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density_1d.f90
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density_1d.f90
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!===============================================================================
! One of Andy Nowacki's Fortran utility modules for dealing with seismic
! anisotropy and other problems.
!
! Andy Nowacki <andy.nowacki@bristol.ac.uk>
!
! See the file LICENCE for licence details.
!===============================================================================
module density_1d
!------------------------------------------------------------------------------
!
! Returns density for some global Earth models, given a depth.
!
!
! ** size constants
integer, parameter, private :: i4 = selected_int_kind(9) ; ! long int
integer, parameter, private :: r4 = selected_real_kind(6,37) ; ! SP
integer, parameter, private :: r8 = selected_real_kind(15,307) ; ! DP
! ** precision selector
integer, parameter, private :: rs = r8
! ** maths constants and other useful things
real(rs), parameter, private :: pi = 3.141592653589793238462643 ;
real(rs), parameter, private :: to_rad = 1.74532925199433e-002 ;
real(rs), parameter, private :: to_deg = 57.2957795130823e0 ;
real(rs), parameter, private :: to_km = 111.194926644559 ;
real(rs), parameter, private :: big_number = 10.e36 ;
contains
!===============================================================================
function ak135den(depth)
!===============================================================================
! Uses AK135 model
implicit none
real(rs),intent(in) :: depth
real(rs) :: dep(136),den(136),ak135den,den1,den2,dep1,dep2
integer :: i
logical :: twodepths
data dep / &
0.0, 20.0, 20.0, 35.0, 35.0, &
77.5, 120.0, 165.0, 210.0, 210.0, &
260.0, 310.0, 360.0, 410.0, 410.0, &
460.0, 510.0, 560.0, 610.0, 660.0, &
660.0, 710.0, 760.0, 809.5, 859.0, &
908.5, 958.0, 1007.5, 1057.0, 1106.5, &
1156.0, 1205.5, 1255.0, 1304.5, 1354.0, &
1403.5, 1453.0, 1502.5, 1552.0, 1601.5, &
1651.0, 1700.5, 1750.0, 1799.5, 1849.0, &
1898.5, 1948.0, 1997.5, 2047.0, 2096.5, &
2146.0, 2195.5, 2245.0, 2294.5, 2344.0, &
2393.5, 2443.0, 2492.5, 2542.0, 2591.5, &
2640.0, 2690.0, 2740.0, 2740.0, 2789.7, &
2839.3, 2891.5, 2891.5, 2939.3, 2989.7, &
3040.0, 3090.3, 3140.7, 3191.0, 3241.3, &
3291.7, 3342.0, 3392.3, 3442.6, 3493.0, &
3543.3, 3593.6, 3644.0, 3694.3, 3744.6, &
3795.0, 3845.3, 3895.6, 3945.9, 3996.3, &
4046.6, 4096.9, 4147.3, 4197.6, 4247.9, &
4298.3, 4348.6, 4398.9, 4449.3, 4499.6, &
4549.9, 4600.3, 4650.6, 4700.9, 4801.6, &
4851.9, 4902.2, 4952.6, 5002.9, 5053.2, &
5103.6, 5153.5, 5153.5, 5204.6, 5255.3, &
5306.0, 5356.8, 5407.5, 5458.2, 5508.9, &
5559.6, 5610.3, 5661.0, 5711.7, 5813.2, &
5863.9, 5914.6, 5965.3, 6016.0, 6066.7, &
6117.4, 6168.1, 6218.9, 6269.6, 6320.3, &
6371.0 /
data den / &
2.44900, 2.44900, 2.71420, 2.71420, 3.29760, &
3.29940, 3.30130, 3.34870, 3.39600, 3.39600, &
3.46520, 3.53430, 3.60340, 3.67260, 3.79760, &
3.86120, 3.92480, 3.98850, 4.05210, 4.11580, &
4.33930, 4.38960, 4.43990, 4.47010, 4.50290, &
4.53500, 4.56640, 4.59700, 4.62700, 4.65630, &
4.68490, 4.71300, 4.74040, 4.76730, 4.79360, &
4.81950, 4.84480, 4.87000, 4.89420, 4.91820, &
4.94230, 4.96530, 4.98820, 5.01090, 5.03330, &
5.05530, 5.07720, 5.09900, 5.12060, 5.14220, &
5.16380, 5.18480, 5.20610, 5.22700, 5.24810, &
5.26980, 5.29070, 5.31220, 5.33380, 5.35600, &
5.37760, 5.39990, 5.42240, 5.42240, 5.42380, &
5.42510, 5.42650, 9.91450, 9.99420, 10.07220, &
10.14850, 10.22330, 10.29640, 10.36790, 10.43780, &
10.50620, 10.57310, 10.63850, 10.70230, 10.76470, &
10.82570, 10.88520, 10.94340, 11.00010, 11.05550, &
11.10950, 11.16230, 11.21370, 11.26390, 11.31270, &
11.36040, 11.40690, 11.45210, 11.49620, 11.53910, &
11.58090, 11.62160, 11.66120, 11.69980, 11.73730, &
11.77370, 11.80920, 11.84370, 11.87720, 11.94140, &
11.97220, 12.00010, 12.03110, 12.05930, 12.08670, &
12.11330, 12.13910, 12.70370, 12.72890, 12.75300, &
12.77600, 12.79800, 12.81880, 12.83870, 12.85740, &
12.87510, 12.89170, 12.90720, 12.92170, 12.94740, &
12.95860, 12.96880, 12.97790, 12.98590, 12.99290, &
12.99880, 13.00360, 13.00740, 13.01000, 13.01170, &
13.01220 /
! Ensure depth is in km and not too large
if (depth > 6371.0) then
write(*,'(a,f9.1,a)') ' ak135den: depth ',depth,' is too large.'
stop
endif
! Look for the specific point first
do i=1,136
if (depth == dep(i)) then
ak135den = den(i)
twodepths = .false.
exit
else
! Otherwise, find the points above and below this depth
if (depth > dep(i) .and. depth < dep(i+1)) then
dep1 = dep(i)
den1 = den(i)
dep2 = dep(i+1)
den2 = den(i+1)
twodepths = .true.
exit
endif
endif
enddo
if (twodepths) then
! Extrapolate linearly to find density
ak135den = den1 + (depth-dep1)*(den2-den1)/(dep2-dep1)
endif
return
end function ak135den
!------------------------------------------------------------------------------
!===============================================================================
function premden(depth)
!===============================================================================
! PREM
implicit none
real(rs),intent(in) :: depth
real(rs) :: dep(88),den(88),premden,den1,den2,dep1,dep2
integer :: i
logical :: twodepths
data dep / 0.00, 15.00, 15.00, 24.40, 24.40, &
40.00, 60.00, 80.00, 115.00, 150.00, 185.00, &
220.00, 220.00, 265.00, 310.00, 355.00, 400.00, &
400.00, 450.00, 500.00, 550.00, 600.00, 635.00, &
670.00, 670.00, 721.00, 771.00, 871.00, 971.00, &
1071.00, 1171.00, 1271.00, 1371.00, 1471.00, 1571.00, &
1671.00, 1771.00, 1871.00, 1971.00, 2071.00, 2171.00, &
2271.00, 2371.00, 2471.00, 2571.00, 2671.00, 2741.00, &
2771.00, 2871.00, 2891.00, 2891.00, 2971.00, 3071.00, &
3171.00, 3271.00, 3371.00, 3471.00, 3571.00, 3671.00, &
3771.00, 3871.00, 3971.00, 4017.00, 4171.00, 4271.00, &
4371.00, 4471.00, 4571.00, 4671.00, 4771.00, 4871.00, &
4971.00, 5071.00, 5149.50, 5149.50, 5171.00, 5271.00, &
5371.00, 5471.00, 5571.00, 5671.00, 5771.00, 5871.00, &
5971.00, 6071.00, 6171.00, 6271.00, 6371.00/
data den / 2.60000, 2.60000, 2.90000, 2.90000, 3.38076, &
3.37906, 3.37688, 3.37471, 3.37091, 3.36710, 3.36330, &
3.35950, 3.43578, 3.46264, 3.48951, 3.51639, 3.54325, &
3.72378, 3.78678, 3.84980, 3.91282, 3.97584, 3.98399, &
3.99214, 4.38071, 4.41241, 4.44317, 4.50372, 4.56307, &
4.62129, 4.67844, 4.73460, 4.78983, 4.84422, 4.89783, &
4.95073, 5.00299, 5.05469, 5.10590, 5.15669, 5.20713, &
5.25729, 5.30724, 5.35706, 5.40681, 5.45657, 5.49145, &
5.50642, 5.55641, 5.56645, 9.90349, 10.02940, 10.18134, &
10.32726, 10.46727, 10.60152, 10.73012, 10.85321, 10.97091, &
11.08335, 11.19067, 11.29298, 11.39042, 11.48311, 11.57119, &
11.65478, 11.73401, 11.80900, 11.87990, 11.94682, 12.00989, &
12.06924, 12.12500, 12.16634, 12.76360, 12.77493, 12.82501, &
12.87073, 12.91211, 12.94912, 12.98178, 13.01009, 13.03404, &
13.05364, 13.06888, 13.07977, 13.08630, 13.08848 /
! Ensure depth is in km and not too large
if (depth > 6371.0) then
write(*,'(a,f9.1,a)') ' premden: depth ',depth,' is too large.'
stop
endif
! Look for the specific point first
do i=1,88
if (depth == dep(i)) then
premden = den(i)
twodepths = .false.
exit
else
! Otherwise, find the points above and below this depth
if (depth > dep(i) .and. depth < dep(i+1)) then
dep1 = dep(i)
den1 = den(i)
dep2 = dep(i+1)
den2 = den(i+1)
twodepths = .true.
exit
endif
endif
enddo
if (twodepths) then
! Extrapolate linearly to find density
premden = den1 + (depth-dep1)*(den2-den1)/(dep2-dep1)
endif
return
end function premden
!------------------------------------------------------------------------------
end module density_1d