Eccentric dipole of the geomagnetic field during the last reversal, last excursions, and the most significant Holocene anomalies

<p>The geomagnetic field is commonly approximated to a geocentric tilted dipole. However, a next step in the approach of the geomagnetic field is the eccentric dipole which takes the first and second terms of the spherical harmonic representation of the geomagnetic field. In this work, we analyze the behavior of the eccentric dipole during the last reversal (Matuyama – Brunhes, 780 ka), the last excursions (Laschamp, 41 ka, and Mono Lake, 34 ka), and during two interesting features of the geomagnetic field observed during the Holocene (the South Atlantic Anomaly, from 1840 AD or older, and the Levantine Iron Age Anomaly, around 1000 BC). The last reversal and excursions are studied by using the IMMAB4 and LSMOD2 paleoreconstructions, respectively. We found that for these events the center of the eccentric dipole follows a common longitude path. The Holocene anomalies have been analyzed by using two of the most up-to-date paleoreconstructions for the last 3 millennia: the SHAWQ2k and the SHAWQ Iron Age paleoreconstructions. A common longitude path has not been observed between these anomalies.</p>

Computing the Orientational-Average of Diffusion-Weighted MRI Signals: A Comparison of Different Techniques

ABSTRACTNumerous applications in diffusion MRI, from multi-compartment modeling to power-law analyses, involves computing the orientationally-averaged diffusion-weighted signal. Most approaches implicitly assume, for a given b-value, that the gradient sampling vectors are uniformly distributed on a sphere (or ‘shell’), computing the orientationally-averaged signal through simple arithmetic averaging. One challenge with this approach is that not all acquisition schemes have gradient sampling vectors distributed over perfect spheres (either by design, or due to gradient non-linearities). To ameliorate this challenge, alternative averaging methods include: weighted signal averaging; spherical harmonic representation of the signal in each shell; and using Mean Apparent Propagator MRI (MAP-MRI) to derive a three-dimensional signal representation and estimate its ‘isotropic part’. This latter approach can be applied to all q-space sampling schemes, making it suitable for multi-shell acquisitions when unwanted gradient non-linearities are present.Here, these different methods are compared under different signal-to-noise (SNR) realizations. With sufficiently dense sampling points (61points per shell), and isotropically-distributed sampling vectors, all methods give comparable results, (accuracy of MAP-MRI-based estimates being slightly higher albeit with slightly elevated bias as b-value increases). As the SNR and number of data points per shell are reduced, MAP-MRI-based approaches give pronounced improvements in accuracy over the other methods.

Global High-Resolution Magnetic Field Inversion Using Spherical Harmonic Representation of Tesseroids as Individual Sources

In this study, we present a novel approach combining the advantages of tesseroids in representing geophysical structures though their voxel-like discretization features with a spherical harmonic representation of the magnetic field. Modelling of the Earth lithospheric magnetic field is challenging since part of the spectra is hidden by the core field and the forward modeled field of a lithospheric magnetization is always biased by the spectral range used. In our approach, a spherical harmonic representation of the magnetic field of spherical prisms (tesseroids) is used for high-resolution magnetic inversion of lithospheric field models. The use of filtered spherical harmonic models of the magnetic field of each tesseroid ensures that the resulting field matches the spectral range of the input data. For the inversion, we use the projected gradient method. The projected gradient method easily allows us to assign an initial guess (i.e., a-priori assumption) for the inversion and avoids negative values of susceptibilities. The latter is providing more plausible models since induced magnetization is assumed to be dominant over the continents and, for the oceans, a remanence model can be subtracted. We show an application of the technique to a synthetic dataset and a satellite-derived lithospheric field model where the model geometry is based on seismic information. We also demonstrate a proof-of-concept for high-resolution tile-wise inversion for the Bangui anomaly in Africa.

A comparison study of tidal prediction techniques for applications in the German Bight

<p>The harmonic representation of inequalities (HRoI) is a technique for tidal analysis and prediction. The HRoI has been used at BSH for over six decades to calculate heights and times of high and low waters for German tide tables. In its original form, it is tailored to predict the vertices of semi-diurnal tides. A more generalized version of the HRoI allows analysing the full tidal curve at equal fractions of the mean lunar day. We compare results from the HRoI with other tidal analysis techniques, e.g. the common harmonic method, for locations in the German Bight. The study includes several tide gauges in the rivers Ems, Weser and Elbe. Short durations of rise and rapid water level changes after low water often characterize the tide curves in these rivers and pose challenges to tidal predictions.</p>

Reassessment of long-period constituents for tidal predictions along the German North Sea coast and its tidally influenced rivers

The harmonic representation of inequalities (HRoI) is a procedure for tidal analysis and prediction that combines aspects of the non-harmonic and the harmonic method. With this technique, the deviations of heights and lunitidal intervals, especially of high and low waters, from their respective mean values are represented by superpositions of long-period tidal constituents. This article documents the preparation of a constituents list for the operational application of the harmonic representation of inequalities. Frequency analyses of observed heights and lunitidal intervals of high and low water from 111 tide gauges along the German North Sea coast and its tidally influenced rivers have been carried out using the generalized Lomb–Scargle periodogram. One comprehensive list of partial tides is realized by combining the separate frequency analyses and by applying subsequent improvements, e.g. through manual inspections of long time series data. The new set of 39 partial tides largely confirms the previously used set with 43 partial tides. Nine constituents are added and 13 partial tides, mostly in the close neighbourhood of strong spectral components, are removed. The effect of these changes has been studied by comparing predictions with observations from 98 tide gauges. Using the new set of constituents, the standard deviations of the residuals are reduced on average by 2.41 % (times) and 2.30 % (heights) for the year 2016. The new set of constituents will be used for tidal analyses and predictions starting with the German tide tables for the year 2020.

Reassessment of long-period constituents for tidal predictions along the German North Sea coast and its tidally influenced rivers

The Harmonic Representation of Inequalities is a method for tidal analysis and prediction. With this technique, the deviations of heights and lunitidal intervals, especially of high and low waters, from their respective mean values are represented by superpositions of long-period tidal constituents. This study documents the preparation of a constituents list for the operational application of the Harmonic Representation of Inequalities. Frequency analyses of observed heights and lunitidal intervals of high and low water from 111 tide gauges along the German North Sea coast and its tidally influenced rivers have been carried out using the generalized Lomb-Scargle periodogram. One comprehensive list of partial tides is realized by combining the separate frequency analyses and by applying subsequent improvements, e.g. through manual inspections of long-time data. The new set of 39 partial tides largely confirms the previously used set with 43 partial tides. Nine constituents are added and 13 partial tides, mostly in close neighbourhood of strong spectral components, are removed. The effect of these changes has been studied by comparing predictions with observations from 98 tide gauges. Using the new set of constituents, the standard deviations of the residuals are reduced by 2.41 % (times) and 2.30 % (heights) for the year 2016. The new set of constituents is used for tidal analyses and predictions starting with the German tide tables for the year 2020.