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LocalizedAdmitCorr.f95
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LocalizedAdmitCorr.f95
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Program LocalizedAdmitCorr
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! This program demonstrates how to calculate localized admittance and
! correlation functions.
!
! Written by Mark Wieczorek (April, 2005)
!
! Copyright (c) 2005, Mark A. Wieczorek
! All rights reserved.
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
use SHTOOLS
use PlanetsConstants
implicit none
character*120 :: topography_file, potential_file, outfile
real*8 :: header(8), mpr, r0_pot, gm, mass, lat, lon, pi, theta0, &
alpha, sn, r
real*8, allocatable :: grav(:,:,:), admit(:), corr(:), admit_error(:), &
corr_error(:), tapers(:,:), &
eigenvalues(:), topo(:,:,:), pot(:,:,:)
integer :: lmax_topo, lmax_pot, lmax, option1, l, lwin, lmaxwin, &
astat(5), K, degmax
integer, allocatable :: taper_order(:)
pi = acos(-1.0d0)
degmax = 360
topography_file = "../../ExampleDataFiles/MarsTopo719.shape"
potential_file = "../../ExampleDataFiles/jgmro_110b_sha.tab"
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Read topography and gravity fields, and from the header information
! determine the mean planetary radius and mass. Verify that these values
! are correct as it is possible the input files could be using a
! different set of base units (i.e., km instead of meters).
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
allocate(topo(2,degmax+1,degmax+1), stat = astat(1))
allocate(pot(2,degmax+1,degmax+1), stat = astat(2))
if (astat(1) /= 0 .or. astat(2) /= 0) then
print*, "Problem allocating arrays TOPO and POT", astat(1), astat(2)
stop
endif
print*, "Reading = ", topography_file
call SHRead(topography_file, topo, lmax_topo)
print*, "Lmax of topography file = ", lmax_topo
mpr = topo(1,1,1)
print*, "Mean planetary radius (km) = ", mpr/1.d3
print*, "Reading = ", potential_file
call SHRead(potential_file, pot, lmax_pot, header=header(1:2))
print*, "Lmax of potential file = ", lmax_pot
r0_pot = header(1)*1.d3
gm = header(2)*1.d9
mass = gm/Grav_constant
print*, "Reference radius of potential coefficients (km) = ", r0_pot/1.d3
print*, "Mass of planet (kg) = ", mass
print*, "Surface gravitational acceleration (m/s2) = ", gm/r0_pot**2
lmax = min(lmax_topo, lmax_pot)
print*, "Maximum spherical harmonic degree to be used in calculations = ", &
lmax
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Get localization parameters from user.
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
print*, "Number of tapers to use > "
read(*,*) K
print*, "Latitude of feature of interest (degrees) > "
read(*,*) lat
print*, "Longitude (degrees) > "
read(*,*) lon
print*, "Angular radius of localization window (degrees) > "
read(*,*) theta0
theta0 = theta0*pi/180.0d0
print*, "Create localization window using"
print*, "(1) Desired concentration factor, alpha"
print*, "(2) Desired (approximate) Shannon number; (Lwin+1) Theta0 / pi)"
print*, "(3) Desired Spectral bandwidth (Lwin)"
read(*,*) option1
if (option1==1) then
print*, "Input desired concentration factor of the Kth taper > "
read(*,*) alpha
lwin = SHFindLWin(theta0, 0, alpha, K)
print*, "Corresponding spherical harmonic bandwidth = ", lwin
print*, "Corresponding approximate Shannon number = ", &
(lwin+1)*theta0/pi
elseif (option1==2) then
print*, "Input Shannon number > "
read(*,*) sn
lwin = nint(sn*pi/theta0) - 1
print*, "Corresponding spherical harmonic bandwidth = ", lwin
elseif (option1==3) then
print*, "Input Lwin > "
read(*,*) lwin
print*, "Corresponding approximate Shannon number = ", &
(lwin+1)*theta0/pi
else
stop
endif
allocate(tapers(lwin+1, (lwin+1)**2), stat = astat(1))
allocate(taper_order((lwin+1)**2), stat = astat(2))
allocate(eigenvalues((lwin+1)**2), stat = astat(3))
if (astat(1) /= 0 .or. astat(2) /= 0 .or. astat(3) /= 0 ) then
print*, "Problem allocatig arrays for tapers, taper_order, or eigenvalues", &
astat(1), astat(2), astat(3)
stop
endif
call SHReturnTapers(theta0, lwin, tapers, eigenvalues, taper_order)
print*, "Concentration factor of first taper = ", eigenvalues(1)
print*, "Taper order = ", taper_order(1)
lmaxwin = lmax+lwin
r = r0_pot
print*, "Gravity field evaluated at R = (km) ", r0_pot/1.d3
print*, "Name of output admittance and correlation file > "
read(*,*) outfile
open(12, file=outfile)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Allocate memory for arrays based on Lmax and Lwin.
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
allocate(grav(2,lmax+1,lmax+1), stat=astat(1))
allocate(admit(lmax+lwin+1), stat=astat(2))
allocate(corr(lmax+lwin+1), stat=astat(3))
allocate(admit_error(lmax+lwin+1), stat=astat(4))
allocate(corr_error(lmax+lwin+1), stat=astat(5))
grav = 0.0d0
admit = 0.0d0
corr = 0.0d0
admit_error = 0.0d0
corr_error = 0.0d0
if (astat(1) /= 0 .or. astat(2) /= 0 .or. astat(3) /= 0 .or. astat(4) /= 0 &
.or. astat(5) /=0) then
print*, "Problem allocating memory"
stop
endif
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Create gravity coefficients in units of mGals. Convert Topography
! coefficients to km.
!
! Cilm(gravity) = 1.d5*G*M*Cilm(potential)*(l+1)*(r0_pot/r)**(l+2)/r0_pot**2
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
do l=0, lmax
grav(1:2,l+1,1:l+1) = pot(1:2,l+1,1:l+1) * dble(l+1) * (r0_pot/r)**(l+2)
enddo
grav = grav * 1.0d5 * gm / (r0_pot**2)
topo = topo / 1.0d3
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Compute localized admittances, and write data to output file.
! Units for the admittance are mgals/km.
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
call SHLocalizedAdmitCorr(tapers, taper_order, lwin, lat, lon, grav, topo, &
lmax, admit, corr, K, admit_error=admit_error, corr_error=corr_error, &
mtdef=1)
if (K==1) then
do l = 0, lmax-lwin
write(12,*) l, admit(l+1), corr(l+1)
enddo
else
do l = 0, lmax - lwin
write(12,*) l, admit(l+1), admit_error(l+1), corr(l+1), &
corr_error(l+1)
enddo
endif
close(12)
deallocate(grav)
deallocate(admit)
deallocate(admit_error)
deallocate(corr)
deallocate(corr_error)
deallocate(tapers)
deallocate(taper_order)
deallocate(eigenvalues)
deallocate(topo)
deallocate(pot)
end program LocalizedAdmitCorr