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seismic_PML_Collino_2D_anisotropic_fourth.f90
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!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Program seismic_PML_Collino_2D_ani_4th, fourth-order accurate in space and second-order accurate in time
!
! This anisotropic code with classical split PML is modified by Jingyi Chen from program 'seismic_PML_Collino_2D_iso'
! written by Dimitri Komatitsch.
!
! Jingyi Chen, Department of Geosciences, University of Tulsa, USA. Email: jingyi-chen AT utulsa DOT edu
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Copyright Universite de Pau et des Pays de l'Adour, CNRS and INRIA, France.
! Contributors: Dimitri Komatitsch, dimitri DOT komatitsch aT univ-pau DOT fr
! Jingyi Chen, jingyi-chen AT utulsa DOT edu
!
! This software is a computer program whose purpose is to solve
! the two-dimensional anisotropic elastic wave equation
! using a finite-difference method with classical split Perfectly Matched
! Layer (PML) conditions.
!
! This software is governed by the CeCILL license under French law and
! abiding by the rules of distribution of free software. You can use,
! modify and/or redistribute the software under the terms of the CeCILL
! license as circulated by CEA, CNRS and INRIA at the following URL
! "http://www.cecill.info".
!
! As a counterpart to the access to the source code and rights to copy,
! modify and redistribute granted by the license, users are provided only
! with a limited warranty and the software's author, the holder of the
! economic rights, and the successive licensors have only limited
! liability.
!
! In this respect, the user's attention is drawn to the risks associated
! with loading, using, modifying and/or developing or reproducing the
! software by the user in light of its specific status of free software,
! that may mean that it is complicated to manipulate, and that also
! therefore means that it is reserved for developers and experienced
! professionals having in-depth computer knowledge. Users are therefore
! encouraged to load and test the software's suitability as regards their
! requirements in conditions enabling the security of their systems and/or
! data to be ensured and, more generally, to use and operate it in the
! same conditions as regards security.
!
! The full text of the license is available at the end of this program
! and in file "LICENSE".
program seismic_PML_Collino_2D_ani_4th
! 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
!
! PML implemented in the two directions (x and y directions).
!
! Version 1.0 July, 2010
! Jingyi Chen,the Department of Geosciences, The University of Tulsa, USA. Email: jingyi-chen@utulsa.edu
!
! The second-order staggered-grid formulation of Madariaga (1976) and Virieux (1986) is used:
!
! ^ y
! |
! |
!
! +-------------------+
! | |
! | |
! | |
! | |
! | v_y |
! sigma_xy +---------+ |
! | | |
! | | |
! | | |
! | | |
! | | |
! +---------+---------+ ---> x
! v_x sigma_xx
! sigma_yy
!
!
! To display the 2D results as color images, use:
!
! " display image* " or " gimp image* "
!
! 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 = 401
integer, parameter :: NY = 401
! size of a grid cell
double precision, parameter :: h = 5.d0
! flags to add PML layers to the edges of the grid
logical, parameter :: USE_PML_XMIN = .true.
logical, parameter :: USE_PML_XMAX = .true.
logical, parameter :: USE_PML_YMIN = .true.
logical, parameter :: USE_PML_YMAX = .true.
! thickness of the PML layer in grid points
integer, parameter :: NPOINTS_PML = 10
! model I from Becache, Fauqueux and Joly, which is stable
! Model was also used in Dimitri Komatitsch and Roland Martin (2007),geophysics
double precision, parameter :: scale_aniso = 1.d10
double precision, parameter :: c11 = 4.d0 * scale_aniso
double precision, parameter :: c12 = 3.8d0 * scale_aniso
double precision, parameter :: c22 = 20.d0 * scale_aniso
double precision, parameter :: c33 = 2.d0 * scale_aniso
double precision, parameter :: rho = 4000.d0 ! used to be 1.
! double precision, parameter :: f0 = 25.d0
! total number of time steps
integer, parameter :: NSTEP = 3000
! time step in seconds
double precision, parameter :: DELTAT = 1.d-3/2
double precision, parameter :: ONE_OVER_DELTAT = 1.d0 / DELTAT
! parameters for the source
double precision, parameter :: f0 = 25.d0
double precision, parameter :: t0 = 1.20d0 / f0
double precision, parameter :: factor = 1.d7
! source
integer, parameter :: ISOURCE = NX - 2*NPOINTS_PML - 1
integer, parameter :: JSOURCE = 2 * NY / 3 + 1
double precision, parameter :: xsource = (ISOURCE - 1) * h
double precision, parameter :: ysource = (JSOURCE - 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 :: xfin = xsource ! last receiver x in meters
double precision, parameter :: yfin = 300.d0 ! last receiver y in meters
! display information on the screen from time to time
integer, parameter :: IT_DISPLAY = 200
! 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
! definition of the split velocity vector and stress tensor:
!
! vx(:,:) = vx_1(:,:) + vx_2(:,:)
! vy(:,:) = vy_1(:,:) + vy_2(:,:)
!
! sigmaxx(:,:) = sigmaxx_1(:,:) + sigmaxx_2(:,:)
! sigmayy(:,:) = sigmayy_1(:,:) + sigmayy_2(:,:)
! sigmaxy(:,:) = sigmaxy_1(:,:) + sigmaxy_2(:,:)
! main arrays
double precision, dimension(NX,NY) :: vx_1,vx_2,vy_1,vy_2, &
sigmaxx_1,sigmaxx_2,sigmayy_1,sigmayy_2,sigmaxy_1,sigmaxy_2
! additional array used for display only
double precision, dimension(NX,NY) :: image_data_2D
double precision, dimension(NX) :: dx_over_two,dx_half_over_two
double precision, dimension(NY) :: dy_over_two,dy_half_over_two
! for stability estimate
double precision :: quasi_cp_max,aniso_stability_criterion,aniso2,aniso3
! for the source
double precision a,t,force_x,force_y,source_term
! for receivers
double precision xspacerec,yspacerec,distval,dist
integer, dimension(NREC) :: ix_rec,iy_rec
double precision, dimension(NREC) :: xrec,yrec
double precision, dimension(NSTEP,NREC) :: sisvx,sisvy
! for evolution of total energy in the medium
double precision :: epsilon_xx,epsilon_yy,epsilon_xy
double precision :: sigmaxx_total,sigmayy_total,sigmaxy_total
double precision, dimension(NSTEP) :: total_energy_kinetic,total_energy_potential
integer :: i,j,it,irec
double precision :: xval,delta,xoriginleft,xoriginright,rcoef,d0,velocnorm,Courant_number,value_dx,value_dy,d
! *******************
! program starts here
! *******************
print *
print *,'2D elastic anisotropic finite-difference code in velocity and stress formulation with split PML'
print *
! display size of the model
print *
print *,'NX = ',NX
print *,'NY = ',NY
print *
print *,'size of the model along X = ',(NX - 1) * h
print *,'size of the model along Y = ',(NY - 1) * h
print *
print *,'Total number of grid points = ',NX * NY
print *
print *,'Velocity of qP along vertical axis. . . . =',sqrt(c22/rho)
print *,'Velocity of qP along horizontal axis. . . =',sqrt(c11/rho)
print *
print *,'Velocity of qSV along vertical axis . . . =',sqrt(c33/rho)
print *,'Velocity of qSV along horizontal axis . . =',sqrt(c33/rho)
print *
! from Becache et al., INRIA report, equation 7 page 5 http://hal.inria.fr/docs/00/07/22/83/PDF/RR-4304.pdf
if(c11*c22 - c12*c12 <= 0.d0) stop 'problem in definition of orthotropic material'
! check intrinsic mathematical stability of PML model for an anisotropic material
! from E. B\'ecache, S. Fauqueux and P. Joly, Stability of Perfectly Matched Layers, group
! velocities and anisotropic waves, Journal of Computational Physics, 188(2), p. 399-433 (2003)
aniso_stability_criterion = ((c12+c33)**2 - c11*(c22-c33)) * ((c12+c33)**2 + c33*(c22-c33))
print *,'PML anisotropy stability criterion from Becache et al. 2003 = ',aniso_stability_criterion
if(aniso_stability_criterion > 0.d0 .and. (USE_PML_XMIN .or. USE_PML_XMAX .or. USE_PML_YMIN .or. USE_PML_YMAX)) &
print *,'WARNING: PML model mathematically intrinsically unstable for this anisotropic material for condition 1'
print *
aniso2 = (c12 + 2*c33)**2 - c11*c22
print *,'PML aniso2 stability criterion from Becache et al. 2003 = ',aniso2
if(aniso2 > 0.d0 .and. (USE_PML_XMIN .or. USE_PML_XMAX .or. USE_PML_YMIN .or. USE_PML_YMAX)) &
print *,'WARNING: PML model mathematically intrinsically unstable for this anisotropic material for condition 2'
print *
aniso3 = (c12 + c33)**2 - c11*c22 - c33**2
print *,'PML aniso3 stability criterion from Becache et al. 2003 = ',aniso3
if(aniso3 > 0.d0 .and. (USE_PML_XMIN .or. USE_PML_XMAX .or. USE_PML_YMIN .or. USE_PML_YMAX)) &
print *,'WARNING: PML model mathematically intrinsically unstable for this anisotropic material for condition 3'
print *
! to compute d0 below, and for stability estimate
quasi_cp_max = max(sqrt(c22/rho),sqrt(c11/rho))
!--- 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 * quasi_cp_max * 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
! print position of the source
print *
print *,'Position of the source:'
print *
print *,'x = ',xsource
print *,'y = ',ysource
print *
! define location of receivers
print *
print *,'There are ',nrec,' receivers'
print *
xspacerec = (xfin-xdeb) / dble(NREC-1)
yspacerec = (yfin-ydeb) / dble(NREC-1)
do irec=1,nrec
xrec(irec) = xdeb + dble(irec-1)*xspacerec
yrec(irec) = ydeb + dble(irec-1)*yspacerec
enddo
! find closest grid point for each receiver
do irec=1,nrec
dist = HUGEVAL
do j = 1,NY
do i = 1,NX
distval = sqrt((h*dble(i-1) - xrec(irec))**2 + (h*dble(j-1) - yrec(irec))**2)
if(distval < dist) then
dist = distval
ix_rec(irec) = i
iy_rec(irec) = j
endif
enddo
enddo
print *,'receiver ',irec,' x_target,y_target = ',xrec(irec),yrec(irec)
print *,'closest grid point found at distance ',dist,' in i,j = ',ix_rec(irec),iy_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 = quasi_cp_max * DELTAT * sqrt(1.d0/h**2 + 1.d0/h**2)
print *,'Courant number is ',Courant_number
print *
if(Courant_number > 1.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 image*.pnm image*.gif')
! initialize arrays
vx_1(:,:) = 0.d0
vy_1(:,:) = 0.d0
vx_2(:,:) = 0.d0
vy_2(:,:) = 0.d0
sigmaxx_1(:,:) = 0.d0
sigmayy_1(:,:) = 0.d0
sigmaxy_1(:,:) = 0.d0
sigmaxx_2(:,:) = 0.d0
sigmayy_2(:,:) = 0.d0
sigmaxy_2(:,:) = 0.d0
! initialize seismograms
sisvx(:,:) = 0.d0
sisvy(:,:) = 0.d0
! initialize total energy
total_energy_kinetic(:) = 0.d0
total_energy_potential(:) = 0.d0
!---
!--- beginning of time loop
!---
do it = 1,NSTEP
!----------------------
! compute stress sigma
!----------------------
do j = 3,NY-1
do i = 2,NX-2
value_dx = (27.d0*vx_1(i+1,j) - 27.d0*vx_1(i,j)-vx_1(i+2,j)+vx_1(i-1,j)) / (24.d0*h) &
+ (27.d0*vx_2(i+1,j) - 27.d0*vx_2(i,j)-vx_2(i+2,j)+vx_2(i-1,j)) / (24.d0*h)
value_dy = (27.d0*vy_1(i,j) - 27.d0*vy_1(i,j-1)-vy_1(i,j+1)+vy_1(i,j-2)) / (24.d0*h) &
+ (27.d0*vy_2(i,j) - 27.d0*vy_2(i,j-1)-vy_2(i,j+1)+vy_2(i,j-2)) / (24.d0*h)
d = dx_half_over_two(i)
sigmaxx_1(i,j) = ( sigmaxx_1(i,j)*(ONE_OVER_DELTAT - d) + c11 * value_dx ) / (ONE_OVER_DELTAT + d)
sigmayy_1(i,j) = ( sigmayy_1(i,j)*(ONE_OVER_DELTAT - d) + c12 * value_dx ) / (ONE_OVER_DELTAT + d)
d = dy_over_two(j)
sigmaxx_2(i,j) = ( sigmaxx_2(i,j)*(ONE_OVER_DELTAT - d) + c12 * value_dy ) / (ONE_OVER_DELTAT + d)
sigmayy_2(i,j) = ( sigmayy_2(i,j)*(ONE_OVER_DELTAT - d) + c22 * value_dy ) / (ONE_OVER_DELTAT + d)
enddo
enddo
do j = 2,NY-2
do i = 3,NX-1
value_dx = (27.d0*vy_1(i,j) - 27.d0*vy_1(i-1,j)-vy_1(i+1,j)+vy_1(i-2,j)) / (24.d0*h) &
+ (27.d0*vy_2(i,j) - 27.d0*vy_2(i-1,j)-vy_2(i+1,j)+vy_2(i-2,j)) / (24.d0*h)
value_dy = (27.d0*vx_1(i,j+1) - 27.d0*vx_1(i,j)-vx_1(i,j+2)+vx_1(i,j-1)) / (24.d0*h) &
+ (27.d0*vx_2(i,j+1) - 27.d0*vx_2(i,j)-vx_2(i,j+2)+vx_2(i,j-1)) / (24.d0*h)
d = dx_over_two(i)
sigmaxy_1(i,j) = ( sigmaxy_1(i,j)*(ONE_OVER_DELTAT - d) + c33 * value_dx ) / (ONE_OVER_DELTAT + d)
d = dy_half_over_two(j)
sigmaxy_2(i,j) = ( sigmaxy_2(i,j)*(ONE_OVER_DELTAT - d) + c33 * value_dy ) / (ONE_OVER_DELTAT + d)
enddo
enddo
!------------------
! compute velocity
!------------------
do j = 3,NY-1
do i = 3,NX-1
value_dx = (27.d0*sigmaxx_1(i,j) - 27.d0*sigmaxx_1(i-1,j)-sigmaxx_1(i+1,j)+sigmaxx_1(i-2,j)) / (24.d0*h) &
+ (27.d0*sigmaxx_2(i,j) - 27.d0*sigmaxx_2(i-1,j)-sigmaxx_2(i+1,j)+sigmaxx_2(i-2,j)) / (24.d0*h)
value_dy = (27.d0*sigmaxy_1(i,j) - 27.d0*sigmaxy_1(i,j-1)-sigmaxy_1(i,j+1)+sigmaxy_1(i,j-2)) / (24.d0*h) &
+ (27.d0*sigmaxy_2(i,j) - 27.d0*sigmaxy_2(i,j-1)-sigmaxy_2(i,j+1)+sigmaxy_2(i,j-2)) / (24.d0*h)
d = dx_over_two(i)
vx_1(i,j) = ( vx_1(i,j)*(ONE_OVER_DELTAT - d) + value_dx / rho ) / (ONE_OVER_DELTAT + d)
d = dy_over_two(j)
vx_2(i,j) = ( vx_2(i,j)*(ONE_OVER_DELTAT - d) + value_dy / rho ) / (ONE_OVER_DELTAT + d)
enddo
enddo
do j = 2,NY-2
do i = 2,NX-2
value_dx = (27.d0*sigmaxy_1(i+1,j) - 27.d0*sigmaxy_1(i,j)-sigmaxy_1(i+2,j)+sigmaxy_1(i-1,j)) / (24.d0*h) &
+ (27.d0*sigmaxy_2(i+1,j) - 27.d0*sigmaxy_2(i,j)-sigmaxy_2(i+2,j)+sigmaxy_2(i-1,j)) / (24.d0*h)
value_dy = (27.d0*sigmayy_1(i,j+1) - 27.d0*sigmayy_1(i,j)-sigmayy_1(i,j+2)+sigmayy_1(i,j-1)) / (24.d0*h) &
+ (27.d0*sigmayy_2(i,j+1) - 27.d0*sigmayy_2(i,j)-sigmayy_2(i,j+2)+sigmayy_2(i,j-1)) / (24.d0*h)
d = dx_half_over_two(i)
vy_1(i,j) = ( vy_1(i,j)*(ONE_OVER_DELTAT - d) + value_dx / rho ) / (ONE_OVER_DELTAT + d)
d = dy_half_over_two(j)
vy_2(i,j) = ( vy_2(i,j)*(ONE_OVER_DELTAT - d) + value_dy / rho ) / (ONE_OVER_DELTAT + d)
enddo
enddo
! 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
! define location of the source
i = ISOURCE
j = JSOURCE
! add the source to one of the two components of the split field
vx_1(i,j) = vx_1(i,j) + force_x * DELTAT / rho
vy_1(i,j) = vy_1(i,j) + force_y * DELTAT / rho
! implement Dirichlet boundary conditions on the four edges of the grid
! xmin
vx_1(1,:) = 0.d0
vy_1(1,:) = 0.d0
vx_2(1,:) = 0.d0
vy_2(1,:) = 0.d0
! xmax
vx_1(NX,:) = 0.d0
vy_1(NX,:) = 0.d0
vx_2(NX,:) = 0.d0
vy_2(NX,:) = 0.d0
! ymin
vx_1(:,1) = 0.d0
vy_1(:,1) = 0.d0
vx_2(:,1) = 0.d0
vy_2(:,1) = 0.d0
! ymax
vx_1(:,NY) = 0.d0
vy_1(:,NY) = 0.d0
vx_2(:,NY) = 0.d0
vy_2(:,NY) = 0.d0
! store seismograms
do irec = 1,NREC
sisvx(it,irec) = vx_1(ix_rec(irec),iy_rec(irec)) + vx_2(ix_rec(irec),iy_rec(irec))
sisvy(it,irec) = vy_1(ix_rec(irec),iy_rec(irec)) + vy_2(ix_rec(irec),iy_rec(irec))
enddo
! compute total energy in the medium (without the PML layers)
! 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(it) = 0.5d0 * sum(rho*( &
(vx_1(NPOINTS_PML+1:NX-NPOINTS_PML,NPOINTS_PML+1:NY-NPOINTS_PML) + &
vx_2(NPOINTS_PML+1:NX-NPOINTS_PML,NPOINTS_PML+1:NY-NPOINTS_PML))**2 + &
(vy_1(NPOINTS_PML+1:NX-NPOINTS_PML,NPOINTS_PML+1:NY-NPOINTS_PML) + &
vy_2(NPOINTS_PML+1:NX-NPOINTS_PML,NPOINTS_PML+1:NY-NPOINTS_PML))**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
total_energy_potential(it) = ZERO
do j = NPOINTS_PML+1, NY-NPOINTS_PML
do i = NPOINTS_PML+1, NX-NPOINTS_PML
! compute total field from split components
sigmaxx_total = sigmaxx_1(i,j) + sigmaxx_2(i,j)
sigmayy_total = sigmayy_1(i,j) + sigmayy_2(i,j)
sigmaxy_total = sigmaxy_1(i,j) + sigmaxy_2(i,j)
epsilon_xx = (c22 * sigmaxx_total - c12 * sigmayy_total) / (c11*c22-c12**2)
epsilon_yy = (c11 * sigmayy_total - c12 * sigmaxx_total) / (c11*c22-c12**2)
epsilon_xy = sigmaxy_total / (2.d0 * c33)
total_energy_potential(it) = total_energy_potential(it) + &
0.5d0 * (epsilon_xx * sigmaxx_total + epsilon_yy * sigmayy_total + 2.d0 * epsilon_xy * sigmaxy_total)
enddo
enddo
! output information
if(mod(it,IT_DISPLAY) == 0 .or. it == 5) then
velocnorm = maxval(sqrt((vx_1 + vx_2)**2 + (vy_1 + vy_2)**2))
print *,'Time step # ',it
print *,'Time: ',sngl((it-1)*DELTAT),' seconds'
print *,'Max norm velocity vector V (m/s) = ',velocnorm
print *,'total energy = ',total_energy_kinetic(it) + total_energy_potential(it)
print *
! check stability of the code, exit if unstable
if(velocnorm > STABILITY_THRESHOLD) stop 'code became unstable and blew up'
image_data_2D = vx_1 + vx_2
call create_color_image(image_data_2D,NX,NY,it,ISOURCE,JSOURCE,ix_rec,iy_rec,nrec, &
NPOINTS_PML,.true.,.true.,.true.,.true.,1)
image_data_2D = vy_1 + vy_2
call create_color_image(image_data_2D,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),sngl(total_energy_kinetic(it)), &
sngl(total_energy_potential(it)),sngl(total_energy_kinetic(it) + total_energy_potential(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 "collino_total_energy_semilog.eps"'
write(20,*) 'set logscale y'
write(20,*) 'plot "energy.dat" us 1:2 t ''Ec'' w l lc 1, "energy.dat" us 1:3 &
& t ''Ep'' w l lc 3, "energy.dat" us 1:4 t ''Total energy'' w l lc 4'
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_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,*)
close(20)
print *
print *,'End of the simulation'
print *
end program seismic_PML_Collino_2D_ani_4th
!----
!---- 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
! amplitude threshold above which we draw the color point
double precision, parameter :: cutvect = 0.01d0
! use black or white background for points that are below the threshold
logical, parameter :: WHITE_BACKGROUND = .true.
! size of cross and square in pixels drawn to represent the source and the receivers
integer, parameter :: width_cross = 5, thickness_cross = 1, size_square = 3
integer NX,NY,it,field_number,ISOURCE,JSOURCE,NPOINTS_PML,nrec
logical USE_PML_XMIN,USE_PML_XMAX,USE_PML_YMIN,USE_PML_YMAX
double precision, dimension(NX,NY) :: image_data_2D
integer, dimension(nrec) :: ix_rec,iy_rec
integer :: ix,iy,irec
character(len=100) :: file_name,system_command
integer :: R, G, B
double precision :: normalized_value,max_amplitude
! open image file and create system command to convert image to more convenient format
! use the "convert" command from ImageMagick http://www.imagemagick.org
if(field_number == 1) then
write(file_name,"('image',i6.6,'_Vx.pnm')") it
write(system_command,"('convert image',i6.6,'_Vx.pnm image',i6.6,'_Vx.gif ; rm image',i6.6,'_Vx.pnm')") it,it,it
else if(field_number == 2) then
write(file_name,"('image',i6.6,'_Vy.pnm')") it
write(system_command,"('convert image',i6.6,'_Vy.pnm image',i6.6,'_Vy.gif ; rm image',i6.6,'_Vy.pnm')") it,it,it
endif
open(unit=27, file=file_name, status='unknown')
write(27,"('P3')") ! write image in PNM P3 format
write(27,*) NX,NY ! write image size
write(27,*) '255' ! maximum value of each pixel color
! compute maximum amplitude
max_amplitude = maxval(abs(image_data_2D))
! image starts in upper-left corner in PNM format
do iy=NY,1,-1
do ix=1,NX
! define data as vector component normalized to [-1:1] and rounded to nearest integer
! keeping in mind that amplitude can be negative
normalized_value = image_data_2D(ix,iy) / max_amplitude
! suppress values that are outside [-1:+1] to avoid small edge effects
if(normalized_value < -1.d0) normalized_value = -1.d0
if(normalized_value > 1.d0) normalized_value = 1.d0
! draw an orange cross to represent the source
if((ix >= ISOURCE - width_cross .and. ix <= ISOURCE + width_cross .and. &
iy >= JSOURCE - thickness_cross .and. iy <= JSOURCE + thickness_cross) .or. &
(ix >= ISOURCE - thickness_cross .and. ix <= ISOURCE + thickness_cross .and. &
iy >= JSOURCE - width_cross .and. iy <= JSOURCE + width_cross)) then
R = 255
G = 157
B = 0
! display two-pixel-thick black frame around the image
else if(ix <= 2 .or. ix >= NX-1 .or. iy <= 2 .or. iy >= NY-1) then
R = 0
G = 0
B = 0
! display edges of the PML layers
else if((USE_PML_XMIN .and. ix == NPOINTS_PML) .or. &
(USE_PML_XMAX .and. ix == NX - NPOINTS_PML) .or. &
(USE_PML_YMIN .and. iy == NPOINTS_PML) .or. &
(USE_PML_YMAX .and. iy == NY - NPOINTS_PML)) then
R = 255
G = 150
B = 0
! suppress all the values that are below the threshold
else if(abs(image_data_2D(ix,iy)) <= max_amplitude * cutvect) then
! use a black or white background for points that are below the threshold
if(WHITE_BACKGROUND) then
R = 255
G = 255
B = 255
else
R = 0
G = 0
B = 0
endif
! represent regular image points using red if value is positive, blue if negative
else if(normalized_value >= 0.d0) then
R = nint(255.d0*normalized_value**POWER_DISPLAY)
G = 0
B = 0
else
R = 0
G = 0
B = nint(255.d0*abs(normalized_value)**POWER_DISPLAY)
endif
! draw a green square to represent the receivers
do irec = 1,nrec
if((ix >= ix_rec(irec) - size_square .and. ix <= ix_rec(irec) + size_square .and. &
iy >= iy_rec(irec) - size_square .and. iy <= iy_rec(irec) + size_square) .or. &
(ix >= ix_rec(irec) - size_square .and. ix <= ix_rec(irec) + size_square .and. &
iy >= iy_rec(irec) - size_square .and. iy <= iy_rec(irec) + size_square)) then
! use dark green color
R = 30
G = 180
B = 60
endif
enddo
! write color pixel
write(27,"(i3,' ',i3,' ',i3)") R,G,B
enddo
enddo
! close file
close(27)
! call the system to convert image to GIF (can be commented out if "call system" is missing in your compiler)
! call system(system_command)
end subroutine create_color_image
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