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flt_module.f90
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flt_module.f90
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module flt_module
use const_module
use input_module
use utils
implicit none
real(8), allocatable :: flt_len_seg(:)
real(8), allocatable :: flt_az_seg(:)
real(8), allocatable :: flt_coor(:,:)
real(8), allocatable :: flt_S_corner(:)
real(8) :: site_coor(2)
real(8), allocatable :: rup_top(:)
real(8), allocatable :: rup_coor(:,:), coor_D(:,:)
real(8), allocatable :: S1(:), S2(:)
real(8), allocatable :: p_locD_arr(:)
real(8), allocatable :: mag_inc_0(:), rate_inc_0(:) ! lower bound of zero
real(8), allocatable :: mag_inc(:), rate_inc(:) ! lower bound of Mmin
real(8) :: flt_area, flt_len, flt_wid
real(8) :: flt_strike_deg, flt_strike_rad
real(8) :: step_D, step_S
real(8) :: step_D_trial, step_S_trial
real(8) :: rup_len, rup_wid, rup_area
real(8) :: rup_len_trial, rup_wid_trial, rup_area_trial
integer :: n_locD, i_locD
integer :: n_locS, i_locS
integer :: n_cor, i_seg
real(8) :: step_D_V, step_D_H
real(8) :: step_D_Hc, step_D_Hs
real(8) :: p_locS, p_locD, ftop
real(8) :: Mw, rate, Rrup, Rjb, Rx
integer :: i_mag, n_mag, i_mag_bin, i_dist_bin, i_eps_bin
integer :: i_freq, i_inten
real(8) :: Tin
contains
subroutine mag_freq_distribution( )
real(8) :: beta, Af, b
real(8) :: c
real(8) :: c2
real(8) :: d
real(8) :: dmag2
real(8) :: K
real(8) :: m_local
real(8) :: M0_Mmax
real(8) :: Mmin0
real(8) :: mu
real(8) :: muAS
real(8), allocatable :: mag_cum(:), rate_cum (:)
real(8), allocatable :: rate_inc_0(:), mag_inc_0(:)
real(8) :: N_Mmin
! magnitude frequency distribution for characteristic recurrence relation
Mmin0 = 0.0 ! Mmin alway set as zero
b = b_value
beta = b * log(10.0)
Af = flt_area * 1.0d10 ! convert km2 to cm**2
c = 1.5
d = 16.05
mu = 3.0d11 ! dyne/cm2
muAS = mu * Af * slip_rate * 0.1 ! slip rate in mm/yr here
M0_Mmax = 10**(Mmax * c + d)
select case ( m_rec_relation) !
case ( EXPONENTIAL) !
call mfd_exp()
case ( CHARACTERISTIC) !
call mfd_char()
case ( DELTA) !
call mfd_delta()
case default
stop 'recurrence relation not supported'
end select
mag_inc = pack(mag_inc_0, mag_inc_0 > Mmin)
rate_inc = pack (rate_inc_0, mag_inc_0 > Mmin)
n_mag = size(mag_inc)
contains
subroutine mfd_delta()
allocate(mag_inc_0(1), rate_inc_0(1))
mag_inc_0(1) = Mmax
rate_inc_0(1) = muAS / M0_Mmax
end subroutine mfd_delta
!>
subroutine mfd_exp()
! Arguments declarations
! Variable declarations
real(8) :: nu
real(8) :: tmp
!
tmp = exp(-beta * (Mmax - Mmin0))
nu = muAS * (1.0d0 - tmp) * (c - b) / b / M0_Mmax / tmp
n_mag = nint(Mmax / mag_step) + 1;
allocate(mag_cum(n_mag))
do i_mag = 1,n_mag
mag_cum (i_mag)= dble(i_mag - 1) * mag_step
end do
allocate(rate_cum(n_mag))
rate_cum = 0.0d0
do i_mag=1,n_mag
m_local = mag_cum(i_mag)
rate_cum(i_mag) = nu * (exp(-beta * (m_local - Mmin0)) - tmp) / (1.0 - tmp)
end do
dmag2 = mag_step / 2.0d0
allocate(mag_inc_0(n_mag - 1))
do i_mag = 1, (n_mag - 1)
mag_inc_0(i_mag) = dmag2 + dble(i_mag-1) * mag_step
end do
!m2f: mag_inc = mag_inc'
allocate(rate_inc_0(n_mag - 1))
rate_inc_0 = rate_cum(1:n_mag-1) - rate_cum(2:n_mag)
end subroutine mfd_exp
subroutine mfd_char()
implicit none
real(8) :: nu_C
real(8) :: nu_NC
real(8) :: tmp_05
real(8) :: tmp_15
real(8) :: tmp_c
tmp_15 = exp(-beta * (Mmax - Mmin0 -1.5))
tmp_05 = exp(-beta * (Mmax - Mmin0 -0.5))
c2 = 0.5 * beta * tmp_15 / (1.0 - tmp_05)
M0_Mmax = 10**(Mmax * c + d)
tmp_c = 10**(-c/2.0)
K = b * tmp_c /(c-b) + b * exp(beta) * (1 - tmp_c) / c
N_Mmin = muAS * (1+c2) * (1-tmp_05) / M0_Mmax / K / tmp_05
nu_NC = muAS * (1.0 - tmp_05) / M0_Mmax / K / tmp_05
nu_C = nu_NC * 0.5 * beta * tmp_15 / (1.0 - tmp_05)
n_mag = nint(Mmax / mag_step) + 1;
allocate(mag_cum(n_mag))
do i_mag = 1,n_mag
mag_cum (i_mag)= dble(i_mag - 1) * mag_step
end do
allocate(rate_cum(n_mag))
rate_cum = 0.0d0
do i_mag=1,n_mag
m_local = mag_cum(i_mag)
if (m_local <= Mmax - 0.5) then
rate_cum(i_mag) = nu_C + nu_NC * &
((exp(-beta*(m_local-Mmin0)) - tmp_05)/(1.0 - tmp_05))
else
rate_cum(i_mag) = nu_C * (Mmax - m_local) / 0.5
end if
end do
dmag2 = mag_step / 2.0
allocate(mag_inc_0(n_mag - 1))
do i_mag = 1, (n_mag - 1)
mag_inc_0(i_mag) = dmag2 + dble(i_mag-1) * mag_step
end do
allocate(rate_inc_0(n_mag - 1))
rate_inc_0 = rate_cum(1:n_mag-1) - rate_cum(2:n_mag)
end subroutine mfd_char
end subroutine mag_freq_distribution
subroutine unit_conversion()
if (m_unit .eq. DEG) then
call deg2km_model()
else if(m_unit .eq. KM ) then
call align_model()
else
stop 'wrong unit, check UNIT section in input '
end if
end subroutine
subroutine calDepthProb ()
implicit none
real(8) :: focal_depth
real(8) :: half_wid
real(8) :: z1
real(8) :: z2
real(8) :: z3
integer(8) :: i_locD
z1 = Smin
z2 = Smin + (Smax-Smin) * depth_param
z3 = Smax
half_wid = rup_wid * sin(flt_dip_rad) / 2.0
do i_locD=1,n_locD
focal_depth = rup_top(i_locD) + half_wid
if (focal_depth < z1) then
p_locD_arr(i_locD) = 0.
else if ( focal_depth < z2 ) then
p_locD_arr(i_locD) = (focal_depth - z1) / (z2 - z1)
else if ( focal_depth < z3 ) then
p_locD_arr(i_locD) = 1. - (focal_depth - z2) / (z3 - z2)
else if ( focal_depth >= z3 ) then
p_locD_arr(i_locD) = 0.
end if
end do
p_locD_arr = p_locD_arr / sum(p_locD_arr)
end subroutine calDepthProb
subroutine deg2km_model()
integer :: i_corner
allocate(flt_coor(flt_n_corner,2))
do i_corner=1,flt_n_corner
call deg2km_simple(flt_coor(i_corner,1), flt_coor(i_corner,2), &
flt_trace(i_corner,1), flt_trace(i_corner,2), &
site(1), site(2))
end do
site_coor = [ 0.0, 0.0 ]
end subroutine deg2km_model
subroutine align_model()
allocate(flt_coor(flt_n_corner,2))
flt_coor(:,1) = flt_trace(:,1) - site(1)
flt_coor(:,2) = flt_trace(:,2) - site(2)
site_coor = [ 0.0,0.0 ]
end subroutine align_model
subroutine flt_ini()
real(8) :: x1, y1, x2, y2, xN, yN
integer :: i_seg
flt_n_corner = size(flt_trace) / 2
flt_n_seg = flt_n_corner - 1
allocate(flt_len_seg(flt_n_seg))
allocate(flt_az_seg(flt_n_seg))
allocate(flt_s_corner(flt_n_corner))
flt_s_corner(1) = 0.0d0
do i_seg = 1, flt_n_seg
y1 = flt_coor(i_seg, 1);
x1 = flt_coor(i_seg, 2);
y2 = flt_coor(i_seg + 1, 1);
x2 = flt_coor(i_seg + 1, 2);
call delaz2_km (y1,x1,y2,x2, flt_len_seg(i_seg), flt_az_seg(i_seg))
flt_s_corner(i_seg+1) = flt_s_corner(i_seg) + flt_len_seg(i_seg)
end do
flt_len = sum(flt_len_seg)
flt_wid = (Smax - Smin) / sin(flt_dip_rad)
flt_area = flt_len * flt_wid
Y1 = flt_coor(1,1)
X1 = flt_coor(1,2)
Yn = flt_coor(flt_n_corner,1)
Xn = flt_coor(flt_n_corner,2)
flt_strike_rad = atan2(Xn - X1, Yn - Y1) ! in radian
flt_strike_deg = flt_strike_rad * RAD2DEG ! in degree
end subroutine flt_ini
subroutine cal_p_locD_arr()
if (allocated(p_locD_arr)) deallocate (p_locD_arr)
allocate(p_locD_arr(n_locD))
p_locD_arr = 0.0d0
select case(m_DEPTH_distribution)
case (UNIFORM)
p_locD_arr = p_locD_arr + 1.0d0 / real(n_locD, 8)
case (TRIANGULAR)
call calDepthProb()
case default
stop 'unsupported depth distribution'
end select
end subroutine
subroutine cal_coor_d()
n_cor = size(rup_coor) / 2
if(allocated(coor_D)) deallocate(coor_D)
allocate(coor_D(n_cor,2))
coor_D = 0.0d0
do i_seg = 1, n_cor
coor_D(i_seg,1) = rup_coor(i_seg,1) + real((i_locD - 1),8) * step_D_Hc;
coor_D(i_seg,2) = rup_coor(i_seg,2) + real((i_locD - 1),8) * step_D_Hs;
end do ! end n_cor
end subroutine
subroutine rupture_location ()
integer :: i_locD, i_locS
step_S_trial = strike_step
step_D_trial = dip_step
call Mw2Arup()
if (rup_area_trial > flt_area) then ! break the entire fault
n_locS = 1; n_locD = 1
step_S = 0.0d0; step_D = 0.0d0
if (allocated(S1)) deallocate(S1)
allocate(S1(n_locS))
if (allocated(S2)) deallocate(S2)
allocate(S2(n_locS))
S1(1) = 0.0d0; S2(1) = flt_len
if (allocated(rup_top)) deallocate(rup_top)
allocate(rup_top(n_locD))
rup_top(1) = Smin
rup_wid = flt_wid
rup_len = flt_len
rup_area = rup_area_trial
else if (rup_wid_trial > flt_wid) then ! break the whole width
n_locD = 1
step_D = 0
if (allocated(rup_top)) deallocate(rup_top)
allocate(rup_top(n_locD))
rup_wid = flt_wid
rup_top(1) = Smin
rup_len = rup_area_trial / rup_wid
if (rup_len > flt_len) then
rup_len = flt_len
n_locS = 1
step_S = 0
if (allocated(S1)) deallocate(S1)
allocate(S1(n_locS))
if (allocated(S2)) deallocate(S2)
allocate(S2(n_locS))
S1(1) = 0.0d0; S2(1) = flt_len
else
n_locS = floor((flt_len - rup_len) / step_S_trial) + 1
step_S = (flt_len - rup_len) / n_locS
n_locS = n_locS + 1
!m2f: S1 = zeros(n_locS,n_locD)
if (allocated(S1)) deallocate(S1)
allocate(S1(n_locS))
S1 = 0.0d0
!m2f: S2 = zeros(n_locS,n_locD)
if (allocated(S2)) deallocate(S2)
allocate(S2(n_locS))
S2 = 0.0d0
do i_locS=1,n_locS
S1(i_locS) = (i_locS - 1)* step_S
S2(i_locS) = S1(i_locS) + rup_len
end do
end if
else
rup_wid = rup_wid_trial
rup_len = rup_len_trial
n_locS = floor((flt_len - rup_len) / step_S_trial) + 1
step_S = (flt_len - rup_len) / n_locS
n_locD = floor((flt_wid - rup_wid) / step_D_trial) + 1
step_D = (flt_wid - rup_wid) / n_locD
step_D_V = step_D * sin(flt_dip_rad)
n_locS = n_locS + 1
n_locD = n_locD + 1
!m2f: S1 = zeros(n_locS,1)
if (allocated(S1)) deallocate(S1)
allocate(S1(n_locS))
S1 = 0.0d0
!m2f: S2 = zeros(n_locS,1)
if (allocated(S2)) deallocate(S2)
allocate(S2(n_locS))
S2 = 0.0d0
do i_locS=1,n_locS
S1(i_locS) = (i_locS - 1)* step_S
S2(i_locS) = S1(i_locS) + rup_len
end do
!m2f: rup_top = zeros(n_locD,1)
if (allocated(rup_top)) deallocate(rup_top)
allocate(rup_top(n_locD))
rup_top = 0.0d0
do i_locD=1,n_locD
rup_top(i_locD) = Smin + (i_locD - 1) * step_D_V
end do
end if
if (S2(n_locS) > flt_len) then
S2(n_locS) = flt_len * 0.99999
end if
step_D_V = step_D * sin(flt_dip_rad)
step_D_H = step_D * cos(flt_dip_rad)
step_D_Hc = step_D_H * cos(flt_strike_rad + PI / 2.0d0)
step_D_Hs = step_D_H * sin(flt_strike_rad + PI / 2.0d0)
end subroutine
subroutine locate_rupture( S1_local, S2_local , rup_coor)
! Arguments declarations
real(8), allocatable, intent(out) :: rup_coor(:,:) ! m2f:check dim(Ntot
real(8), intent(in) :: S1_local, S2_local
! Variable declarations
integer :: N1, N2, Ntot , i
real(8) :: X1, X2, Y1, Y2 !
! S1_local and S2_local are the starting and ending points of the rupture, measured as
! distance to the first corner of the fault
! rup_coor is the fault surface trace between S1_local and S2_local
N1 = count(S1_local >= flt_S_corner)
Y1 = flt_coor(N1,1) + (S1_local - flt_S_corner(N1)) * cos(flt_az_seg(N1))
X1 = flt_coor(N1,2) + (S1_local - flt_S_corner(N1)) * sin(flt_az_seg(N1))
if (S2_local > flt_S_corner(flt_n_corner)) then
stop 'S2_local cannot be greater than fault length'
end if
N2 = count(S2_local > flt_S_corner)
Y2 = flt_coor(N2,1) + (S2_local - flt_S_corner(N2)) * cos(flt_az_seg(N2))
X2 = flt_coor(N2,2) + (S2_local - flt_S_corner(N2)) * sin(flt_az_seg(N2))
Ntot = N2 - N1 + 2
!m2f: rup_coor = zeros(Ntot, 2)
if (allocated(rup_coor)) deallocate(rup_coor)
allocate(rup_coor(Ntot, 2))
if (N1 == N2) then
rup_coor(1,:) = [Y1, X1]
rup_coor(2,:) = [Y2, X2]
else
rup_coor(1,:) = [ Y1,X1 ]
rup_coor(Ntot,:) = [ Y2,X2 ]
do i=2,(Ntot - 1)
rup_coor(i,1) = flt_coor(N1+i-1,1)
rup_coor(i,2) = flt_coor(N1+i-1,2)
end do
end if
end subroutine locate_rupture
subroutine Mw2Arup()
! Variable declarations
real(8) :: AR2
real(8) :: A_rup
! AR is aspect ratio (length to width ratio)
select case ( m_scaling) !
case ( PEER) !
A_rup = 10**(Mw - 4.0)
case (CEUS)
A_rup = 10**(Mw - 4.36)
case (POINT)
A_rup = 1.0d-6
case ( WC94) !
select case ( m_SOF) !
case (SS) !
A_rup = 10**(0.9 * Mw - 3.42)
case ( RV) !
A_rup = 10**(0.98 * Mw - 3.99)
case (NM) !
A_rup = 10**(0.82 * Mw - 2.87)
case (NA) !
A_rup = 10**(0.91 * Mw - 3.49)
case default
stop 'wrong source mechanism '
end select
case default
stop 'wrong scaling model '
end select
AR2 = sqrt(Aspect_Ratio)
rup_len_trial = sqrt(A_rup)*AR2
rup_wid_trial = sqrt(A_rup)/AR2
rup_area_trial = A_rup
end subroutine Mw2Arup
end module flt_module