Fault plane solution
 Gives the orientation of the fault plane and the direction of displacement (slip) on it.
 Based on the radiation pattern, usually of P-waves, from the source. I.e., whether the first
ground motion of the wave is towards the source, dilation (“negative polarity”), or away
from the source, compression (“positive polarity”). Fig. 5.7 in the textbook, Fig. 4.2-4 and
4.2-7b in the book An introduction to seismology, earthquakes, and earth structure by
Stein & Wysession (S&W).
 Two different displacements on two mutually orthogonal planes, the so-called nodal
planes, give the same radiation pattern. One of them is the fault plane, the other is called
the auxiliary plane (and is not a physical plane). Which one of the nodal planes is the fault
plane, is determined from additional information (see below).
 For a P-wave recorded on the vertical instrument at an observatory, dilatation corresponds
to down-motion, and compression corresponds to up-motion. Fig. 4.2-4 (S&W).
 Making a fault plane solution:
1. Introduce the focal sphere, a spherical shell centered at the hypocentre and with a
horizontal equatorial plane. Fig. 5.10 (textbook).
2. Waves arriving at remote observatories intersect the lower hemisphere, whereas those
at nearby observatories intersect the upper hemisphere.
3. For the lower hemisphere: increasing epicentral distance —> decreasing take-off angle
(i.e., angle between ray and vertical at the hypocentre). Fig. 4.2-8 (S&W).
4. An intersection point is given by the take-off angle and the azimuth Ø at the
hypocentre towards the observatory. Ø is the angle, measured clockwise, between
north and the great circle through the hypocentre and the observatory. Fig. 5.10
(textbook).
5. The points of intersection are projected onto the equatorial plane of the focal sphere,
i.e., a horizontal plane through the hypocentre.
6. Usually, each projected point is marked with a plus if the wave had compressional first
motion or a minus in case of dilatational first motion.
7. By using a so-called Schmidt-net, two (if possible) arcs are drawn that separate the
pluses (compression) and minuses (dilatation) into two, three or four quadrants. The
arcs correspond to the projections of the intersections between the nodal planes and
the lower hemisphere. By convention, compressional quadrants are shaded. Fig. 5.9
(textbook); Fig. 4.2-14 and 4.2-17 (S&W).
8. The direction of maximum compressive stress is given by the P-axis (“pressure axis”),
whereas the direction of minimum compressive stress is given by the T-axis (“tension
axis”). The two axes are found by bisecting the dilatational and compressional
quadrants, respectively. Fig. 4.2-16 (S&W).
 The fault plane solution gives two candidates (the nodal planes) for the fault plane. How
to decide which one is the fault plane:
 The fault plane can easily be identified if it breaks the earth’s surface.
 By locating aftershocks; these are usually located on the fault plane.
 By considering the trend of faults in the area and/or fault plane solutions for earlier
earthquakes.