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qspsv.f
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subroutine qspsv(y,k,lup,llw)
implicit none
c
c calculation of response to p-sv source
c y(6,6): solution vector (complex)
c k: wave number
c
integer lup,llw
double precision k
double complex y(6,6)
c
include 'qsglobal.h'
c
c work space
c
integer i,istp,j,l,n,key
double complex cfac,ck,ch0,pwave,swave
double complex y0(4,2),c0(4,2),c1(4,2),b(4,6),b0(4,6)
double complex cinc(4,6)
double complex y1(4,2),yup(4,2),ylw(4,2),orth(2,2)
double complex coef(4,4),cnorm(2),coefrs(2,2),brs(2,6)
logical rsite
c
double complex c2
data c2/(2.d0,0.d0)/
c
ck=dcmplx(k,0.d0)
c
c===============================================================================
c
c matrix propagation from surface to source
c
c determination of starting upper sublayer
c
rsite=.false.
c
if(lup.eq.1.and.isurf.eq.0)then
do j=1,2
do i=1,4
yup(i,j)=(0.d0,0.d0)
enddo
enddo
yup(1,1)=(1.d0,0.d0)
if(vpair.gt.0.d0)yup(2,1)=-accair/kpair
yup(3,2)=(1.d0,0.d0)
else
n=nno(lup)
c
yup(1,1)=kp(n)
yup(2,1)=wa(n)
yup(3,1)=ck
yup(4,1)=wb(n)*kp(n)
c
yup(1,2)=ck
yup(2,2)=wb(n)*ks(n)
yup(3,2)=ks(n)
yup(4,2)=wa(n)
endif
if(lup.eq.lzr)call cmemcpy(yup,y0,8)
c
do l=lup+1,ls
ch0=dcmplx(hp(l-1),0.d0)
n=nno(l-1)
c
c determination of propagation matrix
c
call qsve2am(n,ck,yup,c0,2,rsite)
pwave=cdexp(-kp(n)*ch0)
swave=cdexp(-ks(n)*ch0)
c
c orthonormalization of the p-sv modes
c
cfac=(1.d0,0.d0)/(c0(3,2)*c0(1,1)-c0(1,2)*c0(3,1))
orth(1,1)=c0(3,2)*cfac
orth(1,2)=-c0(1,2)*cfac
orth(2,1)=-c0(3,1)*cfac
orth(2,2)=c0(1,1)*cfac
call caxcb(c0,orth,4,2,2,c1)
c
if(l.gt.lzr)then
c
c additional normalization to avoid overflow
c
do i=1,2
orth(i,1)=orth(i,1)*pwave
orth(i,2)=orth(i,2)*swave
enddo
call caxcb(y0,orth,4,2,2,y1)
call cmemcpy(y1,y0,8)
endif
c
c for partial solution only!
c
if(.not.pup(l-1))then
c1(2,1)=(0.d0,0.d0)
c1(4,1)=(0.d0,0.d0)
if(l.gt.lzr)then
do j=1,4
y0(j,1)=(0.d0,0.d0)
enddo
endif
endif
if(.not.svup(l-1))then
c1(2,2)=(0.d0,0.d0)
c1(4,2)=(0.d0,0.d0)
if(l.gt.lzr)then
do j=1,4
y0(j,2)=(0.d0,0.d0)
enddo
endif
endif
if(.not.pdw(l-1))then
c1(2,1)=(0.d0,0.d0)
c1(2,2)=(0.d0,0.d0)
if(l-1.eq.lzr)then
call qsve2am(n,ck,y0,c0,2,rsite)
c0(2,1)=(0.d0,0.d0)
c0(2,2)=(0.d0,0.d0)
call qsam2ve(n,ck,y0,c0,2,rsite)
endif
endif
if(.not.svdw(l-1))then
c1(4,1)=(0.d0,0.d0)
c1(4,2)=(0.d0,0.d0)
if(l-1.eq.lzr)then
call qsve2am(n,ck,y0,c0,2,rsite)
c0(4,1)=(0.d0,0.d0)
c0(4,2)=(0.d0,0.d0)
call qsam2ve(n,ck,y0,c0,2,rsite)
endif
endif
c
c end partial solution procedure!
c
c c1(1,1)=c1(1,1)
c1(2,1)=c1(2,1)*pwave*pwave
c1(3,1)=(0.d0,0.d0)
c1(4,1)=c1(4,1)*pwave*swave
c
c1(1,2)=(0.d0,0.d0)
c1(2,2)=c1(2,2)*swave*pwave
c c1(3,2)=c1(3,2)
c1(4,2)=c1(4,2)*swave*swave
c
call qsam2ve(n,ck,yup,c1,2,rsite)
c
if(l.eq.lzr)call cmemcpy(yup,y0,8)
enddo
c
c===============================================================================
c
c matrix propagation from half-space to source
c
n=nno(llw)
ylw(1,1)=-kp(n)
ylw(2,1)=wa(n)
ylw(3,1)=ck
ylw(4,1)=-wb(n)*kp(n)
c
ylw(1,2)=ck
ylw(2,2)=-wb(n)*ks(n)
ylw(3,2)=-ks(n)
ylw(4,2)=wa(n)
c
if(llw.gt.ls.and.llw.eq.lzr)call cmemcpy(ylw,y0,8)
c
do l=llw-1,ls,-1
ch0=dcmplx(hp(l),0.d0)
n=nno(l)
c
c determination of propagation matrix
c
call qsve2am(n,ck,ylw,c0,2,rsite)
pwave=cdexp(-kp(n)*ch0)
swave=cdexp(-ks(n)*ch0)
c
c orthonormalization of the p-sv modes
c
cfac=(1.d0,0.d0)/(c0(4,2)*c0(2,1)-c0(2,2)*c0(4,1))
orth(1,1)=c0(4,2)*cfac
orth(1,2)=-c0(2,2)*cfac
orth(2,1)=-c0(4,1)*cfac
orth(2,2)=c0(2,1)*cfac
call caxcb(c0,orth,4,2,2,c1)
c
if(l.lt.lzr)then
c
c additional normalization to avoid overflow
c
do i=1,2
orth(i,1)=orth(i,1)*pwave
orth(i,2)=orth(i,2)*swave
enddo
call caxcb(y0,orth,4,2,2,y1)
call cmemcpy(y1,y0,8)
endif
c
c for partial solution only!
c
if(.not.pup(l))then
c1(1,1)=(0.d0,0.d0)
c1(1,2)=(0.d0,0.d0)
if(l+1.eq.lzr)then
call qsve2am(n,ck,y0,c0,2,rsite)
c0(1,1)=(0.d0,0.d0)
c0(1,2)=(0.d0,0.d0)
call qsam2ve(n,ck,y0,c0,2,rsite)
endif
endif
if(.not.svup(l))then
c1(3,1)=(0.d0,0.d0)
c1(3,2)=(0.d0,0.d0)
if(l+1.eq.lzr)then
call qsve2am(n,ck,y0,c0,2,rsite)
c0(3,1)=(0.d0,0.d0)
c0(3,2)=(0.d0,0.d0)
call qsam2ve(n,ck,y0,c0,2,rsite)
endif
endif
if(.not.pdw(l))then
c1(1,1)=(0.d0,0.d0)
c1(3,1)=(0.d0,0.d0)
if(l.lt.lzr)then
do j=1,4
y0(j,1)=(0.d0,0.d0)
enddo
endif
endif
if(.not.svdw(l))then
c1(1,2)=(0.d0,0.d0)
c1(3,2)=(0.d0,0.d0)
if(l.lt.lzr)then
do j=1,4
y0(j,2)=(0.d0,0.d0)
enddo
endif
endif
c
c end partial solution procedure!
c
c1(1,1)=c1(1,1)*pwave*pwave
c c1(2,1)=c1(2,1)
c1(3,1)=c1(3,1)*pwave*swave
c1(4,1)=(0.d0,0.d0)
c
c1(1,2)=c1(1,2)*swave*pwave
c1(2,2)=(0.d0,0.d0)
c1(3,2)=c1(3,2)*swave*swave
c c1(4,2)=c1(4,2)
c
call qsam2ve(n,ck,ylw,c1,2,rsite)
if(l.gt.ls.and.l.eq.lzr)call cmemcpy(ylw,y0,8)
enddo
c
c===============================================================================
c source function
c===============================================================================
c
do istp=1,6
do i=1,4
c b(i,istp)=dcmplx(sfct0(i,istp)+k*sfct1(i,istp),0.d0)
b(i,istp)=sfct0(i,istp)+ck*sfct1(i,istp)
enddo
enddo
do i=1,4
do j=1,2
coef(i,j)=yup(i,j)
coef(i,j+2)=-ylw(i,j)
enddo
enddo
if(ipath.eq.1)call cmemcpy(b,b0,24)
key=0
call cdgemp(coef,b,4,6,0.d0,key)
if(key.eq.0)then
print *,'warning in qspsv: anormal exit from cdgemp!'
return
endif
if(lzr.le.ls)then
do istp=1,6
do i=1,4
y(i,istp)=(0.d0,0.d0)
do j=1,2
y(i,istp)=y(i,istp)+b(j,istp)*y0(i,j)
enddo
enddo
enddo
else
do istp=1,6
do i=1,4
y(i,istp)=(0.d0,0.d0)
do j=1,2
y(i,istp)=y(i,istp)+b(j+2,istp)*y0(i,j)
enddo
enddo
enddo
endif
c
if(ipath.eq.1)then
n=nno(lpath)
ylw(1,1)=-kp(n)
ylw(2,1)=wa(n)
ylw(3,1)=ck
ylw(4,1)=-wb(n)*kp(n)
c
ylw(1,2)=ck
ylw(2,2)=-wb(n)*ks(n)
ylw(3,2)=-ks(n)
ylw(4,2)=wa(n)
c
if(lpath.gt.ls.and.lpath.eq.lzr)call cmemcpy(ylw,y0,8)
do l=lpath-1,ls,-1
ch0=dcmplx(hp(l),0.d0)
n=nno(l)
c
c determination of propagation matrix
c
call qsve2am(n,ck,ylw,c0,2,rsite)
pwave=cdexp(-kp(n)*ch0)
swave=cdexp(-ks(n)*ch0)
c
c orthonormalization of the p-sv modes
c
cfac=(1.d0,0.d0)/(c0(4,2)*c0(2,1)-c0(2,2)*c0(4,1))
orth(1,1)=c0(4,2)*cfac
orth(1,2)=-c0(2,2)*cfac
orth(2,1)=-c0(4,1)*cfac
orth(2,2)=c0(2,1)*cfac
c
call caxcb(c0,orth,4,2,2,c1)
if(l.lt.lzr)then
c
c additional normalization to avoid overflow
c
do i=1,2
orth(i,1)=orth(i,1)*pwave
orth(i,2)=orth(i,2)*swave
enddo
call caxcb(y0,orth,4,2,2,y1)
call cmemcpy(y1,y0,8)
endif
c
c for partial solution only!
c
if(.not.pup(l))then
c1(1,1)=(0.d0,0.d0)
c1(1,2)=(0.d0,0.d0)
if(l+1.eq.lzr)then
call qsve2am(n,ck,y0,c0,2,rsite)
c0(1,1)=(0.d0,0.d0)
c0(1,2)=(0.d0,0.d0)
call qsam2ve(n,ck,y0,c0,2,rsite)
endif
endif
if(.not.svup(l))then
c1(3,1)=(0.d0,0.d0)
c1(3,2)=(0.d0,0.d0)
if(l+1.eq.lzr)then
call qsve2am(n,ck,y0,c0,2,rsite)
c0(3,1)=(0.d0,0.d0)
c0(3,2)=(0.d0,0.d0)
call qsam2ve(n,ck,y0,c0,2,rsite)
endif
endif
if(.not.pdw(l))then
c1(1,1)=(0.d0,0.d0)
c1(3,1)=(0.d0,0.d0)
if(l.lt.lzr)then
do j=1,4
y0(j,1)=(0.d0,0.d0)
enddo
endif
endif
if(.not.svdw(l))then
c1(1,2)=(0.d0,0.d0)
c1(3,2)=(0.d0,0.d0)
if(l.lt.lzr)then
do j=1,4
y0(j,2)=(0.d0,0.d0)
enddo
endif
endif
c
c end partial solution procedure!
c
c1(1,1)=c1(1,1)*pwave*pwave
c c1(2,1)=c1(2,1)
c1(3,1)=c1(3,1)*pwave*swave
c1(4,1)=(0.d0,0.d0)
c
c1(1,2)=c1(1,2)*swave*pwave
c1(2,2)=(0.d0,0.d0)
c1(3,2)=c1(3,2)*swave*swave
c c1(4,2)=c1(4,2)
c
call qsam2ve(n,ck,ylw,c1,2,rsite)
if(l.gt.ls.and.l.eq.lzr)call cmemcpy(ylw,y0,8)
enddo
do i=1,4
do j=1,2
coef(i,j)=yup(i,j)
coef(i,j+2)=-ylw(i,j)
enddo
enddo
key=0
call cdgemp(coef,b0,4,6,1.d-30,key)
if(key.eq.0)then
print *,'warning in qspsv: anormal exit from cdgemp!'
return
endif
if(lzr.le.ls)then
do istp=1,6
do i=1,4
do j=1,2
y(i,istp)=y(i,istp)-b0(j,istp)*y0(i,j)
enddo
enddo
enddo
else
do istp=1,6
do i=1,4
do j=1,2
y(i,istp)=y(i,istp)-b0(j+2,istp)*y0(i,j)
enddo
enddo
enddo
endif
endif
c
if(n0rs.gt.0)then
c
c for receiver-site structure different from source-site structure
c
n=nno(lzr)
do istp=1,6
call qsve2am(n,ck,y(1,istp),cinc(1,istp),1,rsite)
enddo
c
c determination of starting upper sublayer
c
rsite=.true.
c
if(isurf.eq.0)then
do j=1,2
do i=1,4
yup(i,j)=(0.d0,0.d0)
enddo
enddo
yup(1,1)=(1.d0,0.d0)
if(vpair.gt.0.d0)yup(2,1)=-accair/kpair
yup(3,2)=(1.d0,0.d0)
else
n=nnors(lup)
c
yup(1,1)=kprs(n)
yup(2,1)=wars(n)
yup(3,1)=ck
yup(4,1)=wbrs(n)*kprs(n)
c
yup(1,2)=ck
yup(2,2)=wbrs(n)*ksrs(n)
yup(3,2)=ksrs(n)
yup(4,2)=wars(n)
endif
if(lzrrs.eq.1)call cmemcpy(yup,y0,8)
c
do l=2,lprs
ch0=dcmplx(hprs(l-1),0.d0)
n=nnors(l-1)
c
c
c determination of propagation matrix
c
call qsve2am(n,ck,yup,c0,2,rsite)
pwave=cdexp(-kprs(n)*ch0)
swave=cdexp(-ksrs(n)*ch0)
c
c orthonormalization of the p-sv modes
c
cfac=(1.d0,0.d0)/(c0(3,2)*c0(1,1)-c0(1,2)*c0(3,1))
orth(1,1)=c0(3,2)*cfac
orth(1,2)=-c0(1,2)*cfac
orth(2,1)=-c0(3,1)*cfac
orth(2,2)=c0(1,1)*cfac
c
call caxcb(c0,orth,4,2,2,c1)
if(l.gt.lzrrs)then
c
c additional normalization to avoid overflow
c
do i=1,2
orth(i,1)=orth(i,1)*pwave
orth(i,2)=orth(i,2)*swave
enddo
call caxcb(y0,orth,4,2,2,y1)
call cmemcpy(y1,y0,8)
endif
c c1(1,1)=c1(1,1)
c1(2,1)=c1(2,1)*pwave*pwave
c1(3,1)=(0.d0,0.d0)
c1(4,1)=c1(4,1)*pwave*swave
c
c1(1,2)=(0.d0,0.d0)
c1(2,2)=c1(2,2)*swave*pwave
c c1(3,2)=c1(3,2)
c1(4,2)=c1(4,2)*swave*swave
c
call qsam2ve(n,ck,yup,c1,2,rsite)
if(l.eq.lzrrs)call cmemcpy(yup,y0,8)
enddo
n=nnors(lprs)
call qsve2am(n,ck,yup,c0,2,rsite)
do istp=1,6
brs(1,istp)=cinc(1,istp)
brs(2,istp)=cinc(3,istp)
enddo
coefrs(1,1)=c0(1,1)
coefrs(1,2)=c0(1,2)
coefrs(2,1)=c0(3,1)
coefrs(2,2)=c0(3,2)
key=0
call cdgemp(coefrs,brs,2,6,0.d0,key)
if(key.eq.0)then
print *,'warning in qspsv: anormal exit from cdgemp!'
return
endif
do istp=1,6
do i=1,4
y(i,istp)=(0.d0,0.d0)
do j=1,2
y(i,istp)=y(i,istp)+brs(j,istp)*y0(i,j)
enddo
enddo
enddo
endif
if(isurf.eq.2)then
c
c free surface corrections
c
n=1
if(rsite)then
yup(1,1)=kprs(n)
yup(2,1)=wars(n)
yup(3,1)=ck
yup(4,1)=wbrs(n)*kprs(n)
c
yup(1,2)=ck
yup(2,2)=wbrs(n)*ksrs(n)
yup(3,2)=ksrs(n)
yup(4,2)=wars(n)
c
ylw(1,1)=-kprs(n)
ylw(2,1)=wars(n)
ylw(3,1)=ck
ylw(4,1)=-wbrs(n)*kprs(n)
c
ylw(1,2)=ck
ylw(2,2)=-wbrs(n)*ksrs(n)
ylw(3,2)=-ksrs(n)
ylw(4,2)=wars(n)
else
yup(1,1)=kp(n)
yup(2,1)=wa(n)
yup(3,1)=ck
yup(4,1)=wb(n)*kp(n)
c
yup(1,2)=ck
yup(2,2)=wb(n)*ks(n)
yup(3,2)=ks(n)
yup(4,2)=wa(n)
c
ylw(1,1)=-kp(n)
ylw(2,1)=wa(n)
ylw(3,1)=ck
ylw(4,1)=-wb(n)*kp(n)
c
ylw(1,2)=ck
ylw(2,2)=-wb(n)*ks(n)
ylw(3,2)=-ks(n)
ylw(4,2)=wa(n)
endif
c
do istp=1,6
call qsve2am(1,ck,y(1,istp),b0(1,istp),1,rsite)
b(1,istp)=-yup(2,1)*b0(1,istp)-yup(2,2)*b0(3,istp)
b(2,istp)=-yup(4,1)*b0(1,istp)-yup(4,2)*b0(3,istp)
orth(1,1)=ylw(2,1)
orth(1,2)=ylw(2,2)
orth(2,1)=ylw(4,1)
orth(2,2)=ylw(4,2)
key=0
call cdgemp(orth,b(1,istp),2,1,0.d0,key)
if(key.eq.0)then
print *,'warning in qspsv: anormal exit from cdgemp!'
return
endif
b0(2,istp)=b(1,istp)
b0(4,istp)=b(2,istp)
call qsam2ve(1,ck,y(1,istp),b0(1,istp),1,rsite)
enddo
endif
return
end