Local geoid determination combining gravity disturbances and GPS/levelling: a case study in the Lake Nasser area, Aswan, Egypt

 The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used, as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads. Received: 14 August 2000 / Accepted: 28 February 2001     

New analytical and numerical approaches for geopotential modeling

 The standard analytical approach which is applied for constructing geopotential models OSU86 and earlier ones, is based on reducing the boundary value equation to a sphere enveloping the Earth and then solving it directly with respect to the potential coefficients _n,m . In an alternative procedure, developed by Jekeli and used for constructing the models OSU91 and EGM96, at first an ellipsoidal harmonic series is developed for the geopotential and then its coefficients _n,m ^e are transformed to the unknown _n,m . The second solution is more exact, but much more complicated. The standard procedure is modified and a new simple integral formula is derived for evaluating the potential coefficients. The efficiency of the standard and new procedures is studied numerically. In these solutions the same input data are used as for constructing high-degree parts of the EGM96 models. From two sets of _n,m (n≤360,|m|≤n), derived by the standard and new approaches, different spectral characteristics of the gravity anomaly and the geoid undulation are estimated and then compared with similar characteristics evaluated by Jekeli's approach (`etalon' solution). The new solution appears to be very close to Jekeli's, as opposed to the standard solution. The discrepancies between all the characteristics of the new and `etalon' solutions are smaller than the corresponding discrepancies between two versions of the final geopotential model EGM96, one of them (HDM190) constructed by the block-diagonal least squares (LS) adjustment and the other one (V068) by using Jekeli's approach. On the basis of the derived analytical solution a new simple mathematical model is developed to apply the LS technique for evaluating geopotential coefficients. Received: 12 December 2000 / Accepted: 21 June 2001     

Variation in Coronal Activity from Solar Cycle 24 Minimum to Maximum Using Three-Dimensional Reconstructions of the Coronal Electron Density from STEREO/COR1

Three-dimensional electron density distributions in the solar corona are reconstructed for 100 Carrington rotations (CR 2054?–?2153) during 2007/03?–?2014/08 using the spherically symmetric method from polarized white-light observations with the inner coronagraph (COR1) onboard the twin Solar Terrestrial Relations Observatory (STEREO). These three-dimensional electron density distributions are validated by comparison with similar density models derived using other methods such as tomography and a magnetohydrodynamics (MHD) model as well as using data from the Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph (LASCO)-C2. Uncertainties in the estimated total mass of the global corona are analyzed based on differences between the density distributions for COR1-A and -B. Long-term variations of coronal activity in terms of the global and hemispheric average electron densities (equivalent to the total coronal mass) reveal a hemispheric asymmetry during the rising phase of Solar Cycle 24, with the northern hemisphere leading the southern hemisphere by a phase shift of 7?–?9 months. Using 14 CR (\(\approx13\)-month) running averages, the amplitudes of the variation in average electron density between Cycle 24 maximum and Cycle 23/24 minimum (called the modulation factors) are found to be in the range of 1.6?–?4.3. These modulation factors are latitudinally dependent, being largest in polar regions and smallest in the equatorial region. These modulation factors also show a hemispheric asymmetry: they are somewhat larger in the southern hemisphere. The wavelet analysis shows that the short-term quasi-periodic oscillations during the rising and maximum phases of Cycle 24 have a dominant period of 7?–?8 months. In addition, it is found that the radial distribution of the mean electron density for streamers at Cycle 24 maximum is only slightly larger (by \(\approx30\%\)) than at cycle minimum.     

Scaling procedures for heterogeneous unconfined aquifers

Complex flows in heterogeneous confined and unconfined aquifers is a phenomenon that continues to present difficulties in flow mapping and modelling in the field, laboratory, and through numerical simulations. It is often the case with complicated phenomena that transformative scaling and reduction of the problem through symmetry is of great efficacy in the formation of predictive models in both the laboratory and computational settings. A detailed a study of the application of a broad class of Lie scaling transformations on a set of equations representing the groundwater flows in heterogeneous confined and unconfined aquifers has produced a set of scaling relationships between the spatial variables, hydrologic variables, and parameters. The set of scaling transformations preserve the structure of the equations in the sense that the scaling transformations leave the initial‐boundary value system representing the invariant groundwater flows. This theoretical approach elucidates not only the scaling relationships but also the properties that hydrologic variables and parameters must satisfy in order for calling to be possible. Validation of the theory developed is carried out through a series of four numerical simulations using the USGS modflow ‐2005 software package. The results of these experiments demonstrate that the derived scaling transformations can effectively form predictive models of large‐scale phenomena at small scales with negligible error in many cases. Comments on the limitations of the approach and directions for future research are made in the closing sections. Copyright © 2016 John Wiley & Sons, Ltd.     

Latitude matters: an examination of behavioural plasticity in dietary traits amongst extant and Pleistocene Rangifer tarandus

The geographical distribution of species affects their dietary traits relative to resources available in different latitudes. Dietary traits of Rangifer tarandus, a species with a wide geographical distribution, were investigated using tooth mesowear and microwear methods in eight extant populations from Canada. The data show a latitudinal shift corresponding to a vegetational gradient from the taiga to the tundra, i.e. an increase of lichen consumption from the low to the high latitudes. This pattern is also evidenced in the Pleistocene fossil record of Europe where R. tarandus populations from low latitude localities show a lower consumption of lichen than at higher latitudes.     

Urban seismic stations: soil–structure interaction assessment by spectral ratio analyses

In this work we present and discuss the results of ambient seismic noise analyses computed at four sites where seismic stations, managed by the INGV (Italian Institute for Geophysics and Vulcanology) and the DPC (Italian Department of Civil Protection), are installed inside buildings. The experiments were performed considering different types of installation: sensor located at the bottom of a school, directly installed on rock (case 1); sensor located at the bottom of a medieval fortress, built on an isolate hill, directly installed on rock (case 2); sensor installed on the foundations of a medieval fortress, built on an isolate hill (case 3); sensor installed on the foundations of a school, built on alluvial deposits (case 4). Since recent works proposed the use of spectral ratio techniques to study the dynamic characterization of buildings, ambient seismic-noise measurements were performed for each site close to the stations (at the base of the structures), at the top of the structures and outside the buildings. In order to check the source of vibrations both horizontal to vertical spectral ratio (HVNR) and standard spectral ratio (SSR) techniques were applied. For all stations the results from ambient seismic noise were compared to those obtained from earthquakes (HVSR). In order to detect preferential directions of amplification, for each site average HVNRs and HVSRs were computed considering one azimuth for each set of 5°. We obtain different results for different types of installation: in cases 1 and 2, where the sensors are directly installed on rock, the vibrations of the structure do not affect the noise measures performed close to the stations, which show flat HVNR in the whole frequency range: in both cases the eigenfrequency of the building is given by the HVNR calculated from the measures performed at the top of the structure. In cases 3 and 4, where the sensors are installed on the foundations of the considered structures, both the amplification peaks between 5 and 9 Hz (case 3) and between 5.5 and 7 Hz (case 4) include the contribution of the free oscillations of the buildings. In particular, in case 4, HVNRs performed outside building highlight possible soil–structure resonance effects in case of an earthquake.     

Evaluation of significant sources influencing the variation of physico-chemical parameters in Port Blair Bay,South Andaman,India by using multivariate statistics

Port Blair is the capital city of Andaman & Nicobar Islands, the union territory of India. More than 50% of the population of these islands lives around Port Blair Bay. Therefore the anthropogenic effects in the bay water were studied for monitoring purpose from seven stations. Physico-chemical parameters of seawater were analyzed in samples collected once in every 3 months for 2 years from seven sampling stations located in Port Blair Bay, South Andaman Island to evaluate the spatial and tidal variation. Cluster analysis and factor analysis were applied to the experimental data in an attempt to understand the sources of variation of physico-chemical parameters. In cluster analysis, the stations Junglighat Bay and Phoenix Bay having high anthropogenic influence formed a separate group. The factors obtained from factor analysis indicated that the parameters responsible for physico-chemical variations are mainly related to land run-off, sewage outfall and tidal flow.     

Application of Hilbert‐like transforms for enhanced processing of full tensor magnetic gradient data

Commonly, geomagnetic prospection is performed via scalar magnetometers that measure values of the total magnetic intensity. Recent developments of superconducting quantum interference devices have led to their integration in full tensor magnetic gradiometry systems consisting of planar‐type first‐order gradiometers and magnetometers fabricated in thin‐film technology. With these systems measuring directly the magnetic gradient tensor and field vector, a significantly higher magnetic and spatial resolution of the magnetic maps is yield than those produced via conventional magnetometers. In order to preserve the high data quality in this work, we develop a workflow containing all the necessary steps for generating the gradient tensor and field vector quantities from the raw measurement data up to their integration into high­resolution, low­noise, and artefactless two‐dimensional maps of the magnetic field vector. The gradient tensor components are processed by superposition of the balanced gradiometer signals and rotation into an Earth‐centred Earth‐fixed coordinate frame. As the magnetometers have sensitivity lower than that of gradiometers and the total magnetic intensity is not directly recorded, we employ Hilbert‐like transforms, e.g., integration of the gradient tensor components or the conversion of the total magnetic intensity derived by calibrated magnetometer readings to obtain these values. This can lead to a better interpretation of the measured magnetic anomalies of the Earth's magnetic field that is possible from scalar total magnetic intensity measurements. Our conclusions are drawn from the application of these algorithms on a survey acquired in South Africa containing full tensor magnetic gradiometry data.