| 1 |
""" |
| 2 |
seismic wave propagation |
| 3 |
|
| 4 |
@var __author__: name of author |
| 5 |
@var __licence__: licence agreement |
| 6 |
@var __url__: url entry point on documentation |
| 7 |
@var __version__: version |
| 8 |
@var __date__: date of the version |
| 9 |
""" |
| 10 |
|
| 11 |
__copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
| 12 |
http://www.access.edu.au |
| 13 |
Primary Business: Queensland, Australia""" |
| 14 |
__license__="""Licensed under the Open Software License version 3.0 |
| 15 |
http://www.opensource.org/licenses/osl-3.0.php""" |
| 16 |
__author__="Lutz Gross, l.gross@uq.edu.au" |
| 17 |
__url__="http://www.iservo.edu.au/esys/escript" |
| 18 |
__version__="$Revision$" |
| 19 |
__date__="$Date$" |
| 20 |
|
| 21 |
from esys.escript import * |
| 22 |
from esys.escript.linearPDEs import LinearPDE |
| 23 |
from esys.finley import Brick |
| 24 |
import time |
| 25 |
|
| 26 |
output=False |
| 27 |
n_end=100 |
| 28 |
|
| 29 |
resolution=4000. # number of elements per m |
| 30 |
l=80000. # width and length m |
| 31 |
h=30000. # height in m |
| 32 |
|
| 33 |
rho_bedrock=8e3 |
| 34 |
mu_bedrock=1.7e11 |
| 35 |
lambda_bedrock=1.7e11 |
| 36 |
|
| 37 |
l_x_water=10000 # length of water in x |
| 38 |
l_y_water=10000 # length of water in y |
| 39 |
h_water=max(2000,resolution) # depth of water region |
| 40 |
|
| 41 |
water_tag=2 |
| 42 |
rho_water=1e3 |
| 43 |
mu_water=0. |
| 44 |
lambda_water=1.e9 |
| 45 |
|
| 46 |
d0_sand=10000 # thickness of sand region on surface |
| 47 |
d_sand=max(2000,resolution) # thickness of sand layer under the water |
| 48 |
|
| 49 |
sand_tag=3 |
| 50 |
rho_sand=5e3 |
| 51 |
mu_sand=1.5e10 |
| 52 |
lambda_sand=1.5e10 |
| 53 |
|
| 54 |
|
| 55 |
# location and geometrical size of event: |
| 56 |
xc=[30000.,40000.,10000.] |
| 57 |
src_radius = 0.1*h |
| 58 |
# direction of event: |
| 59 |
event=numarray.array([1.,0.,0.])*1.e6 |
| 60 |
# time and length of the event |
| 61 |
tc_length=2. |
| 62 |
tc=sqrt(5.*tc_length) |
| 63 |
if output: |
| 64 |
print "event location = ",xc |
| 65 |
print "radius of event = ",src_radius |
| 66 |
print "time of event = ",tc |
| 67 |
print "length of event = ",tc_length |
| 68 |
print "direction = ",event |
| 69 |
|
| 70 |
t_end=20. |
| 71 |
|
| 72 |
def getDomain(): |
| 73 |
""" |
| 74 |
this defines a dom as a brick of length and width l and hight h |
| 75 |
|
| 76 |
|
| 77 |
""" |
| 78 |
global netotal |
| 79 |
ne_l=int(l/resolution+0.5) |
| 80 |
ne_h=int(h/resolution+0.5) |
| 81 |
netotal=ne_l*ne_l*ne_h |
| 82 |
if output: print "grid : %s x %s x %s"%(ne_l,ne_l,ne_h) |
| 83 |
dom=Brick(ne_l,ne_l,ne_h,l0=l,l1=l,l2=h,order=1) |
| 84 |
|
| 85 |
fs=Function(dom) |
| 86 |
x=Function(dom).getX() |
| 87 |
fs.setTags(sand_tag,wherePositive(x[0]-(l-l_x_water-d0_sand)) \ |
| 88 |
*wherePositive(x[1]-(l-l_y_water-d0_sand)) \ |
| 89 |
*wherePositive(x[2]-(h-h_water-d_sand))) |
| 90 |
fs.setTags(water_tag,wherePositive(x[0]-(l-l_x_water)) \ |
| 91 |
*wherePositive(x[1]-(l-l_y_water)) \ |
| 92 |
*wherePositive(x[2]-(h-h_water))) |
| 93 |
return dom |
| 94 |
|
| 95 |
def getMaterialProperties(dom): |
| 96 |
rho =Scalar(rho_bedrock,Function(dom)) |
| 97 |
rho.setTaggedValue(sand_tag,rho_sand) |
| 98 |
rho.setTaggedValue(water_tag,rho_water) |
| 99 |
|
| 100 |
lame_mu =Scalar(mu_bedrock,Function(dom)) |
| 101 |
lame_mu.setTaggedValue(sand_tag,mu_sand) |
| 102 |
lame_mu.setTaggedValue(water_tag,mu_water) |
| 103 |
|
| 104 |
lame_lambda=Scalar(lambda_bedrock,Function(dom)) |
| 105 |
lame_lambda.setTaggedValue(sand_tag,lambda_sand) |
| 106 |
lame_lambda.setTaggedValue(water_tag,lambda_water) |
| 107 |
|
| 108 |
return rho,lame_mu,lame_lambda |
| 109 |
|
| 110 |
|
| 111 |
def wavePropagation(dom,rho,lame_mu,lame_lambda): |
| 112 |
x=Function(dom).getX() |
| 113 |
# ... open new PDE ... |
| 114 |
mypde=LinearPDE(dom) |
| 115 |
mypde.setSolverMethod(LinearPDE.LUMPING) |
| 116 |
k=kronecker(Function(dom)) |
| 117 |
mypde.setValue(D=k*rho) |
| 118 |
|
| 119 |
v_p=sqrt((2*lame_mu+lame_lambda)/rho) |
| 120 |
if output: print "v_p=",v_p |
| 121 |
v_s=sqrt(lame_mu/rho) |
| 122 |
if output: print "v_s=",v_s |
| 123 |
dt=(1./5.)*inf(dom.getSize()/v_p) |
| 124 |
if output: print "time step size = ",dt |
| 125 |
# ... set initial values .... |
| 126 |
n=0 |
| 127 |
t=0 |
| 128 |
# initial value of displacement at point source is constant (U0=0.01) |
| 129 |
# for first two time steps |
| 130 |
u =Vector(0.,Solution(dom)) |
| 131 |
u_last=Vector(0.,Solution(dom)) |
| 132 |
|
| 133 |
starttime = time.clock() |
| 134 |
while t<t_end and n<n_end: |
| 135 |
if output: print n+1,"-th time step t ",t+dt," max u and F: ",Lsup(u), |
| 136 |
# ... get current stress .... |
| 137 |
eps=symmetric(grad(u)) |
| 138 |
stress=lame_lambda*trace(eps)*k+2*lame_mu*eps |
| 139 |
# ... force due to event: |
| 140 |
F=exp(-((t-tc)/tc_length)**2)*exp(-(length(x-xc)/src_radius)**2)*event |
| 141 |
if output: print Lsup(F) |
| 142 |
# ... get new acceleration .... |
| 143 |
mypde.setValue(X=-stress,Y=F) |
| 144 |
a=mypde.getSolution() |
| 145 |
# ... get new displacement ... |
| 146 |
u_new=2*u-u_last+dt**2*a |
| 147 |
# ... shift displacements .... |
| 148 |
u_last,u=u,u_new |
| 149 |
# ... save current acceleration in units of gravity and displacements |
| 150 |
if output: |
| 151 |
if n%10==0: saveVTK("disp.%i.vtu"%(n/10),displacement=u, amplitude=length(u)) |
| 152 |
|
| 153 |
t+=dt |
| 154 |
n+=1 |
| 155 |
|
| 156 |
endtime = time.clock() |
| 157 |
totaltime = endtime-starttime |
| 158 |
global netotal |
| 159 |
print ">>number of elements: %s, total time: %s, per time step: %s <<"%(netotal,totaltime,totaltime/n) |
| 160 |
if __name__ =="__main__": |
| 161 |
dom=getDomain() |
| 162 |
rho,lame_mu,lame_lambda=getMaterialProperties(dom) |
| 163 |
wavePropagation(dom,rho,lame_mu,lame_lambda) |
Parent Directory
| 
Revision Log