Focal Mechanism Diagrams in a Nutshell
Focal Mechanism of an Earthquake
The focal mechanism of an earthquake sums up (1) the slip motion of the rocks underground and (2) the orientation of the fault that the slip occurred on. (See Fault Types in a Nutshell for a quick explanation of the three basic fault types.)
Beachball Earthquake Diagram Explained
The "beachball" earthquake diagram is built from seismograms recorded around an earthquake. The first motion of the arriving P-waves is checked for each seismograph station to see if it's a pushing (upward/away from the source) or a pulling (downward/toward the source) motion. Pushing is compression; pulling is tension. This first-motion information is plotted as it would appear on a hollow half-sphere sunk in the ground and shows what directionboth compass direction and vertical angle these ismic waves left the earthquake focus to reach each station. (The half- sphere is represented on flat paper as an equal-area projection.) Compressions are shown in black, while tensions are marked in white. Both are graphed as circles, which from when viewed from above, create the pattern of a stereotypical beachball. In a well-behaved earthquake with well-recorded data, all the compressions cluster in two opposite quadrants. The same goes for the tensions, which occupy the other two quadrants.
The fault that created the compression and tension runs exactly between the black and white, where tension and compression balance. That's what the top diagrams (A) show, with the compressive areas shown black and tension areas shown white. The motion of the rocks at the source of the earthquake goes from white toward the black. (The P and T axes, shown by dots marking one end, are part of the moment tensor, which is the ultimate boiled-down mathematical description of the earthquake motions. You can ignore them.)
Earthquake Diagram Solutions
The trouble is that there are two solutions to the diagram. There are two planes along which earthquake motions could yield the same seismographic results. One is the real fault plane, whereas the other, called the auxiliary plane, has no physical meaning. Seismographic evidence alone isn't enough to choose the right one. That's why in (B) there are two different slip diagrams shown for each focal mechanism. Usually there are enough clues in the local geology or aftershock patterns to pick the right solution.
Though universities teach this basic earthquake diagram material to geology majors, not every student retains it. Many must consult this diagram several times a year as a refresher. For a much more thorough treatment of the subject including exercises, see this PDF by Vince Cronin of Baylor University, "A Draft Primer on Focal Mechanism Solutions for Geologists."