This is the flat, hand-drawable version of the focal mechanism: a Lambert equal-area (Schmidt) lower-hemisphere projection, exactly what a seismologist plots on a stereonet. Every take-off direction γ̂ on the lower focal hemisphere (colatitude θ from straight-down, azimuth φ from North) maps to one point on the disk at radius ρ = √2·sin(θ/2), angle φ — the same equal-area formula used since the 1950s to plot fold axes, fault poles and earthquake radiation by hand.
Fault normal n̂, slip d̂ — identical double-couple geometry as the 3D version.
Radiation: A(γ̂) = 2 (γ̂·n̂)(γ̂·d̂)
Projection (forward): ρ = √2 sin(θ/2), disk(x,y) = ρ(sinφ, cosφ)
Projection (inverse, per-pixel): θ = 2 asin(ρ/√2), γ̂ = (sinθ cosφ, sinθ sinφ, cosθ) [N,E,Down]
Every pixel inside the unit disk is independently inverse-projected back to a take-off direction γ̂, then colored red (compressional) or cream (dilatational) by the sign of A(γ̂) — this is a per-pixel scalar field on a 2D grid, not a photograph of a rotating sphere. The two curves where A(γ̂)=0 are the nodal planes (fault + auxiliary plane, projected as circular arcs through the rim); P and T axes plot as fixed marker dots. A conservation check: since n̂⊥d̂ always, ∫A dΩ over the whole sphere is exactly zero — the compressional and dilatational lobes always balance.
The probe station sits at a fixed 55° take-off angle from vertical and sweeps azimuth around the rim, reporting the same first-motion polarity a real seismogram's initial P-pulse would show.