Apparent dip in cross-section drawing

True dip

The true dip is the maximum inclination of a bed to the horizontal, measured in a direction perpendicular to the strike.

Apparent dip

The apparent dip is the inclination of the bed measured along any direction other than the true dip direction. It is smaller than the true dip and is related by $\tan \delta_a = \tan \delta \sin\alpha$, where $\alpha$ is the angle between the strike and the section line.

Why apparent dip is needed in a cross-section

A geological cross-section is a vertical slice along a chosen line. The bed in this slice shows only the dip that exists in the direction of the section line.

• If the section line is perpendicular to the strike, the section shows the true dip.
• If the line is oblique to the strike, the bed in the section has the apparent dip. Drawing the true dip there would make the bed too steep, so the thickness, depth and position of the bed at depth would be wrong.

 Plan:        strike
        ----------------
          \ alpha |
           \      | true dip direction
 section    \     v
 line  -------> (apparent dip direction)

 Section along oblique line:
   true dip 40 deg (wrong)  /|
   apparent dip 22.8 (correct)/__|

Illustration by numbers

True dip = 40°, section line at $\alpha = 30°$ to the strike.

$$\tan\delta_a = \tan 40° \times \sin 30° = 0.8391 \times 0.5 = 0.4195 \Rightarrow \delta_a = 22.8°$$

If the true dip of 40° were drawn, the bed would reach a depth much greater than the real depth, so a wrong depth of the rock bed is predicted for a tunnel or foundation. For $\alpha = 60°$ the apparent dip is 36.0°, and for $\alpha = 90°$ it equals the true dip (40°).

Hence, for oblique sections the apparent dip must be calculated (or taken from a chart or the stereographic net) before drawing the beds.