Mixed finite element discretization and Newton iteration for a reactive contaminant transport model with nonequilibrium sorption: convergence analysis and error estimates

We present a numerical scheme for reactive contaminant transport with nonequilibrium sorption in porous media. The mass conservative scheme is based on Euler implicit, mixed finite elements, and Newton method. We consider the case of a Freundlich-type sorption. In this case, the sorption isotherm is not Lipschitz but just Hölder continuous. To deal with this, we perform a regularization step. The convergence of the scheme is analyzed. An explicit order of convergence depending only on the regularization parameter, the time step, and the mesh size is derived. We give also a sufficient condition for the quadratic convergence of the Newton method. Finally, relevant numerical results are presented.     

exofit: orbital parameters of extrasolar planets from radial velocities

Retrieval of orbital parameters of extrasolar planets poses considerable statistical challenges. Due to sparse sampling, measurement errors, parameters degeneracy and modelling limitations, there are no unique values of basic parameters, such as period and eccentricity. Here, we estimate the orbital parameters from radial velocity data in a Bayesian framework by utilizing Markov Chain Monte Carlo (MCMC) simulations with the Metropolis–Hastings algorithm. We follow a methodology recently proposed by Gregory and Ford. Our implementation of MCMC is based on the object-oriented approach outlined by Graves. We make our resulting code, exofit , publicly available with this paper. It can search for either one or two planets as illustrated on mock data. As an example we re-analysed the orbital solution of companions to HD 187085 and HD 159868 from the published radial velocity data. We confirm the degeneracy reported for orbital parameters of the companion to HD 187085, and show that a low-eccentricity orbit is more probable for this planet. For HD 159868, we obtained slightly different orbital solution and a relatively high 'noise' factor indicating the presence of an unaccounted signal in the radial velocity data. exofit is designed in such a way that it can be extended for a variety of probability models, including different Bayesian priors.     

Insights into the high-pressure behavior of kaolinite from infrared spectroscopy and quantum-mechanical calculations

The high-pressure behavior of Keokuk kaolinite has been studied to 9.5 GPa by infrared spectroscopy using synchrotron radiation. The kaolinite-I → kaolinite-II and kaolinite-II → kaolinite-III transformations have clear spectroscopic expression, with discontinuities coinciding with the transformation pressures bracketed by X-ray diffraction (Welch and Crichton in Am Mineral 95:651–654, 2010). The experimental spectra have been interpreted from band assignments derived from density functional theory for the structures of kaolinite-II and kaolinite-III, using as starting models the ab initio structures reported by Mercier and Le Page (Acta Crystallogr A B64:131–143, 2008, Mater Sci Technol 25:437–442, 2009) and unit-cell parameters from Welch and Crichton (Am Mineral 95:651–654, 2010). The relaxed theoretical structures are very similar to those reported by Mercier and Le Page (Acta Crystallogr A B64:131–143, 2008, Mater Sci Technol 25:437–442, 2009) in their theoretical investigation of kaolinite polytypes at high pressure. The vibrational spectra calculated from the quantum-mechanical analysis allow band assignments of the IR spectra to be made and provide insights into the behavior of different OH environments in the two high-pressure polytypes. The single perpendicular-interlayer OH group of kaolinite-III has a distinctive spectroscopic signature that is diagnostic of this polytype (ν = 3,595 cm⁻¹ at 9.5 GPa) and is sensitive to the compression/expansion of the interlayer space. This OH group also has a distinctive signature in the calculated spectra. The spectra collected on decompression are those of kaolinite-III and persist largely unchanged to 4.6 GPa, except for a continuous blue shift of the 3,595 cm⁻¹ band to 3,613 cm⁻¹. Finally, kaolinite-I is recovered at 0.6 GPa, confirming the kaolinite-III → kaolinite-I transformation previously observed by X-ray diffraction, and the irreversibility of the kaolinite-II → kaolinite-III transformation. The ambient spectra collected at the start and finish of the experiment are those of kaolinite-I, and start/finish band frequencies agree to within 6 cm⁻¹.     

Iron isotope fractionation between pyrite (FeS2), hematite (Fe2O3) and siderite (FeCO3): A first-principles density functional theory study

In addition to equilibrium isotopic fractionation factors experimentally derived, theoretical predictions are needed for interpreting isotopic compositions measured on natural samples because they allow exploring more easily a broader range of temperature and composition. For iron isotopes, only aqueous species were studied by first-principles methods and the combination of these data with those obtained by different methods for minerals leads to discrepancies between theoretical and experimental isotopic fractionation factors. In this paper, equilibrium iron isotope fractionation factors for the common minerals pyrite, hematite, and siderite were determined as a function of temperature, using first-principles methods based on the density functional theory (DFT). In these minerals belonging to the sulfide, oxide and carbonate class, iron is present under two different oxidation states and is involved in contrasted types of interatomic bonds. Equilibrium fractionation factors calculated between hematite and siderite compare well with the one estimated from experimental data (ln α⁵⁷Fe/⁵⁴Fe = 4.59 ± 0.30‰ and 5.46 ± 0.63‰ at 20 °C for theoretical and experimental data, respectively) while those for Fe(III)_aq-hematite and Fe(II)_aq-siderite are significantly higher that experimental values. This suggests that the absolute values of the reduced partition functions (β-factors) of aqueous species are not accurate enough to be combined with those calculated for minerals. When compared to previous predictions derived from Mössbauer or INRXS data [Polyakov V. B., Clayton R. N., Horita J. and Mineev S. D. (2007) Equilibrium iron isotope fractionation factors of minerals: reevaluation from the data of nuclear inelastic resonant X-ray scattering and Mössbauer spectroscopy. Geochim. Cosmochim. Acta71, 3833-3846], our iron β-factors are in good agreement for siderite and hematite while a discrepancy is observed for pyrite. However, the detailed investigation of the structural, electronic and vibrational properties of pyrite as well as the study of sulfur isotope fractionation between pyrite and two other sulfides (sphalerite and galena) indicate that DFT-derived β-factors of pyrite are as accurate as for hematite and siderite. We thus suggest that experimental vibrational density of states of pyrite should be re-examined.     

Bi-normalized response spectra and seismic intensity in Bucharest for 1986 and 1990 Vrancea seismic events

The Vrancea subcrustal earthquakes of August 30,1986 and May 30,1990 are the two most recent seismic events that have occurred in Romania with moment magnitudes M W ≥ 6.9.The spectral analysis of the strong ground motions recorded in Bucharest reveals that despite small differences in magnitude between the 1986 and 1990 earthquakes,their frequency contents are very different,sometimes even opposing.The main focus of this study is to conduct a comparative analysis of the response spectra in terms of the bi-normalized response spectra(BNRS) proposed by Xu and Xie(2004 and 2007) for strong ground motions recorded in Bucharest during these two seismic events.The mean absolute acceleration and relative velocity response spectra for the two earthquakes are discussed and compared.Furthermore,the mean bi-normalized absolute acceleration and normalized relative velocity response spectra with respect to the control period T C are computed for the ground motions recorded in Bucharest in 1986 and 1990.The predominant period T P is also used in this study for the normalization of the spectral period axis.Subsequently,the methodology proposed by Martinez-Perreira and Bommer(1998) is applied in order to estimate the seismic intensity of the two events.The results are discussed and several conclusions regarding the possibility of using the bi-normalized response spectra(BNRS) are given.     

Effects of fluctuating daily surface fluxes on the time-mean oceanic circulation

The effect of fluctuating daily surface fluxes on the time-mean oceanic circulation is studied using an empirical flux model. The model produces fluctuating fluxes resulting from atmospheric variability and includes oceanic feedbacks on the fluxes. Numerical experiments were carried out by driving an ocean general circulation model with three different versions of the empirical model. It is found that fluctuating daily fluxes lead to an increase in the meridional overturning circulation (MOC) of the Atlantic of about 1 Sv and a decrease in the Antarctic circumpolar current (ACC) of about 32 Sv. The changes are approximately 7% of the MOC and 16% of the ACC obtained without fluctuating daily fluxes. The fluctuating fluxes change the intensity and the depth of vertical mixing. This, in turn, changes the density field and thus the circulation. Fluctuating buoyancy fluxes change the vertical mixing in a non-linear way: they tend to increase the convective mixing in mostly stable regions and to decrease the convective mixing in mostly unstable regions. The ACC changes are related to the enhanced mixing in the subtropical and the mid-latitude Southern Ocean and reduced mixing in the high-latitude Southern Ocean. The enhanced mixing is related to an increase in the frequency and the depth of convective events. As these events bring more dense water downward, the mixing changes lead to a reduction in meridional gradient of the depth-integrated density in the Southern Ocean and hence the strength of the ACC. The MOC changes are related to more subtle density changes. It is found that the vertical mixing in a latitudinal strip in the northern North Atlantic is more strongly enhanced due to fluctuating fluxes than the mixing in a latitudinal strip in the South Atlantic. This leads to an increase in the density difference between the two strips, which can be responsible for the increase in the Atlantic MOC.     

Assessment of seismic risk scenarios for Bucharest,Romania

In this paper, seismic risk scenarios for Bucharest, the capital city of Romania, are proposed and assessed. Bucharest has one of the highest seismic risk levels in Europe, and this is due to a combination of relatively high seismic hazard and a building stock built mainly before the devastating Vrancea 1977 earthquake. In this study, the seismic risk of Bucharest is assessed using the most recent information regarding the characteristics of the residential building stock. The ground motion amplitudes are evaluated starting from random fields obtained by coupling a ground motion model derived for the Vrancea intermediate-depth seismic source with a spatial correlation model. The seismic risk evaluation method applied in this study is based on the well-known macroseismic method. For several structural typologies, the vulnerability parameters are evaluated based on a damage survey performed on 18,000 buildings in Bucharest after the March 1977 earthquake. Subsequently, the risk metrics are compared with those from other studies in the literature that apply a different risk assessment methodology in order to gain a better view of the uncertainties associated with a seismic risk study at city level. Finally, the impact of several Vrancea intermediate-depth earthquake scenarios is evaluated and the results show that the earthquake which has the closest epicenter to Bucharest appears to be the most damaging.

     

Amplitude Preserving Kirchhoff Migration: A Traveltime Based Strategy

Amplitude versus offset information is a key feature to seismic reservoir characterization. Therefore amplitude preserving migration was developed to obtain this information from seismic reflection data. For complex 3-D media, however, this process is computationally expensive. In this paper we present an efficient traveltime based strategy for amplitude preserving migration of the Kirchhoff type. Its foundations are the generation of traveltime tables using a wavefront-oriented ray-tracing technique, and a generalized moveout relation for 3-D heterogeneous media. All required quantities for the amplitude preserving migration are computed from coarsely gridded traveltime tables. The migration includes the interpolation from the coarsely gridded input traveltimes onto the fine migration grid, the computation of amplitude preserving weight functions, and, optionally, the evaluation of an optimized migration aperture. Since ray tracing is employed for the traveltime computation the input velocity model needs to be smooth, i.e. velocity variations of spatial dimensions below the wavelength of the considered reflection signals are removed. Numerical examples on simple generic models validate the technique and an application to the Marmousi model demonstrates its potential to complex media. The major advantage of the traveltime based strategy consists of its computational efficiency by maintaining sufficient accuracy. Considerable savings in storage space (10⁵ and more for 3-D data with respect to no interpolation at all) can be achieved. The computational time for the stack can be substantially reduced (up to 90% in 3-D) with the optimized migration aperture since only those traces are stacked which really contribute to the image point under consideration.     

Low-temperature evolution of OH bands in synthetic forsterite, implication for the nature of H defects at high pressure

We performed in situ infrared spectroscopic measurements of OH bands in a forsterite single crystal between ?194 and 200 °C. The crystal was synthesized at 2 GPa from a cooling experiment performed between 1,400 and 1,275 °C at a rate of 1 °C per hour under high silica-activity conditions. Twenty-four individual bands were identified at low temperature. Three different groups can be distinguished: (1) Most of the OH bands between 3,300 and 3,650 cm^?1 display a small frequency lowering (<4 cm^?1) and a moderate broadening (<10 cm^?1) as temperature is increased from ?194 to 200 °C. The behaviour of these bands is compatible with weakly H-bonded OH groups associated with hydrogen substitution into silicon tetrahedra; (2) In the same frequency range, two bands at 3,617 and 3,566 cm^?1 display a significantly anharmonic behaviour with stronger frequency lowering (42 and 27 cm^?1 respectively) and broadening (~30 cm^?1) with increasing temperature. It is tentatively proposed that the defects responsible for these OH bands correspond to H atoms in interstitial position; (3) In the frequency region between 3,300 and 3,000 cm^?1, three broad bands are identified at 3,151, 3,178 and 3,217 cm^?1, at ?194 °C. They exhibit significant frequency increase (~20 cm^?1) and broadening (~70 cm^?1) with increasing temperature, indicating moderate H bonding. These bands are compatible with (2H)_Mg defects. A survey of published spectra of forsterite samples synthesized above 5 GPa shows that about 75 % of the incorporated hydrogen belongs to type (1) OH bands associated with Si substitution and 25 % to the broad band at 3,566 cm^?1 (type (2); 3,550 cm^?1 at room temperature). The contribution of OH bands of type (3), associated to (2H)_Mg defects, is negligible. Therefore, solubility of hydrogen in forsterite (and natural olivine compositions) cannot be described by a single solubility law, but by the combination of at least two laws, with different activation volumes and water fugacity exponents.