= Solution
For a <double-couple seismic source>, measure <P-wave first-motion polarity> signs and use source-to-station takeoff angles from the location and <velocity> model to plot them on a <focal sphere>. Fit the alternating radiation-sign quadrants, optionally adding amplitude ratios and waveform information. The two nodal planes determine a <focal mechanism>, conventionally expressed by <fault strike>, <fault dip> and <fault rake>.
A more general waveform inversion fits a <seismic moment tensor> to several components and stations. Its double-couple part supplies candidate slip and normal <vectors>, but a general moment <tensor> should not be forced to be double-couple without justification. Polarity calibration, near-nodal observations, path effects and takeoff-angle errors limit the result.
\b[Point-source radiation alone interchanges the <fault plane> and auxiliary plane without changing the double couple.] Resolve this <fault-plane ambiguity> using mapped rupture, aftershock geometry, <geodesy> or finite-rupture directivity. A dense set of polarity picks does not by itself remove that fundamental ambiguity.
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