Wavelet-based directional analysis of the gravity field: evidence for large-scale undulations

International audienceIn the eighties, the analysis of satellite altimetry data leads to the major discovery of gravity lineations in the oceans, with wavelengths between 200 and 1400 km. While the existence of the 200 km scale undulations is widely accepted, undulations at scales larger than 400 km are still a matter of debate. In this paper, we revisit the topic of the large-scale geoid undulations over the oceans in the light of the satellite gravity data provided by the GRACE mission, considerably more precise than the altimetry data at wavelengths larger than 400 km. First, we develop a dedicated method of directional Poisson wavelet analysis on the sphere with significance testing, in order to detect and characterize directional structures in geophys-ical data on the sphere at different spatial scales. This method is particularly well suited for potential field analysis. We validate it on a series of synthetic tests, and then apply it to analyze recent gravity models, as well as a bathymetry data set independent from gravity. Our analysis confirms the existence of gravity undulations at large scale in the oceans, with characteristic scales between 600 and 2000 km. Their direction correlates well with present-day plate motion over the Pacific ocean, where they are particularly clear, and associated with a conjugate direction at 1500 km scale. A major finding is that the 2000 km scale geoid undulations dominate and had never been so clearly observed previously. This is due to the great precision of GRACE data at those wavelengths. Given the large scale of these undulations, they are most likely related to mantle processes. Taking into account observations and models from other geophysical information, as seismological tomography, convection and geochemical models and electrical conductivity in the mantle, we conceive that all these inputs indicate a directional fabric of the mantle flows at depth, reflecting how the history of subduction influences the organization of lower mantle upwellings

Discovery of starspots on Vega - First spectroscopic detection of surface structures on a normal A-type star

The theoretically studied impact of rapid rotation on stellar evolution needs to be confronted with the results of high resolution spectroscopy-velocimetry observations. A weak surface magnetic field had recently been detected in the A0 prototype star Vega, potentially leading to a (yet undetected) structured surface. The goal of this article is to present a thorough analysis of the line profile variations and associated estimators in the early-type standard star Vega (A0) in order reveal potential activity tracers, exoplanet companions and stellar oscillations. Vega was monitored in high-resolution spectroscopy with the velocimeter Sophie/OHP. A total of 2588 high S/N spectra was obtained during 5 nights (August 2012) at R = 75000 and covering the visible domain. For each reduced spectrum, Least Square Deconvolved (LSD) equivalent photospheric profiles were calculated with a Teff = 9500 and logg = 4.0 spectral line mask. Several methods were applied to study the dynamic behavior of the profile variations (evolution of radial velocity, bisectors, vspan, 2D profiles, amongst others). We present the discovery of a starspotted stellar surface in an A-type standard star with faint spot amplitudes Delta F/Fc ~5 10^{-4}. A rotational modulation of spectral lines with a period of rotation P = 0.68 d has clearly been exhibited, confirming the results of previous spectropolarimetric studies. Either a very thin convective layer can be responsible for magnetic field generation at small amplitudes, or a new mechanism has to be invoked in order to explain the existence of activity tracing starspots. This first strong evidence that standard A-type stars can show surface structures opens a new field of research and asks the question about a potential link with the recently discovered weak magnetic field discoveries in this category of stars.Comment: accepted for publication by Astronomy & Astrophysics (23rd of March 2015

Detection of trend changes in time series using Bayesian inference

Change points in time series are perceived as isolated singularities where two regular trends of a given signal do not match. The detection of such transitions is of fundamental interest for the understanding of the system's internal dynamics. In practice observational noise makes it difficult to detect such change points in time series. In this work we elaborate a Bayesian method to estimate the location of the singularities and to produce some confidence intervals. We validate the ability and sensitivity of our inference method by estimating change points of synthetic data sets. As an application we use our algorithm to analyze the annual flow volume of the Nile River at Aswan from 1871 to 1970, where we confirm a well-established significant transition point within the time series.Comment: 9 pages, 12 figures, submitte

General theory for integer-type algorithm for higher order differential equations

Based on functional analysis, we propose an algorithm for finite-norm solutions of higher-order linear Fuchsian-type ordinary differential equations (ODEs) P(x,d/dx)f(x)=0 with P(x,d/dx):=[\sum_m p_m (x) (d/dx)^m] by using only the four arithmetical operations on integers. This algorithm is based on a band-diagonal matrix representation of the differential operator P(x,d/dx), though it is quite different from the usual Galerkin methods. This representation is made for the respective CONSs of the input Hilbert space H and the output Hilbert space H' of P(x,d/dx). This band-diagonal matrix enables the construction of a recursive algorithm for solving the ODE. However, a solution of the simultaneous linear equations represented by this matrix does not necessarily correspond to the true solution of ODE. We show that when this solution is an l^2 sequence, it corresponds to the true solution of ODE. We invent a method based on an integer-type algorithm for extracting only l^2 components. Further, the concrete choice of Hilbert spaces H and H' is also given for our algorithm when p_m is a polynomial or a rational function with rational coefficients. We check how our algorithm works based on several numerical demonstrations related to special functions, where the results show that the accuracy of our method is extremely high.Comment: Errors concerning numbering of figures are fixe

Multiscale theory of turbulence in wavelet representation

We present a multiscale description of hydrodynamic turbulence in incompressible fluid based on a continuous wavelet transform (CWT) and a stochastic hydrodynamics formalism. Defining the stirring random force by the correlation function of its wavelet components, we achieve the cancellation of loop divergences in the stochastic perturbation expansion. An extra contribution to the energy transfer from large to smaller scales is considered. It is shown that the Kolmogorov hypotheses are naturally reformulated in multiscale formalism. The multiscale perturbation theory and statistical closures based on the wavelet decomposition are constructed.Comment: LaTeX, 27 pages, 3 eps figure

Fractal Spectrum of a Quasi_periodically Driven Spin System

We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time behaviour of various dynamical quantities, such as the moments of the distribution of the wave packet. Our data suggest a close similarity between the information dimension of the spectrum and the exponent ruling the algebraic growth of the 'entropic width' of wavepackets.Comment: 17 pages, RevTex, 5 figs. available on request from [email protected]

Acetylcholinesterase inhibition interacts with training to reverse spatial learning deficits after cortical impact injury

Cholinergic mechanisms are known to play a key role in cognitive functions that are profoundly altered in traumatic brain injury (TBI). The present investigation was designed to test the ability of continuous administration, starting at the time of injury, of physostigmine (PHY), an acetylcholinesterase (AChE) inhibitor that crosses the blood-brain barrier (BBB), to ameliorate the alterations of learning and memory induced by cerebral cortex impact injury in rats under isoflurane anesthesia. Learning and memory were assessed with the Morris water maze implemented during days 7-11 (WM1), and days 21-25 post-TBI (WM2), with four trials per day for 3 days, followed by target reversal and 2 additional days of training. These groups of Sprague-Dawley male rats were used: TBI treated with PHY at 3.2 μmol/kg/day (TBI-PHY3.2), or 6.4 μmol/kg/day (TBI-PHY6.4), by subcutaneous osmotic pumps, or TBI and no injury (Sham) treated with saline. AChE activity was measured in brain tissue samples of non-traumatized animals that received PHY at the doses used in the TBI animals. In WM1 tests, PHY3.2 improved learning within sessions, but not between sessions, in the recall of the target position, while PHY6.4 had no significant effects. In WM2 tests, PHY improved within- and between-sessions performance at both dose levels. We found that continuous AChE inhibition interacted with repeated training on the water maze task to completely reverse the deficits seen in learning and memory induced by TBI. The PHY treatment also reduced the amount of brain tissue loss as measured using cresyl violet staining.Fil: Scremin, Oscar Umberto. University of California at Los Angeles. School of Medicine; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Norman, Keith M.. No especifíca;Fil: Roch, Margareth. No especifíca;Fil: Holschneider, Daniel P.. No especifíca;Fil: Scremin, A. M. Erika. University of California at Los Angeles. School of Medicine; Estados Unido

Quantum Return Probability for Substitution Potentials

We propose an effective exponent ruling the algebraic decay of the average quantum return probability for discrete Schrodinger operators. We compute it for some non-periodic substitution potentials with different degrees of randomness, and do not find a complete qualitative agreement with the spectral type of the substitution sequences themselves, i.e., more random the sequence smaller such exponent.Comment: Latex, 13 pages, 6 figures; to be published in Journal of Physics

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App

Fractional differentiability of nowhere differentiable functions and dimensions

Weierstrass's everywhere continuous but nowhere differentiable function is shown to be locally continuously fractionally differentiable everywhere for all orders below the `critical order' 2-s and not so for orders between 2-s and 1, where s, 1<s<2 is the box dimension of the graph of the function. This observation is consolidated in the general result showing a direct connection between local fractional differentiability and the box dimension/ local Holder exponent. Levy index for one dimensional Levy flights is shown to be the critical order of its characteristic function. Local fractional derivatives of multifractal signals (non-random functions) are shown to provide the local Holder exponent. It is argued that Local fractional derivatives provide a powerful tool to analyze pointwise behavior of irregular signals.Comment: minor changes, 19 pages, Late