The seismogram U = Source * Propagation * Site

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

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

EXTENDED SOURCE FAULT PARAMETERS

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

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

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

COMPLEX SOURCE PHENOMENA Asperities and barriers asperities barriers

 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

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 2.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 4.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 6.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 8.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 10.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 12.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 14.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 16.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 18.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 20.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 22.0

KINEMATICS EXTENDED SOURCE Slip on an earthquake fault: second 24.0

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

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

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

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

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

Displacement Field from a double couple x1 x2 x3 x1 x2 x3 x2 x1

NODAL PLANE AND POLARITIES x3 x1 x2 dilatation compression + - x3 x2 x1 + -

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

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

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

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

Radiation pattern

Radiation pattern Far Field Onde P Onde S

Radiation pattern Far Field S P Nodal Planes

Directivity COMPLEX SOURCE PHENOMENA directive Non directive antidirective

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

Fraunhofer Approximation The error in this approximation is