Gravity potential spherical harmonic series

Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested.

Gravity mapping in the southern Weddell Sea region, Antarctica (Scale 1:2 000 000)

New maps of free-air and the Bouguer gravity anomalies on the Weddell Sea sector (70-81° S, 6-75° W) of Antarctica are presented. These maps are based on the first computer compilation of available gravity data collected by ''Sevmorgeologia'' in 1976-89 in the southern Weddell Sea and adjacent coasts of western Dronning Maud Land (WDML) and Coats Land. The accomplished gravity studies comprise airborne observations with a line spacing of about 20 km and conventional measurements at over-the-ice points, which were spaced at 10-30 km and supplemented by seismic soundings. Hence, anomalies on the maps represent mainly large-scale and deep crustal features. The dominant feature in free-air gravity map is a large dipolar gravity anomaly stretching along the continental margin. Following the major grain of seabed morphology this shelf-edge/slope anomaly (SESA) is clearly divided into three segments characterized by diverse anomaly amplitudes, wavelengths and trends. They are associated with continental margins of different geotectonic provinces of Antarctica surrounding the Weddell Sea. Apparent distinctions in the SESA signatures are interpreted as the gravity expression of tectonic, deep crustal structure segmentation of the continental margin. The prominent gravity highs (100-140 mGal) of the shelf edge anomaly mapped along WDML are assumed to represent high-density mantle injections intruded into the middle/lower crust during initial rifting of continental breakup. Enlarged wavelengths and diminished amplitudes of the gravity anomaly westwards, along the Weddell Sea embayment (WSE) margin, reflect a widening of the continental slope and a significant increase in thickness of underlying sediment strata. Low amplitude, negative free-air anomalies in the Filchner-Ronne Ice Shelves (FRIS) contrast sharply with the dominating positive anomalies offshore. This indicates a greater sedimentary thickness of the basin in this area. Crustal response to the enlarged sediment load is impressed in mostly positive features of the Bouguer gravity field observed here. Two pronounced positive Bouguer anomalies of 50-70 mGal and an average widths of 200 km dominate the Weddell Sea embayment margins towards the Antarctic Peninsula and the East Antarctic craton. They correlate well with very deep seabed troughs (> 1000 m below sea level). The gravity highs are most likely caused by a shallow upper mantle underneath graben-rift structures evolved at the margins of the WSE basin. A regional zone (> 100 km in width) of the prominent Bouguer and free-air negative anomalies (-40 to -60 mGal) adjacent Coats Land to the north of the ice shelf edge may indicate the presence of the thick old cratonic crust far offshore beneath the Weddell Sea Embayment.

Mean dynamic topography and oceanographic parameters estimated from an inverse model and satellite geodesy, with link to model result in one single NetCDF file (392 MB), including the inverse data error covariance

Geostrophic surface velocities can be derived from the gradients of the mean dynamic topography-the difference between the mean sea surface and the geoid. Therefore, independently observed mean dynamic topography data are valuable input parameters and constraints for ocean circulation models. For a successful fit to observational dynamic topography data, not only the mean dynamic topography on the particular ocean model grid is required, but also information about its inverse covariance matrix. The calculation of the mean dynamic topography from satellite-based gravity field models and altimetric sea surface height measurements, however, is not straightforward. For this purpose, we previously developed an integrated approach to combining these two different observation groups in a consistent way without using the common filter approaches (Becker et al. in J Geodyn 59(60):99-110, 2012, doi:10.1016/j.jog.2011.07.0069; Becker in Konsistente Kombination von Schwerefeld, Altimetrie und hydrographischen Daten zur Modellierung der dynamischen Ozeantopographie, 2012, http://nbn-resolving.de/nbn:de:hbz:5n-29199). Within this combination method, the full spectral range of the observations is considered. Further, it allows the direct determination of the normal equations (i.e., the inverse of the error covariance matrix) of the mean dynamic topography on arbitrary grids, which is one of the requirements for ocean data assimilation. In this paper, we report progress through selection and improved processing of altimetric data sets. We focus on the preprocessing steps of along-track altimetry data from Jason-1 and Envisat to obtain a mean sea surface profile. During this procedure, a rigorous variance propagation is accomplished, so that, for the first time, the full covariance matrix of the mean sea surface is available. The combination of the mean profile and a combined GRACE/GOCE gravity field model yields a mean dynamic topography model for the North Atlantic Ocean that is characterized by a defined set of assumptions. We show that including the geodetically derived mean dynamic topography with the full error structure in a 3D stationary inverse ocean model improves modeled oceanographic features over previous estimates.

(Table 2) Chemical composition of quenched glasses from the Mohns and Knipovich Ridges

The aim of this project was a petrogeochemical study of igneous rocks in the areas of the Mohns and Knipovich Ridges, both being the northern extensions of the Mid-Atlantic Ridge (MAR), using data available for quenching glass samples collected during Cruises 36 and 38 of R/V Akademic Mstislav Keldysh and during Cruise 15 of R/V Professor Logachev. Results of igneous rock studying from the Mohns and Knipovich Ridges at the background of evolution of the total North Atlantic Province, which had been identified earlier from tectonic and geophysical data, showed that igneous rocks of the Knipovich Ridge can be ranked as shallow tholeiites, primary melts of which were relatively rich in Na and Si and poor in Fe. This type of magma is characteristic of colder regions of the oceanic lithosphere. Its occurrence in the Knipovich Ridge and its potential propagation up to the Gakkel Ridge suggest that igneous rocks of this region originated under conditions of passive spreading in contrast to the MAR region in vicinity of Iceland and Azores, where substantial contribution of hotter material of a rising plume contributed to formation of the oceanic crust. The North Atlantic Ocean is the youngest province in terms of ocean-floor opening. Geologically and geophysically it is one of well studied regions of the World Ocean. Nevertheless some basic key items of its origin still remain to be clarified. In 1975 Scatler et al. proved specifics of this region manifested in growth of the gravity field, and also in relative height of the ocean floor in the region of 33-70°N, which was associated by them with rise of the hotter mantle, as compared with common regions of the Mid-Atlantic Ridge. Later this view was confirmed by character of magmatism, which differed in depth of generation and by melting degree of the resulting primary magma. Uniqueness of the North Atlantic region was also proved by the fact that this region was marked by extensive geochemical anomalies associated with Azores, Iceland, and Jan Mayen. All of these data allow to consider the northern part of the MAR (north of 33°N) as an united global geotectonic province. The Mohns and Knipovich Ridges located north of Iceland locate at the northern end of this province. This is the least known region. Therefore, new data for ridge areas of 73-77°N are needed for more complete geologic history of the Arctic Basin. The aim of this study was to carry out a complex comparison of magmatism at the Mohns and Knipovich Ridges with magmatism at large segments of the MAR northern province and to reconstruct mechanisms of primary magma formation, as well as conditions of their fractionation. This paper was based on results of studying quenched glasses, which reflect evolution of melt in the course of its formation.

Ice loss in the Canadian Arctic Archipelago

Though much attention has been focused in recent years on the melting of ice from Greenland and Antarctica, nearly half of the ice volume currently being lost to the ocean is actually coming from other mountain glaciers and ice caps. Ice loss from a group of islands in northern Canada accounts for much of that volume. In a study published in April 2011 in the journal Nature, a team of researchers led by Alex Gardner of the University of Michigan found that land ice in both the northern and southern Canadian Arctic Archipelago has declined sharply. The maps above show ice loss from surface melting for the northern portion of the archipelago from 2004-2006 (left) and 2007-2009 (right). Blue indicates ice gain, and red indicates ice loss. In the six years studied, the Canadian Arctic Archipelago lost an average of approximately 61 gigatons of ice per year. (A gigaton is a billion tons of ice.) The research team also found the rate of ice loss was accelerating. From 2004 to 2006, the average mass loss was roughly 31 gigatons per year; from 2007 to 2009, the loss increased to 92 gigatons per year. Gardner and colleagues used three independent methods to assess ice mass, all of which showed the same trends. The team used a model to estimate the surface mass balance of ice and the amount of ice discharged. They also compiled and analyzed measurements from NASA's Ice, Cloud and Land Elevation Satellite (ICESat) to assess changes in the surface height of ice. Finally, they gathered observations from NASA's Gravity Recovery and Climate Experiment (GRACE) to determine changes in the gravity field in the region, an indicator of the amount of ice gained or lost. The Canadian Arctic Archipelago generally receives little precipitation, and the amount of snowfall changes little from year to year. But the rate of snow and ice melting varies considerably, so changes in ice mass come largely from changes in summertime melt. During the 2004 to 2009 study period, the Canadian Arctic Archipelago experienced four of its five warmest years since 1960, likely fueling the melting. Gardner notes that from 2001 to 2004, the sum of melting from all mountain glaciers and ice caps around the world (but not the Greenland and Antarctic ice sheets) contributed an estimated 1 millimeter per year to global sea level rise. Recent estimates suggest the Greenland and Antarctic ice sheets add another 1.3 millimeters per year to sea level. "This means 1 percent of the land ice volume-mountain glaciers and ice caps-account for about half of all ice loss to the world's oceans," Gardner said. "Most of the ice loss is coming from the Canadian Arctic Archipelago, Alaska, Patagonia, the Himalayas, and the smaller ice masses surrounding the main Greenland and Antarctic ice sheets."

Code and readme of a MATLAB-based graphical user interface program for computing functionals of the geopotential

We present a novel graphical user interface program GrafLab (GRAvity Field LABoratory) for spherical harmonic synthesis (SHS) created in MATLAB®. This program allows to comfortably compute 38 various functionals of the geopotential up to ultra-high degrees and orders of spherical harmonic expansion. For the most difficult part of the SHS, namely the evaluation of the fully normalized associated Legendre functions (fnALFs), we used three different approaches according to required maximum degree: (i) the standard forward column method (up to maximum degree 1800, in some cases up to degree 2190); (ii) the modified forward column method combined with Horner's scheme (up to maximum degree 2700); (iii) the extended-range arithmetic (up to an arbitrary maximum degree). For the maximum degree 2190, the SHS with fnALFs evaluated using the extended-range arithmetic approach takes only approximately 2-3 times longer than its standard arithmetic counterpart, i.e. the standard forward column method. In the GrafLab, the functionals of the geopotential can be evaluated on a regular grid or point-wise, while the input coordinates can either be read from a data file or entered manually. For the computation on a regular grid we decided to apply the lumped coefficients approach due to significant time-efficiency of this method. Furthermore, if a full variance-covariance matrix of spherical harmonic coefficients is available, it is possible to compute the commission errors of the functionals. When computing on a regular grid, the output functionals or their commission errors may be depicted on a map using automatically selected cartographic projection.

Geology, geochemistry, and mineralogy of sediments from the Trans Indian Ocean Geotraverse

The monograph is devoted to the main results of research on the Trans Indian Ocean Geotraverse from the Maskarene Basin to the north-western margin of Australia. These results were obtained by Russian specialists and together with Indian specialists during 15 years of cooperation in investigation of geological structure and mineral resources of the Indian Ocean. The monograph includes materials on information support of marine geological and geophysical studies, composition and structure of information resources on the Indian Ocean, bathymetry and geomorphology, structure and geological nature of the magnetic field, gravity field, plate tectonics, crustal structure and sedimentary cover, seismic stratigraphy, perspectives for detecting oil and gas, solid minerals, sediment composition, composition and properties of clay minerals, stratigraphy and sediment age, chemical composition of sediments, composition of and prospects for solid minerals.

Atmospheric, oceanic and hydrological polar motion excitation mechanisms based on a combination of geometric and gravimetric space observations

The goal of our study is to determine accurate time series of geophysical Earth rotation excitations to learn more about global dynamic processes in the Earth system. For this purpose, we developed an adjustment model which allows to combine precise observations from space geodetic observation systems, such as Satellite Laser Ranging (SLR), Global Navigation Satellite Systems (GNSS), Very Long Baseline Interferometry (VLBI), Doppler Orbit determination and Radiopositioning Integrated on Satellite (DORIS), satellite altimetry and satellite gravimetry in order to separate geophysical excitation mechanisms of Earth rotation. Three polar motion time series are applied to derive the polar motion excitation functions (integral effect). Furthermore we use five time variable gravity field solutions from Gravity Recovery and Climate Experiment (GRACE) to determine not only the integral mass effect but also the oceanic and hydrological mass effects by applying suitable filter techniques and a land-ocean mask. For comparison the integral mass effect is also derived from degree 2 potential coefficients that are estimated from SLR observations. The oceanic mass effect is also determined from sea level anomalies observed by satellite altimetry by reducing the steric sea level anomalies derived from temperature and salinity fields of the oceans. Due to the combination of all geodetic estimated excitations the weaknesses of the individual processing strategies can be reduced and the technique-specific strengths can be accounted for. The formal errors of the adjusted geodetic solutions are smaller than the RMS differences of the geophysical model solutions. The improved excitation time series can be used to improve the geophysical modeling.

Improved geoid solution for the Weddell Sea region

We present a geoid solution for the Weddell Sea and adjacent continental Antarctic regions. There, a refined geoid is of interest, especially for oceanographic and glaciological applications. For example, to investigate the Weddell Gyre as a part of the Antarctic Circumpolar Current and, thus, of the global ocean circulation, the mean dynamic topography (MDT) is needed. These days, the marine gravity field can be inferred with high and homogeneous resolution from altimetric height profiles of the mean sea surface. However, in areas permanently covered by sea ice as well as in coastal regions, satellite altimetry features deficiencies. Focussing on the Weddell Sea, these aspects are investigated in detail. In these areas, ground-based data that have not been used for geoid computation so far provide additional information in comparison with the existing high-resolution global gravity field models such as EGM2008. The geoid computation is based on the remove-compute-restore approach making use of least-squares collocation. The residual geoid with respect to a release 4 GOCE model adds up to two meters and more in the near-coastal and continental areas of the Weddell Sea region, also in comparison with EGM2008. Consequently, the thus refined geoid serves to compute new estimates of the regional MDT and geostrophic currents.

Mean dynamic topography of the North Indian Ocean

A satellite-only Mean Dynamic Topography (MDT) of the North Indian Ocean is estimated from the DIRR5 geoid and CNES_CLS11 mean sea surface (Schaffer et al. 2012). DIRR5 geoid is estimated from the latest release (Release 5) of GOCE gravity data according to previous studies (e.g., Johannessen et al. 2003; Raj, 2014). Note that this MDT estimated is referenced to a time period of 7 years (1993-1999). A correction data obtained from AVISO is later used to convert the MDT to a time reference of 20 years (1993-2012). More details are given in Raj (2016).

Magnetic and gravity measurements on North-South profiles across the Grosse Meteor Bank, North Atlantic

During the first section of the "Meteor" cruise No. 2 a profile was run from the Azores to the south across the flanks of the Mid-Atlantic Ridge with a chain of seamounts. The profile extended between the Cruiser (living) and the Hyeres seamounts, which, according to our soundings, form a connected massif, and across the centre of the Grosse Meteor Bank (30°N, 28.5 °W). These seamounts rise from a depth of more than 4000 m up till close to the surface of the sea forming there a large almost flat plateau. In the case of the Grosse Meteor Bank, this plateau has a N-S extension of approx. 30 nautical miles and an E-W extension of approx. 20 nautical miles and reaches a height of 275 m in water depth. The gravity measurements yielded a density of the topographic masses of 2.6 g/cm**3 for the Grosse Meteor Bank. Magnitude and shape of the measured free-air anomaly are very well shown in a model computation with this density. The theoretical gravity effects of the seismically detected swell of cristalline rock and of the Moho depression (mountain root) are not indicated by the observational data. It can, therefore, be assumed that the latter two neutralize each other. It seems, accordingly, that there is no local isostatic compensation of the topographic masses. Hence, the density of 2.6 g/cm**3 obtained would be about the true density of rock. In connection with the mean velocity of P waves (Aric et al., 1968) obtained by seismic refraction methods it must be concluded that the material of the 1200-4000 m thick surface layer of the Grosse Meteor Bank consists of consolidated sediments. This finding is supported by the total intensity of the Earth's magnetic field over the Grosse Meteor Bank. On the assumption of a homogeneous magnetization in the direction of the present Earth's field, the computed anomaly of the massif deviates considerably from the measured anomaly while the magnetic field of the seismically detected crystalline body is capable of interpreting the observed data. Deviating from the prevailing interpretation of the seamounts' plateau as a volcanic cone with submarine abrasion, the Grosse Meteor Bank and the seamounts in the vicinity are assumed to be of continental origin. The questions whether these seamounts submerged later on or whether the sealevel has risen subsequently are, therefore, largely nonexistent.