Fault plane solution
Ø Gives the orientation of the fault plane and the direction of displacement (slip) on it.
Ø Is 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”). See 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).
Ø Displacement (slip) on each of two mutually orthogonal planes, the so-called nodal planes, gives the same radiation pattern. One of them is the actual fault plane, the other is called the auxiliary plane (and is not a physical plane). Which one of the nodal planes that is the fault plane, is determined from additional information (see below).
Ø For a P-wave recorded on the vertical instrument at an observatory, dilatation corresponds to down-motion, and compression corresponds to up-motion. See first two slides in ppt-presentation and Fig. 4.2-4 (S&W).
Ø Making a fault plane solution:
1. Introduce the focal sphere, which is a small, 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. The position of 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, using a so-called equal area map projection.
6. Usually, each projected point is marked with a plus or a closed circle if the wave had compressional first motion, or a minus or open circle 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 sectors. The arcs correspond to the projections of the intersections between the nodal planes and the lower hemisphere. By convention, compressional sectors 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 sectors, respectively. Fig. 4.2-16 (S&W).
Ø 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.