No abstract

No abstract

In this study, mathematical models for the self and relative neighborhoods of spatial point configurations have been proposed. This was intended for data/check elevation point patterns. These models were based on some realized point patterns within an illustrative rectangular geographical window. This window includes the Nile Valley, Eastern Desert and South Sinai in Egypt. The investigated data and check patterns had point elevation values, which were based on the SRTM30 global elevation model. The trends of the neighborhood models agreed with those of the interpolation quality, as expressed in terms of the standard deviation of discrepancies. Moreover, closed expressions were proposed, which relate the terrain interpolation qualities with the relevant neighborhood models. It is recommended to use such criterion for planning the spatial distributions of elevation point patterns in digital terrain modeling.

In this study, some stochastic and deterministic models have been proposed for the assessment of the regularity and isotropy of geodetic point patterns. These models utilized realized point configurations within a rectangular window, leaning on stochastic geometry. As an illustrative example, the geographical extent of the Egyptian Territory was selected as a test window. The proposed models have agreed with the visual and qualitative characteristics of the investigated patterns. Also, it has been found that the stochastic and deterministic models for regularity and isotropy have very strong mutual correlation coefficients. Furthermore, the proposed models were applied to some geoid interpolation algorithms. In particular, the relationships among the data/check point distributions and the geoid interpolation accuracies, were investigated. Finally, a closed expression was proposed, which efficiently describes the relations among such features. So, it is recommended to use such approach for the pre-analysis and planning of the geographic distributions of point patterns in similar and other geodetic applications.

In this paper, the effect of integration cap size on geoid determination was studied, when using gravity disturbances and vertical deflection as input data. For this purpose, a series of varying cap radii was used to predict gravimetric geoidal heights at discrete GPS-Benchmarks, using both the Hotine and deflection-geoid techniques. In both cases, the results showed significant dependence of the resulting geoid accuracy on the integration cap size. The two methods showed comparable behavior in the vicinity of the cap radius, which i s consistent wit? the maximal resolution of the reference geopotential model. At larger cap sizes, the perfomance of the deflection data type was significantly better than the gravity disturbances, which in turn showed a dramatic degradation of the geoid accuracy. Therefore, when solving for the geoid without modifying the integration kemel, it is strongly recommended to nse large cap sizes along with the deflection-geoid method. If gravity disturbances are to be used for geoid determination, then it is recommended to use as small integration cap as possible.