Mathematics and Geomatics Flashcards

The Combined Scale Factor (CSF) used to convert ground distances to grid distances is computed as:

Answer: Grid Scale Factor × Elevation Factor

CSF = Grid Scale Factor × Elevation Factor; it converts ground (surface) distances directly to grid distances.

A random error in surveying measurements is best characterized as:

Answer: Unpredictable in sign and magnitude, following a normal distribution

Random errors are accidental, vary in sign and size, and follow a normal (Gaussian) distribution — they are minimized by redundant observations.

In the method of least squares adjustment, the condition minimized is:

Answer: The sum of the squares of the residuals (v'Pv)

Least squares minimizes Σ(p·v²), the weighted sum of squared residuals, to produce the most probable solution.

The vanishing bearing in a closed traverse survey occurs when the latitude or departure of a course equals zero. If a course has a bearing of N 90°00' E, its latitude is:

Answer: 0.00 ft

Latitude = L × cos(bearing); cos(90°) = 0, so the latitude of a due-east course is zero.

A digital elevation model (DEM) is most commonly used in GIS-based surveying to:

Answer: Represent the bare-earth terrain surface for topographic analysis

A DEM represents the bare-earth surface as a raster grid of elevation values, enabling slope, aspect, watershed, and visibility analyses.

The parallax difference method in stereophotogrammetry is used to determine:

Answer: Elevation differences between points using the change in x-parallax

Height differences are calculated from the difference in x-parallax between the target point and a reference point using the parallax bar formula.

In Bowditch (Compass Rule) traverse adjustment, the correction to each course's latitude is proportional to:

Answer: The length of that course divided by the total traverse perimeter

Bowditch Rule distributes closure errors in proportion to each course's length relative to the total traverse length.