Groebner-basis solution of the three-dimensional resection problem (P4P)

The three-dimensional (3-D) resection problem is usually solved by first obtaining the distances connecting the unknown point P{X,Y,Z} to the known points P_i{X_i,Y_i,Z_i}i=1,2,3 through the solution of the three nonlinear Grunert equations and then using the obtained distances to determine the position {X,Y,Z} and the 3-D orientation parameters {,, }. Starting from the work of the German J. A. Grunert (1841), the Grunert equations have been solved in several substitutional steps and the desire as evidenced by several publications has been to reduce these number of steps. Similarly, the 3-D ranging step for position determination which follows the distance determination step involves the solution of three nonlinear ranging (`Bogenschnitt') equations solved in several substitution steps. It is illustrated how the algebraic technique of Groebner basis solves explicitly the nonlinear Grunert distance equations and the nonlinear 3-D ranging (`Bogenschnitt') equations in a single step once the equations have been converted into algebraic (polynomial) form. In particular, the algebraic tool of the Groebner basis provides symbolic solutions to the problem of 3-D resection. The various forward and backward substitution steps inherent in the classical closed-form solutions of the problem are avoided. Similar to the Gauss elimination technique in linear systems of equations, the Groebner basis eliminates several variables in a multivariate system of nonlinear equations in such a manner that the end product normally consists of a univariate polynomial whose roots can be determined by existing programs e.g. by using the roots command in Matlab.Acknowledgments.The first author wishes to acknowledge the support of JSPS (Japan Society of Promotion of Science) for the financial support that enabled the completion of the write-up of the paper at Kyoto University, Japan. The author is further grateful for the warm welcome and the good working atmosphere provided by his hosts Professors S. Takemoto and Y. Fukuda of the Department of Geophysics, Graduate School of Science, Kyoto University, Japan.     

Conjoint modeling of residential group preferences: A comparison of the internal validity of hierarchical information integration approaches

 In this paper, two approaches for measuring residential group preferences, based on the method of Hierarchical Information Integration (HII), are compared. In particular, the hypothesis that group-based preference models estimated from integrated HII experiments better predict group preferences than part individual-based group models estimated from classical HII experiments is tested. To that effect, the models' ability to predict group preferences for new residential alternatives is compared in a study of residential preferences of co-ops. Results indicate that integrated HII group experiments indeed result in better predictions of residential preferences.     

GPS network monitors the Western Alps' deformation over a five-year period: 1993–1998

  The Western Alps are among the best studied collisional belts with both detailed structural mapping and also crustal geophysical investigations such as the ECORS and EGT seismic profile. By contrast, the present-day kinematics of the belt is still largely unknown due to small relative motions and the insufficient accuracy of the triangulation data. As a consequence, several tectonic problems still remain to be solved, such as the amount of N–S convergence in the Occidental Alps, the repartition of the deformation between the Alpine tectonic units, and the relation between deformation and rotation across the Alpine arc. In order to address these problems, the GPS ALPES group, made up of French, Swiss and Italian research organizations, has achieved the first large-scale GPS surveys of the Western Alps. More than 60 sites were surveyed in 1993 and 1998 with a minimum observation of 3 days at each site. GPS data processing has been done by three independent teams using different software. The different solutions have horizontal repeatabilities (N–E) of 4–7 mm in 1993 and 2–3 mm in 1998 and compare at the 3–5-mm level in position and 2-mm/yr level in velocity. A comparison of 1993 and 1998 coordinates shows that residual velocities of the GPS marks are generally smaller than 2 mm/yr, precluding a detailed tectonic interpretation of the differential motions. However, these data seem to suggest that the N–S compression of the Western Alps is quite mild (less than 2 mm/yr) compared to the global convergence between the African and Eurasian plate (6 mm/yr). This implies that the shortening must be accomodated elsewhere by the deformation of the Maghrebids and/or by rotations of Mediterranean microplates. Also, E–W velocity components analysis supports the idea that E–W extension exists, as already suggested by recent structural and seismotectonic data interpretation. Received: 27 November 2000 / Accepted: 17 September 2001     

The effects of frequency-dependent quasar variability on the celestial reference frame

We examine the relationship between source position stability and astrophysical properties of radio-loud quasars making up the International Celestial Reference Frame (ICRF2). Understanding this relationship is important for improving quasar selection and analysis strategies, and therefore reference frame stability. We construct flux density time series, known as light curves, for 95 of the most frequently observed ICRF2 quasars at both the 2.3 and 8.4 GHz geodetic very long baseline interferometry (VLBI) observing bands. Because the appearance of new quasar components corresponds to an increase in quasar flux density, these light curves alert us about potential changes in source structure before they appear in VLBI images. We test how source position stability depends on three astrophysical parameters: (1) flux density variability at X band; (2) time lag between flares in S and X bands; (3) spectral index root-mean-square (rms), defined as the variability in the ratio between S and X band flux densities. We find that the time lag between S and X band light curves provides a good indicator of position stability: sources with time lags $<$ 0.06 years are significantly more stable ( $>$ 20 % improvement in weighted rms) than sources with larger time lags. A similar improvement is obtained by observing sources with low $(<$ 0.12) spectral index variability. On the other hand, there is no strong dependence of source position stability on flux density variability in a single frequency band. These findings can be understood by interpreting the time lag between S and X band light curves as a measure of the size of the source structure. Monitoring of source flux density at multiple frequencies therefore appears to provide a useful probe of quasar structure on scales important to geodesy. The observed astrometric position of the brightest quasar component (the core) is known to depend on observing frequency. We show how multi-frequency flux density monitoring may allow the dependence on frequency of the relative core positions along the jet to be elucidated. Knowledge of the position–frequency relation has important implications for current and future geodetic VLBI programs, as well as the alignment between the radio and optical celestial reference frames.     

Satellite remote sensing of forest type and landcover in the subalpine forest region,Kananaskis Valley,Alberta

Landsat Thematic Mapper (TM) imagery and a digital elevation model (DEM) of the Kananaskis Valley in southwestern Alberta have been used to separate three forest types and eight landcover classes with mapping accuracies up to 76% overall. Image transformations based on a principal components analysis (PCA) were used to distinguish vegetation type and separate surface features in visual interpretations, and to reduce the 10 channel data set (TM 1–7, elevation, slope and incidence) to a more manageable 7 channel data set (PCA 1–4, elevation, slope and incidence). The DEM was shown to be critical in providing explanation of surface cover variability even though the original model was produced from medium scale aerial photography on a relatively coarse 100 metre grid. Discrimination increased up to 50% for pure stands of Lodgepole Pine (Pinus contorta Dougl.) and Englemann Spruce (Picea englemanii Parry) based on analysis of 100 pixels in test areas. Overall increases in map accuracy were between 2 and 11%. Success at this level of classification is required prior to detailed ecological study and modelling of mountain vegetation productivity at the community level using current satellite and aerial remote sensing technology.     

EXPERIENCE IN COMPILING LARGE-SCALE MAPS OF EROSION-PRONE AREAS

Specific criteria used in the compilation of large-scale maps of erosion-prone areas are defined and evaluated for tracts of land representing a number of different agricultural cover types. Formulas are derived which facilitate the mapping of such areas based on such readily observable morphometric characteristics as slope length and steepness. Translated by Edward Torrey, Alexandria, VA 22308 from: Vestnik Moskovskogo Universiteta, geografiya, 1988, No. 5, pp. 25-31.     

A global inventory of coral reef stressors based on satellite observed nighttime lights

In this article, we present a satellite-based approach to gather information about the threat to coral reefs worldwide. Three chosen reef stressors – development, gas flaring and heavily lit fishing boat activity – are analysed using nighttime lights data derived from the Defense Meteorological Satellite Program (DMSP) produced at the National Oceanic & Atmospheric Administration, National Geophysical Data Center (NOAA/NGDC). Nighttime lights represent a direct threat to coral reef ecosystems and are an excellent proxy measure for associated human-caused stressors. A lights proximity index (LPI) is calculated, measuring the distance of coral reef sites to each of the stressors and incorporating the stressor's intensity. Colourized maps visualize the results on a global scale. Area rankings clarify the effects of artificial night lighting on coral reefs on a regional scale. The results should be very useful for reef managers and for state administrations to implement coral reef conservation projects and for the scientific world to conduct further research.     

Enriching the semantics of the directed polyline–polygon topological relationships: the $$\mathcal {}$$-intersection matrix

In this paper, we define an intersection matrix for enriching the semantics of the topological relationships between a directed polyline and a polygon. In particular, we propose the \(\mathcal {DLP}\)-intersection matrix which enables us to model the origin and destination points, as well as the right- and left-hand sides of the directed polyline. This matrix overcomes the limitation of the well-known DE-9IM, because it allows the representation of the different dimensions of the intersection results at the same time. Accordingly, the geo-operators have been revised and extended in order to address the notions of right- and left-hand sides of a directed polyline, as well as additional notions related to the orientation of the polyline. The \(\mathcal {DLP}\)-intersection matrix has been implemented by extending the Java Topology Suite methods in order to address the new geo-operators based on the notion of orientation.     

Geodetic intersection on the ellipsoid

Through each of two known points on the ellipsoid a geodesic is passing in a known azimuth. We solve the problem of intersection of the two geodesics. The solution for the latitude is obtained as a closed formula for the sphere plus a small correction, of the order of the eccentricity of the ellipsoid, which is determined by numerical integration. The solution is iterative. Once the latitude is obtained, the longitude is determined without iteration.     

Comparison of Deep Underwater Measurements and Radar Observations of Rainfall

Deep-water acoustical measurements of rainfall are compared to high-resolution ground radar observations for the first time. The measurements of underwater ambient sound were made from a subsurface mooring near Methoni, Greece, in 2004. The acoustical measurements were at 60-, 200-, 1000-, and 2000-m depths. Simultaneous ground-based polarimetric -band radar observations were made over the acoustic mooring. Comparisons show acoustic detection of rain events and storm structure that are in agreement with the radar observations. Results from a comparison between the underwater sound pressure level at different depths and the observed radar reflectivities are presented.