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seismic_PML_Collino_3D_isotropic_OpenMP.f90
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seismic_PML_Collino_3D_isotropic_OpenMP.f90
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!
! SEISMIC_CPML Version 1.1.1, November 2009.
!
! Copyright Universite de Pau et des Pays de l'Adour, CNRS and INRIA, France.
! Contributors: Dimitri Komatitsch, komatitsch aT lma DOT cnrs-mrs DOT fr
! and Roland Martin, roland DOT martin aT get DOT obs-mip DOT fr
!
! This software is a computer program whose purpose is to solve
! the three-dimensional isotropic elastic wave equation
! using a finite-difference method with classical split Perfectly Matched
! Layer (PML) conditions.
!
! This program is free software; you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation; either version 3 of the License, or
! (at your option) any later version.
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along
! with this program; if not, write to the Free Software Foundation, Inc.,
! 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
!
! The full text of the license is available in file "LICENSE".
program seismic_PML_Collino_3D_iso
! IMPORTANT : all our CPML codes work fine in single precision as well (which is significantly faster).
! If you want you can thus force automatic conversion to single precision at compile time
! or change all the declarations and constants in the code from double precision to single.
implicit none
!
! 3D explicit PML velocity-stress FD code based upon INRIA report for the 2D case:
!
! Francis Collino and Chrysoula Tsogka
! Application of the PML Absorbing Layer Model to the Linear
! Elastodynamic Problem in Anisotropic Heteregeneous Media
! INRIA Research Report RR-3471, August 1998
! http://hal.inria.fr/docs/00/07/32/19/PDF/RR-3471.pdf
!
! and
!
! @ARTICLE{CoTs01,
! author = {F. Collino and C. Tsogka},
! title = {Application of the {PML} absorbing layer model to the linear elastodynamic
! problem in anisotropic heterogeneous media},
! journal = {Geophysics},
! year = {2001},
! volume = {66},
! number = {1},
! pages = {294-307}}
!
! PML implemented in the three directions (x, y and z).
!
! Dimitri Komatitsch and Roland Martin, University of Pau, France, April 2007.
!
! The second-order staggered-grid formulation of Madariaga (1976) and Virieux (1986) is used.
!
! Parallel implementation based on OpenMP.
! Type for instance "setenv OMP_NUM_THREADS 4" before running in OpenMP if you want 4 tasks.
!
! To display the results as color images in the selected 2D cut plane, use:
!
! " display image*.gif " or " gimp image*.gif "
!
! or
!
! " montage -geometry +0+3 -rotate 90 -tile 1x21 image*Vx*.gif allfiles_Vx.gif "
! " montage -geometry +0+3 -rotate 90 -tile 1x21 image*Vy*.gif allfiles_Vy.gif "
! then " display allfiles_Vx.gif " or " gimp allfiles_Vx.gif "
! then " display allfiles_Vy.gif " or " gimp allfiles_Vy.gif "
!
! total number of grid points in each direction of the grid
integer, parameter :: NX = 101
integer, parameter :: NY = 641
integer, parameter :: NZ = 640
! size of a grid cell
double precision, parameter :: h = 10.d0
! thickness of the PML layer in grid points
integer, parameter :: NPOINTS_PML = 10
! P-velocity, S-velocity and density
double precision, parameter :: cp = 3300.d0
double precision, parameter :: cs = cp / 1.732d0
double precision, parameter :: rho = 2800.d0
double precision, parameter :: mu = rho*cs*cs
double precision, parameter :: lambda = rho*(cp*cp - 2.d0*cs*cs)
double precision, parameter :: lambda_plus_two_mu = rho*cp*cp
! total number of time steps
integer, parameter :: NSTEP = 2500
! time step in seconds
double precision, parameter :: DELTAT = 1.6d-3
double precision, parameter :: ONE_OVER_DELTAT = 1.d0 / DELTAT
! parameters for the source
double precision, parameter :: f0 = 7.d0
double precision, parameter :: t0 = 1.20d0 / f0
double precision, parameter :: factor = 1.d7
! source
! if one wants to put the source at another location, one can invert the formulas below
! and define the grid point (ISOURCE, JSOURCE, KSOURCE) to use as:
! double precision, parameter :: xsource = ...put here the coordinate you want...
! double precision, parameter :: ysource = ...put here the coordinate you want...
! double precision, parameter :: zsource = ...put here the coordinate you want...
! integer, parameter :: ISOURCE = xsource / h + 1
! integer, parameter :: JSOURCE = ysource / h + 1
! integer, parameter :: KSOURCE = zsource / h + 1
! (h is the size of mesh cells)
integer, parameter :: ISOURCE = NX - 2*NPOINTS_PML - 1
integer, parameter :: JSOURCE = 2 * NY / 3 + 1
integer, parameter :: KSOURCE = NZ / 2
double precision, parameter :: xsource = (ISOURCE - 1) * h
double precision, parameter :: ysource = (JSOURCE - 1) * h
double precision, parameter :: zsource = (KSOURCE - 1) * h
! angle of source force clockwise with respect to vertical (Y) axis
double precision, parameter :: ANGLE_FORCE = 135.d0
! receivers
integer, parameter :: NREC = 2
double precision, parameter :: xdeb = xsource - 100.d0 ! first receiver x in meters
double precision, parameter :: ydeb = 2300.d0 ! first receiver y in meters
double precision, parameter :: zdeb = zsource ! first receiver y in meters
double precision, parameter :: xfin = xsource ! last receiver x in meters
double precision, parameter :: yfin = 300.d0 ! last receiver y in meters
double precision, parameter :: zfin = zsource ! last receiver y in meters
! display information on the screen from time to time
integer, parameter :: IT_DISPLAY = 100
! value of PI
double precision, parameter :: PI = 3.141592653589793238462643d0
! conversion from degrees to radians
double precision, parameter :: DEGREES_TO_RADIANS = PI / 180.d0
! zero
double precision, parameter :: ZERO = 0.d0
! large value for maximum
double precision, parameter :: HUGEVAL = 1.d+30
! velocity threshold above which we consider that the code became unstable
double precision, parameter :: STABILITY_THRESHOLD = 1.d+25
! main arrays
double precision, dimension(NX,NY,NZ) :: vx_1,vx_2,vx_3, &
vy_1,vy_2,vy_3, &
vz_1,vz_2,vz_3, &
sigmaxx_1,sigmaxx_2,sigmaxx_3, &
sigmayy_1,sigmayy_2,sigmayy_3, &
sigmazz_1,sigmazz_2,sigmazz_3, &
sigmaxy_1,sigmaxy_2, &
sigmaxz_1,sigmaxz_3, &
sigmayz_2,sigmayz_3
double precision, dimension(NX) :: dx_over_two,dx_half_over_two
double precision, dimension(NY) :: dy_over_two,dy_half_over_two
double precision, dimension(NZ) :: dz_over_two,dz_half_over_two
! for the source
double precision a,t,force_x,force_y,force_z,source_term
! for receivers
double precision xspacerec,yspacerec,zspacerec,distval,dist
integer, dimension(NREC) :: ix_rec,iy_rec,iz_rec
double precision, dimension(NREC) :: xrec,yrec,zrec
double precision, dimension(NSTEP,NREC) :: sisvx,sisvy
! for evolution of total energy in the medium
double precision :: epsilon_xx,epsilon_yy,epsilon_zz,epsilon_xy,epsilon_xz,epsilon_yz
double precision :: sigmaxx_total,sigmayy_total,sigmazz_total
double precision :: sigmaxy_total,sigmaxz_total,sigmayz_total
double precision :: total_energy_kinetic,total_energy_potential
double precision, dimension(NSTEP) :: total_energy
integer :: i,j,k,it,irec,iplane
double precision :: xval,delta,xoriginleft,xoriginright,rcoef,d0,Vsolidnorm,Courant_number,value_dx,value_dy,value_dz,d
! timer to count elapsed time
character(len=8) datein
character(len=10) timein
character(len=5) :: zone
integer, dimension(8) :: time_values
integer ihours,iminutes,iseconds,int_tCPU
double precision :: time_start,time_end,tCPU
! names of the time stamp files
character(len=150) outputname
! main I/O file
integer, parameter :: IOUT = 41
!---
!--- program starts here
!---
!--- define profile of absorption in PML region
! thickness of the layer in meters
delta = NPOINTS_PML * h
! reflection coefficient (INRIA report section 6.1) http://hal.inria.fr/docs/00/07/32/19/PDF/RR-3471.pdf
Rcoef = 0.001d0
! compute d0 from INRIA report section 6.1 http://hal.inria.fr/docs/00/07/32/19/PDF/RR-3471.pdf
d0 = 3.d0 * cp * log(1.d0/Rcoef) / (2.d0 * delta)
print *,'d0 = ',d0
print *
! origin of the PML layer (position of right edge minus thickness, in meters)
xoriginleft = delta
xoriginright = (NX-1)*h - delta
do i=1,NX
xval = h*dble(i-1)
if (xval < xoriginleft) then
dx_over_two(i) = d0 * ((xoriginleft-xval)/delta)**2
dx_half_over_two(i) = d0 * ((xoriginleft-xval-h/2.d0)/delta)**2
! fix problem with dx_half_over_two() exactly on the edge
else if (xval >= 0.9999d0*xoriginright) then
dx_over_two(i) = d0 * ((xval-xoriginright)/delta)**2
dx_half_over_two(i) = d0 * ((xval+h/2.d0-xoriginright)/delta)**2
else
dx_over_two(i) = 0.d0
dx_half_over_two(i) = 0.d0
endif
enddo
! divide the whole profile by two once and for all
dx_over_two(:) = dx_over_two(:) / 2.d0
dx_half_over_two(:) = dx_half_over_two(:) / 2.d0
! origin of the PML layer (position of right edge minus thickness, in meters)
xoriginleft = delta
xoriginright = (NY-1)*h - delta
do j=1,NY
xval = h*dble(j-1)
if (xval < xoriginleft) then
dy_over_two(j) = d0 * ((xoriginleft-xval)/delta)**2
dy_half_over_two(j) = d0 * ((xoriginleft-xval-h/2.d0)/delta)**2
! fix problem with dy_half_over_two() exactly on the edge
else if (xval >= 0.9999d0*xoriginright) then
dy_over_two(j) = d0 * ((xval-xoriginright)/delta)**2
dy_half_over_two(j) = d0 * ((xval+h/2.d0-xoriginright)/delta)**2
else
dy_over_two(j) = 0.d0
dy_half_over_two(j) = 0.d0
endif
enddo
! divide the whole profile by two once and for all
dy_over_two(:) = dy_over_two(:) / 2.d0
dy_half_over_two(:) = dy_half_over_two(:) / 2.d0
! origin of the PML layer (position of right edge minus thickness, in meters)
xoriginleft = delta
xoriginright = (NZ-1)*h - delta
do k=1,NZ
xval = h*dble(k-1)
if (xval < xoriginleft) then
dz_over_two(k) = d0 * ((xoriginleft-xval)/delta)**2
dz_half_over_two(k) = d0 * ((xoriginleft-xval-h/2.d0)/delta)**2
! fix problem with dy_half_over_two() exactly on the edge
else if (xval >= 0.9999d0*xoriginright) then
dz_over_two(k) = d0 * ((xval-xoriginright)/delta)**2
dz_half_over_two(k) = d0 * ((xval+h/2.d0-xoriginright)/delta)**2
else
dz_over_two(k) = 0.d0
dz_half_over_two(k) = 0.d0
endif
enddo
! divide the whole profile by two once and for all
dz_over_two(:) = dz_over_two(:) / 2.d0
dz_half_over_two(:) = dz_half_over_two(:) / 2.d0
! print position of the source
print *
print *,'Position of the source:'
print *
print *,'x = ',xsource
print *,'y = ',ysource
print *,'z = ',zsource
print *
! define location of receivers
print *
print *,'There are ',nrec,' receivers'
print *
xspacerec = (xfin-xdeb) / dble(NREC-1)
yspacerec = (yfin-ydeb) / dble(NREC-1)
zspacerec = (zfin-zdeb) / dble(NREC-1)
do irec=1,nrec
xrec(irec) = xdeb + dble(irec-1)*xspacerec
yrec(irec) = ydeb + dble(irec-1)*yspacerec
zrec(irec) = zdeb + dble(irec-1)*zspacerec
enddo
! find closest grid point for each receiver
do irec=1,nrec
dist = HUGEVAL
do k = 1,NZ
do j = 1,NY
do i = 1,NX
distval = sqrt((h*dble(i-1) - xrec(irec))**2 + (h*dble(j-1) - yrec(irec))**2 + (h*dble(k-1) - zrec(irec))**2)
if (distval < dist) then
dist = distval
ix_rec(irec) = i
iy_rec(irec) = j
iz_rec(irec) = k
endif
enddo
enddo
enddo
print *,'receiver ',irec,' x_target,y_target,z_target = ',xrec(irec),yrec(irec),zrec(irec)
print *,'closest grid point found at distance ',dist,' in i,j,k = ',ix_rec(irec),iy_rec(irec),iz_rec(irec)
print *
enddo
! check the Courant stability condition for the explicit time scheme
! R. Courant et K. O. Friedrichs et H. Lewy (1928)
Courant_number = cp * DELTAT / h
print *,'Courant number is ',Courant_number
print *
if (Courant_number > 1.d0/sqrt(3.d0)) stop 'time step is too large, simulation will be unstable'
! suppress old files (can be commented out if "call system" is missing in your compiler)
! call system('rm -f Vx_*.dat Vy_*.dat Vz_*.dat image*.pnm image*.gif timestamp*')
! initialize arrays
vx_1(:,:,:) = 0.d0
vy_1(:,:,:) = 0.d0
vz_1(:,:,:) = 0.d0
vx_2(:,:,:) = 0.d0
vy_2(:,:,:) = 0.d0
vz_2(:,:,:) = 0.d0
vx_3(:,:,:) = 0.d0
vy_3(:,:,:) = 0.d0
vz_3(:,:,:) = 0.d0
sigmaxx_1(:,:,:) = 0.d0
sigmayy_1(:,:,:) = 0.d0
sigmazz_1(:,:,:) = 0.d0
sigmaxy_1(:,:,:) = 0.d0
sigmaxz_1(:,:,:) = 0.d0
sigmaxx_2(:,:,:) = 0.d0
sigmayy_2(:,:,:) = 0.d0
sigmazz_2(:,:,:) = 0.d0
sigmaxy_2(:,:,:) = 0.d0
sigmayz_2(:,:,:) = 0.d0
sigmaxx_3(:,:,:) = 0.d0
sigmayy_3(:,:,:) = 0.d0
sigmazz_3(:,:,:) = 0.d0
sigmaxz_3(:,:,:) = 0.d0
sigmayz_3(:,:,:) = 0.d0
! initialize seismograms
sisvx(:,:) = 0.d0
sisvy(:,:) = 0.d0
! initialize total energy
total_energy(:) = 0.d0
call date_and_time(datein,timein,zone,time_values)
! time_values(3): day of the month
! time_values(5): hour of the day
! time_values(6): minutes of the hour
! time_values(7): seconds of the minute
! time_values(8): milliseconds of the second
! this fails if we cross the end of the month
time_start = 86400.d0*time_values(3) + 3600.d0*time_values(5) + &
60.d0*time_values(6) + time_values(7) + time_values(8) / 1000.d0
!---
!--- beginning of time loop
!---
do it = 1,NSTEP
print *,'it = ',it
!----------------------
! compute stress sigma
!----------------------
!$OMP PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,d,value_dx,value_dy,value_dz) &
!$OMP SHARED(vx_1,vx_2,vx_3,vy_1,vy_2,vy_3,vz_1,vz_2,vz_3,sigmaxx_1,sigmaxx_2,sigmaxx_3, &
!$OMP sigmayy_1,sigmayy_2,sigmayy_3,sigmazz_1,sigmazz_2,sigmazz_3,dx_half_over_two,dy_over_two,dz_over_two)
do k=2,NZ
do j = 2,NY
do i = 1,NX-1
value_dx = (vx_1(i+1,j,k) - vx_1(i,j,k)) / h &
+ (vx_2(i+1,j,k) - vx_2(i,j,k)) / h &
+ (vx_3(i+1,j,k) - vx_3(i,j,k)) / h
value_dy = (vy_1(i,j,k) - vy_1(i,j-1,k)) / h &
+ (vy_2(i,j,k) - vy_2(i,j-1,k)) / h &
+ (vy_3(i,j,k) - vy_3(i,j-1,k)) / h
value_dz = (vz_1(i,j,k) - vz_1(i,j,k-1)) / h &
+ (vz_2(i,j,k) - vz_2(i,j,k-1)) / h &
+ (vz_3(i,j,k) - vz_3(i,j,k-1)) / h
d = dx_half_over_two(i)
sigmaxx_1(i,j,k) = ( sigmaxx_1(i,j,k)*(ONE_OVER_DELTAT - d) + lambda_plus_two_mu * value_dx ) / (ONE_OVER_DELTAT + d)
sigmayy_1(i,j,k) = ( sigmayy_1(i,j,k)*(ONE_OVER_DELTAT - d) + lambda * value_dx ) / (ONE_OVER_DELTAT + d)
sigmazz_1(i,j,k) = ( sigmazz_1(i,j,k)*(ONE_OVER_DELTAT - d) + lambda * value_dx ) / (ONE_OVER_DELTAT + d)
d = dy_over_two(j)
sigmaxx_2(i,j,k) = ( sigmaxx_2(i,j,k)*(ONE_OVER_DELTAT - d) + lambda * value_dy ) / (ONE_OVER_DELTAT + d)
sigmayy_2(i,j,k) = ( sigmayy_2(i,j,k)*(ONE_OVER_DELTAT - d) + lambda_plus_two_mu * value_dy ) / (ONE_OVER_DELTAT + d)
sigmazz_2(i,j,k) = ( sigmazz_2(i,j,k)*(ONE_OVER_DELTAT - d) + lambda * value_dy ) / (ONE_OVER_DELTAT + d)
d = dz_over_two(k)
sigmaxx_3(i,j,k) = ( sigmaxx_3(i,j,k)*(ONE_OVER_DELTAT - d) + lambda * value_dz ) / (ONE_OVER_DELTAT + d)
sigmayy_3(i,j,k) = ( sigmayy_3(i,j,k)*(ONE_OVER_DELTAT - d) + lambda * value_dz ) / (ONE_OVER_DELTAT + d)
sigmazz_3(i,j,k) = ( sigmazz_3(i,j,k)*(ONE_OVER_DELTAT - d) + lambda_plus_two_mu * value_dz ) / (ONE_OVER_DELTAT + d)
enddo
enddo
enddo
!$OMP END PARALLEL DO
!$OMP PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,d,value_dx,value_dy) SHARED(vx_1,vx_2,vx_3,vy_1, &
!$OMP vy_2,vy_3,sigmaxy_1,sigmaxy_2,dy_half_over_two,dx_over_two)
do k=1,NZ
do j = 1,NY-1
do i = 2,NX
value_dx = (vy_1(i,j,k) - vy_1(i-1,j,k)) / h &
+ (vy_2(i,j,k) - vy_2(i-1,j,k)) / h &
+ (vy_3(i,j,k) - vy_3(i-1,j,k)) / h
value_dy = (vx_1(i,j+1,k) - vx_1(i,j,k)) / h &
+ (vx_2(i,j+1,k) - vx_2(i,j,k)) / h &
+ (vx_3(i,j+1,k) - vx_3(i,j,k)) / h
d = dx_over_two(i)
sigmaxy_1(i,j,k) = ( sigmaxy_1(i,j,k)*(ONE_OVER_DELTAT - d) + mu * value_dx ) / (ONE_OVER_DELTAT + d)
d = dy_half_over_two(j)
sigmaxy_2(i,j,k) = ( sigmaxy_2(i,j,k)*(ONE_OVER_DELTAT - d) + mu * value_dy ) / (ONE_OVER_DELTAT + d)
enddo
enddo
enddo
!$OMP END PARALLEL DO
!$OMP PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,d,value_dx,value_dz) SHARED(vx_1,vx_2,vx_3, &
!$OMP vz_1,vz_2,vz_3,sigmaxz_1,sigmaxz_3,dz_half_over_two,dx_over_two)
do k=1,NZ-1
do j = 1,NY
do i = 2,NX
value_dx = (vz_1(i,j,k) - vz_1(i-1,j,k)) / h &
+ (vz_2(i,j,k) - vz_2(i-1,j,k)) / h &
+ (vz_3(i,j,k) - vz_3(i-1,j,k)) / h
value_dz = (vx_1(i,j,k+1) - vx_1(i,j,k)) / h &
+ (vx_2(i,j,k+1) - vx_2(i,j,k)) / h &
+ (vx_3(i,j,k+1) - vx_3(i,j,k)) / h
d = dx_over_two(i)
sigmaxz_1(i,j,k) = ( sigmaxz_1(i,j,k)*(ONE_OVER_DELTAT - d) + mu * value_dx ) / (ONE_OVER_DELTAT + d)
d = dz_half_over_two(k)
sigmaxz_3(i,j,k) = ( sigmaxz_3(i,j,k)*(ONE_OVER_DELTAT - d) + mu * value_dz ) / (ONE_OVER_DELTAT + d)
enddo
enddo
enddo
!$OMP END PARALLEL DO
!$OMP PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,d,value_dy,value_dz) SHARED(vy_1,vy_2,vy_3, &
!$OMP vz_1,vz_2,vz_3,sigmayz_2,sigmayz_3,dy_half_over_two,dz_half_over_two)
do k=1,NZ-1
do j = 1,NY-1
do i = 1,NX
value_dy = (vz_1(i,j+1,k) - vz_1(i,j,k)) / h &
+ (vz_2(i,j+1,k) - vz_2(i,j,k)) / h &
+ (vz_3(i,j+1,k) - vz_3(i,j,k)) / h
value_dz = (vy_1(i,j,k+1) - vy_1(i,j,k)) / h &
+ (vy_2(i,j,k+1) - vy_2(i,j,k)) / h &
+ (vy_3(i,j,k+1) - vy_3(i,j,k)) / h
d = dy_half_over_two(j)
sigmayz_2(i,j,k) = ( sigmayz_2(i,j,k)*(ONE_OVER_DELTAT - d) + mu * value_dy ) / (ONE_OVER_DELTAT + d)
d = dz_half_over_two(k)
sigmayz_3(i,j,k) = ( sigmayz_3(i,j,k)*(ONE_OVER_DELTAT - d) + mu * value_dz ) / (ONE_OVER_DELTAT + d)
enddo
enddo
enddo
!$OMP END PARALLEL DO
!------------------
! compute velocity
!------------------
!$OMP PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,d,value_dx,value_dy,value_dz) SHARED(vx_1,vx_2, &
!$OMP vx_3,sigmaxx_1,sigmaxx_2,sigmaxx_3,sigmaxy_1,sigmaxy_2,sigmaxz_1,sigmaxz_3,dx_over_two,dy_over_two,dz_over_two)
do k = 2,NZ
do j = 2,NY
do i = 2,NX
value_dx = (sigmaxx_1(i,j,k) - sigmaxx_1(i-1,j,k)) / h &
+ (sigmaxx_2(i,j,k) - sigmaxx_2(i-1,j,k)) / h &
+ (sigmaxx_3(i,j,k) - sigmaxx_3(i-1,j,k)) / h
value_dy = (sigmaxy_1(i,j,k) - sigmaxy_1(i,j-1,k)) / h &
+ (sigmaxy_2(i,j,k) - sigmaxy_2(i,j-1,k)) / h
value_dz = (sigmaxz_1(i,j,k) - sigmaxz_1(i,j,k-1)) / h &
+ (sigmaxz_3(i,j,k) - sigmaxz_3(i,j,k-1)) / h
d = dx_over_two(i)
vx_1(i,j,k) = ( vx_1(i,j,k)*(ONE_OVER_DELTAT - d) + value_dx / rho ) / (ONE_OVER_DELTAT + d)
d = dy_over_two(j)
vx_2(i,j,k) = ( vx_2(i,j,k)*(ONE_OVER_DELTAT - d) + value_dy / rho ) / (ONE_OVER_DELTAT + d)
d = dz_over_two(k)
vx_3(i,j,k) = ( vx_3(i,j,k)*(ONE_OVER_DELTAT - d) + value_dz / rho ) / (ONE_OVER_DELTAT + d)
enddo
enddo
enddo
!$OMP END PARALLEL DO
!$OMP PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,d,value_dx,value_dy,value_dz) SHARED(vy_1,vy_2, &
!$OMP vy_3,sigmayy_1,sigmayy_2,sigmayy_3,sigmaxy_1,sigmaxy_2,sigmayz_2,sigmayz_3,dx_half_over_two,dy_half_over_two,dz_over_two)
do k = 2,NZ
do j = 1,NY-1
do i = 1,NX-1
value_dx = (sigmaxy_1(i+1,j,k) - sigmaxy_1(i,j,k)) / h &
+ (sigmaxy_2(i+1,j,k) - sigmaxy_2(i,j,k)) / h
value_dy = (sigmayy_1(i,j+1,k) - sigmayy_1(i,j,k)) / h &
+ (sigmayy_2(i,j+1,k) - sigmayy_2(i,j,k)) / h &
+ (sigmayy_3(i,j+1,k) - sigmayy_3(i,j,k)) / h
value_dz = (sigmayz_2(i,j,k) - sigmayz_2(i,j,k-1)) / h &
+ (sigmayz_3(i,j,k) - sigmayz_3(i,j,k-1)) / h
d = dx_half_over_two(i)
vy_1(i,j,k) = ( vy_1(i,j,k)*(ONE_OVER_DELTAT - d) + value_dx / rho ) / (ONE_OVER_DELTAT + d)
d = dy_half_over_two(j)
vy_2(i,j,k) = ( vy_2(i,j,k)*(ONE_OVER_DELTAT - d) + value_dy / rho ) / (ONE_OVER_DELTAT + d)
d = dz_over_two(k)
vy_3(i,j,k) = ( vy_3(i,j,k)*(ONE_OVER_DELTAT - d) + value_dz / rho ) / (ONE_OVER_DELTAT + d)
enddo
enddo
enddo
!$OMP END PARALLEL DO
!$OMP PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,d,value_dx,value_dy,value_dz) SHARED(vz_1,vz_2, &
!$OMP vz_3,sigmazz_1,sigmazz_2,sigmazz_3,sigmaxz_1,sigmaxz_3,sigmayz_2,sigmayz_3,dx_half_over_two,dy_over_two,dz_half_over_two)
do k = 1,NZ-1
do j = 2,NY
do i = 1,NX-1
value_dx = (sigmaxz_1(i+1,j,k) - sigmaxz_1(i,j,k)) / h &
+ (sigmaxz_3(i+1,j,k) - sigmaxz_3(i,j,k)) / h
value_dy = (sigmayz_2(i,j,k) - sigmayz_2(i,j-1,k)) / h &
+ (sigmayz_3(i,j,k) - sigmayz_3(i,j-1,k)) / h
value_dz = (sigmazz_1(i,j,k+1) - sigmazz_1(i,j,k)) / h &
+ (sigmazz_2(i,j,k+1) - sigmazz_2(i,j,k)) / h &
+ (sigmazz_3(i,j,k+1) - sigmazz_3(i,j,k)) / h
d = dx_half_over_two(i)
vz_1(i,j,k) = ( vz_1(i,j,k)*(ONE_OVER_DELTAT - d) + value_dx / rho ) / (ONE_OVER_DELTAT + d)
d = dy_over_two(j)
vz_2(i,j,k) = ( vz_2(i,j,k)*(ONE_OVER_DELTAT - d) + value_dy / rho ) / (ONE_OVER_DELTAT + d)
d = dz_half_over_two(k)
vz_3(i,j,k) = ( vz_3(i,j,k)*(ONE_OVER_DELTAT - d) + value_dz / rho ) / (ONE_OVER_DELTAT + d)
enddo
enddo
enddo
!$OMP END PARALLEL DO
! add the source (force vector located at a given grid point)
a = pi*pi*f0*f0
t = dble(it-1)*DELTAT
! Gaussian
! source_term = factor * exp(-a*(t-t0)**2)
! first derivative of a Gaussian
source_term = - factor * 2.d0*a*(t-t0)*exp(-a*(t-t0)**2)
! Ricker source time function (second derivative of a Gaussian)
! source_term = factor * (1.d0 - 2.d0*a*(t-t0)**2)*exp(-a*(t-t0)**2)
force_x = sin(ANGLE_FORCE * DEGREES_TO_RADIANS) * source_term
force_y = cos(ANGLE_FORCE * DEGREES_TO_RADIANS) * source_term
force_z = 0.d0
! add the source to one of the two components of the split field
vx_1(ISOURCE,JSOURCE,KSOURCE) = vx_1(ISOURCE,JSOURCE,KSOURCE) + force_x * DELTAT / rho
vy_1(ISOURCE,JSOURCE,KSOURCE) = vy_1(ISOURCE,JSOURCE,KSOURCE) + force_y * DELTAT / rho
! implement Dirichlet boundary conditions on the six edges of the grid
!$OMP PARALLEL WORKSHARE
! xmin
vx_1(1,:,:) = 0.d0
vy_1(1,:,:) = 0.d0
vz_1(1,:,:) = 0.d0
vx_2(1,:,:) = 0.d0
vy_2(1,:,:) = 0.d0
vz_2(1,:,:) = 0.d0
vx_3(1,:,:) = 0.d0
vy_3(1,:,:) = 0.d0
vz_3(1,:,:) = 0.d0
! xmax
vx_1(NX,:,:) = 0.d0
vy_1(NX,:,:) = 0.d0
vz_1(NX,:,:) = 0.d0
vx_2(NX,:,:) = 0.d0
vy_2(NX,:,:) = 0.d0
vz_2(NX,:,:) = 0.d0
vx_3(NX,:,:) = 0.d0
vy_3(NX,:,:) = 0.d0
vz_3(NX,:,:) = 0.d0
! ymin
vx_1(:,1,:) = 0.d0
vy_1(:,1,:) = 0.d0
vz_1(:,1,:) = 0.d0
vx_2(:,1,:) = 0.d0
vy_2(:,1,:) = 0.d0
vz_2(:,1,:) = 0.d0
vx_3(:,1,:) = 0.d0
vy_3(:,1,:) = 0.d0
vz_3(:,1,:) = 0.d0
! ymax
vx_1(:,NY,:) = 0.d0
vy_1(:,NY,:) = 0.d0
vz_1(:,NY,:) = 0.d0
vx_2(:,NY,:) = 0.d0
vy_2(:,NY,:) = 0.d0
vz_2(:,NY,:) = 0.d0
vx_3(:,NY,:) = 0.d0
vy_3(:,NY,:) = 0.d0
vz_3(:,NY,:) = 0.d0
! zmin
vx_1(:,:,1) = 0.d0
vy_1(:,:,1) = 0.d0
vz_1(:,:,1) = 0.d0
vx_2(:,:,1) = 0.d0
vy_2(:,:,1) = 0.d0
vz_2(:,:,1) = 0.d0
vx_3(:,:,1) = 0.d0
vy_3(:,:,1) = 0.d0
vz_3(:,:,1) = 0.d0
! zmax
vx_1(:,:,NZ) = 0.d0
vy_1(:,:,NZ) = 0.d0
vz_1(:,:,NZ) = 0.d0
vx_2(:,:,NZ) = 0.d0
vy_2(:,:,NZ) = 0.d0
vz_2(:,:,NZ) = 0.d0
vx_3(:,:,NZ) = 0.d0
vy_3(:,:,NZ) = 0.d0
vz_3(:,:,NZ) = 0.d0
!$OMP END PARALLEL WORKSHARE
! store seismograms
do irec = 1,NREC
sisvx(it,irec) = vx_1(ix_rec(irec),iy_rec(irec),iz_rec(irec)) + &
vx_2(ix_rec(irec),iy_rec(irec),iz_rec(irec)) + vx_3(ix_rec(irec),iy_rec(irec),iz_rec(irec))
sisvy(it,irec) = vy_1(ix_rec(irec),iy_rec(irec),iz_rec(irec)) + &
vy_2(ix_rec(irec),iy_rec(irec),iz_rec(irec)) + vy_3(ix_rec(irec),iy_rec(irec),iz_rec(irec))
enddo
! compute total energy in the medium (without the PML layers)
total_energy_kinetic = ZERO
total_energy_potential = ZERO
!$OMP PARALLEL DO DEFAULT(NONE) PRIVATE(i,j,k,sigmaxx_total,sigmayy_total, &
!$OMP sigmazz_total,sigmaxy_total,sigmaxz_total,sigmayz_total,epsilon_xx,epsilon_yy,epsilon_zz,epsilon_xy,epsilon_xz,epsilon_yz) &
!$OMP SHARED(vx_1,vx_2,vx_3,vy_1,vy_2,vy_3,vz_1,vz_2,vz_3,sigmaxx_1,sigmaxx_2, &
!$OMP sigmaxx_3,sigmayy_1,sigmayy_2,sigmayy_3,sigmazz_1,sigmazz_2,sigmazz_3, &
!$OMP sigmaxy_1,sigmaxy_2,sigmaxz_1,sigmaxz_3,sigmayz_2,sigmayz_3) REDUCTION(+:total_energy_kinetic,total_energy_potential)
do k = NPOINTS_PML+1, NZ-NPOINTS_PML
do j = NPOINTS_PML+1, NY-NPOINTS_PML
do i = NPOINTS_PML+1, NX-NPOINTS_PML
! compute kinetic energy first, defined as 1/2 rho ||v||^2
! in principle we should use rho_half_x_half_y instead of rho for vy
! in order to interpolate density at the right location in the staggered grid cell
! but in a homogeneous medium we can safely ignore it
total_energy_kinetic = total_energy_kinetic + 0.5d0 * rho*( &
(vx_1(i,j,k) + vx_2(i,j,k) + vx_3(i,j,k))**2 + &
(vy_1(i,j,k) + vy_2(i,j,k) + vy_3(i,j,k))**2 + &
(vz_1(i,j,k) + vz_2(i,j,k) + vz_3(i,j,k))**2)
! add potential energy, defined as 1/2 epsilon_ij sigma_ij
! in principle we should interpolate the medium parameters at the right location
! in the staggered grid cell but in a homogeneous medium we can safely ignore it
! compute total field from split components
sigmaxx_total = sigmaxx_1(i,j,k) + sigmaxx_2(i,j,k) + sigmaxx_3(i,j,k)
sigmayy_total = sigmayy_1(i,j,k) + sigmayy_2(i,j,k) + sigmayy_3(i,j,k)
sigmazz_total = sigmazz_1(i,j,k) + sigmazz_2(i,j,k) + sigmazz_3(i,j,k)
sigmaxy_total = sigmaxy_1(i,j,k) + sigmaxy_2(i,j,k)
sigmaxz_total = sigmaxz_1(i,j,k) + sigmaxz_3(i,j,k)
sigmayz_total = sigmayz_2(i,j,k) + sigmayz_3(i,j,k)
epsilon_xx = (2.d0*(lambda + mu) * sigmaxx_total - lambda * sigmayy_total -lambda*sigmazz_total) / &
(2.d0 * mu * (3.d0*lambda + 2.d0*mu))
epsilon_yy = (2.d0*(lambda + mu) * sigmayy_total - lambda * sigmaxx_total -lambda*sigmazz_total) / &
(2.d0 * mu * (3.d0*lambda + 2.d0*mu))
epsilon_zz = (2.d0*(lambda + mu) * sigmazz_total - lambda * sigmaxx_total -lambda*sigmayy_total) / &
(2.d0 * mu * (3.d0*lambda + 2.d0*mu))
epsilon_xy = sigmaxy_total / (2.d0 * mu)
epsilon_xz = sigmaxz_total / (2.d0 * mu)
epsilon_yz = sigmayz_total / (2.d0 * mu)
total_energy_potential = total_energy_potential + &
0.5d0 * (epsilon_xx * sigmaxx_total + epsilon_yy * sigmayy_total + &
epsilon_yy * sigmayy_total+ 2.d0 * epsilon_xy * sigmaxy_total + &
2.d0*epsilon_xz * sigmaxz_total+2.d0*epsilon_yz * sigmayz_total)
enddo
enddo
enddo
!$OMP END PARALLEL DO
total_energy(it) = total_energy_kinetic + total_energy_potential
! output information
if (mod(it,IT_DISPLAY) == 0 .or. it == 5) then
Vsolidnorm = maxval(sqrt((vx_1 + vx_2 + vx_3)**2 + (vy_1 + vy_2 + vy_3)**2+(vz_1 + vz_2 + vz_3)**2))
print *,'Time step # ',it,' out of ',NSTEP
print *,'Time: ',sngl((it-1)*DELTAT),' seconds'
print *,'Max norm velocity vector V (m/s) = ',Vsolidnorm
print *,'Total energy = ',total_energy(it)
! check stability of the code, exit if unstable
if (Vsolidnorm > STABILITY_THRESHOLD) stop 'code became unstable and blew up'
iplane=1
! count elapsed wall-clock time
call date_and_time(datein,timein,zone,time_values)
! time_values(3): day of the month
! time_values(5): hour of the day
! time_values(6): minutes of the hour
! time_values(7): seconds of the minute
! time_values(8): milliseconds of the second
! this fails if we cross the end of the month
time_end = 86400.d0*time_values(3) + 3600.d0*time_values(5) + &
60.d0*time_values(6) + time_values(7) + time_values(8) / 1000.d0
! elapsed time since beginning of the simulation
tCPU = time_end - time_start
int_tCPU = int(tCPU)
ihours = int_tCPU / 3600
iminutes = (int_tCPU - 3600*ihours) / 60
iseconds = int_tCPU - 3600*ihours - 60*iminutes
write(*,*) 'Elapsed time in seconds = ',tCPU
write(*,"(' Elapsed time in hh:mm:ss = ',i4,' h ',i2.2,' m ',i2.2,' s')") ihours,iminutes,iseconds
write(*,*) 'Mean elapsed time per time step in seconds = ',tCPU/dble(it)
write(*,*)
! write time stamp file to give information about progression of simulation
write(outputname,"('timestamp',i6.6)") it
open(unit=IOUT,file=outputname,status='unknown')
write(IOUT,*) 'Time step # ',it
write(IOUT,*) 'Time: ',sngl((it-1)*DELTAT),' seconds'
write(IOUT,*) 'Max norm velocity vector V (m/s) = ',Vsolidnorm
write(IOUT,*) 'Total energy = ',total_energy(it)
write(IOUT,*) 'Elapsed time in seconds = ',tCPU
write(IOUT,"(' Elapsed time in hh:mm:ss = ',i4,' h ',i2.2,' m ',i2.2,' s')") ihours,iminutes,iseconds
write(IOUT,*) 'Mean elapsed time per time step in seconds = ',tCPU/dble(it)
close(IOUT)
! save seismograms
print *,'saving seismograms'
print *
call write_seismograms(sisvx,sisvy,NSTEP,NREC,DELTAT)
! here we represent the cut plane that is in the middle of the model along the Z direction, in NZ/2
call create_color_image(vx_1(:,:,NZ/2) + vx_2(:,:,NZ/2) + vx_3(:,:,NZ/2),NX,NY,it,ISOURCE,JSOURCE,ix_rec,iy_rec,nrec, &
NPOINTS_PML,.true.,.true.,.true.,.true.,1)
call create_color_image(vy_1(:,:,NZ/2) + vy_2(:,:,NZ/2) +vy_3(:,:,NZ/2),NX,NY,it,ISOURCE,JSOURCE,ix_rec,iy_rec,nrec, &
NPOINTS_PML,.true.,.true.,.true.,.true.,2)
endif
enddo ! end of time loop
! save seismograms
call write_seismograms(sisvx,sisvy,NSTEP,NREC,DELTAT)
! save total energy
open(unit=20,file='energy.dat',status='unknown')
do it = 1,NSTEP
write(20,*) sngl(dble(it-1)*DELTAT),total_energy(it)
enddo
close(20)
! create script for Gnuplot for total energy
open(unit=20,file='plot_energy',status='unknown')
write(20,*) '# set term x11'
write(20,*) 'set term postscript landscape monochrome dashed "Helvetica" 22'
write(20,*)
write(20,*) 'set xlabel "Time (s)"'
write(20,*) 'set ylabel "Total energy"'
write(20,*)
write(20,*) 'set output "collino3D_total_energy_semilog.eps"'
write(20,*) 'set logscale y'
write(20,*) 'plot "energy.dat" t ''Total energy'' w l lc 1'
write(20,*) 'pause -1 "Hit any key..."'
write(20,*)
close(20)
! create script for Gnuplot
open(unit=20,file='plotgnu',status='unknown')
write(20,*) 'set term x11'
write(20,*) '# set term postscript landscape monochrome dashed "Helvetica" 22'
write(20,*)
write(20,*) 'set xlabel "Time (s)"'
write(20,*) 'set ylabel "Amplitude (m / s)"'
write(20,*)
write(20,*) 'set output "v_sigma_Vx_receiver_001.eps"'
write(20,*) 'plot "Vx_file_001.dat" t ''Vx C-PML'' w l lc 1'
write(20,*) 'pause -1 "Hit any key..."'
write(20,*)
write(20,*) 'set output "v_sigma_Vy_receiver_001.eps"'
write(20,*) 'plot "Vy_file_001.dat" t ''Vy C-PML'' w l lc 1'
write(20,*) 'pause -1 "Hit any key..."'
write(20,*)
write(20,*) 'set output "v_sigma_Vz_receiver_001.eps"'
write(20,*) 'plot "Vz_file_001.dat" t ''Vz C-PML'' w l lc 1'
write(20,*) 'pause -1 "Hit any key..."'
write(20,*)
write(20,*) 'set output "v_sigma_Vx_receiver_002.eps"'
write(20,*) 'plot "Vx_file_002.dat" t ''Vx C-PML'' w l lc 1'
write(20,*) 'pause -1 "Hit any key..."'
write(20,*)
write(20,*) 'set output "v_sigma_Vy_receiver_002.eps"'
write(20,*) 'plot "Vy_file_002.dat" t ''Vy C-PML'' w l lc 1'
write(20,*) 'pause -1 "Hit any key..."'
write(20,*)
write(20,*) 'set output "v_sigma_Vz_receiver_002.eps"'
write(20,*) 'plot "Vz_file_002.dat" t ''Vz C-PML'' w l lc 1'
write(20,*) 'pause -1 "Hit any key..."'
write(20,*)
close(20)
print *
print *,'End of the simulation'
print *
end program seismic_PML_Collino_3D_iso
!----
!---- save the seismograms in ASCII text format
!----
subroutine write_seismograms(sisvx,sisvy,nt,nrec,DELTAT)
implicit none
integer nt,nrec
double precision DELTAT
double precision sisvx(nt,nrec)
double precision sisvy(nt,nrec)
integer irec,it
character(len=100) file_name
! X component
do irec=1,nrec
write(file_name,"('Vx_file_',i3.3,'.dat')") irec
open(unit=11,file=file_name,status='unknown')
do it=1,nt
write(11,*) sngl(dble(it-1)*DELTAT),' ',sngl(sisvx(it,irec))
enddo
close(11)
enddo
! Y component
do irec=1,nrec
write(file_name,"('Vy_file_',i3.3,'.dat')") irec
open(unit=11,file=file_name,status='unknown')
do it=1,nt
write(11,*) sngl(dble(it-1)*DELTAT),' ',sngl(sisvy(it,irec))
enddo
close(11)
enddo
end subroutine write_seismograms
!----
!---- routine to create a color image of a given vector component
!---- the image is created in PNM format and then converted to GIF
!----
subroutine create_color_image(image_data_2D,NX,NY,it,ISOURCE,JSOURCE,ix_rec,iy_rec,nrec, &
NPOINTS_PML,USE_PML_XMIN,USE_PML_XMAX,USE_PML_YMIN,USE_PML_YMAX,field_number)
implicit none
! non linear display to enhance small amplitudes for graphics
double precision, parameter :: POWER_DISPLAY = 0.30d0