SME
Physical Geology · Problem type
Apparent dip
Use this for “A bed dips 40°. What dip does it show in a road cut 30° from its strike?”
This is an example. Type your own values to start a new problem.
tan(
δₐ
°)
=
tan(
δ
°)
×
sin(
β
°)
Formulas
tan(δₐ°)
=
tan(
δ
°)
×
sin(
β
°)
tan(22.76°) = tan(40°) × sin(30°)
Assumptions
•
β is the angle in map view between the bed’s strike and the section, from 0° to 90°.
•
A section along the dip direction (β = 90°) shows the true dip; any other shows less.
•
Along strike (β = 0°) the bed looks flat, so the apparent dip falls to 0°.
Step-by-step
WE KNOW
δ = 40°, β = 30°
FIND
apparent dip (δₐ)
Step 1 · Find apparent dip (δₐ)
Use tan(δₐ°) = tan(δ°) × sin(β°)
The
section
cuts
the
dip
slope
at
β
,
so
its
slope
is
the
true
slope
tan
δ
shrunk
by
sin
β
.
δₐ
=
tan⁻¹(tan(
δ
°)
×
sin(
β
°))
δₐ = tan⁻¹(tan(40°) × sin(30°))
tan(40°) = 0.8391
sin(30°) = 0.5
0.8391 × 0.5 = 0.4195
δₐ = 22.76°
Check
Put the numbers back in. Both sides should match.
tan(22.76°) = tan(40°) × sin(30°) ✓
← Previous lesson
Geologic structures (folds, faults, strike and dip)
Next lesson →
Thickness of a dipping bed
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