Structural Geology

Stereographic Projection & Apparent Dip

Plot planes and lines on the stereonet and convert true dip to the apparent dip seen in any cross-section or mine drift.

PART 1

Topic Breakdown & Traps

The Engineering Principle

Orientations of planes and lines are analysed on a stereonet (equal-area Schmidt net). A plane plots as a great circle; its pole (normal) plots as a single point. The true dip is the steepest inclination on a plane, measured perpendicular to strike. In any other vertical section the bed appears gentler — the apparent dip — given by

tan δ_{a pp} = tan δ_{t r u e} sin β

, where

β

is the angle between the section line and the strike. When

β = 9 0^{\circ}

(section ⟂ strike) the apparent dip equals the true dip.

The Core Formula Matrix

Apparent dip:

tan δ_{a pp} = tan δ_{t r u e} sin β

(

β

= angle between section line and strike).

Dip direction (right-hand rule): strike

+ 9 0^{\circ}

.

True thickness (horizontal traverse ⟂ strike, width

w

t = w sin δ

A bed dipping 45° plotted as a great circle.

The ‘IIT Traps’

⚠
Apparent ≤ true. The apparent dip is always smaller than (or equal to) the true dip.
⚠
β from strike, not dip direction. $β$ is measured from the strike line; mixing it with the dip direction inverts the sine.
⚠
Plane = great circle; pole = point. Don't plot a plane as a point.

📚 Standard references

The Mapping of Geological Structures — K.R. McClay
An Outline of Structural Geology — Hobbs, Means & Williams

PART 2

Progressive 3-Tier Question Suite

Q1MEDIUM2 Marks · NAT

A bed has a true dip of

4 5^{\circ}

. In a vertical section making

3 0^{\circ}

with the strike, the apparent dip is _____ degrees.

Section at 30° to strike.

Q2BASIC1 Mark · MCQ

On a stereonet, a dipping plane is represented by a

Q3HARD2 Marks · NAT

A bed dipping

3 0^{\circ}

crops out across a horizontal width of

500

m perpendicular to strike. Its true thickness is _____ m.