Journal of Surveying Engineering

A high-resolution quartz tiltmeter was developed for measurement of small movements. It is used to record earth deformation during many months. This deformation is due particularly to earth tides. The fast Fourier transform and the least-squares method are used to analyze the groups of waves composing the tilt signal. It is found two groups of waves, diurnal, and semidiurnal are the principal components of this tilt.

Volume calculations based on a digital elevation model (DEM) are widely used instead of traditional handmade cross-sectioning methods on contour maps. Cross sections can be derived from a DEM performed in a computer, when the cross-sectioning method is preferred. Although many studies have been performed on the accuracy of DEM, accuracy of volume calculation based on a DEM is still unfamiliar to users. Therefore, in the concept of this study, accuracies of the DEM based volume calculations are tested on four selected theoretical surfaces for various data patterns. Volume calculations with triangular prisms, rectangular prisms, and cross sections are applied. Rational true errors are derived for the DEM based volume calculations.

By means of constructing equivalent linear problems, Greenfeld (1997) derived closed-form formulas for four- and six-parameter least squares coordinate transformations between two planar systems, so that users can obtain direct solutions on spreadsheets. However, the three- and five-parameter cases cannot be converted to equivalent linear problems for explicit solutions. An alternative approach is developed here to fully utilize the power inside spreadsheets and solve transformation problems more directly and efficiently, without reformulating the problems for linearity. The new approach is insensitive to the number of parameters, and handles the transformation problems in a unified way. It offers not only the full rigor of least squares, but also the simplicity of being completely spreadsheet based, and eliminates the usual linearization and programming requirements on the part of the user. The new method is further extended to three-dimensional conformal transformations, while practical hints on obtaining provisional solutions and fine-tuning solver parameters to avoid numerical hazards are also discussed.

Due to its high spatial resolution, IKONOS imagery has the highest potential for large-scale topographic mapping of the resource satellites currently available. The orthorectification of IKONOS images thus becomes an important task. Since raw image data would, in general, not be provided by the satellite company, we have developed a method that performs the rectification of IKONOS GEO images. The proposed scheme includes the following steps: (1) the correction of relief displacement for ground control points (GCPs); (2) the performing of affine transformation between the ground coordinate system and the image coordinate system; (3) the performing of back projection for each pixel in the orthoimage; (4) the use of digital terrain model to calculate the relief displacement for the pixel in the previous step; and (5) image resampling. The experimental results indicate that the generated orthoimage may reach an accuracy of 2 m, when 6 GCPs are used.

The Delaunay triangulation is a widely appreciated and investigated mathematical model for topographic surface representation. After a brief theoretical description, six possible basic algorithms to construct a Delaunay triangulation are analyzed and properties that can be exploited for multibeam echosounder data processing are investigated. Two concepts will be treated in more depth: the divide-and-conquer construction algorithm and the incremental method. The calculation speed of the divide-and-conquer method makes it an ideal candidate to construct the initial triangulation of multibeam data. Its runtime performance is compared to that of the incremental algorithm to demonstrate this. The algorithm’s merge step appears to be useful also in replacing triangulated areas of existing triangulations by new data. The incremental algorithm does not seem an effective construction method but it can easily be adapted to accommodate insertion of individual vertices into an existing triangulation and as such it is useful for editing purposes.

Zonal analysis in geographic information systems is a useful and convenient tool to study the accuracy of the digital elevation model (DEM) in terms of topographic complexity, which is defined in this paper as the change in terrain slope or slope change. The accuracy of the U.S. Geological Survey 1-degree DEM over two test areas is studied by comparing it with the USGS 7.5-min DEM. The statistical quantities of the DEM errors are studied and modeled using various mathematical functions. It is shown that the standard deviation of the 1-degree DEM can be largely approximated with a linear function of the slope change, while its minimum and maximum errors remain almost unchanged and occur in all slope change zones as a behavior independent of the terrain complexity.