Model of the Northridge earthquake, based on early hypocentral and focal mechanism information from Berkeley. Delta_CFF is calculated on optimal failure planes at 10km depth and for E-W striking reverse faults at 10km depth. Illustrates makemodel, elfgrid, stroop, strop, modellines, bblines, gclrx.
Note that answers given in [square braces] are defaults which will be used if no answer is supplied (just hit the carriage return).
First we use makemodel. Note that a projection is specified and the coordinates are entered as longitude and latitude. Because the information used to make the model is preliminary, we expect that the model will need revision. In particular, because our model will be a single dislocation surface centered on the hypocenter, it may not represent the actual distribution of slip very well, expecially if the rupture started at depth and move upward or at one end and spread unilaterally. These factors will probably be most important close to the rupture. We hope that at distances equal to several rupture widths, the details of the slip distribution will be less important in calculating the stress changes accurately.
> makemodel
Program MAKEMODEL outputs two files defining a dislocation model.
Name for .PAR parameter file: [nr.par]
Name for .DLC dislocation file: [nr.dlc]
Give DLC format:
1 = Dunbar (type 1) dislocation format (obsolete)
2 = Normal (type 2) dislocation format
3 = Ends (type 3) dislocation format
4 = Triangle (type 4) dislocation format
e = Earthquake input (to type 2 format)
Format (1/2/3/4/e): [2] e
Poisson's ratio: [0.25]
Shear Modulus (bars): [300000.]
Projection number (99 for help): [0] 4
Give coordinates in decimal degrees or d:m or d:m:s
(e.g. -120.52 or -120:31.2 or -120:31:12)
Central meridian: [0.] -118
Base latitude: 32
New azimuth of North-direction: [0.]
Title (80 chars): Early S-dipping Berkeley Solution for the Northridge Earthquake
Give coordinates in decimal degrees or d:m or d:m:s
(e.g. -120.52 or -120:31.2 or -120:31:12)
Lon of earthquake (- for W): [-120.] -118.45
Lat of earthquake: [37.] 34.31
Depth (km) of earthquake: [15.] 14
Specify fault plane orientation by dip-direction or strike? (d/s): [s]
Strike, Dip of fault plane (eg. 320, 45NE): [N41W, 90] 123,44S
Specify slip direction by giving rake-angle or aux-plane? (r/a): [r]
Rake angle (0=LL; +/-180=RL; +90=Reverse; -90=Normal): [-180.] 105
Horizontal length of rupture (km): [1.] 10
Down-dip length of rupture (km): [1.] 10
Give moment or magnitude? (mom/mag): [mom]
Moment: [0.] 1.2E26
Strike slip: LL is +, RL is -
Give strike-slip displacement (m): [-1.03528]
Dip slip: Normal is +, Reverse is -
Give dip-slip displacement (m): [-3.8637]
** converting moment to magnitude using:
** mag = (log10(mom) - 16.0)/1.5
** moment = 1.20000E+26
** magnitude = 6.71945
Want to review parameters? (y/n): [n]
Another? (y/n): [n]
STOP:
The output model files nr.par and nr.dlc look like this:
nr.par:
=======
*ELASTIC
! pr shear-modulus
0.25 3.00E+05
*PROJECTION
! iprj cm bl rot xcen ycen
4 -118.0000 32.0000 0.0000 0.0000 0.0000
*END
nr.dlc:
=======
#TYP LONCEN LATCEN DCEN STR DIP HORLEN DIPLEN SS(m) DS(m) OP(m) RAKE
! Early S-dipping Berkeley Solution for the Northridge Earthquake
-2 -118.4500 34.3100 14.0000 123.0000 44.000 10.0000 10.0000 -1.0353 -3.8637 0. 105.
We need to know where we are in projected km in order to run subsequent programs:
> ptprj
West longitudes should be negative...
Give large numbers to stop...
Projection number (99 for help): [0] 4
Give coordinates in decimal degrees or d:m or d:m:s
(e.g. -120.52 or -120:31.2 or -120:31:12)
Central meridian: [0.] -118
Base latitude: 32
Forward or inverse projection (f/i): [f]
__________________________________________________
Give lon: -118.45
Give lat: 34.31
xkm, ykm = -41.3360 256.2373
xdeg,ydeg = -118.4500 34.3100
__________________________________________________
Give lon: -999
STOP:
Next we run elfgrid to calculate the stress tensor on a horizontal observation plane at a depth of 10km. The output is six Standard Grids, one for each component of the tensor.
> elfgrid
Parameter file: [nr.par]
Dislocation file: [nr.dlc]
Number of dislocations read = 1
Field to calculate:
s = stress tensor
u = displacements
e = strain tensor
d = dilatation
r = rotation
t = tilts
w = strain energy
Give field type (s/u/e/d/r/t/w/a/q): [s]
Is grid of observation points horizontal or dipping? (h/d): [h]
Left (west) bound (km): -140
Right (east) bound (km): 60
Bottom (south) bound (km): 150
Top (north) bound (km): 350
Grid interval (km): 2
ncol, nrow = 101 101
Depth for horizontal grid (km): [0.] 10
Starting Stress grid(s)...
** Done: 4% 10% 20% 31% 41% 51% 61% 71% 80% 90% 100%
Done with Stress grid(s).
STOP:
Now we calculate the change in the Coulomb Failure Function (CFF) on optimal failure planes at 10km depth by running stroop (stress_on_optimal_planes). There are some subtle assumptions in the calculation of DeltaCFF and the different ways of calculating it that are discussed in the CFF page. Note that a regional stress field is specified as the initial field (for calculation CFFo). The final stress field is the sum of the regional field and the stress changes generated by our model of the earthquake.
> stroop
Stress or Strain? (s/e): [s]
Root for stress grid filenames: [nr]
Add regional stresses? (y/n): [n] y
Poissons ratio: [0.25]
Regional options:
h = general (with 2 axes horizontal)
p = general (with 2 axes horizontal, asks for phi)
s = regional Shear stress
u = regional uniaxial tensional or compressive stress
t = regional Tectonic (e or c) stress
l = Lithostatic stress (no hor disp)
i = Lithostatic stress (isotropic)
c = Continue: exit from regional options.
Give regional option (g/h/p/s/e/f/d/t/l/i/c): [c] u
Azimuth of tension or compression: [0.] 0
Magnitude of stress (bar, + is tension): [0.] -100
Give regional option (g/h/p/s/e/f/d/t/l/i/c): [c]
** Give negative fric to include max pore pressure effect...
Friction (- for pore pressure): [0.75]
Cohesion: [0.]
** Angle of fracture relative to compression axis = 27.
Output grid of Coulomb failure function? (y/n): [n] y
Want to difference Coulomb criteria? (y/n): [y]
Coulomb criterion grid: [nr.delcff]
Output grid of phi value? (y/n): [n]
Output grids of principal components? (y/n): [n]
Output grids of ~horizontal components? (y/n): [n]
Want beachball lines (y/n): [y] n
Want lines showing near-horizontal axes? (y/n): [n]
Reading input grids and calculating...
** Done: 2% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
STOP:
Before plotting we run modellines:
> modellines
Parameter file: [nr.par]
Dislocation file: [nr.dlc]
Number of dislocations = 1
File for model lines: [nr.lin]
Grid to project lines onto (n if horizontal): [nr.s12]
------------------------------------------------------------------------------
ID = Stress12 depth = 10.0 year = 0.0 PGM=d3dgrid
ntot= 10201 nz= 1
ncol= 101 xo= -140.00000 dx= 2.0000000 xmax= 60.000000
nrow= 101 yo= 150.00000 dy= 2.0000000 ymax= 350.00000
projection= 4 cm= -118.0000 bl= 32.0000
------------------------------------------------------------------------------
Show Burger's vectors? (y/n): [n]
STOP:
Then run bblines to save as a linefile the orientations of the final stress tensor (represented as beachballs) on the observation plane. The final stress tensor is the sum of the regional stress, specified in stroop, and the stress change calculated for our Northridge model.
> bblines
Makes a file of beach-ball lines to indicate
orientation of principal axes of a tensor...
Stress or Strain Tensor? (s/e): [s]
Root for stress grid filenames: [nr]
Add regional stresses? (y/n): [n] y
Poissons ratio: [0.25]
Regional options:
h = general (with 2 axes horizontal)
p = general (with 2 axes horizontal, asks for phi)
s = regional Shear stress
u = regional uniaxial tensional or compressive stress
t = regional Tectonic (e or c) stress
l = Lithostatic stress (no hor disp)
i = Lithostatic stress (isotropic)
c = Continue: exit from regional options.
Give regional option (g/h/p/s/e/f/d/t/l/i/c): [c] u
Azimuth of tension or compression: [0.]
Magnitude of stress (bar, + is tension): [0.] -100
Give regional option (g/h/p/s/e/f/d/t/l/i/c): [c]
Want beachball lines (y/n): [y]
Beachball file: [nr.ball_lin]
** Beachball line file will be in .lin format
Coulomb Criterion threshold to print beachballs? (y/n): [n]
Radius of beach balls (km): [10.] 5
Skip columns between beachballs: [20]
Want to color in beach balls (slow)? (y/n): [y]
** Extensional quadrants will be shaded ...
Want lines showing near-horizontal axes? (y/n): [n]
Reading input grids...
** Done: 2% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
STOP:
Finally we plot the DeltaCFF grid on the screen using gclrx:
> gclrx p == >Plot-only, Plot-and-Save, or Save-only? (P/p/Ps/ps/s) c == Give task (c/q/gs/cs/m/x/sr/cr/df/w) nr.delcff == Grid (n for none) w == Background white or black? (w/b) h == Show colorscale (h=horiz, v=vert, n=none)? (h/v/n) 0.75 0.75 1.20 0.50 == Minimum margins around data window in inches (l,r,b,t) -1. == Give map scale 12.ymc == Color file (h for help) 11 == Give number of contours (0 for file) -2.5 == Give MIN level 0.5 == Give INTerval bars == Colorbar units label (or n for none) 0.1 == Ht of labels on colorbar li == ?Option (h or he = help) nr.lin == Line file (h for help with abbrevs) n == Project lines? (y/n) km == ?Option (h or he = help) 5 == x-spacing between edge-tics in km 5 == y-spacing between edge-tics in km 0.05 == Height for tics in inches o == Plot tics inside or outside box? (i/o) y == Label tics? (y/n) 2 == Number to skip 0.09 == Label height li == ?Option (h or he = help) caout == Line file (h for help with abbrevs) y == Project lines? (y/n) id == ?Option (h or he = help) t == Title at bottom or top? (b/t/bp/tp) .15 == Title height + at 10 km Depth (Fric=0.75) == Title lw == ?Option (h or he = help) .5 == Line width factor (Units of 0.005in) li == ?Option (h or he = help) cafaults == Line file (h for help with abbrevs) y == Project lines? (y/n) li == ?Option (h or he = help) nr.ball_lin == Line file (h for help with abbrevs) .LIN == Give line type (.OLN/.BOLN/.BLN/.LIN/.GEN/.QP/.OPP/.AXYZ/.XYZ/.BLXYZ/QUIT) n == Project lines? (y/n)
Here is the stroop plot:
As a variation, Delta CFF can be calculated on planes of fixed orientation if it is known that there is a fabric of existing faults or fractures which are likely to provide planes of failure. In this case we assume that E-W trending, south dipping reverse faults in the Transverse Ranges will be of interest as candidates for failure. We use strop (stress_on_planes) in this run to calculate DeltaCFF on planes of specified orientation at 10km depth:
> strop
** STROP calculates STRess changes On fixed Planes
and outputs delta_cff and delta_tractions.
Stress or Strain? (s/e): [s]
Root for stress grids: [nr]
------------------------------------------------------------------------------
ID = Stress11 depth = 10.0 year = 0.0 PGM=d3dgrid
ntot= 10201 nz= 1
ncol= 101 xo= -140.00000 dx= 2.0000000 xmax= 60.000000
nrow= 101 yo= 150.00000 dy= 2.0000000 ymax= 350.00000
projection= 4 cm= -118.0000 bl= 32.0000
------------------------------------------------------------------------------
Root for output grids: [nr]
** Strike is in direction of left hand looking down-dip...
Strike,dip of planes (eg. N60W,34SE or 300,34SE): [0.0, 90.0] 90,45S
Specify a failure direction by giving:
Rake on planes or a regional Field (r/f): [r]
Rake angle (0=LL; +/-180=RL; +90=Reverse; -90=Normal): [0.] 90
Give negative fric to include max pore pressure effect...
Friction (- for pore pressure): [0.75]
Cohesion: [0.]
Delta_CFF grid: [nr.deltacff]
Want delta stress component (traction) grids? (y/n): [n]
Want pore term grid? (y/n): [n]
Reading stress grids...
** Done: 2% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
STOP:
> gclrx
p == >Plot-only, Plot-and-Save, or Save-only? (P/p/Ps/ps/s)
c == Give task (c/q/gs/cs/m/x/sr/cr/df/w)
nr.deltacff == Grid (n for none)
w == Background white or black? (w/b)
h == Show colorscale (h=horiz, v=vert, n=none)? (h/v/n)
0.75 0.75 1.20 0.50 == Minimum margins around data window in inches (l,r,b,t)
-1. == Give map scale
12.ymc == Color file (h for help)
11 == Give number of contours (0 for file)
-2.5 == Give MIN level
0.5 == Give INTerval
bars == Colorbar units label (or n for none)
0.1 == Ht of labels on colorbar
li == ?Option (h or he = help)
nr.lin == Line file (h for help with abbrevs)
n == Project lines? (y/n)
km == ?Option (h or he = help)
5 == x-spacing between edge-tics in km
5 == y-spacing between edge-tics in km
0.05 == Height for tics in inches
o == Plot tics inside or outside box? (i/o)
y == Label tics? (y/n)
2 == Number to skip
0.09 == Label height
li == ?Option (h or he = help)
caout == Line file (h for help with abbrevs)
y == Project lines? (y/n)
id == ?Option (h or he = help)
t == Title at bottom or top? (b/t/bp/tp)
.15 == Title height
+ at 10 km Depth == Title
lw == ?Option (h or he = help)
.5 == Line width factor (Units of 0.005in)
li == ?Option (h or he = help)
cafaults == Line file (h for help with abbrevs)
y == Project lines? (y/n)
Here is the strop figure:
