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# |
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# $Id$ |
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# |
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####################################################### |
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# |
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# Copyright 2003-2007 by ACceSS MNRF |
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# Copyright 2007 by University of Queensland |
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# |
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# http://esscc.uq.edu.au |
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# Primary Business: Queensland, Australia |
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# Licensed under the Open Software License version 3.0 |
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# http://www.opensource.org/licenses/osl-3.0.php |
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# |
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####################################################### |
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# |
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|
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""" |
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seismic wave propagation |
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|
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@var __author__: name of author |
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@var __licence__: licence agreement |
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@var __url__: url entry point on documentation |
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@var __version__: version |
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@var __date__: date of the version |
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""" |
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|
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__copyright__=""" Copyright (c) 2006 by ACcESS MNRF |
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http://www.access.edu.au |
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Primary Business: Queensland, Australia""" |
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__license__="""Licensed under the Open Software License version 3.0 |
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http://www.opensource.org/licenses/osl-3.0.php""" |
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__author__="Lutz Gross, l.gross@uq.edu.au" |
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__url__="http://www.iservo.edu.au/esys/escript" |
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__version__="$Revision$" |
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__date__="$Date$" |
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|
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from esys.escript import * |
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from esys.escript.linearPDEs import LinearPDE |
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from esys.finley import Brick |
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import time |
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|
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WORKDIR="/raid2/lutz/waves/" |
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output=True |
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n_end=10000 |
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|
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resolution=1000. # number of elements per m in the finest region |
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resolution=400. # number of elements per m in the finest region |
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o=1 # element order |
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|
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l=100000. # width and length m (without obsorber) |
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h=30000. # height in m (without obsorber) |
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d_absorber=l*0.10 # thickness of absorbing layer |
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|
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l_sand=20000. # thickness of sand region on surface |
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h_sand=5000. # thickness of sand layer under the water |
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|
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l_x_water=10000. # length of water in x |
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l_y_water=10000. # length of water in y |
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h_water=2000. # depth of water region |
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|
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x_sand=l/2-l_x_water/2-l_sand # x coordinate of location of sand region (without obsorber) |
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y_sand=l/2-l_y_water/2-l_sand # y coordinate of location of sand region (without obsorber) |
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|
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|
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# origin |
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origin={"x": -d_absorber, "y" : -d_absorber , "z" : -h-d_absorber } |
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# location and geometrical size of event reltive to origin: |
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xc=[l*0.2,l*0.3,-h*0.7] |
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src_radius = 2*resolution |
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# direction of event: |
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event=numarray.array([0.,0.,1.])*1.e6 |
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# time and length of the event |
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tc=2. |
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tc_length=0.5 |
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|
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# material properties: |
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bedrock=0 |
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absorber=1 |
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water=2 |
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sand=3 |
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|
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rho_tab={} |
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rho_tab[bedrock]=8e3 |
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rho_tab[absorber]=rho_tab[bedrock] |
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rho_tab[water]=1e3 |
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rho_tab[sand]=5e3 |
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|
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mu_tab={} |
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mu_tab[bedrock]=1.7e11 |
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mu_tab[absorber]=mu_tab[bedrock] |
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mu_tab[water]=0. |
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mu_tab[sand]=1.5e10 |
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|
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lmbd_tab={} |
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lmbd_tab[bedrock]=1.7e11 |
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lmbd_tab[absorber]=lmbd_tab[bedrock] |
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lmbd_tab[water]=1.e9 |
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lmbd_tab[sand]=1.5e10 |
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|
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eta_tab={} |
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eta_tab[absorber]=-log(0.05)*sqrt(rho_tab[absorber]*(lmbd_tab[absorber]+2*mu_tab[absorber]))/d_absorber |
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eta_tab[sand]=eta_tab[absorber]/40. |
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eta_tab[water]=eta_tab[absorber]/40. |
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eta_tab[bedrock]=eta_tab[absorber]/40. |
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|
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|
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# material properties: |
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bedrock=0 |
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absorber=1 |
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water=2 |
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sand=3 |
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|
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rho={} |
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rho[bedrock]=8e3 |
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rho[absorber]=rho[bedrock] |
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rho[water]=1e3 |
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rho[sand]=5e3 |
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|
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mu={} |
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mu[bedrock]=1.7e11 |
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mu[absorber]=mu[bedrock] |
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mu[water]=0. |
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mu[sand]=1.5e10 |
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|
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lmbd={} |
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lmbd[bedrock]=1.7e11 |
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lmbd_absorber=lmbd[bedrock] |
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lmbd[water]=1.e9 |
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lmbd[sand]=1.5e10 |
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|
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eta={} |
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eta[absorber]=-log(0.05)*sqrt(rho[absorber]*(lmbd_absorber+2*mu[absorber]))/d_absorber |
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eta[sand]=eta[absorber]/40. |
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eta[water]=eta[absorber]/40. |
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eta[bedrock]=eta[absorber]/40. |
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|
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if output: |
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print "event location = ",xc |
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print "radius of event = ",src_radius |
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print "time of event = ",tc |
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print "length of event = ",tc_length |
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print "direction = ",event |
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|
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t_end=30. |
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dt_write=0.1 |
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|
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|
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def getDomain(): |
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""" |
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this defines a dom as a brick of length and width l and hight h |
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|
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|
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""" |
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global netotal |
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|
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v_p={} |
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for tag in rho_tab.keys(): |
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v_p[tag]=sqrt((2*mu_tab[tag]+lmbd_tab[tag])/rho_tab[tag]) |
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v_p_ref=min(v_p.values()) |
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print "velocities: bedrock = %s, sand = %s, water =%s, absorber =%s, reference =%s"%(v_p[bedrock],v_p[sand],v_p[water],v_p[absorber],v_p_ref) |
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|
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sections={} |
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sections["x"]=[d_absorber, x_sand, l_sand, l_x_water, l_sand, l-x_sand-2*l_sand-l_x_water, d_absorber] |
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sections["y"]=[d_absorber, y_sand, l_sand, l_y_water, l_sand, l-y_sand-2*l_sand-l_y_water, d_absorber] |
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sections["z"]=[d_absorber,h-h_water-h_sand,h_sand,h_water] |
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if output: |
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print "sections x = ",sections["x"] |
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print "sections y = ",sections["y"] |
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print "sections z = ",sections["z"] |
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|
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mats= [ |
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[ [absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber] ], |
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|
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[ [absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber] ], |
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|
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[ [absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, bedrock , sand , sand , sand , bedrock , absorber], |
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[absorber, bedrock , sand , sand , sand , bedrock , absorber], |
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[absorber, bedrock , sand , sand , sand , bedrock , absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber] ], |
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|
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[ [absorber, absorber, absorber, absorber, absorber, absorber, absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, bedrock , sand , sand , sand , bedrock , absorber], |
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[absorber, bedrock , sand , water , sand , bedrock , absorber], |
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[absorber, bedrock , sand , sand , sand , bedrock , absorber], |
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[absorber, bedrock , bedrock , bedrock , bedrock , bedrock , absorber], |
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[absorber, absorber, absorber, absorber, absorber, absorber, absorber] ] ] |
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|
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num_elem={} |
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for d in sections: |
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num_elem[d]=[] |
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for i in range(len(sections[d])): |
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if d=="x": |
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v_p_min=v_p[mats[0][0][i]] |
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for q in range(len(sections["y"])): |
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for r in range(len(sections["z"])): |
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v_p_min=min(v_p[mats[r][q][i]],v_p_min) |
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elif d=="y": |
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v_p_min=v_p[mats[0][i][0]] |
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for q in range(len(sections["x"])): |
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for r in range(len(sections["z"])): |
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v_p_min=min(v_p[mats[r][i][q]],v_p_min) |
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elif d=="z": |
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v_p_min=v_p[mats[i][0][0]] |
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for q in range(len(sections["x"])): |
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for r in range(len(sections["y"])): |
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v_p_min=min(v_p[mats[i][r][q]],v_p_min) |
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num_elem[d].append(max(1,int(sections[d][i] * v_p_ref/v_p_min /resolution+0.5))) |
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|
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ne_x=sum(num_elem["x"]) |
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ne_y=sum(num_elem["y"]) |
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ne_z=sum(num_elem["z"]) |
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netotal=ne_x*ne_y*ne_z |
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if output: print "grid : %s x %s x %s (%s elements)"%(ne_x,ne_y,ne_z,netotal) |
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dom=Brick(ne_x,ne_y,ne_z,l0=o*ne_x,l1=o*ne_y,l2=o*ne_z,order=o) |
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x_old=dom.getX() |
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x_new=0 |
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|
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for d in sections: |
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if d=="x": |
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i=0 |
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f=[1,0,0] |
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if d=="y": |
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i=1 |
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f=[0,1,0] |
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if d=="z": |
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i=2 |
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f=[0,0,1] |
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x=x_old[i] |
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|
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p=origin[d] |
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ne=0 |
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s=0. |
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|
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for i in range(len(sections[d])-1): |
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msk=whereNonPositive(x-o*ne+0.5) |
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s=s*msk + (sections[d][i]/(o*num_elem[d][i])*(x-o*ne)+p)*(1.-msk) |
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ne+=num_elem[d][i] |
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p+=sections[d][i] |
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x_new=x_new + s * f |
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dom.setX(x_new) |
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|
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fs=Function(dom) |
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x=Function(dom).getX() |
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x0=x[0] |
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x1=x[1] |
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x2=x[2] |
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p_z=origin["z"] |
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for i in range(len(mats)): |
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f_z=wherePositive(x2-p_z)*wherePositive(x2-p_z+sections["z"][i]) |
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p_y=origin["y"] |
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for j in range(len(mats[i])): |
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f_y=wherePositive(x1-p_y)*wherePositive(x1-p_z+sections["y"][j]) |
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p_x=origin["x"] |
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for k in range(len(mats[i][j])): |
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f_x=wherePositive(x0-p_x)*wherePositive(x0-p_x+sections["x"][k]) |
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fs.setTags(mats[i][j][k],f_x*f_y*f_z) |
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p_x+=sections["x"][k] |
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p_y+=sections["y"][j] |
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p_z+=sections["z"][i] |
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return dom |
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|
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def getMaterialProperties(dom): |
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rho =Scalar(rho_tab[bedrock],Function(dom)) |
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eta =Scalar(eta_tab[bedrock],Function(dom)) |
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mu =Scalar(mu_tab[bedrock],Function(dom)) |
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lmbd=Scalar(lmbd_tab[bedrock],Function(dom)) |
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tags=Scalar(bedrock,Function(dom)) |
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|
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for tag in rho_tab.keys(): |
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rho.setTaggedValue(tag,rho_tab[tag]) |
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eta.setTaggedValue(tag,eta_tab[tag]) |
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mu.setTaggedValue(tag,mu_tab[tag]) |
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lmbd.setTaggedValue(tag,lmbd_tab[tag]) |
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tags.setTaggedValue(tag,tag) |
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return rho,mu,lmbd,eta |
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|
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def wavePropagation(dom,rho,mu,lmbd,eta): |
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x=Function(dom).getX() |
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# ... open new PDE ... |
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mypde=LinearPDE(dom) |
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mypde.setSolverMethod(LinearPDE.LUMPING) |
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k=kronecker(Function(dom)) |
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mypde.setValue(D=k*rho) |
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|
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dt=(1./5.)*inf(dom.getSize()/sqrt((2*mu+lmbd)/rho)) |
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if output: print "time step size = ",dt |
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# ... set initial values .... |
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n=0 |
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t=0 |
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t_write=0. |
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n_write=0 |
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# initial value of displacement at point source is constant (U0=0.01) |
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# for first two time steps |
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u=Vector(0.,Solution(dom)) |
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v=Vector(0.,Solution(dom)) |
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a=Vector(0.,Solution(dom)) |
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a2=Vector(0.,Solution(dom)) |
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v=Vector(0.,Solution(dom)) |
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|
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starttime = time.clock() |
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while t<t_end and n<n_end: |
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if output: print n+1,"-th time step t ",t+dt," max u and F: ",Lsup(u), |
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# prediction: |
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u_pr=u+dt*v+(dt**2/2)*a+(dt**3/6)*a2 |
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v_pr=v+dt*a+(dt**2/2)*a2 |
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a_pr=a+dt*a2 |
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# ... get current stress .... |
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eps=symmetric(grad(u_pr)) |
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stress=lmbd*trace(eps)*k+2*mu*eps |
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# ... force due to event: |
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if abs(t-tc)<5*tc_length: |
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F=exp(-((t-tc)/tc_length)**2)*exp(-(length(x-xc)/src_radius)**2)*event |
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if output: print Lsup(F) |
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else: |
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if output: print 0. |
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# ... get new acceleration .... |
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mypde.setValue(X=-stress,Y=F-eta*v_pr) |
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a=mypde.getSolution() |
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# ... get new displacement ... |
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da=a-a_pr |
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u=u_pr+(dt**2/12.)*da |
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v=v_pr+(5*dt/12.)*da |
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a2+=da/dt |
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# ... save current acceleration in units of gravity and displacements |
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if output: |
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if t>=t_write: |
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saveVTK(WORKDIR+"disp.%i.vtu"%n_write,displacement=u, amplitude=length(u)) |
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t_write+=dt_write |
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n_write+=1 |
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t+=dt |
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n+=1 |
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|
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endtime = time.clock() |
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totaltime = endtime-starttime |
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global netotal |
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print ">>number of elements: %s, total time: %s, per time step: %s <<"%(netotal,totaltime,totaltime/n) |
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if __name__ =="__main__": |
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dom=getDomain() |
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rho,mu,lmbd,eta=getMaterialProperties(dom) |
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wavePropagation(dom,rho,mu,lmbd,eta) |
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