/
minos_bran.f
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minos_bran.f
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c
c MINEOS version 1.0 by Guy Masters, John Woodhouse, and Freeman Gilbert
c
c This program is free software; you can redistribute it and/or modify
c it under the terms of the GNU General Public License as published by
c the Free Software Foundation; either version 2 of the License, or
c (at your option) any later version.
c
c This program is distributed in the hope that it will be useful,
c but WITHOUT ANY WARRANTY; without even the implied warranty of
c MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
c GNU General Public License for more details.
c
c You should have received a copy of the GNU General Public License
c along with this program; if not, write to the Free Software
c Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
c
c****************************************************************************
c minos_bran program produces the solution of the seismic normal mode
c eigenvalue-eigenfunction problem.
c
c****************************************************************************
c this program uses one input and two output files
c the input file contains the model
c the output files are 1) a model listing + a summary of mode properties
c and 2) a file for the eigenfunctions
c the program then asks for some control info described below
c
c structure of model file
c card 1 : title (up to 256 chars long)
c card 2 : ifanis,tref,ifdeck (unformatted)
c ifanis=1 for anisotropic model, 0 for isotropic
c tref=ref period(secs) of model for dispersion correction.
c if tref is .le. 0. no correction is made.
c ifdeck=1 for card deck model, 0 for polynomial model.
c *** card deck model ***
c card 3 : n,nic,noc (unformatted)
c n=no of levels,nic=index of solid side of icb,noc=index of
c fluid side of mcb.note that n must be .le. 223.
c card 4-n: r,rho,vpv,vsv,qkappa,qshear,vph,vsh,eta (f8.0,3f9.2,2f9.1,2f9.2,
c f9.5)
c if isotropic vp=vpv,vs=vsv and vph,vsh,eta are unspecified.
c if the q model is not specified then no disp. correction is made.
c s.i. units are used,e.g. radius in metres and velocities in m/s.
c *** polynomial model ***
c card 3 : nreg,nic,noc,rx (unformatted)
c nreg is the number of regions in the model,nic and noc as before
c and rx is the normalising radius for the polynomials.
c rx is given in kms and is usually 6371.
c card 4 : nlay,r1,r2 (unformatted)
c nlay is the number of levels to be used in the region extending
c from radius r1 to r2 (in kms).
c card 5-9(iso) or card 5-12(ani) : coefs (5f9.5)
c 5 sets of coefficients are required for each region of an isotropic
c model and 8 sets for an anisotropic model.each polynomial can be
c up to a quartic in r/rx ( 5 coefficients) and are ordered thusly:
c rho,vpv,vsv,qkappa,qshear,vph,vsh,eta. the coeffs are given in the
c usual mixed seismological units (rho in g/cc,vel in km/s etc.)
c conversion to s.i. is done by the program.
c cards 4-9(iso) or 4-12(ani) are repeated for each region of the
c model
c
c control parameters (from screen)
c eps,wgrav
c eps controls the accuracy of the runge-kutta integration scheme.
c the relative accuracy of an eigen frequency will be 2-3 x eps.
c it also controls the precision with which a root is found and
c the minimum relative separation of two roots with the same angular
c order.it is safe to set eps=1.d-7.
c wgrav is the frequency in millihertz above which gravitational terms
c are neglected-this gives about a factor of 3 increase in speed.
c jcom
c jcom=1 radial modes, 2 toroidal modes, 3 spheroidal modes,
c 4 inner core toroidal modes.
c lmin,lmax,wmin,wmax,nmin,nmax
c lmin - lmax defines the range of angular orders to be computed.
c if jcom=1 this is ignored. wmin - wmax defines the frequency range
c to be computed (in millihertz)
c nmin-nmax specifies the branch numbers to be computed -- nmin=0
c is the fundamental mode
c
c model listing
c this is an ascii file which lists the model and mode properties
c i.e. phase velocity in km/s,frequency,period,group velocity in km/s,
c q and a parameter which is the ratio of kinetic to potential energy
c minus 1 which should be small ( of order eps )if the eigenfunction is
c accurate and if there are enough radial knots in the model to allow
c quodratures to be done accurately. (you will probably see some degradation
c in this parameter for strongly exponential modes such as stoneley modes ).
c
c eigenfunction file
c****** file name "none" will suppress calculation of eigenfunctions
c this is a fixed record length binary file with an entry for each mode
c written as
c write(ioeig) (abuf(i),i=1,nvec)
c where nvec is 5+6*npts for spheroidal modes and 5+2*npts for toroidal
c and radial modes. the first five words of abuf are n,l,frequecy,q and
c group velocity. the rest of abuf contains w(1..npts) and wp(1..npts)
c for toroidal modes and u(1..npts),up(1..npts),v(1..npts),vp(1..npts),
c p(1..npts) and pp(1..npts) for spheroidal modes. these are as in
c woodhouse and dahlen 1978 except that w,wp,v and vp must be divided
c by sqrt(l*(l+1)). the normalisation is such that
c frequency**2 times integral(rho*w*w*r*r) is 1 for toroidal modes
c frequency**2 times integral(rho*(u*u+l*(l+1)*v*v)*r*r) is 1 for
c spheroidal modes
c the model has been normalised such that a density of 5515 mg/m**3 = 1 ;
c pi*g=1 where g is the grav constant (6.6723e-11) and the radius of the
c earth (rn=6371000 m) is 1. these normalizations result in
c acceleration normalisation = pi*g*rhobar*rn
c velocity normalisation = rn*sqrt(pi*g*rhobar)= vn
c frequency normalization = vn/rn
c
c**************************************************************************
character*256 filnam
print *,'input model file:'
read(5,100) filnam
100 format(a256)
c MB added one line below
print *,filnam(1:lnblnk(filnam))
open(7,file=filnam,status='old',form='formatted',iostat=iret)
print *,'output file:'
read(5,100) filnam
c MB added one line below
print *,filnam(1:lnblnk(filnam))
open(8,file=filnam,form='formatted',iostat=iret)
call model(7,8)
close(7)
print *,'eigenfunction file (output):'
read(5,100) filnam
c MB added one line below
print *,filnam(1:lnblnk(filnam))
ifreq=1
if(filnam(1:4).eq.'none') ifreq=0
open(3,file=filnam,form='unformatted',iostat=iret)
call wtable(8,3,ifreq)
close(8)
close(3)
stop
end
subroutine wtable(iout,ioeig,ifreq)
c*** makes up table of frequencies ***
implicit real*8(a-h,o-z)
common/bits/pi,rn,vn,wn,w,wsq,wray,qinv,cg,wgrav,tref,fct,eps,fl,
+ fl1,fl2,fl3,sfl3,jcom,nord,l,kg,kount,knsw,ifanis,iback
common/shanks/b(46),c(10),dx,step(8),stepf,maxo,in
common/mtab/we(2),de(2),ke(2),wtry,bm
dimension wt(2)
data inss/5/
cmhz=pi/500.d0
stepf=1.d0
print *,'enter eps and wgrav'
read(*,*) eps,wgrav
c MB added one line below
print *,eps,wgrav
eps=max(eps,1.d-12)
eps1=eps
eps2=eps
wgrav=wgrav*cmhz
write(iout,100) eps,eps1,wgrav
100 format(/,'integration precision =',g12.4,' root precision =',
+ g12.4,' gravity cut off =',g12.4,' rad/s',///,6x,'mode',
+ 8x,'phs vel',7x,'w(mhz)',10x,'t(secs)',6x,'grp vel(km/s)',
+ 8x,'q',13x,'raylquo',/)
call steps(eps)
print *,'enter jcom (1=rad;2=tor;3=sph;4=ictor)'
read(*,*) jcom
c MB added one line below
print *,jcom
if(jcom.lt.1.or.jcom.gt.4) jcom=3
print *,'enter lmin,lmax,wmin,wmax,nmin,nmax'
read(*,*) lmin,lmax,wmin,wmax,normin,normax
c MB added one line below
print *,lmin,lmax,wmin,wmax,normin,normax
wmin=max(wmin,0.1d0)
wmin=wmin*cmhz
wmax=wmax*cmhz
if(lmin.le.0) lmin=1
if(jcom.eq.1) then
lmin=0
lmax=0
end if
normin=max(normin,0)
normax=max(normax,normin)
ncall = 0
do 50 nor=normin,normax
wt(1)=wmin
wt(2)=wmax
wtry=0.d0
bm=0.d0
do 10 l=lmin,lmax
if(wt(1).ge.wmax) goto 50
nord=nor
nup=nor
ndn=nor-1
if(l.eq.1) then
nup=ndn
ndn=ndn-1
end if
knsw=1
maxo=inss
fl=l
fl1=fl+1.d0
fl2=fl+fl1
fl3=fl*fl1
sfl3=sqrt(fl3)
we(1)=wt(1)
we(2)=wt(2)
if(wtry.ne.0.d0) we(2)=wtry
call detqn(we(1),ke(1),de(1),0)
if(ke(1).gt.ndn) goto 10
call detqn(we(2),ke(2),de(2),0)
if(ke(2).lt.nup) then
we(2)=wt(2)
call detqn(we(2),ke(2),de(2),0)
if(ke(2).lt.nup) goto 50
end if
c*** bracket this mode ***
wx=0.5d0*(we(1)+we(2))
ktry=0
15 if(ke(1).eq.ndn.and.ke(2).eq.nup) goto 40
ktry=ktry+1
if(ktry.gt.50) goto 10
call detqn(wx,kx,dx,0)
if(kx.le.ndn) then
we(1)=wx
ke(1)=kx
de(1)=dx
else
we(2)=wx
ke(2)=kx
de(2)=dx
end if
wx=0.5d0*(we(1)+we(2))
goto 15
c*** find roots ***
40 knsw=0
maxo=8
c added argument for number of times called (mhr)
ncall = ncall + 1
call rotspl(eps1,wt,iout,ioeig,ifreq,ncall)
10 continue
50 continue
return
end
subroutine rotspl(eps1,wt,iout,ioeig,ifreq,ncall)
c*** find roots by spline interpolation ***
implicit real*8(a-h,o-z)
common/bits/pi,rn,vn,wn,w,wsq,wray,qinv,cg,wgrav,tref,fct,eps,fl,
+ fl1,fl2,fl3,sfl3,jcom,nord,l,kg,kount,knsw,ifanis,iback
common/mtab/we(2),de(2),ke(2),wtry,bm
dimension x(20),det(20),qx(3,20),wrk(60),wt(*),kchar(4)
character*2 kchar
data tol/1.d-9/,itmax/15/,kchar/' s',' t',' s',' c'/
if(de(1)*de(2).gt.0.d0) return
nord=ke(2)
if(l.eq.1) nord=nord+1
det(1)=de(1)
det(2)=de(2)
x(1)=we(1)
x(2)=we(2)
5 c=x(1)
if(dabs(det(1)).gt.dabs(det(2))) c=x(2)
10 ntry=2
grad=(x(1)-x(2))/(det(1)-det(2))
b=x(1)-det(1)*grad
15 t=dabs(b*eps1)
if(dabs(b-c).lt.t) goto 65
call detqn(b,knt,fb,0)
ind=1
do 20 m=2,ntry
ind=ind+1
20 if(b.lt.x(m)) goto 25
25 ntry=ntry+1
j2=ntry
30 j1=j2-1
x(j2)=x(j1)
det(j2)=det(j1)
if(j1.eq.ind) goto 35
j2=j2-1
goto 30
35 x(ind)=b
det(ind)=fb
idn=0
do 40 m=2,ntry
idn=idn+1
iup=idn+1
40 if(det(idn)*det(iup).le.0.d0) goto 45
45 ind=iup
if(dabs(det(idn)).lt.dabs(det(iup))) ind=idn
c=x(ind)
if(ntry.ge.itmax) goto 60
call dsplin(ntry,x,det,qx,wrk)
del=-det(ind)/qx(1,ind)
50 delx=-det(ind)/(qx(1,ind)+del*qx(2,ind))
if(dabs(delx-del).lt.tol) goto 55
if(del*delx.lt.0.d0) goto 60
del=delx
goto 50
55 b=c+delx
if(b.ge.x(idn).and.b.le.x(iup)) goto 15
60 x(1)=x(idn)
x(2)=x(iup)
det(1)=det(idn)
det(2)=det(iup)
goto 10
c*** write out frequencies ***
65 call detqn(b,knt,fb,ifreq)
tcom=2.d0*pi/b
wmhz=1000.d0/tcom
cvel=b*rn/(l+0.5)/1000.
if(ifreq.eq.1) then
wdiff=(b-wray*wn)/b
gcom=vn*cg/1000.d0
qmod=0.d0
if(qinv.gt.0.d0) qmod=1.d0/qinv
c remove writing resulting to stnd output (mhr)
c print 200,nord,kchar(jcom),l,cvel,wmhz,tcom,gcom,qmod,wdiff
write(iout,200) nord,kchar(jcom),l,cvel,wmhz,tcom,gcom,qmod,
+ wdiff
200 format(i5,a2,i5,6g16.7)
call modout(b,qmod,gcom,ioeig,ncall)
else
cg=5000./vn
c*** we estimate group velocity using previous frequencies
if(bm.ne.0.d0) cg=(b-bm)/wn
gcom=vn*cg/1000.d0
c added print of gcom. qmod & wdiff not computed w/o egnfcns. (mhr)
c remove writing resulting to stnd output (mhr)
c print 200,nord,kchar(jcom),l,cvel,wmhz,tcom,gcom
write(iout,200) nord,kchar(jcom),l,cvel,wmhz,tcom,gcom
end if
wtry=b+2.d0*cg*wn
wt(1)=b
bm=b
return
end
subroutine modout(wcom,qmod,gcom,ioeig,ncall)
implicit real*8(a-h,o-z)
parameter (mk=350)
real*4 abuf,buf,ww,qq,gc
common/bits/pi,rn,vn,wn,w,wsq,wray,qinv,cg,wgrav,tref,fct,eps,fl,
+ fl1,fl2,fl3,sfl3,jcom,nord,l,kg,kount,knsw,ifanis,iback
common/rindx/nic,noc,nsl,nicp1,nocp1,nslp1,n
common/eifx/a(14,mk),dum(mk)
c common block name changes from buf$ to c_buf (mhr)
common/c_buf/nn,ll,ww,qq,gc,buf(6*mk)
dimension abuf(6*mk+5)
equivalence (nn,abuf)
nn=nord
ll=l
ww=wcom
qq=qmod
gc=gcom
if(jcom.eq.3) then
nvec=6*n+5
do i=1,n
buf(i)=a(1,i)
buf(i+n)=a(2,i)
buf(i+n+n)=a(3,i)
buf(i+3*n)=a(4,i)
buf(i+4*n)=a(5,i)
buf(i+5*n)=a(6,i)
enddo
else
nvec=2*n+5
if(jcom.eq.2) then
do i=1,noc
a(1,i)=0.d0
a(2,i)=0.d0
enddo
end if
do i=1,n
buf(i)=a(1,i)
buf(i+n)=a(2,i)
enddo
end if
c include writing egfcns (mhr)
write(ioeig) (abuf(i),i=1,nvec)
return
end
subroutine model(iin,iout)
implicit real*8(a-h,o-z)
parameter (mk=350)
save
integer*4 ititle(20)
real*8 lcon,ncon,lspl,nspl
common r(mk),fmu(mk),flam(mk),qshear(mk),qkappa(mk),
+ xa2(mk),xlam(mk),rho(mk),qro(3,mk),g(mk),qg(3,mk),
+ fcon(mk),fspl(3,mk),lcon(mk),lspl(3,mk),ncon(mk),
+ nspl(3,mk),ccon(mk),cspl(3,mk),acon(mk),aspl(3,mk)
common/bits/pi,rn,vn,wn,w,wsq,wray,qinv,cg,wgrav,tref,fct,eps,fl,
+ fl1,fl2,fl3,sfl3,jcom,nord,l,kg,kount,knsw,ifanis,iback
common/eifx/vpv(mk),vph(mk),vsv(mk),vsh(mk),eta(mk),wrk(mk*10)
common/rindx/nic,noc,nsl,nicp1,nocp1,nslp1,n
data bigg,tau/6.6723d-11,1.d3/,rhobar/5515.d0/
pi=3.14159265358979d0
read(iin,100) (ititle(i),i=1,20)
100 format(20a4)
read(iin,*) ifanis,tref,ifdeck
if(ifdeck.eq.0) go to 1000
c*** card deck model ***
read(iin,*) n,nic,noc
read(iin,*) (r(i),rho(i),vpv(i),vsv(i),
+ qkappa(i),qshear(i),vph(i),vsh(i),eta(i),i=1,n)
105 format(f8.0, 3f9.2, 2f9.1, 2f9.2, f9.5)
cc 105 format(f10.1,3f10.3,2f10.1,2f10.3,f10.5)
go to 2000
c*** polynomial model ***
1000 read(iin,*) nreg,nic,noc,rx
rx=rx*tau
n=0
knt=0
jj=5
if(ifanis.ne.0) jj=8
do nn=1,nreg
read(iin,*) nlay,r1,r2
r1=r1*tau
r2=r2*tau
dr=(r2-r1)/float(nlay-1)
do i=1,nlay
n=n+1
r(n)=r1+dr*float(i-1)
enddo
do j=1,jj
read(iin,110) (wrk(i),i=1,5)
110 format(5f9.5)
if(ifanis.eq.2) then
do i=1,nlay
ind=knt+i
rt=r(ind)/rx
val=wrk(1)+rt*(wrk(2)+rt*(wrk(3)+rt*(wrk(4)+rt*wrk(5))))
if(j.eq.1) rho(ind)=val*tau
if(j.eq.2) vph(ind)=val*tau
if(j.eq.3) vsv(ind)=val*tau
if(j.eq.4) qkappa(ind)=val
if(j.eq.5) qshear(ind)=val
if(j.eq.6) vpv(ind)=sqrt(val)*vph(ind)
if(j.eq.7) vsh(ind)=sqrt(val)*vsv(ind)
if(j.eq.8) eta(ind)=val
enddo
else
do i=1,nlay
ind=knt+i
rt=r(ind)/rx
val=wrk(1)+rt*(wrk(2)+rt*(wrk(3)+rt*(wrk(4)+rt*wrk(5))))
if(j.eq.1) rho(ind)=val*tau
if(j.eq.2) vpv(ind)=val*tau
if(j.eq.3) vsv(ind)=val*tau
if(j.eq.4) qkappa(ind)=val
if(j.eq.5) qshear(ind)=val
if(j.eq.6) vph(ind)=val*tau
if(j.eq.7) vsh(ind)=val*tau
if(j.eq.8) eta(ind)=val
enddo
end if
enddo
knt=knt+nlay
enddo
2000 if(ifanis.eq.0) then
do i=1,n
vph(i)=vpv(i)
vsh(i)=vsv(i)
eta(i)=1.d0
enddo
end if
if(iout.ge.0) then
c*** write out model ***
write(iout,900) (ititle(k),k=1,20),tref
900 format(1x,20a4,' ref per =',f6.1,' secs',///,2x,'level',
1 4x,'radius',8x,'rho',9x,'vpv',9x,'vph',9x,'vsv',
2 9x,'vsh',9x,'eta',9x,'qmu ',8x,'qkap',/)
write(iout,905) (i,r(i),rho(i),vpv(i),vph(i),vsv(i),vsh(i),
1 eta(i),qshear(i),qkappa(i),i=1,n)
905 format(3x,i3,f12.1,5f12.2,f12.5,2f12.2)
end if
c*** normalise and spline ***
rn=r(n)
gn=pi*bigg*rhobar*rn
vn2=gn*rn
vn=sqrt(vn2)
wn=vn/rn
do i=1,n
r(i)=r(i)/rn
if(i.gt.1.and.dabs(r(i)-r(i-1)).lt.1.d-7) r(i)=r(i-1)
if(qshear(i).gt.0.d0) qshear(i)=1.d0/qshear(i)
if(qkappa(i).gt.0.d0) qkappa(i)=1.d0/qkappa(i)
rho(i)=rho(i)/rhobar
acon(i)=rho(i)*vph(i)*vph(i)/vn2
ccon(i)=rho(i)*vpv(i)*vpv(i)/vn2
lcon(i)=rho(i)*vsv(i)*vsv(i)/vn2
ncon(i)=rho(i)*vsh(i)*vsh(i)/vn2
fcon(i)=eta(i)*(acon(i)-2.d0*lcon(i))
fmu(i)=(acon(i)+ccon(i)-2.d0*fcon(i)+5.d0*ncon(i)
+ +6.d0*lcon(i))/15.d0
flam(i)=(4.d0*(acon(i)+fcon(i)-ncon(i))+ccon(i))/9.d0
+ -2.d0*fmu(i)/3.d0
rat=4.d0*fmu(i)/(3.d0*(flam(i)+2.d0*fmu(i)))
xlam(i)=((1.d0-rat)*qkappa(i)-.5d0*rat*qshear(i))/(1.d0
+ -1.5d0*rat)
xa2(i)=(1.d0-rat)*qkappa(i)+rat*qshear(i)
enddo
call drspln(1,n,r,rho,qro,wrk)
call grav(g,rho,qro,r,n)
call drspln(1,n,r,g,qg,wrk)
call drspln(1,n,r,fcon,fspl,wrk)
call drspln(1,n,r,lcon,lspl,wrk)
if(ifanis.ne.0) then
call drspln(1,n,r,acon,aspl,wrk)
call drspln(1,n,r,ccon,cspl,wrk)
call drspln(1,n,r,ncon,nspl,wrk)
end if
nsl=n+1
65 nsl=nsl-1
if(vsv(nsl).le.0.d0) go to 65
nicp1=nic+1
nocp1=noc+1
nslp1=nsl+1
tref=0.5d0*tref/pi
return
end
subroutine detqn(wdim,knt,det,ifeif)
c**** supevises the integration of the equations,it returns the value
c**** of the secular determinant as det and the count of zero crossings.
implicit real*8(a-h,o-z)
parameter (mk=350)
save
real*8 lcon,ncon,lspl,nspl
common r(mk),fmu(mk),flam(mk),qshear(mk),qkappa(mk),
+ xa2(mk),xlam(mk),rho(mk),qro(3,mk),g(mk),qg(3,mk),
+ fcon(mk),fspl(3,mk),lcon(mk),lspl(3,mk),ncon(mk),
+ nspl(3,mk),ccon(mk),cspl(3,mk),acon(mk),aspl(3,mk)
common/bits/pi,rn,vn,wn,w,wsq,wray,qinv,cg,wgrav,tref,fct,eps,fl,
+ fl1,fl2,fl3,sfl3,jcom,nord,l,kg,kount,knsw,ifanis,iback
common/eifx/a(14,mk),dum(mk)
common/rindx/nic,noc,nsl,nicp1,nocp1,nslp1,n
dimension ass(14),vf(mk),zi(4)
iback=0
w=wdim/wn
wsq=w*w
iexp=0
kount=0
kg=0
fct=0.d0
if(tref.gt.0.d0) fct=2.d0*dlog(tref*wdim)/pi
goto (2,3,1,3),jcom
1 if(wdim.le.wgrav) kg=1
nvefm=2+kg*3
nvesm=5+kg*9
call sdepth(wdim,ls)
if(ls.le.2) then
r10=4.5d-4*(fl+.5d0)/wdim
if(r10.lt.r(2)) then
r(1)=r10
g(1)=rho(1)*r(1)*1.333333333333333d0
ls=1
end if
end if
if(ls.le.nic) then
c*** propagate through inner core ***
call spsm(ls,nvesm,ass)
call sprpmn(ls,nic,ass,vf,nvesm,iexp)
r(1)=0.d0
g(1)=0.d0
call sfbm(ass,kg,iback)
end if
if(ls.le.noc) then
c*** propagate through outer core ***
is=max(ls,nicp1)
if(is.eq.ls) call fpsm(ls,nvefm,ass)
call fprpmn(is,noc,ass,vf,nvefm,iexp)
call fsbm(ass,kg,iback)
end if
is=max(ls,nocp1)
if(is.eq.ls) call spsm(ls,nvesm,ass)
c*** propagate through mantle ***
call sprpmn(is,nsl,ass,vf,nvesm,iexp)
if(nsl.eq.n) then
dnorm=a(1,nsl)*a(1,nsl)
do i=2,nvesm
dnorm=dnorm+a(i,nsl)*a(i,nsl)
enddo
det=a(5,nsl)/sqrt(dnorm)
else
call sfbm(ass,kg,iback)
c*** propagate through ocean ***
call fprpmn(nslp1,n,ass,vf,nvefm,iexp)
if(kg.eq.0) then
det=a(2,n)/sqrt(a(1,n)*a(1,n)+a(2,n)*a(2,n))
else
det=a(5,n)/sqrt(a(1,n)**2+a(2,n)**2+a(3,n)**2+
+ a(4,n)**2+a(5,n)**2)
end if
end if
if(ls.gt.noc) det=-det
if(knsw.eq.1) then
if(ls.gt.noc) kount=kount-2
irem=mod(kount,2)
if(irem.eq.0.and.det.lt.0.d0) kount=kount+1
if(irem.ne.0.and.det.gt.0.d0) kount=kount+1
knt=kount
end if
if(ifeif.eq.0) return
c*** this does eigenfunction calculation for spheroidal modes ***
iback=1
jexp=0
nbakf=1+kg*3
nbaks=4+kg*10
do i=1,nbaks
ass(i)=0.d0
enddo
if(n.ne.nsl) then
if(kg.eq.0) then
ass(1)=dsign(1.d0,a(1,n))
else
asi1=a(3,n)*a(3,n)
asi2=a(4,n)*a(4,n)
if(asi2.le.asi1) ass(1)=dsign(1.d0,a(3,n))
if(asi2.gt.asi1) ass(2)=dsign(1.d0,a(2,n))
end if
call fprpmn(n,nslp1,ass,vf,nbakf,jexp)
call fsbm(ass,kg,iback)
else
asi1=a(3,n)*a(3,n)
asi2=a(4,n)*a(4,n)
if(kg.ne.0) then
asi1=asi1+a(12,n)*a(12,n)
asi2=asi2+a(11,n)*a(11,n)
end if
if(asi2.le.asi1) ass(1)=dsign(1.d0,a(3,n))
if(asi2.gt.asi1) ass(2)=dsign(1.d0,a(2,n))
end if
nto=max(ls,nocp1)
call sprpmn(nsl,nto,ass,vf,nbaks,jexp)
if(nto.eq.ls) goto 90
call sfbm(ass,kg,iback)
nto=max(ls,nicp1)
call fprpmn(noc,nto,ass,vf,nbakf,jexp)
if(nto.eq.ls) goto 90
call fsbm(ass,kg,iback)
nto=max(ls,2)
call sprpmn(nic,nto,ass,vf,nbaks,jexp)
90 if(dabs(det).gt.1.d-4.and.ls.le.noc) call remedy(ls)
call eifout(ls)
return
c*** radial modes ***
2 ls=2
call rps(ls,ass)
call rprop(ls,n,ass)
det=a(2,n)/dsqrt(a(1,n)*a(1,n)+a(2,n)*a(2,n))
knt=kount-1
if(ifeif.eq.0) return
a(1,1)=0.d0
a(2,1)=0.d0
do i=ls,n
ff=fcon(i)*(1.d0+xlam(i)*fct)
cc=ccon(i)*(1.d0+xa2(i)*fct)
a(2,i)=(a(2,i)-2.d0*ff*a(1,i)/r(i))/cc
enddo
zi(1)=0.d0
zi(2)=0.d0
zi(3)=0.d0
do i=ls,n
im=i-1
if(r(i).ne.r(im)) call gauslv(r(im),r(i),im,zi,3)
enddo
rnrm=1.d0/(w*dsqrt(zi(1)))
cg=0.d0
qinv=zi(2)/(wsq*zi(1))
wray=dsqrt(zi(3)/zi(1))
do i=2,n
do j=1,2
a(j,i)=a(j,i)*rnrm
enddo
enddo
return
c*** toroidal modes ***
3 if(jcom.eq.2) then
nb=nocp1
n2=nsl
ass(1)=1.d0
ass(2)=0.d0
else
nb=2
a(1,1)=0.d0
a(2,1)=0.d0
n2=nic
end if
q=0.d0
ls=nb
call startl(ls,n2,fmu,ls,q)
if(ls.ne.nocp1) call tps(ls,ass)
call tprop(ls,n2,ass)
det=a(2,n2)/dsqrt(a(1,n2)*a(1,n2)+a(2,n2)*a(2,n2))
if(knsw.eq.1) then
knt=kount-2
if(jcom.ne.4) then
if(l.ne.1) then
knt=knt+1
irem=mod(knt,2)
if(irem.eq.0.and.det.gt.0.d0) knt=knt+1
if(irem.ne.0.and.det.lt.0.d0) knt=knt+1
end if
end if
end if
if(ifeif.eq.0) return
do i=ls,n2
a(2,i)=a(1,i)/r(i)+a(2,i)/(lcon(i)*(1.d0+qshear(i)*fct))
enddo
if(ls.ne.nb) then
do i=nb,ls-1
a(1,i)=0.d0
a(2,i)=0.d0
enddo
end if
do i=1,4
zi(i)=0.d0
enddo
do i=ls,n2
im=i-1
if(r(i).ne.r(im)) call gauslv(r(im),r(i),im,zi,4)
enddo
rnrm=1.d0/(w*dsqrt(zi(1)))
cg=(fl+0.5d0)*zi(2)/(w*zi(1))
qinv=zi(3)/(wsq*zi(1))
wray=dsqrt(zi(4)/zi(1))
do i=ls,n2
do j=1,2
a(j,i)=a(j,i)*rnrm
enddo
enddo
return
end
subroutine sprpmn(jf,jl,f,h,nvesm,iexp)
c*** propagate a minor vector in a solid region from level jf to jl ***
implicit real*8(a-h,o-z)
parameter (mk=350)
save
real*8 lcon,ncon,lspl,nspl
common r(mk),fmu(mk),flam(mk),qshear(mk),qkappa(mk),
+ xa2(mk),xlam(mk),rho(mk),qro(3,mk),g(mk),qg(3,mk),
+ fcon(mk),fspl(3,mk),lcon(mk),lspl(3,mk),ncon(mk),
+ nspl(3,mk),ccon(mk),cspl(3,mk),acon(mk),aspl(3,mk)
common/bits/pi,rn,vn,wn,w,wsq,wray,qinv,cg,wgrav,tref,fct,eps,fl,
+ fl1,fl2,fl3,sfl3,jcom,nord,l,kg,kount,knsw,ifanis,iback
common/eifx/ar(14,mk),inorm(mk),jjj(mk)
common/shanks/b(46),c(10),dx,step(8),stepf,maxo,in
dimension f(*),h(nvesm,*),s(14),fp(14),rne(6)
data econst/1048576.d0/
maxo1=maxo-1
jud=1
if(jl.lt.jf) jud=-1
y=r(jf)
i=jf
go to 45
10 x=y
y=r(i)
if(y.eq.x) goto 45
iq=min(i,i-jud)
qff=1.d0+xlam(iq)*fct
qll=1.d0+qshear(iq)*fct
qaa=1.d0+xa2(iq)*fct
xi=g(i)/y
vpsq=(flam(i)+2.d0*fmu(i))/rho(i)
vssq=fmu(i)/rho(i)
alfsq=(wsq+4.d0*rho(i)+xi)/vpsq
betasq=wsq/vssq
delsq=sqrt((betasq-alfsq)**2+4.d0*fl3*xi*xi/(vssq*vpsq))
fksq=.5d0*(alfsq+betasq+delsq)-fl3/(x*x)
qt=sqrt(abs(fksq))+sqrt(abs(fksq-delsq))+2.d0/r(iq)
q=(qt+float(kg)*sfl3/x)/stepf
del=float(jud)*step(maxo)/q
dxs=0.d0
15 y=x+del
if(float(jud)*(y-r(i)).gt.0.d0) y=r(i)
dx=y-x
if(dx.ne.dxs) call baylis(q,maxo1)
dxs=dx
do j=1,nvesm
s(j)=f(j)
enddo
do ni=1,in
z=x+c(ni)
call derms(iq,z,f,h(1,ni),0,qff,qll,qaa)
call rkdot(f,s,h,nvesm,ni)
enddo
if(knsw.eq.1) then
call derms(iq,y,f,fp,1,qff,qll,qaa)
call zknt(s,h,f,fp,x,y,1)
end if
x=y
if(y.ne.r(i)) goto 15
45 size=abs(f(1))
do j=2,nvesm
size=max(size,dabs(f(j)))
enddo
55 if(size.lt.1024.d0) goto 65
do j=1,nvesm
f(j)=f(j)/econst
enddo
size=size/econst
iexp=iexp+20
goto 55
65 if(iback.ne.0) then
inorm(i)=inorm(i)+iexp
if(kg.ne.0) then
t1=f(4)+f(8)
t2=t1+f(4)
t1=t1+f(8)
t3=f(8)-f(4)
rne(1)=ar(6,i)*f(10)-ar(14,i)*f(9)+ar(13,i)*t3
1 -ar(1,i)*f(7)-ar(7,i)*f(6)+ar(8,i)*f(5)
2 +ar(12,i)*f(3)-ar(2,i)*f(2)+ar(3,i)*f(1)
rne(2)=ar(6,i)*f(13)+ar(14,i)*t2+ar(13,i)*f(12)
1 -ar(1,i)*f(11)-ar(9,i)*f(6)-ar(7,i)*f(5)
2 +ar(11,i)*f(3)-ar(4,i)*f(2)-ar(2,i)*f(1)
rne(3)=ar(6,i)*f(14)-ar(7,i)*t1-ar(8,i)*f(12)
1 +ar(13,i)*f(11)-ar(9,i)*f(9)+ar(14,i)*f(7)
2 +ar(10,i)*f(3)+ar(11,i)*f(2)+ar(12,i)*f(1)
rne(4)=ar(14,i)*f(14)+ar(7,i)*f(13)+ar(12,i)*f(12)
1 -ar(2,i)*f(11)-ar(9,i)*f(10)-ar(11,i)*t3
2 +ar(4,i)*f(7)+ar(10,i)*f(5)+ar(5,i)*f(1)
rne(5)=ar(13,i)*f(14)+ar(8,i)*f(13)-ar(12,i)*t2
1 -ar(3,i)*f(11)+ar(7,i)*f(10)-ar(11,i)*f(9)
2 -ar(2,i)*f(7)+ar(10,i)*f(6)+ar(5,i)*f(2)
rne(6)=ar(1,i)*f(14)+ar(13,i)*f(13)-ar(2,i)*t1
1 -ar(3,i)*f(12)+ar(14,i)*f(10)-ar(4,i)*f(9)
2 -ar(11,i)*f(6)-ar(12,i)*f(5)+ar(5,i)*f(3)
else
rne(1)=-ar(1,i)*f(3)+ar(2,i)*f(2)-ar(3,i)*f(1)
rne(2)=-ar(1,i)*f(4)+ar(4,i)*f(2)+ar(2,i)*f(1)
rne(3)=-ar(2,i)*f(4)+ar(4,i)*f(3)-ar(5,i)*f(1)
rne(4)=-ar(3,i)*f(4)-ar(2,i)*f(3)-ar(5,i)*f(2)
end if
do jj=1,6
ar(jj,i)=rne(jj)
enddo
else
inorm(i)=iexp
do j=1,nvesm
ar(j,i)=f(j)
enddo
end if
if(i.eq.jl) return
i=i+jud
go to 10
end
subroutine fprpmn(jf,jl,f,h,nvefm,iexp)
c*** propagate the minor vector in a fluid region from level jf to jl ***
implicit real*8(a-h,o-z)
parameter (mk=350)
save
real*8 lcon,ncon,lspl,nspl
common r(mk),fmu(mk),flam(mk),qshear(mk),qkappa(mk),
+ xa2(mk),xlam(mk),rho(mk),qro(3,mk),g(mk),qg(3,mk),
+ fcon(mk),fspl(3,mk),lcon(mk),lspl(3,mk),ncon(mk),
+ nspl(3,mk),ccon(mk),cspl(3,mk),acon(mk),aspl(3,mk)
common/bits/pi,rn,vn,wn,w,wsq,wray,qinv,cg,wgrav,tref,fct,eps,fl,
+ fl1,fl2,fl3,sfl3,jcom,nord,l,kg,kount,knsw,ifanis,iback
common/eifx/ar(14,mk),inorm(mk),jjj(mk)
common/shanks/b(46),c(10),dx,step(8),stepf,maxo,in
dimension f(*),h(nvefm,1),s(5),fp(5)
data econst/1048576.d0/
if(nvefm.eq.1) then
do i=jl,jf
inorm(i)=inorm(i)+iexp
do j=1,2
ar(j,i)=ar(j,i)*f(1)
enddo
enddo
return
end if
maxo1=maxo-1
jud=1
if(jl.lt.jf) jud=-1
y=r(jf)
i=jf
go to 45
10 x=y
y=r(i)
if(y.eq.x) goto 45
iq=min(i,i-jud)
qff=1.d0+xlam(iq)*fct
xi=g(i)/y
alfsq=(wsq+4.d0*rho(i)+xi-fl3*xi*xi/wsq)*rho(i)/flam(i)
q=(sqrt(abs(alfsq-fl3/(x*x)))+1.d0/r(iq)+float(kg)*sfl3/x)/stepf
del=float(jud)*step(maxo)/q
dxs=0.d0
15 y=x+del
if(float(jud)*(y-r(i)).gt.0.d0) y=r(i)
dx=y-x
if(dx.ne.dxs) call baylis(q,maxo1)
dxs=dx
do j=1,nvefm
s(j)=f(j)
enddo
do ni=1,in
z=x+c(ni)
call dermf(iq,z,f,h(1,ni),0,qff)
call rkdot(f,s,h,nvefm,ni)
enddo
if(knsw.eq.1) then
call dermf(iq,y,f,fp,1,qff)
call zknt(s,h,f,fp,x,y,0)
end if
x=y
if(y.ne.r(i)) go to 15
45 size=dabs(f(1))
do j=2,nvefm
size=dmax1(size,dabs(f(j)))
enddo
55 if(size.lt.1024.d0) goto 65
do j=1,nvefm
f(j)=f(j)/econst
enddo
size=size/econst
iexp=iexp+20
goto 55
65 if(iback.ne.0) then
inorm(i)=inorm(i)+iexp
rne2 =-ar(1,i)*f(4)+ar(4,i)*f(2)+ar(2,i)*f(1)
ar(1,i)=-ar(1,i)*f(3)+ar(2,i)*f(2)-ar(3,i)*f(1)
rne3 =-ar(2,i)*f(4)+ar(4,i)*f(3)-ar(5,i)*f(1)
ar(4,i)=-ar(3,i)*f(4)-ar(2,i)*f(3)-ar(5,i)*f(2)
ar(2,i)=rne2
ar(3,i)=rne3
else
inorm(i)=iexp
do j=1,nvefm
ar(j,i)=f(j)
enddo
end if
if(i.eq.jl) return
i=i+jud
go to 10
end
subroutine derms(iq,z,f,fp,iknt,qff,qll,qaa)
c*** calculates minor vector derivative (fp) in a solid ***
implicit real*8(a-h,o-z)
parameter (mk=350)
save
real*8 nn,ll,lcon,ncon,lspl,nspl
common r(mk),fmu(mk),flam(mk),qshear(mk),qkappa(mk),
+ xa2(mk),xlam(mk),rho(mk),qro(3,mk),g(mk),qg(3,mk),
+ fcon(mk),fspl(3,mk),lcon(mk),lspl(3,mk),ncon(mk),
+ nspl(3,mk),ccon(mk),cspl(3,mk),acon(mk),aspl(3,mk)
common/bits/pi,rn,vn,wn,w,wsq,wray,qinv,cg,wgrav,tref,fct,eps,fl,
+ fl1,fl2,fl3,sfl3,jcom,nord,l,kg,kount,knsw,ifanis,iback
dimension f(*),fp(*)
if(iknt.ne.0) then
if(kg.eq.0) then
fp(3)=s22*f(1)-2.d0*t12*f(2)+b33*f(3)+c11*f(5)
fp(4)=-s11*f(1)+2.d0*t21*f(2)-b33*f(4)-c22*f(5)
fp(5)=-2.d0*s12*f(2)+s11*f(3)-s22*f(4)-b11*f(5)
else
fp(3)=s22*f(1)+b32*f(2)+b33*f(3)+c11*f(5)+b313*f(13)
fp(4)=-s11*f(1)+b42*f(2)+b44*f(4)-c22*f(5)+b414*f(14)
fp(5)=b52*f(2)+s11*f(3)-s22*f(4)+b55*f(5)-b313*f(11)
+ +b414*f(12)
end if
return
end if
t=z-r(iq)
if(t.eq.0.d0) then
ro=rho(iq)
gr=g(iq)
ff=fcon(iq)*qff
ll=lcon(iq)*qll
nn=ncon(iq)*qll
cc=ccon(iq)*qaa
aa=acon(iq)*qaa
else
ro=rho(iq)+t*(qro(1,iq)+t*(qro(2,iq)+t*qro(3,iq)))
gr=g(iq)+t*(qg(1,iq)+t*(qg(2,iq)+t*qg(3,iq)))
ff=(fcon(iq)+t*(fspl(1,iq)+t*(fspl(2,iq)+t*fspl(3,iq))))*qff
ll=(lcon(iq)+t*(lspl(1,iq)+t*(lspl(2,iq)+t*lspl(3,iq))))*qll
if(ifanis.eq.0) then
nn=ll
cc=ff+ll+ll
aa=cc
else
nn=(ncon(iq)+t*(nspl(1,iq)+t*(nspl(2,iq)+t*nspl(3,iq))))*qll
cc=(ccon(iq)+t*(cspl(1,iq)+t*(cspl(2,iq)+t*cspl(3,iq))))*qaa
aa=(acon(iq)+t*(aspl(1,iq)+t*(aspl(2,iq)+t*aspl(3,iq))))*qaa
end if
end if
zr=1.d0/z
sfl3z=sfl3*zr
rogr=ro*gr
c11=1.d0/cc
c22=1.d0/ll
dmg=aa-nn-ff*ff*c11
zdmg=zr*dmg
t11=-2.d0*ff*zr*c11+zr