Calculating apparent dip from true dip

Apparent dip is the inclination of a bed measured in a vertical section that is not perpendicular to the strike. It is always smaller than the true dip.

Formula

Let $\delta$ be the true dip, and $\alpha$ be the horizontal angle between the strike line and the direction (section line) in which the apparent dip $\delta_a$ is wanted.

$$\tan \delta_a = \tan \delta \times \sin \alpha$$

Derivation

        strike
   A --------------- B
    \      |       /
     \     | h(depth)
      \    |
       C ------- D
   true dip: CD is perpendicular to strike

Take a point on the strike line at height 0 and go a horizontal distance $x$ in the apparent-dip direction. The bed falls by $h$.

• Along the true-dip direction (perpendicular to strike): the horizontal distance is $d = x\sin\alpha$ for the same fall $h$, so $\tan\delta = h/d$.
• Along the apparent-dip direction: $\tan\delta_a = h/x$.
• Hence $\tan\delta_a = \tan\delta \cdot d/x = \tan\delta \sin\alpha$.

Procedure

1. Measure strike and true dip from the compass.
2. Measure the bearing of the section line and find $\alpha$ = difference between the two bearings (use the acute angle).
3. Apply the formula and take the inverse tangent.

Example

True dip = 30°, section line makes $\alpha = 45°$ with the strike.

$$\tan \delta_a = \tan 30° \times \sin 45° = 0.5774 \times 0.7071 = 0.4082 \Rightarrow \delta_a = 22.2°$$

Check: for $\alpha = 90°$, $\delta_a = \delta$ (true dip); for $\alpha = 0°$ (along the strike), $\delta_a = 0°$.