7 Commits
v1.2 ... v1.3

Author SHA1 Message Date
Hongjian Fang
e72b1205d1 Update manual again 2018-07-04 16:13:08 -04:00
Hongjian Fang
a42952b9ad Update manual 2018-07-04 16:09:03 -04:00
Hongjian Fang
f4bef435fe V1.3 release
Fix some bugs in jointly invert both phase and group velocity
2018-07-04 15:56:43 -04:00
Hongjian Fang
6b943f362a fix problem using both Rayleigh and Love data
Increase 'NP' in surfdisp.f. Change kmax to kmaxLC
2018-05-17 10:49:14 -04:00
Hongjian Fang
2b73597aea nothing important
change the script for generating true model and add script for ploting
paths
2018-02-03 11:38:11 -05:00
Hongjian Fang
6b00b85ba0 revise the weighting scheme
constant smoothing weight for all iterations now
2017-12-18 20:23:13 +08:00
Hongjian Fang
6e1c1016b6 change weight scheme 2017-12-12 14:26:42 +08:00
14 changed files with 131 additions and 209 deletions

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1
bin/DSurfTomo Symbolic link
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@@ -0,0 +1 @@
../src/DSurfTomo

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doc/ManualDSurfTomoV1.3.pdf Normal file

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@@ -1,10 +0,0 @@
# GMT common arguments shelf
-Ba0.2f0.1:S velocity (km/s):
-JM2i
-R121.35/121.605/24.975/25.2
-x2.3i
-Y5i
-y-2.7i
-jM2i
EOF

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@@ -1,107 +0,0 @@
#
# GMT-SYSTEM 4.5.15 [64-bit] Defaults file
#
#-------- Plot Media Parameters -------------
PAGE_COLOR = white
PAGE_ORIENTATION = landscape
PAPER_MEDIA = a4
#-------- Basemap Annotation Parameters ------
ANNOT_MIN_ANGLE = 20
ANNOT_MIN_SPACING = 0
ANNOT_FONT_PRIMARY = Helvetica
ANNOT_FONT_SIZE_PRIMARY = 6p
ANNOT_OFFSET_PRIMARY = 0.2c
ANNOT_FONT_SECONDARY = Helvetica
ANNOT_FONT_SIZE_SECONDARY = 16p
ANNOT_OFFSET_SECONDARY = 0.2c
DEGREE_SYMBOL = ring
HEADER_FONT = Helvetica
HEADER_FONT_SIZE = 36p
HEADER_OFFSET = 0.5c
LABEL_FONT = Helvetica
LABEL_FONT_SIZE = 5p
LABEL_OFFSET = 0.1c
OBLIQUE_ANNOTATION = 1
PLOT_CLOCK_FORMAT = hh:mm:ss
PLOT_DATE_FORMAT = yyyy-mm-dd
PLOT_DEGREE_FORMAT = ddd:mm:ss
Y_AXIS_TYPE = hor_text
#-------- Basemap Layout Parameters ---------
BASEMAP_AXES = WESN
BASEMAP_FRAME_RGB = black
BASEMAP_TYPE = fancy
FRAME_PEN = 1.25p
FRAME_WIDTH = 0.1c
GRID_CROSS_SIZE_PRIMARY = 0c
GRID_PEN_PRIMARY = 0.25p
GRID_CROSS_SIZE_SECONDARY = 0c
GRID_PEN_SECONDARY = 0.5p
MAP_SCALE_HEIGHT = 0.2c
POLAR_CAP = 85/90
TICK_LENGTH = 0.1c
TICK_PEN = 0.3p
X_AXIS_LENGTH = 25c
Y_AXIS_LENGTH = 15c
X_ORIGIN = 2.5c
Y_ORIGIN = 2.5c
UNIX_TIME = FALSE
UNIX_TIME_POS = BL/-2c/-2c
UNIX_TIME_FORMAT = %Y %b %d %H:%M:%S
#-------- Color System Parameters -----------
COLOR_BACKGROUND = black
COLOR_FOREGROUND = white
COLOR_NAN = 128
COLOR_IMAGE = adobe
COLOR_MODEL = rgb
HSV_MIN_SATURATION = 1
HSV_MAX_SATURATION = 0.1
HSV_MIN_VALUE = 0.3
HSV_MAX_VALUE = 1
#-------- PostScript Parameters -------------
CHAR_ENCODING = ISOLatin1+
DOTS_PR_INCH = 300
GLOBAL_X_SCALE = 1
GLOBAL_Y_SCALE = 1
N_COPIES = 1
PS_COLOR = rgb
PS_IMAGE_COMPRESS = lzw
PS_IMAGE_FORMAT = ascii
PS_LINE_CAP = butt
PS_LINE_JOIN = miter
PS_MITER_LIMIT = 35
PS_VERBOSE = FALSE
TRANSPARENCY = 0
#-------- I/O Format Parameters -------------
D_FORMAT = %.12lg
FIELD_DELIMITER = tab
GRIDFILE_FORMAT = nf
GRIDFILE_SHORTHAND = FALSE
INPUT_CLOCK_FORMAT = hh:mm:ss
INPUT_DATE_FORMAT = yyyy-mm-dd
IO_HEADER = FALSE
N_HEADER_RECS = 1
NAN_RECORDS = pass
OUTPUT_CLOCK_FORMAT = hh:mm:ss
OUTPUT_DATE_FORMAT = yyyy-mm-dd
OUTPUT_DEGREE_FORMAT = D
XY_TOGGLE = FALSE
#-------- Projection Parameters -------------
ELLIPSOID = WGS-84
MAP_SCALE_FACTOR = default
MEASURE_UNIT = cm
#-------- Calendar/Time Parameters ----------
TIME_FORMAT_PRIMARY = full
TIME_FORMAT_SECONDARY = full
TIME_EPOCH = 2000-01-01T12:00:00
TIME_IS_INTERVAL = OFF
TIME_INTERVAL_FRACTION = 0.5
TIME_LANGUAGE = us
TIME_UNIT = d
TIME_WEEK_START = Sunday
Y2K_OFFSET_YEAR = 1950
#-------- Miscellaneous Parameters ----------
HISTORY = TRUE
INTERPOLANT = akima
LINE_STEP = 0.025c
VECTOR_SHAPE = 0
VERBOSE = FALSE

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@@ -5,11 +5,11 @@ surfdataTB.dat c: data file
18 18 9 c: nx ny nz (grid number in lat lon and depth direction)
25.2 121.35 c: goxd gozd (upper left point,[lat,lon])
0.015 0.017 c: dvxd dvzd (grid interval in lat and lon direction)
25 c: nsrc*maxf
4.0 0.0 c: weight damp
3 c: nsublayer (numbers of sublayers for each grid interval:grid --> layer)
0.5 2.8 c: minimum velocity, maximum velocity
10 c: maxiter (iteration number)
20 c: max(sources, receivers)
4.0 0.1 c: weight damp
3 c: sablayers (for computing depth kernel, 2~5)
0.5 2.8 c: minimum velocity, maximum velocity (a priori information)
10 c: maximum iteration
0.2 c: sparsity fraction
26 c: kmaxRc (followed by periods)
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0
@@ -18,4 +18,4 @@ surfdataTB.dat c: data file
0 c: kmaxLg
0 c: synthetic flag(0:real data,1:synthetic)
0.02 c: noiselevel
2.5 c: threshold
0.5 c: threshold

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@@ -1,49 +0,0 @@
#!/bin/csh
#-----------------------------------------------------------
# 2015-06-08 Hongjian Fang
# example:csh plotslicenewVs.gmt DSurfTomo.inMeasure.dat 0.2 0.4 0.8 1.1
#-----------------------------------------------------------
gmtset ANOT_FONT_SIZE 6
gmtset LABEL_FONT_SIZE 6
gmtset FRAME_WIDTH=0.1c
gmtset LABEL_OFFSET=0.1c
gmtset LABEL_FONT_SIZE=5p
gmtset TICK_LENGTH=0.1c
gmtset TICK_PEN=0.3p
set inp3D = $1
set ps = horizVs.ps
set J = -JM2i #size for plot
set cpt = slice.cpt
# start
makecpt -Cseis -T0.6/1.5/0.1 > $cpt #velocity boundary
set RMAP = `minmax -C $inp3D | awk '{print "-R"$1"/"$2"/"$3"/"$4}'`
psbasemap $RMAP $J -Ba0.1f0.05WseN -P -K -Y5i >$ps
awk '{if($3==depth1) print $1,$2,$4}' depth1=$2 $inp3D|xyz2grd -R -I0.017/0.015 -Gtmp.grd
grdimage tmp.grd $J $RMAP -BSenW -E100 -C$cpt -O -K >> $ps
rm -rf tmp.grd
psscale -Cslice.cpt -Ba0.1f0.05:'S velocity (km/s)': -D1.0i/-0.15i/3.00/0.2h -O -K -P >> $ps
makecpt -Cseis -T0.8/1.8/0.1 > $cpt #velocity boundary
psbasemap $RMAP $J -Ba0.1f0.05NwsE -P -K -O -X2.3i >>$ps
awk '{if($3==depth2) print $1,$2,$4}' depth2=$3 $inp3D|xyz2grd -R -I0.017/0.015 -Gtmp.grd
grdimage tmp.grd $J $RMAP -BSenW -E100 -C$cpt -O -K >> $ps
psscale -Cslice.cpt -Ba0.2f0.1:'S velocity (km/s)': -D1.0i/-0.15i/3.00/0.2h -O -K -P >> $ps
makecpt -Cseis -T1.1/2.0/0.1 > $cpt #velocity boundary
psbasemap $RMAP $J -Ba0.1f0.05WneS -P -K -O -Y-2.7i -X-2.3i >>$ps
awk '{if($3==depth2) print $1,$2,$4}' depth2=$4 $inp3D|xyz2grd -R -I0.017/0.015 -Gtmp.grd
grdimage tmp.grd $J $RMAP -BSenW -E100 -C$cpt -O -K >> $ps
psscale -Cslice.cpt -Ba0.2f0.1:'S velocity (km/s)': -D1.0i/-0.25i/3.00/0.2h -O -K -P >> $ps
makecpt -Cseis -T1.3/2.4/0.1 > $cpt #velocity boundary
psbasemap $RMAP $J -Ba0.1f0.05SwnE -P -K -O -X2.3i >>$ps
awk '{if($3==depth2) print $1,$2,$4}' depth2=$5 $inp3D|xyz2grd -R -I0.017/0.015 -Gtmp.grd
grdimage tmp.grd $J $RMAP -BSenW -E100 -C$cpt -O -K >> $ps
psscale -Cslice.cpt -Ba0.2f0.1:'S velocity (km/s)': -D1.0i/-0.25i/3.00/0.2h -O -P >> $ps
rm *cpt *grd
ps2eps -f $ps
evince *eps &

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@@ -6,20 +6,19 @@ import numpy as np
#parameters need to be changed
#start
nx=75
ny=96
nz=17
nx=18
ny=18
nz=8
minvel=0.8
velgrad=0.5
dep1=1.5+np.array([-1.5, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0,10.0,11.0,13.0,16.0,20.0,30.0])
vel1=np.loadtxt('mod.1d')
dep1=np.array([0,0.2,0.4,0.6,0.8,1.1,1.4,1.8,2.5])
#end
vs1=np.zeros(nz)
mod=np.zeros((nz*ny,nx))
for k in range(nz):
for j in range(ny):
for i in range(nx):
mod[k*ny+j,i]= vel1[k]/1.75#minvel+dep1[k]*velgrad
mod[k*ny+j,i]= minvel+dep1[k]*velgrad
with open('MOD','w') as fp:
for i in range(nz):
fp.write('%5.1f' % dep1[i])

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@@ -12,11 +12,12 @@ nz=9
minvel=0.9
velgrad=0.6
dep1=[0,0.2,0.4,0.6,0.8,1.1,1.4,1.8,2.5]
anosize=1.0
anosize=0.5
amplitude=0.4
#end
x=range(1,nx+1)
y=range(1,ny+1)
nmax = np.max([nx,ny])
x=range(1,nmax+1)
y=range(1,nmax+1)
z=range(1,nz+1)
z=np.ones(nz)
bg=np.zeros((nz,nx,ny))
@@ -24,7 +25,7 @@ cross=np.zeros((nz,ny))
vs1=np.zeros(nz)
xy=np.kron(np.sin(anosize*np.array(y)),np.sin(anosize*np.array(x)))
xyz=np.kron(z,xy)
pxy=xyz.reshape(nz,nx,ny)
pxy=xyz.reshape(nz,nmax,nmax)
for k in range(nz):
for j in range(ny):
for i in range(nx):
@@ -35,7 +36,7 @@ for k in range(nz):
for i in range(nx):
mod[(k)*ny+j,i]=bg[k,i,j]+pxy[k,i,j]*amplitude
k=5
plt.imshow(mod[k*ny:(k+1)*ny,:],cmap='jet_r',interpolation='bicubic')
plt.imshow(mod[k*ny:(k+1)*ny,:],cmap='jet_r')
np.savetxt('MOD.true',mod,fmt='%4.4f')
plt.colorbar()
plt.show()

33
scripts/plotpath.py Normal file
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@@ -0,0 +1,33 @@
#!/usr/bin/env python
import numpy as np
from matplotlib import pylab as plt
#parameters you need to change
#begin
numray = 3320 # how many rays do you have (all periods)
rb = 1 # ray index for some period (first one)
re = 50 # ray index for some period (last one)
maxseg = 500 #
#end
n = 0
numseg = np.zeros(numray,)
raylat = np.zeros((numray,maxseg))
raylon = np.zeros((numray,maxseg))
with open('raypath.out') as ray:
for line in ray:
linseg = line.split()
if linseg[0]=='#':
n = n+1
seg = 0
numseg[n-1] = float(linseg[1])
else:
seg = seg+1
raylat[n-1,seg-1] = float(linseg[0])
raylon[n-1,seg-1] = float(linseg[1])
for ii in range(rb,re):
plt.plot(raylon[ii,0:numseg[ii]],raylat[ii,0:numseg[ii]],'k-')
plt.show()

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@@ -92,6 +92,17 @@ subroutine depthkernel(nx,ny,nz,vel,pvRc,sen_vsRc,sen_vpRc,sen_rhoRc, &
dlncg_dlnvs(nn,i) = (cg2(nn)-cg1(nn))/(dlnVs*vsz(i))
enddo
!note here, no integral from z1 to z2 is needed. The grid based nodes
! have already taken into consideration of it. Layer based need integration.
! Test passed
!if (i == 1) then
! dlncg_dlnvs(1:kmaxRc,i) = dlncg_dlnvs(1:kmaxRc,i)*thkm(1)/2.0
!else if (i == mmax) then
! dlncg_dlnvs(1:kmaxRc,i) = dlncg_dlnvs(1:kmaxRc,i)*thkm(mmax-1)/2.0
!else
! dlncg_dlnvs(1:kmaxRc,i) = dlncg_dlnvs(1:kmaxRc,i)*(thkm(i-1)+thkm(i))/2.0
!endif
vpm(i) = vpz(i) - 0.5*dlnVp*vpz(i)
call refineGrid2LayerMdl(minthk,mmax,depm,vpm,vsm,rhom,&
@@ -110,6 +121,16 @@ subroutine depthkernel(nx,ny,nz,vel,pvRc,sen_vsRc,sen_vpRc,sen_rhoRc, &
! cga = 0.5*(cg1(nn)+cg2(nn))
dlncg_dlnvp(nn,i) = (cg2(nn)-cg1(nn))/(dlnVp*vpz(i))
enddo
!if (i == 1) then
! dlncg_dlnvp(1:kmaxRc,i) = dlncg_dlnvp(1:kmaxRc,i)*thkm(1)/2.0
!else if (i == mmax) then
! dlncg_dlnvp(1:kmaxRc,i) = dlncg_dlnvp(1:kmaxRc,i)*thkm(mmax-1)/2.0
!else
! dlncg_dlnvp(1:kmaxRc,i) = dlncg_dlnvp(1:kmaxRc,i)*(thkm(i-1)+thkm(i))/2.0
!endif
rhom(i) = rhoz(i) - 0.5*dlnrho*rhoz(i)
call refineGrid2LayerMdl(minthk,mmax,depm,vpm,vsm,rhom,&
rmax,rdep,rvp,rvs,rrho,rthk)
@@ -127,6 +148,15 @@ subroutine depthkernel(nx,ny,nz,vel,pvRc,sen_vsRc,sen_vpRc,sen_rhoRc, &
! cga = 0.5*(cg1(nn)+cg2(nn))
dlncg_dlnrho(nn,i) = (cg2(nn)-cg1(nn))/(dlnrho*rhoz(i))
enddo
! if (i == 1) then
! dlncg_dlnrho(1:kmaxRc,i) = dlncg_dlnrho(1:kmaxRc,i)*thkm(1)/2.0
! else if (i == mmax) then
! dlncg_dlnrho(1:kmaxRc,i) = dlncg_dlnrho(1:kmaxRc,i)*thkm(mmax-1)/2.0
! else
! dlncg_dlnrho(1:kmaxRc,i) = dlncg_dlnrho(1:kmaxRc,i)*(thkm(i-1)+thkm(i))/2.0
! endif
enddo
sen_vsRc((jj-1)*nx+ii,1:kmaxRc,1:mmax)=dlncg_dlnvs(1:kmaxRc,1:mmax)
sen_vpRc((jj-1)*nx+ii,1:kmaxRc,1:mmax)=dlncg_dlnvp(1:kmaxRc,1:mmax)
@@ -1088,7 +1118,7 @@ subroutine CalSurfG(nx,ny,nz,nparpi,vels,iw,rw,col,dsurf, &
iwave=1
igr=0
call depthkernel(nx,ny,nz,vels,pvLc,sen_vsLc,sen_vpLc, &
sen_rhoLc,iwave,igr,kmax,tLc,depz,minthk)
sen_rhoLc,iwave,igr,kmaxLc,tLc,depz,minthk)
endif
if(kmaxLg.gt.0) then

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@@ -121,7 +121,7 @@ program SurfTomo
! OUTPUT PROGRAM INFOMATION
write(*,*)
write(*,*),' S U R F T O M O'
write(*,*),' DSurfTomo (v1.3)'
write(*,*),'PLEASE contact Hongjain Fang &
(fanghj@mail.ustc.edu.cn) if you find any bug'
write(*,*)
@@ -181,9 +181,9 @@ program SurfTomo
if (checkstat > 0) stop 'error allocating RP'
read(10,*)(tRc(i),i=1,kmaxRc)
write(*,*)'Rayleigh wave phase velocity used,periods:(s)'
write(*,'(50f6.2)')(tRc(i),i=1,kmaxRc)
write(*,'(50f7.1)')(tRc(i),i=1,kmaxRc)
write(66,*)'Rayleigh wave phase velocity used,periods:(s)'
write(66,'(50f6.2)')(tRc(i),i=1,kmaxRc)
write(66,'(50f7.1)')(tRc(i),i=1,kmaxRc)
endif
read(10,*)kmaxRg
if(kmaxRg.gt.0)then
@@ -191,9 +191,9 @@ program SurfTomo
if (checkstat > 0) stop 'error allocating RP'
read(10,*)(tRg(i),i=1,kmaxRg)
write(*,*)'Rayleigh wave group velocity used,periods:(s)'
write(*,'(50f6.2)')(tRg(i),i=1,kmaxRg)
write(*,'(50f7.1)')(tRg(i),i=1,kmaxRg)
write(66,*)'Rayleigh wave group velocity used,periods:(s)'
write(66,'(50f6.2)')(tRg(i),i=1,kmaxRg)
write(66,'(50f7.1)')(tRg(i),i=1,kmaxRg)
endif
read(10,*)kmaxLc
if(kmaxLc.gt.0)then
@@ -201,9 +201,9 @@ program SurfTomo
if (checkstat > 0) stop 'error allocating RP'
read(10,*)(tLc(i),i=1,kmaxLc)
write(*,*)'Love wave phase velocity used,periods:(s)'
write(*,'(50f6.2)')(tLc(i),i=1,kmaxLc)
write(*,'(50f7.1)')(tLc(i),i=1,kmaxLc)
write(66,*)'Love wave phase velocity used,periods:(s)'
write(66,'(50f6.2)')(tLc(i),i=1,kmaxLc)
write(66,'(50f7.1)')(tLc(i),i=1,kmaxLc)
endif
read(10,*)kmaxLg
if(kmaxLg.gt.0)then
@@ -211,9 +211,9 @@ program SurfTomo
if (checkstat > 0) stop 'error allocating RP'
read(10,*)(tLg(i),i=1,kmaxLg)
write(*,*)'Love wave group velocity used,periods:(s)'
write(*,'(50f6.2)')(tLg(i),i=1,kmaxLg)
write(*,'(50f7.1)')(tLg(i),i=1,kmaxLg)
write(66,*)'Love wave group velocity used,periods:(s)'
write(66,'(50f6.2)')(tLg(i),i=1,kmaxLg)
write(66,'(50f7.1)')(tLg(i),i=1,kmaxLg)
endif
read(10,*)ifsyn
read(10,*)noiselevel
@@ -333,7 +333,7 @@ program SurfTomo
enddo
close(10)
write(*,*) 'grid points in depth direction:(km)'
write(*,'(50f6.2)') depz
write(*,'(50f7.1)') depz
@@ -382,12 +382,36 @@ program SurfTomo
cbst(i) = obst(i) - dsyn(i)
enddo
threshold = threshold0+(maxiter/2-iter)/3*0.5
! write out rw, iw and cbst for testing
!open(44,file='iw.dat')
!write(44,*) nar
!do i = 2,nar+1
!write(44,*) iw(i)
!enddo
!do i = 1,nar
!write(44,*) col(i)
!enddo
!close(44)
!open(44,file='rw.dat')
!do i = 1,nar
!write(44,*) rw(i)
!enddo
!close(44)
!open(44,file='residal.dat')
!do i = 1,dall
!write(44,*) cbst(i)
!enddo
!close(44)
!threshold = threshold0+(maxiter/2-iter)/3*0.5
do i = 1,dall
datweight(i) = 1.0
if(abs(cbst(i)) > threshold) then
datweight(i) = exp(-(abs(cbst(i))-threshold))
endif
! datweight(i) = 1.0
! if(abs(cbst(i)) > threshold) then
! datweight(i) = exp(-(abs(cbst(i))-threshold))
! endif
datweight(i) = 0.01+1.0/(1+0.05*exp(cbst(i)**2*threshold0))
cbst(i) = cbst(i)*datweight(i)
enddo
@@ -429,7 +453,8 @@ program SurfTomo
! ADDING REGULARIZATION TERM
weight=dnrm2(dall,cbst,1)**2/dall*weight0
!weight=dnrm2(dall,cbst,1)**2/dall*weight0
weight=weight0
nar_tmp=nar
nars=0

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@@ -56,7 +56,7 @@ c-----
integer NL, NL2, NLAY
parameter(NL=200,NLAY=200,NL2=NL+NL)
integer NP
parameter (NP=60)
parameter (NP=80)
c-----
c LIN - unit for FORTRAN read from terminal
@@ -500,7 +500,7 @@ c 2 - Rayleigh Wave
c iflag I*4 0 - Initialize
c 1 - Make model for Love or Rayleigh Wave
c-----
parameter(NL=200,NP=60)
parameter(NL=200,NP=80)
real*4 d(NL),a(NL),b(NL),rho(NL),rtp(NL),dtp(NL),btp(NL)
integer mmax,llw
c common/modl/ d,a,b,rho,rtp,dtp,btp
@@ -563,7 +563,7 @@ c nev = 0 force interval halving
c nev = 1 permit neville iteration if conditions are proper
c nev = 2 neville iteration is being used
c-----
parameter (NL=200,NP=60)
parameter (NL=200,NP=80)
implicit double precision (a-h,o-z)
real*4 d(NL),a(NL),b(NL),rho(NL),rtp(NL),dtp(NL),btp(NL)
dimension x(20),y(20)
@@ -704,7 +704,7 @@ c
function dltar1(wvno,omega,d,a,b,rho,rtp,dtp,btp,mmax,llw,twopi)
c find SH dispersion values.
c
parameter (NL=200,NP=60)
parameter (NL=200,NP=80)
implicit double precision (a-h,o-z)
real*4 d(NL),a(NL),b(NL),rho(NL),rtp(NL),dtp(NL),btp(NL)
integer llw,mmax
@@ -768,7 +768,7 @@ c
c & a0,cpcq,cpy,cpz,cqw,cqx,xy,xz,wy,wz)
c find P-SV dispersion values.
c
parameter (NL=200,NP=60)
parameter (NL=200,NP=80)
implicit double precision (a-h,o-z)
dimension e(5),ee(5),ca(5,5)
real*4 d(NL),a(NL),b(NL),rho(NL),rtp(NL),dtp(NL),btp(NL)