TY - JOUR A1 - Hayn, Michael A1 - Panet, I. A1 - Diament, M. A1 - Holschneider, Matthias A1 - Mandea, Mioara A1 - Davaille, A. T1 - Wavelet-based directional analysis of the gravity field evidence for large-scale undulations JF - Geophysical journal international N2 - In 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 geophysical 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. KW - Wavelet transform KW - Satellite geodesy KW - Gravity anomalies and Earth structure KW - Pacific Ocean Y1 - 2012 U6 - https://doi.org/10.1111/j.1365-246X.2012.05455.x SN - 0956-540X SN - 1365-246X VL - 189 IS - 3 SP - 1430 EP - 1456 PB - Oxford Univ. Press CY - Oxford ER - TY - JOUR A1 - Rocha, Marcia R. A1 - Vasseur, David A. A1 - Hayn, Michael A1 - Holschneider, Matthias A1 - Gaedke, Ursula T1 - Variability patterns differ between standing stock and process rates JF - Oikos N2 - Standing stocks are typically easier to measure than process rates such as production. Hence, stocks are often used as indicators of ecosystem functions although the latter are generally more strongly related to rates than to stocks. The regulation of stocks and rates and thus their variability over time may differ, as stocks constitute the net result of production and losses. Based on long-term high frequency measurements in a large, deep lake we explore the variability patterns in primary and bacterial production and relate them to those of the corresponding standing stocks, i.e. chlorophyll concentration, phytoplankton and bacterial biomass. We employ different methods (coefficient of variation, spline fitting and spectral analysis) which complement each other for assessing the variability present in the plankton data, at different temporal scales. In phytoplankton, we found that the overall variability of primary production is dominated by fluctuations at low frequencies, such as the annual, whereas in stocks and chlorophyll in particular, higher frequencies contribute substantially to the overall variance. This suggests that using standing stocks instead of rate measures leads to an under- or overestimation of food shortage for consumers during distinct periods of the year. The range of annual variation in bacterial production is 8 times greater than biomass, showing that the variability of bacterial activity (e.g. oxygen consumption, remineralisation) would be underestimated if biomass is used. The P/B ratios were variable and although clear trends are present in both bacteria and phytoplankton, no systematic relationship between stock and rate measures were found for the two groups. Hence, standing stock and process rate measures exhibit different variability patterns and care is needed when interpreting the mechanisms and implications of the variability encountered. Y1 - 2011 U6 - https://doi.org/10.1111/j.1600-0706.2010.18786.x SN - 0030-1299 VL - 120 IS - 1 SP - 17 EP - 25 PB - Wiley-Blackwell CY - Malden ER - TY - JOUR A1 - Geese, Anne A1 - Mandea, Mioara A1 - Lesur, Vincent A1 - Hayn, Michael T1 - Regional modelling of the Southern African geomagnetic field using harmonic splines N2 - Over the southern African region the geomagnetic field is weak and changes rapidly. For this area series of geomagnetic field measurements exist since the 1950s. We take advantage of the existing repeat station surveys and observatory annual means, and clean these data sets by eliminating jumps and minimizing external field contributions in the original time-series. This unique data set allows us to obtain a detailed view of the geomagnetic field behaviour in space and time by computing a regional model. For this, we use a system of representation similar to harmonic splines. Initially, the technique is systematically tested on synthetic data. After systematically testing the method on synthetic data, we derive a model for 1961-2001 that gives a detailed view of the fast changes of the geomagnetic field in this region. Y1 - 2010 UR - http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1365-246X U6 - https://doi.org/10.1111/j.1365-246X.2010.04575.x SN - 0956-540X ER - TY - THES A1 - Hayn, Michael T1 - Wavelet analysis and spline modeling of geophysical data on the sphere Y1 - 2010 CY - Potsdam ER - TY - JOUR A1 - Hayn, Michael A1 - Holschneider, Matthias T1 - Directional spherical multipole wavelets N2 - We construct a family of admissible analysis reconstruction pairs of wavelet families on the sphere. The construction is an extension of the isotropic Poisson wavelets. Similar to those, the directional wavelets allow a finite expansion in terms of off-center multipoles. Unlike the isotropic case, the directional wavelets are not a tight frame. However, at small scales, they almost behave like a tight frame. We give an explicit formula for the pseudodifferential operator given by the combination analysis-synthesis with respect to these wavelets. The Euclidean limit is shown to exist and an explicit formula is given. This allows us to quantify the asymptotic angular resolution of the wavelets. Y1 - 2009 UR - http://jmp.aip.org/ U6 - https://doi.org/10.1063/1.3177198 SN - 0022-2488 ER -