Seismology · Interactive Lecture

Focal Mechanisms

Geometry of earthquake sources — from double couples to beach balls

01 — Interactive

The Beach Ball

Drag sliders to change fault geometry. The lower-hemisphere Wulff projection updates in real time, showing compressional (dark) and dilatational (light) quadrants.

Strike
Dip 90°
Rake
Right-lateral Strike-slip
Presets
P-axis Az.
T-axis Az.
M₀ Proxy
1.0
The nodal planes separate compressional from dilatational first motions. One is the fault plane; the other is the auxiliary plane — seismology alone cannot distinguish them.
02 — Classification

Fault Type Gallery

Click a fault type to explore its beach ball signature and tectonic setting.

Strike-slip (R)

Right-lateral · Transform margins

Strike-slip (L)

Left-lateral · Transform margins

Normal

Extensional · Rifts, MORs

Reverse / Thrust

Compressional · Subduction, collision

03 — First Motions

P-wave First Motion Polarity

Upward first motion (compression) = filled circle; downward (dilatation) = open circle. The pattern constrains the nodal planes.

Compression
Dilatation
SYNTHETIC P-WAVE FIRST MOTIONS
Each trace corresponds to a station. Upward deflection = compression.
04 — Stress Axes

Principal Stress Axes

P

P-axis (Pressure)

Maximum compressive stress. Bisects the compressional (dark) quadrants. Located 45° from both nodal planes.

T

T-axis (Tension)

Maximum tensile stress. Bisects the dilatational (white) quadrants. Perpendicular to the P-axis in the fault plane.

B

B-axis (Null / Intermediate)

Lies along the intersection of the two nodal planes. Perpendicular to both P and T.

The P and T axes are not the principal stresses of the ambient field — they are axes of the moment tensor. Stress inversion from many mechanisms recovers the actual stress tensor.
05 — Anderson's Theory of Faulting

Anderson's Theory of Faulting

Anderson (1905, 1951): the Earth's free surface forces one principal stress to be vertical. The relative magnitude of the vertical stress determines which fault style is favoured.

Thrust / Reverse
σ₁ horizontal · σ₃ vertical
Normal / Extensional
σ₁ vertical · σ₃ horizontal
Strike-slip / Wrench
σ₁ horiz · σ₂ vertical · σ₃ horiz
FAULT ANGLE GEOMETRY (COULOMB)

Faults nucleate at θ = 45°+φ/2 from σ₃ (i.e. 45°−φ/2 from σ₁). Adjust internal friction angle φ to see how fault orientation changes for each tectonic regime.

Friction angle φ 30°
MOHR CIRCLE & COULOMB FAILURE ENVELOPE

Normal stress (σₙ) vs shear stress (τ) on all possible planes. Failure where the circle touches τ = C + μσₙ.

σ₁ 150 MPa
σ₃ 40 MPa
05b — Stress Inversion

Focal Mechanism Ensemble

Add mechanisms consistent with the selected regime. As the ensemble grows, the accumulated pattern reveals the dominant stress configuration — the basis of formal stress tensor inversion.

CURRENT REGIME