Sub-Gaussian model of processes with heavy-tailed distributions applied to air permeabilities of fractured tuff

Earth and environmental variables are commonly taken to have multivariate Gaussian or heavy-tailed distributions in space and/or time. This is based on the observation that univariate frequency distributions of corresponding samples appear to be Gaussian or heavy-tailed. Of particular interest to us is the well-documented but heretofore little noticed and unexplained phenomenon that whereas the frequency distribution of log permeability data often seems to be Gaussian, that of corresponding increments tends to exhibit heavy tails. The tails decay as powers of ? $ \alpha $ where 1 <  $ \alpha $  < 2 is either constant or grows monotonically toward an asymptote with increasing separation distance or lag. We illustrate the latter phenomenon on 1-m scale log air permeabilities from pneumatic tests in 6 vertical and inclined boreholes completed in unsaturated fractured tuff near Superior, Arizona. We then show theoretically and demonstrate numerically, on synthetically generated signals, that whereas the case of constant $ \alpha $ is consistent with a collection of samples from truncated sub-Gaussian fractional Lévy noise, a random field (or process) subordinated to truncated fractional Gaussian noise, the case of variable $ \alpha $ is consistent with a collection of samples from truncated sub-Gaussian fractional Lévy motion (tfLm), a random field subordinated to truncated fractional Brownian motion. Whereas the first type of signal is relatively regular and characterized by Lévy index $ \alpha $ , the second is highly irregular (punctuated by spurious spikes) and characterized by the asymptote of $ \alpha $ values associated with its increments. We describe a procedure to estimate the parameters of univariate distributions characterizing such signals and apply it to our log air permeability data. The latter are found to be consistent with a collection of samples from tfLm with $ \alpha $ slightly smaller than 2, which is easily confused with a Gaussian field (characterized by constant $ \alpha $  = 2). The irregular (spiky) nature of this signal is typical of observed fractured rock properties. We propose that distributions of earth and environmental variable be inferred jointly from measured values and their increments in a way that insures consistency between these two sets of data.     

SLA–chlorophyll-a variability and covariability in the Algero-Provençal Basin (1997–2007) through combined use of EOF and wavelet analysis of satellite data

Data reduction and signal decomposition techniques have been applied to a large bio-physical remotely sensed dataset covering the decade 1997–2007. The aim was the estimation of the spatial (basin and sub-basin scales) and temporal (seasonal and interannual) variability of sea level anomalies and chlorophyll-a concentration in the Algero-Provençal Basin, as well as the study of their covariability. Empirical orthogonal functions, wavelet analysis, singular value decomposition and correlation maps have been successfully used to individuate the patterns of (co)variability of the investigated fields. The seasonal variability of the phytoplanktonic biomass is divided in two distinct modes, timewise and spacewise separated. Positive interannual events are related to anomalies in 1999 and 2005, while the main (negative) anomaly is that of summer 2003, associated to the European 2003 heatwave. The analysis of the sea level anomalies shows a minimum in the formation of anticyclonic Algerian eddies during that period. The largest anticorrelation between sea level anomalies and phytoplanktonic biomass is found in the central zone of the basin, suggesting a clear biological response to the shoaling/deepening of the isopycnae and so to the nutrient injection into the euphotic layer. The analysis suggests that the driver of the variability of the nutricline depth in this central area is the displacement (seasonal) of the North Balearic Front and the formation/action of the frontal eddies.     

An Origin for the Linear Magnetic Anomalies on Mars through Accretion of Terranes: Implications for Dynamo Timing

The proposed existence of magnetic lineations in the Terra Cimmeria and Terra Sirenum regions of Mars was initially explained by Earth-like sea-floor spreading. Here we argue instead that these lineations could have been formed at a convergent plate margin through collision and accretion of terranes. A similar process produced banded magnetic anomalies, similar in geometry and even in size to those in Earth's North American Cordillera. Because only sparse and generally weak anomalies have been detected in the martian northern lowlands, which could constitute an analog to the terrestrial oceanic crust, it is possible that the magnetic field stopped its activity while crustal recycling was still active in Mars.     

Scilla e Cariddi e le correnti di marea nello Stretto di Messina

Riassunto L'A. sottopone ad una dettagliata analisi idrodinamica i fenomeni relativi alle maree ed alle correnti di marea dello Stretto di Messina, appoggiandosi sui dati mareografici dei due mari adiacenti nonchè sulle misure ed osservazioni di F. Vercelli e G. Mazzarelli. I risultati mostrano come il fenomeno delle maree nello Stretto di Messina consista nell'accoppiamento delle maree proprie delle masse d'acque dello Stretto con gli impulsi che le stesse masse ricevono dai due mari Jonio e Tirreno. In tale processo i fenomeni d'attrito (attrito esterno e turbolenza) rivelano un'importanza fondamentale. La sovrapposizione di una corrente generale più forte con la corrente di marea dà luogo nell'imbocco Nord dello Stretto a quelle convergenze di corrente alle quali si connettono i «tagli» e le «scale di mare», nonchè i vortici di Capo Peloro (Cariddi), Scilla e San Raineri. Seguono considerazioni sulla possibilità di alterazioni morfologiche dello Stretto di Messina da epoche preistoriche con abbassamento del fondo o con allargamento delle sponde in guisa da spiegare l'indebolimento dei medesimi fenomeni.

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Zusammenfassung Die Gezeiten und Gezeitenströmungen in der Strasse von Messina, an die sich die bekannten Schilderungen der alten Sagen der Scylla und Charybdis knüpfen, werden hier einer eingehenden hydrodynamischen Analyse unterzogen. Die Grundlagen für diese bilden einerseits die bekannten Grundwerte der vertikalen Gezeit in den angrenzenden Meeren im Norden und Süden der Strasse, andererseits die neueren Messungen der Gezeitenströme im engsten Querschnitt der Strasse durch Prof. Vercelli und die Beobachtungen von Prof. G. Mazzarelli. Die Ergebnisse dieser Analyse zeigen, dass das Phänomen der Gezeiten in der Meeresstrasse nichts anderes ist, als die Mitschwingungsgezeiten der Wassermassen der Strasse mit den Impulsen, die sie vom Jonischen und Thyrrhenischen Meer her empfagen. Dabei spielen die Reibungseinflüsse (äussere Reibung und Turbulenz) im engsten Teil der Strasse für die Intensität und Phase der Ströme eine ausschlaggebende Rolle. Die Superposition einer stärkeren allgemeinen Strömung und des Gezeitenstromes gibt am Nordausgang der Meeresstrasse an der Meeresoberfläche zweimal in jeder Mondperiode jene Stromkonvergenzen, an die die bekannten Sprungwellen (tagli o scale di mare) gebunden sind. Mit ihnen in Zusammenhang stehen such die Wirbel vor Cap Peloro (Charybdis), vor Scilla und vor San Raineri. Dieser Zusammenhang wird in der Arbeit näher erörtert, sowie Betrachtungen darüber angestellt, ob nicht möglicherweise morphologische Aenderungen in der Strasse von Messina seit vorhistorischer Zeit durch Vertiefung und vielleicht auch Verbreiterung der Meeresstrasse eine Schwächung der Phänomens bewirkt haben könnten. So könnte man verstehen, dass «Scylla und Charybdis» das sind die von Homer so eindrucksvoll geschilderten Gefahren für die Schiffahrt allmählich verloren gegangen sind.

     

Corrections stemming from the non-osculating character of the Andoyer variables used in the description of rotation of the elastic Earth

We explore the evolution of the angular velocity of an elastic Earth model, within the Hamiltonian formalism. The evolution of the rotation state of the Earth is caused by the tidal deformation exerted by the Moon and the Sun. It can be demonstrated that the tidal perturbation to spin depends not only upon the instantaneous orientation of the Earth, but also upon its instantaneous angular velocity. Parameterizing the orientation of the Earth figure axis with the three Euler angles, and introducing the canonical momenta conjugated to these, one can then show that the tidal perturbation depends both upon the angles and the momenta. This circumstance complicates the integration of the rotational motion. Specifically, when the integration is carried out in terms of the canonical Andoyer variables (which are the rotational analogues to the orbital Delaunay variables), one should keep in mind the following subtlety: under the said kind of perturbations, the functional dependence of the angular velocity upon the Andoyer elements differs from the unperturbed dependence (Efroimsky in Proceedings of Journées 2004: Systèmes de référence spatio-temporels. l’Observatoire de Paris, pp 74–81, 2005; Efroimsky and Escapa in Celest. Mech. Dyn. Astron. 98:251–283, 2007). This happens because, under angular velocity dependent perturbations, the requirement for the Andoyer elements to be canonical comes into a contradiction with the requirement for these elements to be osculating, a situation that parallels a similar antinomy in orbital dynamics. Under the said perturbations, the expression for the angular velocity acquires an additional contribution, the so called convective term. Hence, the time variation induced on the angular velocity by the tidal deformation contains two parts. The first one comes from the direct terms, caused by the action of the elastic perturbation on the torque-free expressions of the angular velocity. The second one arises from the convective terms. We compute the variations of the angular velocity through the approach developed in Getino and Ferrándiz (Celest. Mech. Dyn. Astron. 61:117–180, 1995), but considering the contribution of the convective terms. Specifically, we derive analytical formulas that determine the elastic perturbations of the directional angles of the angular velocity with respect to a non-rotating reference system, and also of its Cartesian components relative to the Tisserand reference system of the Earth. The perturbation of the directional angles of the angular velocity turns out to be different from the evolution law found in Kubo (Celest. Mech. Dyn. Astron. 105:261–274, 2009), where it was stated that the evolution of the angular velocity vector mimics that of the figure axis. We investigate comprehensively the source of this discrepancy, concluding that the difference between our results and those obtained in Ibid. stems from an oversimplification made by Kubo when computing the direct terms. Namely, in his computations Kubo disregarded the motion of the tide raising bodies with respect to a non-rotating reference system when compared with the Earth rotational motion. We demonstrate that, from a numerical perspective, the convective part provides the principal contribution to the variation of the directional angles and of length of day. In the case of the x and y components in the Tisserand system, the convective contribution is of the same order of magnitude as the direct one. Finally, we show that the approximation employed in Kubo (Ibid.) leads to significant numerical differences at the level of a hundred micro-arcsecond.     

Age and origin of the lowlands of Mars

One of the many significant findings of the Mars Global Surveyor mission is the presence of hundreds of quasi-circular depressions (QCDs) observed from high-resolution MOLA topography data. Their presence has recently been interpreted to reflect a northern lowlands that archive some of the earliest recorded rocks on Mars, mostly below a veneer of Hesperian and Amazonian materials. Here we analyze these data, coupled with a recent synthesis of geologic, geophysical, geomorphic, topographic, and magnetic information. Such analysis allows us to suggest a potential plate tectonic phase during the recorded Early into Middle Noachian martian history that transitioned into a monoplate world with episodic magmatic-driven activity persisting to present. This working hypothesis is based on: (1) the observation that the basement of the northern plains is younger than the basement of the southern highlands, but older than the material exposures of the cratered highlands, suggesting different formational ages for each one of the three geologic-time units; (2) the observation that parts of the very ancient highland's crust are highly magnetized, thus suggesting that most if not all of the formation of the lowlands basement postdates the shut off of the martian dynamo, some 4 Gyr ago, and so allowing hundreds of millions of years for the shaping of the buried lowlands. Consequently, the role of endogenic processes in the earliest geological evolution of Mars (Early perhaps into Middle Noachian) requires reconsideration, since MOLA topographic and MGS magnetic data afford a temporal window sufficient for very early, non-primordial shaping of the northern lowlands' basement.     

Putative Meteoritic Craters in Río Cuarto (Central Argentina) Interpreted as Eolian Structures

Ten oblong aligned depressions in the Río Cuarto area (provincia de Córdoba, Argentina) were supposed to be the result of very-low-angle Holocene meteoroid impacts. However, we consider that authors that studied the structures did not demonstrated their extraterrestrial origin. We suggest that an eolian origin for the structures of Río Cuarto is more likely. Actually, these landforms integrate large systems of similar deflation/accumulation geoforms aligned according to predominant winds during different periods.     

The helicity constraint in turbulent dynamos with shear

The evolution of magnetic fields is studied using simulations of forced helical turbulence with strong imposed shear. After some initial exponential growth, the magnetic field develops a large-scale travelling wave pattern. The resulting field structure possesses magnetic helicity, which is conserved in a periodic box by the ideal magnetohydrodynamics equations and can hence only change on a resistive time-scale. This strongly constrains the growth time of the large-scale magnetic field, but less strongly constrains the length of the cycle period. Comparing this with the case without shear, the time-scale for large-scale field amplification is shortened by a factor Q , which depends on the relative importance of shear and helical turbulence, and which also controls the ratio of toroidal to poloidal field. The results of the simulations can be reproduced qualitatively and quantitatively with a mean-field α Ω-dynamo model with alpha-effect and turbulent magnetic diffusivity coefficients that are less strongly quenched than in the corresponding α ²-dynamo.