (23.8 AB mag), F555W (26.5 Vega mag) and F814W (24.5–25 Vega mag) are derived. The distance to the Antennae galaxy is surprisingly poorly known, with almost a factor of 2 difference between the latest distance based on the tip of the red giant branch (13.3 Mpc) and the distance derived from the 2007sr light curve (25 Mpc). Using these distances we derive limits on absolute optical and UV magnitudes of any progenitor but these are still above the brightest (symbiotic) proposed progenitors. From the Chandra data a 3σ upper limit to the X-ray luminosity of  0.5–8.0 × 10³⁷ erg s⁻¹  in the 0.3–1 keV range is found. This is below the X-ray luminosity of the potential progenitor of the Type Ia supernova 2007on that we recently discovered and for which we report a corrected X-ray luminosity. If that progenitor is confirmed it suggests the two supernovae have different progenitors. The X-ray limit is comparable to the brightest supersoft X-ray sources in the Galaxy, the Large Magellanic Cloud (LMC) and the Small Magellanic Cloud (SMC) and significantly below the luminosities of the brightest supersoft and quasi-soft X-ray sources found in nearby galaxies, ruling out such sources as progenitors of this Type Ia supernova.     

Hydraulic Conductivity and Coefficient of Consolidation of Two Sulphide Clays in Sweden

The variation and anisotropy in hydraulic conductivity and the coefficient of consolidation was investigated for two Swedish sulphide clays. A series of constant rate of strain oedometer tests was performed on samples trimmed in the vertical and horizontal direction. A methodology to evaluate the horizontal coefficients of consolidation c _h via the horizontal hydraulic conductivity k _h and the vertical compression modulus M _v is proposed. Laboratory evaluations of c _h are also compared with determinations of c _h from in situ piezometer measurements in vertically drained sulphide clay. Furthermore, the validity of the empirical correlation between hydraulic conductivity change index C _k and initial void ratio e ₀, C _k  = 0.5e ₀ (Tavenas et al. in Can Geotech J 20(4):645–660, 1983b), was investigated for the sulphide clays. The results from the investigation show large ranges in measured hydraulic conductivities and coefficients of consolidation. However, the results indicate that the correlation C _k  = 0.5e ₀ is valid. The anisotropy in hydraulic conductivity and the coefficient of consolidation of the sulphide clays tested seems to be small. For design purposes, multiple tests for assessment of hydraulic conductivity and the coefficient of consolidation should be made, and a partial factor of safety, depending on the requisite level of safety and the spatial variability of the parameters, should be introduced. For design purposes in this type of clay, k _h  = k _v and c _h  = c _v are suggested.     

Magma plumbing systems in large igneous provinces: Inferences from cyclical variations in Palaeogene East Greenland basalts

We present compositional data on a 1,250-m-thick sequence of sparsely porphyritic lavas that comprise the Geikie Plateau Formation, part of the ~55-Ma break-up-related flood basalts in East Greenland. Major element compositions are relatively restricted (6.3–7.6 wt% MgO; 2.2–2.4 wt% TiO₂), with two excursions to more evolved compositions (2.4–3.4 wt% TiO₂) that are similar to the inferred parental magma of the nearby Skaergaard Intrusion. Major and trace element calculations show that fractional crystallisation is the principal control on magma compositions, and the cyclical sequential variations imply regular magma chamber replenishment events. Isotopic data indicate minor crustal assimilation, but with different contaminants for the main group (amphibolitic gneiss) and evolved cycles (granulitic gneiss). Rifting episodes may have allowed more primitive magmas to ascend to shallow crustal levels and subsequently fractionate to more evolved compositions in a separate chamber, which was perhaps similar to the source of the Skaergaard Intrusion.Electronic Supplementary Material Supplementary material is available in the online version of this article at Editorial responsibility: I. Parsons