Notes on Hori Method for Non-Canonical Systems

In this paper the new approach for the integration theory of the canonical version of Hori method recently proposed is extended to the non-canonical one. It will be shown that the non-homogeneous ordinary differential equation with an auxiliary parameter t* associated with the mth order equation of the algorithm can also be replaced by a non-homogeneous partial differential equation in the time t. Using a generalized canonical approach, the general algorithm proposed by Sessin is then revised; as well as the Lagrange variational equations for the non-canonical version of Hori method. A simplified algorithm derived from Sessin's algorithm is presented for non-linear oscillations problem.     

Tracing salinization processes in coastal aquifers using an isotopic and geochemical approach: comparative studies in western Morocco and southwest Portugal

Environmental stable and radioactive isotopes (δ²H, δ¹³C, δ¹⁸O; ³H and ¹⁴C), together with physical and geochemical data, were used in the determination of the origins of groundwater salinization and geochemical evolution processes in coastal regions. Two case studies on the Atlantic Coast are discussed, one located in the Essaouira sedimentary basin, western Morocco, and the second, in the Lower Tagus–Sado sedimentary basin, southwest Portugal. In both regions, groundwater degradation occurs by salinization increase to different concentrations and in relation to different origins. The main quality issues for the groundwater resources are related to seawater intrusion, dissolution of diapiric structures intruding the aquifer layers, brine dissolution at depth, and/or evaporation of irrigation water. Anthropogenic pollution ascribed to agricultural activities is another source for groundwater degradation, affecting mainly the shallow aquifers. The apparent ¹⁴C age of the analysed samples ranges from 2.9?±?0.3 up to 45.6?±?0.6 pmC in the Miocene groundwater samples from the basin in Portugal; at the Essaouira basin in Morocco, the ¹⁴C content varies from 60 to 86 pmC. In most of the water samples, the ³H concentration is below the detection limit. In both basins, the isotopic results together with the geochemical data provided an effective label for tracing the mineralization origin and groundwater degradation processes. Further, the isotopic signatures were used in the identification of a paleoclimate (colder period), recorded in the stable isotopic composition and corroborated with the ¹⁴C data.     

Estimates of eruption velocity and plume height from infrasonic recordings of the 2006 eruption of Augustine Volcano,Alaska

The 2006 eruption of Augustine Volcano, Alaska, began with an explosive phase comprising 13 discrete Vulcanian blasts. These events generated ash plumes reaching heights of 3–14 km. The eruption was recorded by a dense geophysical network including a pressure sensor located 3.2 km from the vent. Infrasonic signals recorded in association with the eruptions have maximum pressures ranging from 13–111 Pa. Eruption durations are estimated to range from 55–350 s. Neither of these parameters, however, correlates with eruption plume height. The pressure record, however, can be used to estimate the velocity and flux of material erupting from the vent, assuming that the sound is generated as a dipole source. Eruptive flux, in turn, is used to estimate plume height, assuming that the plume rises as a buoyant thermal. Plume heights estimated in this way correlate well with observations. Events that exhibit strongly impulsive waveforms are underestimated by the model, suggesting that flow may have been supersonic.     

Observations of shocked H2 and [FeII] line profiles in orion bullet wakes

New observations of H₂ velocity profiles in the Orion bullet wakes are extremely difficult to reconcile with existing steady-state shock models. We have observed [FeII] 1.644µm velocity profiles of selected bullets and H₂ 1-0 S(1) 2.122µm velocity profiles for a series of positions along and across the corresponding bow-shock wakes. Integrated [FeII] velocity profiles of the brightest bullets are consistent with theoretical bow shock predictions. Observations of broad, singly-peaked H₂ 1-0 S(1) profiles in the most clearly resolved bullet wakes challenge our understanding of molecular shocks. It may be necessary to model the effects of instabilities and turbulence in the Orion bullet wakes in order to fit our observations.     

Fast error analysis of continuous GNSS observations with missing data

One of the most widely used method for the time-series analysis of continuous Global Navigation Satellite System (GNSS) observations is Maximum Likelihood Estimation (MLE) which in most implementations requires $\mathcal{O }(n^3)$ operations for $n$ observations. Previous research by the authors has shown that this amount of operations can be reduced to $\mathcal{O }(n^2)$ for observations without missing data. In the current research we present a reformulation of the equations that preserves this low amount of operations, even in the common situation of having some missing data.Our reformulation assumes that the noise is stationary to ensure a Toeplitz covariance matrix. However, most GNSS time-series exhibit power-law noise which is weakly non-stationary. To overcome this problem, we present a Toeplitz covariance matrix that provides an approximation for power-law noise that is accurate for most GNSS time-series.Numerical results are given for a set of synthetic data and a set of International GNSS Service (IGS) stations, demonstrating a reduction in computation time of a factor of 10–100 compared to the standard MLE method, depending on the length of the time-series and the amount of missing data.