1. The seismogram
U = Source * Propagation * Site

3. POINT SOURCE APPROXIMATION
Distance r
Wavelength l
Fault dimension L
Far field terms dominates because r is relatively large

4. N dip Fault dip Fault azimuth Strike foot wall Hanging wall
EXTENDED SOURCE
FAULT PARAMETERS
surface
foot wall
Hanging wall
depth
length L
dip
Fault dip
width W
fault N
NUCLEATION POINT POSITION
Fault azimuth
Strike

5. EXTENDED SOURCE
FAULT PARAMETERS

6. EXTENDED SOURCE PARAMETERIZATION
An extended source is represented by the distribution of point sources at the each grid point
surface

7. EXTENDED SOURCE
FAULT PARAMETERS: Rupture Velocity
surface
fault
Rupture velocity (vr)

8. EXTENDED SOURCE
FAULT PARAMETERS: Slip
surface
fault d
rake y t

9. COMPLEX SOURCE PHENOMENA
Asperities and barriers
asperities
barriers

10.  100 km Distance along the fault plane Surface of the earth Depth
KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault
Surface of the earth
Depth
Into the
earth 
Snapshots every 2 seconds during the rupture
Starts in southern part of fault
100 km
Distance along the fault plane

11. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 2.0

12. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 4.0

13. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 6.0

14. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 8.0

15. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 10.0

16. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 12.0

17. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 14.0

18. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 16.0

19. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 18.0

20. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 20.0

21. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 22.0

22. KINEMATICS EXTENDED SOURCE
Slip on an earthquake fault: second 24.0

23. Rupture on a Fault KINEMATICS EXTENDED SOURCE
Final dislocation on the fault
Rupture on a Fault
Total slip during the 1992 Landers earthquake
Total distribution of slip after earthquake happened.
Red is a lot of slip, blue is no slip
You can see that the whole surface did not slip the same amount
Nor did it slip all at the same time, as you will see in this movie

24. Rupture velocity is few km/s. By default, seismologist uses 3 km/s
EXTENDED SOURCE
FAULT PARAMETERS: Slip Velocity
surface
fault
Rupture velocity (vr)
Rupture velocity is few km/s. By default, seismologist uses 3 km/s
The maximum duration d of the rupture is :
The slip amplitude on the fault scales with the length.
Slip velocity is around 1 m/s L t
Tr = rise time
D(t) . t tr

25. CAVEAT: Using Appropriate Source Time Functions
Examples of single-window STF’s:
SOURCE TIME FUNCTIONS:
The slip velocity history on each point on the fault is determined by the shape of the a priori assumed source time function.
Examples of multi-window STF’s:
time

26. Kinematic relations: Finite duration Fast initial acceleration
Asymmetric shape
Large peak value
N.B. This parameterization allow us to constrain the time of positive slip acceleration, i.e. time of Vpeak

27. Focal Mechanism Focal Sphere around the source A. Kelly, USGS azimuth
S. Stein and M. Wysession

28. Displacement Field from a double couplex1 x2 x3 x1 x2 x3 x2 x1

29. NODAL PLANE AND POLARITIESx3 x1 x2
dilatation
compression + - x3 x2 x1 + -

30. Polarities of first arrivals
The focal mechanism
Polarities of first arrivals - + + -

31. FOCAL MECHANISM DISPLACEMENT   DISLOCATION
compression
Dilatation + - - +

34. Focal Mechanism & Radiation pattern
b) Polarities of first P wave arrival
Stereographic projection

35. Focal Mechanims & Radiation pattern Calculation
From polarities of first arrivals P-waves
From waveform modeling through moment tensor

36. Radiation pattern

37. Radiation pattern Far Field
Onde P
Onde S

38. Radiation pattern Far FieldS P
Nodal Planes

39. Directivity COMPLEX SOURCE PHENOMENA directive Non directive
antidirective

40. Directivity effect on radiation
COMPLEX SOURCE PHENOMENA
Directivity effect on radiation
Hirasawa (1965)

41. Fraunhofer Approximation
The error in this approximation is