Kinematic source example - 1994 Northridge earthquake

We use this earthquake to demonstrate how to set up dynamic rupture model with a kinematic rupture source in SeisSol.

The 1994 Northridge earthquake occurred on January 17, at 4:30:55 a.m. PST and had its epicenter in Reseda, a neighborhood in the north-central San Fernando Valley region of Los Angeles, California, USA. It had a duration of approximately 10–20 seconds. The blind thrust earthquake had a magnitude of 6.7 (Mw). This is a typical reverse-slip earthquake. The fault orients to N122\(^\circ\)E and dips at 40\(^\circ\). The simulation can be used to build a similar model with moderate modifications.

Geometry

The fault geometry is made in Gmsh. Fault: plane fault 20 km*25 km dipping at 40-degree.

Region: 100 km*100 km *60 km.

Geometry of 1994 northridge earthquake.

Geometry of 1994 Northridge earthquake. A planar fault orients at 122 degrees and dip at 40 degrees. The dimension of the fault is 20 km along strike and 25 km along down-dip.

Kinematic rupture Source

The kinematic source of the earthquake can be found at . The standard rupture format can be used directly in SeisSol, with the following lines in parameter.par file.

&SourceType
Type = 42
FileName=’northridge.nrf’
/

Download standard rupture format file (northridge.srf) can be found in https://scec.usc.edu/scecpedia/Standard_Rupture_Format. Please note that the SCEC units are different with SeisSol units in some aspect.

The fault is divided into 20 grids along the strike and 25 grids
along the dip. The source time function (STF) of each rectangular elements is given in the file , whose format looks like the following:
verison (1.0)
PLANE 1
ELON ELAT NSTK NDIP LEN WID STK DIP DTOP SHYP DHYP
POINTS 500
LON LAT DEP STK DIP AREA TINIT DT
RAKE SLIP1 NT1 SLIP2 NT2 SLIP3 NT3
SR1[1] SR1[2] SR1[3] . . . SR1[NT1]
SR2[1] SR2[2] SR2[3] . . . SR2[NT3]
SR3[1] SR3[2] SR3[3] . . . SR3[NT3]
...

Explanations for the input file:

Line 1: version

Line 2: Number of fault planes

Line 3: ELON top center longitude ELAT top center latitude NSTK number of point sources (subfaults) along strike NDIP number of point sources (subfaults) down-dip LEN segment length (km) WID segment width (km) STK segment strike DIP segment dip DTOP depth to top of fault segment (km) SHYP along strike location (from top center) of hypocenter for this segment (km) DHYP down-dip location (from top edge) of hypocenter for this segment (km)

Line 4: Number of points per fault plane

Line 5-9: LON: longitude of subfault center LAT: latitude of subfault center DEP: depth of subfault center (km) STK: strike DIP: dip AREA: area of subfault (cm2) TINIT: initiation time when rupture reaches subfault center (sec) DT: time step in slip velocity function (sec) RAKE: direction of u1 axis (rake direction) SLIP1: total slip in u1 direction (cm) NT1: number of time points in slip rate function for u1 direction SLIP2: total slip in u2 direction (cm) NT2: number of time points in slip rate function for u2 direction SLIP3: total slip in u3 (surface normal) direction (cm) NT3: number of time points in slip rate function for u3 direction SR1[1],…,SR1[NT1] slip rate at each time step for u1 direction (cm/sec) SR2[1],…,SR2[NT2] slip rate at each time step for u2 direction (cm/sec) SR3[1],…,SR3[NT3] slip rate at each time step for u3 direction (cm/sec)

Project geographic coordinates

The geographic coordinates of the source model are projected to Cartesian coordinates wit the pre-processing tool rconv.

rconv -i northridge.srf -o northridge.nrf -m “+proj=merc +lon_0=-118 +y_0=-4050981.42 +x_0=57329.54 +units=m +axis=enu” -x visualization.xdmf

To find the center of fault, use cs2cs in proj.4 to convert the cooridinates:

echo -118.5150 34.3440 0.0 | cs2cs +proj=lonlat +axis=enu +units=m +to +proj=merc +lon_0=-118 +axis=enu +units=m

This cooperation will project the coordinates and shift the center of fault to the origin (0,0) in Cartesian coordinates.

Results

Source rupture starts at 7.0 s and propagates in the domain. A snapshot of velocity is shown in Figure [fig:northridge1]. The surface velocity output is refined by subdividing each triangle into 4 subtriangles while the domain output is not.

Cross-section of vertical velocity

Cross-section of vertical velocity at the surface at 7 s. The surface velocity output is refined by subdividing each triangle into 4 subtriangles while the domain output is not. The plane demonstrates the fault orientation.