1. Fault Plane Solution
Focal Mechanism

2. Fault Geometry
The seismic waves radiated from an earthquake reflect the geometry of the fault and the motion on it.
To describe the geometry of a fault it is assumed that the fault is a planar surface across which relative motion occurred during an earthquake.
Fault geometry:
Dip angle (d);
Strike angle (f);
Slip angle (l).
Stein and Wysession, 2003

3. Fault Geometry
Slip directions (l) in case of the basic fault geometries:
sinistral fault
dextral fault
Stein and Wysession, 2003

4. Fault-Plane Solution
A fault-plane solution tells the orientation and nature of the fault that caused an earthquake.
These are found from the directions of the first arrivals at a number of receivers encircling the epicenter.
As an example we consider a peg struck with a hammer moving northwards:

5. Fault-Plane Solution P-ways are in the direction of propagation.
No P-ways to either the east or west.
Maximum amplitudes are to the north and south.
The first arrival or movement to the north is a compression while to the south is a dilatation:

6. Earthquake First Arrivals
First arrivals of P-waves at a seismic station:
Push corresponds to the compression.
Pull corresponds to the dilatation.

7. Fault-Plane Solution
After an earthquake the fault displacement is more complex:
In the above example there is a N-S trending right-lateral (dextral) strike slip fault surrounded by a circle of seismometers.
When this fault moves, the seismometers will record a “first motion”.
In the top left quadrant this is up, in the bottom left quadrant this is down.

8. Fault-Plane Solution
However, there is ambiguity, as a left lateral strike slip fault trending E-W would also fit these first motions.
This is where one might also consider the local geology – are there any dominant trends? Surface rupture?
Is there a cluster of aftershocks that illuminates a particular plane.

9. First Motions
First motions of P-waves observed at seismometers located in various directions about the earthquake.
The two nodal planes separate regions of compressional and dilatational first arrivals.
Stein and Wysession, 2003

10. Fault-Plane Solution
For any fault types the radiation pattern is similar.
The fault and auxiliary planes cut the focal sphere into four quadrants.
The lower hemisphere is usually used.
In this particular case the lower hemisphere has only three parts.

11. Fault-Plane Solution
A projection of the lower hemisphere on the plane is used.
The lines where two nodal planes cut the focal sphere appear as arcs:

12. Fault-Plane Solution
Because of its appearance, the fault-plane solution is often called a beach ball.
Different faults produce different beach-ball figures:

13. Focal Mechanism Seismic rays travel away from the focus.
Each ray “samples” a dilatational or compressional quadrant around the focus.
Seismic stations at different distances record up or down first motions:

14. Focal Mechanism
Seismograms recorded at various distances and azimuths are used to study the geometry of faulting during an earthquake.
This geometry is known as the focal mechanism.

15. Take-off Angle
The angle of incidence at the earthquake source is the angle from the vertical at which the ray leaves the source.
This is the angle at which the ray intersects the lower focal sphere:
Stein and Wysession, 2003

16. Focal Mechanism
Focal mechanisms and some seismograms from three different earthquakes.
Compressional quadrants are shown shaded.
In some cases the first arrivals are small.
The stations near the center are at large distances from the source.
Stein and Wysession, 2003

17. Focal Mechanism Focal mechanisms for different fault systems.
The Olympia, Washington, M 6.8 earthquake of Feb. 28,

18. Focal Mechanism Focal mechanisms for different fault systems.
Stein and Wysession, 2003

19. World Wide Earthquakes
Focal solutions for shallow earthquakes,

20. Queen Charlotte Fault
The resultant movement along the Queen Charlotte Fault is primarily strike-slip, like that of the San Andreas Fault, but with a slight component of convergence.

21. Earthquakes in PNG
Papua New Guinea earthquakes:

22. Himalayan Seismicity
Earthquakes in Tibet and Himalaya:

23. Surface Displacement

24. Surface Deformation
Ground movement in North America.

25. Surface Deformation
Horizontal displacements due to large thrust earthquake, Nankaido, Japan, 1946.
The surface displacement usually has complex geometry.

26. Surface Deformation
Surface displacement can be tracked using GPS signals.
Measuring how the ground moves over intervals from hours to years.

27. Deformation Measurements
More precise measurements can be obtained by InSAR satellites.
Interferogram that shows the color band pattern around the Landers (California) fault line.
MW 7.3 Landers earthquake (28 June, 1992).

28. Synthetic Aperture Radar
A synthetic aperture radar (SAR) image is obtained using radar backscatter returns from the surface.
If the surface deforms between two SAR image acquisitions, a radar interferogram is obtained.
The point by point product of two images produces a fringe pattern associated with phase differences.
MW 7.3 Landers earthquake (28 June, 1992).

29. Synthetic Aperture Radar
A satellite makes a radar image of the ground at two times time1, time2 separated by a few weeks during which the ground moves.
The paths from A remain the same but those for B and C change.
On summing the radar reflections those from A are in phase and the sum shows large amplitude.
Those from B and C are shifted in phase and their sum is smaller (even zero).
The pattern of the image differences gives rise to what are called interference fringes.

30. Synthetic Aperture Radar
InSAR (Interferometric Synthetic Aperture Radar).
Multiple passes of a single satellite:
Sends out a signal;
Then listens for the echo;
Scans the ground with 100 m square pixels;
Repeat survey:
Looks for changes.

31. Synthetic Aperture Radar
The dark lines represent surface ruptures associated with the earthquake.
The maximum surface displacement was 5.1 m.
Each interferometric fringe corresponds to a displacement 0f 28 mm.
The images were acquired by the ERS-1 satellite on April 24 and August 7, 1992.
MW 7.3 Landers earthquake (28 June, 1992).

32. Synthetic Aperture Radar
Example of InSAR image for deformation due to the Hector Mine MW 7.1 Earthquake in October of 1999.
Each interferometric fringe corresponds to a displacement 0f mm.

33. Synthetic Aperture Radar
Interferogram from the MW 7.3 Landers, California, earthquake.
Each fringe is 5 cm displacement.

34. Surface Displacement
South Sisters, Oregon volcano uplift of 10 cm in 4 years.