The spacetime gravitational field of a deformable body

The high-resolution analysis of orbit perturbations of terrestrial artificial satellites has documented that the eigengravitation of a massive body like the Earth changes in time, namely with periodic and aperiodic constituents. For the space-time variation of the gravitational field the action of internal and external volume as well as surface forces on a deformable massive body are responsible. Free of any assumption on the symmetry of the constitution of the deformable body we review the incremental spatial (“Eulerian”) and material (“Lagrangean”) gravitational field equations, in particular the source terms (two constituents: the divergence of the displacement field as well as the projection of the displacement field onto the gradient of the reference mass density function) and the `jump conditions' at the boundary surface of the body as well as at internal interfaces both in linear approximation. A spherical harmonic expansion in terms of multipoles of the incremental Eulerian gravitational potential is presented. Three types of spherical multipoles are identified, namely the dilatation multipoles, the transport displacement multipoles and those multipoles which are generated by mass condensation onto the boundary reference surface or internal interfaces. The degree-one term has been identified as non-zero, thus as a “dipole moment” being responsible for the varying position of the deformable body's mass centre. Finally, for those deformable bodies which enjoy a spherically symmetric constitution, emphasis is on the functional relation between Green functions, namely between Fourier-/ Laplace-transformed volume versus surface Love-Shida functions (h(r),l(r) versus h ^′(r),l ^′(r)) and Love functions k(r) versus k ^′(r). The functional relation is numerically tested for an active tidal force/potential and an active loading force/potential, proving an excellent agreement with experimental results. Received: December 1995 / Accepted: 1 February 1997     

The truth about Ground Truth

This paper presents a critical appreciation of the book edited by Pickles called Ground Truth . It offers a response in defence of GIS, written from the perspective of a quantitative geographer's unavoidably academic view of the strengths and weaknesses of GIS and Ground Truth. In essence, there is a growing need for a multi-partisan approach to improving rather than rubbishing a geoinformation technology that is an expanding global industry of considerable relevance both to the present and to the future.     

Multiplotting With Images from the Kodak DCS420 Digital Camera

This paper explores the potential of a digital camera to produce multiple images suitable for plotting. The objective was to build a three dimensional database by linking triangulated images from a Kodak DCS420 digital camera with a computer aided measurement system. The system then supplied X, Y, Z data from x, y image co-ordinates captured off two or more images. Relative accuracy in object space was around 1;50 000.     

Innovations in Automation for Vision Metrology Systems

The advantages of vision metrology (VM) systems over their film-based counterparts, in terms of the degree of automation within the measurement process, were initially confined to the image mensuration stage. Of late, however, the potential of significantly raising the level of automation of offline and real time VM systems has been more fully exploited, to the point where full automation of the offline procedure has been realized. Innovative features such as automatic image point identification via coded targets, exterior orientation through automatically recognizable "control" groupings of target points, determination of image point correspondences within unlabelled point clouds, and real time tracking of multipoint, handheld measurement probes are now incorporated in industrial VM systems. Another significant innovation is the development of "smart" cameras with incorporated image processing and measurement capabilities which remove the necessity for transmitting image data to the host computer. This paper reviews recent innovations in automation and discusses their operational impact on practical VM applications. The concepts discussed are illustrated through reference to a modern VM system which supports offline and real time measurement.     

An integrated approach for ground water investigation in part of Fatehpur Sikri of district agra-a case study

The Fatehpur Sikri area infringing the western UP, Rajasthan border was investigated for its water supply crisis in respect of poor quality and quantity as well. The study has indicated presence of two parallel quartz reefs running in NE-SW direction. Geohydrological and photogeological studies have revealed the possibility of subsurface extension of quartz reefs. However, this weathered area along reefs is promising water bearing zone. Paleo channels are also marked during studies and the area found suitable for ground water exploitation. A map showing various categories is also presented.     

Relative utility of Landsat-TM and MSS data small scale soil mapping

The Landsat MSS and TM data in the form of false colour composite (FCC) prints at 1∶250,000 scale over parts of Mirzapur (U.P.) and Rohtas district of (Bihar) were interpreted monoscopically in concert with the collateral data and limited field check for soilscape boundary delineation. The study has revealed that at the mapping scale, except for improved image contrast and capturing features of relatively smaller dimensions, no additional advantage has been noticed with TM data over MSS data with respect to exhibition of soilscape boundaries. However, the capability of TM data to withstand enlargement upto 1∶50,000 which is not feasible with MSS data is an additional feature from soil mapping viewpoint.     

The ellipsoidal corrections to the topographic geoid effects

The topographic effects by Stokes formula are typically considered for a spherical approximation of sea level. For more precise determination of the geoid, sea level is better approximated by an ellipsoid, which justifies the consideration of the ellipsoidal corrections of topographic effects for improved geoid solutions. The aim of this study is to estimate the ellipsoidal effects of the combined topographic correction (direct plus indirect topographic effects) and the downward continuation effect. It is concluded that the ellipsoidal correction to the combined topographic effect on the geoid height is far less than 1 mm. On the contrary, the ellipsoidal correction to the effect of downward continuation of gravity anomaly to sea level may be significant at the 1-cm level in mountainous regions. Nevertheless, if Stokes formula is modified and the integration of gravity anomalies is limited to a cap of a few degrees radius around the computation point, nor this effect is likely to be significant.AcknowledgementsThe author is grateful for constructive remarks by J Ågren and the three reviewers.     

Response of GPS occultation signals to atmospheric gravity waves and retrieval of gravity wave parameters

We show that the amplitude of the Global Positioning System (GPS) signals in the radio occultation (RO) experiments is an indicator of the activity of the gravity waves (GW) in the atmosphere. The amplitude of the GPS RO signals is more sensitive to the atmospheric wave structures than is the phase. Early investigations used only the phase of the GPS occultation signals for statistical investigation of the GW activity in the height interval 10–40 km on a global scale. In this study, we use the polarization equations and Hilbert transform to find the 1-D GW radio image in the atmosphere by analyzing the amplitude of the RO signal. The radio image, also called the GW portrait, consists of the phase and amplitude of the GW as functions of height. We demonstrate the potential of this method using the amplitude data from GPS/Meteorology (GPS/MET) and satellite mission Challenge Mini-satellite Payload (CHAMP) RO events. The GW activity is nonuniformly distributed with the main contribution associated with the tropopause and the secondary maximums related to the GW breaking regions. Using our method we find the vertical profiles of the horizontal wind perturbations and its vertical gradient associated with the GW influence. The estimated values of the horizontal wind perturbations are in fairly good agreement with radiosonde data. The horizontal wind perturbations v(h) are ±1 to ±5 m s with vertical gradients dv/dh ±0.5 to ±15 m s km at height 10–40 km. The height dependence of the GW vertical wavelength was inferred through the differentiation of the GW phase. Analysis of this dependence using the dispersion relationship for the GW gives the estimation of the projection of the horizontal background wind velocity on the direction of the GW propagation. For the event considered, the magnitude of this projection changes between 1.5 and 10 m s at heights of 10–40 km. We conclude that the amplitude of the GPS occultation signals contain important information about the wave processes in the atmosphere on a global scale.     

Uniting space, ground, and underwater measurements for improved estimates of rain rate

Global precipitation is monitored from a variety of platforms including spaceborne, ground-, and ocean-based platforms. Intercomparisons of these observations are crucial to validating the measurements and providing confidence for each measurement technique. Probability distribution functions of rain rates are used to compare satellite and ground-based radar observations. A preferred adjustment technique for improving rain rate distribution estimates is identified using measurements from ground-based radar and rain gauges within the coverage area of the radar. The underwater measurement of rainfall shows similarities to radar measurements, but with intermediate spatial resolution and high temporal resolution. Reconciling these different measurement techniques provides understanding and confidence for all of the methods.     

An update on the IEM surface backscattering model

The integral equation approach to modeling scattering from rough surfaces was introduced in 1992. At that time, it was noted that there was a need to find a transition reflection coefficient that could change its argument from the incident angle to the specular angle as frequency or roughness scale got large. One such reflection coefficient was published in 2001. In this letter, we would like to include this reflection coefficient in the integral equation model to interpret several multifrequency backscattering measurements from surfaces with surface parameters defined by the investigators who acquired the data.