Which tool would primarily be used to establish elevation differences during a survey?

The leveling rod is primarily used to establish elevation differences during a survey because it is specifically designed for this purpose. Typically, a leveling rod is a graduated rod that can be read through a leveling instrument. When used in conjunction with a level or total station, it allows surveyors to determine height differences between points.

The use of a leveling rod provides precise readings of elevation, which is essential for tasks such as establishing grades for land development, construction, and any project requiring accurate elevation data. It is usually held vertically at a point on the ground, and readings are taken from the instrument to accurately determine its elevation relative to other points.

Other tools listed, such as the compass, theodolite, and tape measure, serve different functions in surveying. The compass is mainly for direction and orientation; the theodolite is primarily for measuring horizontal and vertical angles, while the tape measure is used for linear distance measurements. None of these tools directly measure elevation differences as effectively as the leveling rod does.