def TestFilter():
half = 80
r = constants.Moon.r.value
d = r - 40.e3
deglist = np.arange(1, 200, 1)
wl = np.zeros(len(deglist) + 1)
wlcurv = np.zeros(len(deglist) + 1)
for l in deglist:
wl[l] = gravmag.DownContFilterMA(l, half, r, d)
wlcurv[l] = gravmag.DownContFilterMC(l, half, r, d)
fig = plt.figure()
plt.plot(deglist, wl[1:], 'b-', label='Minimum amplitude')
plt.plot(deglist, wlcurv[1:], 'r-', label='Minimum curvature')
plt.xlabel('degree, l')
plt.ylabel('W')
plt.legend()
fig.savefig('Filter.png')
def TestCrustalThickness():
"""
Example routine that calculates the crustal thickness of Mars
"""
delta_max = 5.0
nmax = 6
degmax = 50
lmax = 200
rho_c = 2900.0
rho_m = 3500.0
filter_type = 0
half = 0
gravfile = '../../ExampleDataFiles/gmm3_120_sha.tab'
pot, lmaxp, header = shio.shread(gravfile, lmax=degmax, header=True)
gm = float(header[1]) * 1.e9
mass = gm / constant.G.value
r_grav = float(header[0]) * 1.e3
print(r_grav, gm, mass, lmaxp)
topofile = '../../ExampleDataFiles/MarsTopo719.shape'
hlm, lmaxt = shio.shread(topofile)
r0 = hlm[0, 0, 0]
d = r0 - 45.217409924028445e3
print(r0, lmaxt)
for l in range(2, lmaxp + 1):
pot[:, l, :l + 1] = pot[:, l, :l + 1] * (r_grav / r0)**l
topo_grid = expand.MakeGridDH(hlm, lmax=lmax, sampling=2,
lmax_calc=degmax)
print("Maximum radius (km) = ", topo_grid.max() / 1.e3)
print("Minimum radius (km) = ", topo_grid.min() / 1.e3)
bc, r0 = gravmag.CilmPlusDH(topo_grid, nmax, mass, rho_c, lmax=degmax)
ba = pot - bc
moho_c = np.zeros([2, degmax + 1, degmax + 1], dtype=float)
moho_c[0, 0, 0] = d
for l in range(1, degmax + 1):
if filter_type == 0:
moho_c[:, l, :l + 1] = ba[:, l, :l + 1] * mass * (2 * l + 1) * \
((r0 / d)**l) \
/ (4.0 * np.pi * (rho_m - rho_c) * d**2)
elif filter_type == 1:
moho_c[:, l, :l + 1] = gravmag.DownContFilterMA(l, half, r0, d) * \
ba[:, l, :l + 1] * mass * (2 * l + 1) * \
((r0 / d)**l) / \
(4.0 * np.pi * (rho_m - rho_c) * d**2)
else:
moho_c[:, l, :l + 1] = gravmag.DownContFilterMC(l, half, r0, d) * \
ba[:, l, :l + 1] * mass * (2 * l + 1) *\
((r0 / d)**l) / \
(4.0 * np.pi * (rho_m - rho_c) * d**2)
moho_grid3 = expand.MakeGridDH(moho_c, lmax=lmax, sampling=2,
lmax_calc=degmax)
print('Maximum Crustal thickness (km) = ',
(topo_grid - moho_grid3).max() / 1.e3)
print('Minimum Crustal thickness (km) = ',
(topo_grid - moho_grid3).min() / 1.e3)
moho_c = gravmag.BAtoHilmDH(ba, moho_grid3, nmax, mass, r0,
(rho_m - rho_c), lmax=lmax,
filter_type=filter_type, filter_deg=half,
lmax_calc=degmax)
moho_grid2 = expand.MakeGridDH(moho_c, lmax=lmax, sampling=2,
lmax_calc=degmax)
print('Delta (km) = ', abs(moho_grid3 - moho_grid2).max() / 1.e3)
temp_grid = topo_grid - moho_grid2
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
iter = 0
delta = 1.0e9
while delta > delta_max:
iter += 1
print('Iteration ', iter)
moho_grid = (moho_grid2 + moho_grid3) / 2.0
print("Delta (km) = ", abs(moho_grid - moho_grid2).max() / 1.e3)
temp_grid = topo_grid - moho_grid
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
moho_grid3 = moho_grid2
moho_grid2 = moho_grid
iter += 1
print('Iteration ', iter)
moho_c = gravmag.BAtoHilmDH(ba, moho_grid2, nmax, mass, r0,
rho_m - rho_c, lmax=lmax,
filter_type=filter_type, filter_deg=half,
lmax_calc=degmax)
moho_grid = expand.MakeGridDH(moho_c, lmax=lmax, sampling=2,
lmax_calc=degmax)
delta = abs(moho_grid - moho_grid2).max()
print('Delta (km) = ', delta / 1.e3)
temp_grid = topo_grid - moho_grid
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
moho_grid3 = moho_grid2
moho_grid2 = moho_grid
if temp_grid.max() > 100.e3:
print('Not converging')
exit(1)
fig_map = plt.figure()
plt.imshow(temp_grid)
fig_map.savefig('Mars_CrustalThicknes.png')
def TestCrustalThickness():
"""
calculates the crustal thickness of the Moon
"""
delta_max = 5.0 # Default = 5 [m] for convergence criteria
nmax = 10
degmax = 600
lmax = 1200
rho_c = 2550.0
rho_m = 3220.0
filter_type = 1
half = 110
Tc_mean = 35e3 # [m] assumed mean crustal thickness
# gravfile = '../../ExampleDataFiles/gmm3_120_sha.tab'
gravfile = 'gggrx_1200a_sha.tab'
pot, lmaxp, header = shio.shread(gravfile, lmax=degmax, header=True)
gm = float(header[1]) * 1.e9
mass = gm / constant.G.value
r_grav = float(header[0]) * 1.e3
print(r_grav, gm, mass, lmaxp)
# topofile = '../../ExampleDataFiles/MarsTopo719.shape'
topofile = 'lro_ltm05_2050_sha.tab'
hlm, lmaxt = shio.shread(topofile)
r0 = hlm[0, 0, 0]
d = r0 - Tc_mean
print(r0, lmaxt)
for l in range(2, lmaxp + 1):
pot[:, l, :l + 1] = pot[:, l, :l + 1] * (r_grav / r0)**l
topo_grid = expand.MakeGridDH(hlm, lmax=lmax, sampling=2, lmax_calc=degmax)
print("Maximum radius (km) = ", topo_grid.max() / 1.e3)
print("Minimum radius (km) = ", topo_grid.min() / 1.e3)
bc, r0 = gravmag.CilmPlusDH(topo_grid, nmax, mass, rho_c, lmax=degmax)
## save BA coefficients before correcting for mare
ba_tmp = pot - bc
for l in range(2, lmaxp + 1):
ba_tmp[:, l, :l + 1] = ba_tmp[:, l, :l + 1] * (r0 / r_grav)**l
Cba_grid = expand.MakeGridDH(ba_tmp,
lmax=degmax,
sampling=2,
lmax_calc=degmax)
np.savetxt('BAcoef_UniformDensity.out', Cba_grid)
ba = pot - bc
moho_c = np.zeros([2, degmax + 1, degmax + 1], dtype=float)
moho_c[0, 0, 0] = d
for l in range(1, degmax + 1):
if filter_type == 0:
moho_c[:, l, :l + 1] = ba[:, l, :l + 1] * mass * (2 * l + 1) * \
((r0 / d)**l) \
/ (4.0 * np.pi * (rho_m - rho_c) * d**2)
elif filter_type == 1:
moho_c[:, l, :l + 1] = gravmag.DownContFilterMA(l, half, r0, d) * \
ba[:, l, :l + 1] * mass * (2 * l + 1) * \
((r0 / d)**l) / \
(4.0 * np.pi * (rho_m - rho_c) * d**2)
else:
moho_c[:, l, :l + 1] = gravmag.DownContFilterMC(l, half, r0, d) * \
ba[:, l, :l + 1] * mass * (2 * l + 1) *\
((r0 / d)**l) / \
(4.0 * np.pi * (rho_m - rho_c) * d**2)
moho_grid3 = expand.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
print('Maximum Crustal thickness (km) = ',
(topo_grid - moho_grid3).max() / 1.e3)
print('Minimum Crustal thickness (km) = ',
(topo_grid - moho_grid3).min() / 1.e3)
moho_c = gravmag.BAtoHilmDH(ba,
moho_grid3,
nmax,
mass,
r0, (rho_m - rho_c),
lmax=lmax,
filter_type=filter_type,
filter_deg=half,
lmax_calc=degmax)
moho_grid2 = expand.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
print('Delta (km) = ', abs(moho_grid3 - moho_grid2).max() / 1.e3)
temp_grid = topo_grid - moho_grid2
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
iter = 0
delta = 1.0e9
while delta > delta_max:
iter += 1
print('Iteration ', iter)
moho_grid = (moho_grid2 + moho_grid3) / 2.0
print("Delta (km) = ", abs(moho_grid - moho_grid2).max() / 1.e3)
temp_grid = topo_grid - moho_grid
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
moho_grid3 = moho_grid2
moho_grid2 = moho_grid
iter += 1
print('Iteration ', iter)
moho_c = gravmag.BAtoHilmDH(ba,
moho_grid2,
nmax,
mass,
r0,
rho_m - rho_c,
lmax=lmax,
filter_type=filter_type,
filter_deg=half,
lmax_calc=degmax)
moho_grid = expand.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
delta = abs(moho_grid - moho_grid2).max()
print('Delta (km) = ', delta / 1.e3)
temp_grid = topo_grid - moho_grid
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
moho_grid3 = moho_grid2
moho_grid2 = moho_grid
if temp_grid.max() > 100.e3:
print('Not converging')
exit(1)
temp_grid = temp_grid * 1e-3
# fig_map = plt.figure()
# im = plt.imshow(temp_grid,cmap='jet')
# fig_map.colorbar(im, orientation='horizontal')
# fig_map.savefig('InvCrustalThickness.png')
np.savetxt('CrustalThickness_UniformDensity.out', temp_grid)
def InvMoho():
"""
Invert for the Moho relief from FAA map
"""
delta_max = 5.0 # Default = 5 [m] for convergence criteria
nmax = 10 #7
degmax = 600 # [310]
lmax = 1200 # [930]2*degmax ~ nmax*degmax
#rho_c = 2550.0 # crustal density for use in the first iteration
rho_m = 3220.0
filter_type = 1
half = 80 #80; max=110
# Tc_mean = 44e3 # [m] assumed mean crustal thickness
Tc_mean = 35e3 # [m] assumed mean crustal thickness
# load gravity file
#gravfile = '../../ExampleDataFiles/gmm3_120_sha.tab'
#gravfile = 'JGGRAIL_1200C12A_SHA.TAB'
gravfile = 'gggrx_1200a_sha.tab'
pot, lmaxp, header = shio.shread(gravfile, lmax=degmax, header=True)
gm = float(header[1]) * 1.e9
mass = gm / constant.G.value
r_grav = float(header[0]) * 1.e3
print(r_grav, gm, mass, lmaxp)
# load topography file
#topofile = '../../ExampleDataFiles/MarsTopo719.shape'
topofile = 'lro_ltm05_2050_sha.tab'
hlm, lmaxt = shio.shread(topofile, lmax=degmax)
r0 = hlm[0, 0, 0] # degree-0 radius (reference)
d = r0 - Tc_mean
print(r0, lmaxt)
# load crusatal denisty variation grid (from the current folder)
rho_grid = np.loadtxt('rhoc.in')
# first expand the density grid to spherical harmonics
rho = expand.SHExpandDH(rho_grid, sampling=2, lmax_calc=degmax)
# # consider varible crustal density with resolution better than 5 degree (l = 36)
# lrhomax = 36
# rho[:,lrhomax+1:,:]=0
# # back to grid file
# rho_grid = expand.MakeGridDH(rho, lmax=lmax, sampling=2,lmax_calc=lrhomax)
# fig_map = plt.figure()
# im = plt.imshow(rho_grid,cmap='jet')
# fig_map.colorbar(im, orientation='horizontal')
# fig_map.savefig('rhoc_tmp.png')
# change the reference of the gravity file from r_grav to r0
for l in range(2, lmaxp + 1):
pot[:, l, :l + 1] = pot[:, l, :l + 1] * (r_grav / r0)**l
# expand the toopgraphy
topo_grid = expand.MakeGridDH(hlm, lmax=lmax, sampling=2, lmax_calc=degmax)
print("Maximum radius (km) = ", topo_grid.max() / 1.e3)
print("Minimum radius (km) = ", topo_grid.min() / 1.e3)
# calculate the Bouguer correction
#bc, r0 = gravmag.CilmPlusDH(topo_grid, nmax, mass, rho_c, lmax=degmax)
bc, r0 = gravmag.CilmPlusRhoHDH(topo_grid,
nmax,
mass,
rho_grid,
lmax=degmax)
# calculate the gravitational contribution from the lateral variations in density
# of the shell between the two radii r0 and d, referenced to r0
# calculate the gravity terms (from Wieczoerk 2003 SM Equation 19)
shellc = np.zeros([2, degmax + 1, degmax + 1], dtype=float)
for l in range(1, degmax + 1):
shellc[:, l, :l + 1] = rho[:, l, :l + 1]* 4 * np.pi * r0**3 / mass / \
(2 * l + 1) / (l + 3) * (1 - (d / r0)**(l + 3))
# shellc_grid,_, _, _, _ = gravmag.MakeGravGridDH(shellc, gm, r0, lmax=degmax)
# shellc_grid = -shellc_grid*1e5
#
# shellc1 = np.load('Clm_rho.npy')
# shellc = np.zeros([2, degmax + 1, degmax + 1], dtype=float)
# shellc[:,0:311,0:311] = shellc1
#
# shellc1_grid,_, _, _, _ = gravmag.MakeGravGridDH(shellc, gm, r0, lmax=degmax)
# shellc1_grid = -shellc1_grid*1e5
#
#
# fig, (ax1,ax2) = plt.subplots(2,1)
# pos = ax1.imshow(shellc_grid,cmap='jet')
# cbar = fig.colorbar(pos, ax=ax1,orientation='vertical')
#
# pos = ax2.imshow(shellc1_grid,cmap='jet')
# cbar = fig.colorbar(pos,ax=ax2,orientation='vertical')
#
# fig.savefig('DensityShell.png')
#
#
#
# print('Maximum misfit = ', abs(shellc_grid-shellc1_grid).max())
## """
## Forward modeling of gravity attraction due to mare loading
## Pasted from ForwardMare_VariableDrhom.py
##
## """
# # load mare bottom topography from the current folder
# marethick_grid = np.loadtxt('marethick.in')
#
# # load crusatal for shallow part
# rho_shallow_grid = np.loadtxt('rhoc_shallow.in')
#
#
# # calculate the gravity attaction due to surface with variable density
# gt, r1 = gravmag.CilmPlusRhoHDH(topo_grid, nmax, mass, 3150-rho_shallow_grid, lmax=degmax)
#
# # calculate the gravity attaction due to mare bottom topography with variable density
# gb, r2 = gravmag.CilmPlusRhoHDH(topo_grid-marethick_grid, nmax, mass, 3150-rho_shallow_grid, lmax=degmax)
#
# # calculate the overall contribution
# grav = gt - gb
#
# grav_grid,_, _, _, _ = gravmag.MakeGravGridDH(grav, gm, r0, lmax=degmax)
# grav_grid = -grav_grid*1e5 # convert unit from m/s^2 to mGal; convert upward positive to downward positive
#
## fig_map = plt.figure()
## im = plt.imshow(grav_grid,cmap='jet')
## plt.clim(0, 100)
## fig_map.colorbar(im, orientation='horizontal')
## fig_map.savefig('grav_centralmare.png')
## np.savetxt('grav_centralmare.out',grav_grid)
## save BA coefficients before correcting for mare
# ba_tmp = pot - bc
# for l in range(2, lmaxp + 1):
# ba_tmp[:, l, :l + 1] = ba_tmp[:, l, :l + 1] * (r0 / r_grav)**l
#
# Cba_grid = expand.MakeGridDH(ba_tmp, lmax=degmax, sampling=2,lmax_calc=degmax)
# np.savetxt('BAcoef.out',Cba_grid)
#
## save BA coefficients after correcting for mare
# ba_tmp = pot - bc - 0.3*grav
# for l in range(2, lmaxp + 1):
# ba_tmp[:, l, :l + 1] = ba_tmp[:, l, :l + 1] * (r0 / r_grav)**l
#
# Cba_grid = expand.MakeGridDH(ba_tmp, lmax=degmax, sampling=2,lmax_calc=degmax)
# np.savetxt('BAcoef_MareCorrected.out',Cba_grid)
# # calculate the BA after subtracting bc & bs
# ba = pot - bc - shellc - 0.3*grav
#
#
# """
# End of mare loading modeling
# """
ba = pot - bc - shellc
ba_grid, _, _, _, _ = gravmag.MakeGravGridDH(ba, gm, r0, lmax=degmax)
ba_grid = -ba_grid * 1e5
# np.savetxt('BA.out',ba_grid)
# """
# Plot the three gravity components
# """
#
# bc_grid,_, _, _, _ = gravmag.MakeGravGridDH(bc, gm, r0, lmax=degmax)
# bc_grid = -bc_grid*1e5
#
# shellc_grid,_, _, _, _ = gravmag.MakeGravGridDH(shellc, gm, r0, lmax=degmax)
# shellc_grid = -shellc_grid*1e5
#
# ba_grid,_, _, _, _ = gravmag.MakeGravGridDH(ba, gm, r0, lmax=degmax)
# ba_grid = -ba_grid*1e5
#
# pot_grid,_, _, _, _ = gravmag.MakeGravGridDH(pot, gm, r0, lmax=degmax)
# pot_grid = -pot_grid*1e5
#
# fig, (ax1,ax2,ax3,ax4) = plt.subplots(4,1)
# pos = ax1.imshow(bc_grid,cmap='jet',vmin=-500,vmax=500)
# cbar = fig.colorbar(pos, ax=ax1,orientation='vertical')
#
# pos = ax2.imshow(shellc_grid,cmap='jet',vmin=-500,vmax=500)
# cbar = fig.colorbar(pos,ax=ax2,orientation='vertical')
#
# pos = ax3.imshow(ba_grid,cmap='jet',vmin=-500,vmax=500)
# cbar = fig.colorbar(pos,ax=ax3,orientation='vertical')
#
# pos = ax4.imshow(pot_grid,cmap='jet',vmin=-500,vmax=500)
# cbar = fig.colorbar(pos,ax=ax4,orientation='vertical')
#
# fig.savefig('GravComponets.png')
#
#
# """
# end plot
# """
moho_c = np.zeros([2, degmax + 1, degmax + 1], dtype=float)
# initial h*drho, degree 1 to degmax (h is not moho, moho = d+h)
for l in range(1, degmax + 1):
if filter_type == 0:
moho_c[:, l, :l + 1] = ba[:, l, :l + 1] * mass * (2 * l + 1) * \
((r0 / d)**l) \
/ (4.0 * np.pi * d**2)
elif filter_type == 1:
moho_c[:, l, :l + 1] = gravmag.DownContFilterMA(l, half, r0, d) * \
ba[:, l, :l + 1] * mass * (2 * l + 1) * \
((r0 / d)**l) / \
(4.0 * np.pi * d**2)
else:
moho_c[:, l, :l + 1] = gravmag.DownContFilterMC(l, half, r0, d) * \
ba[:, l, :l + 1] * mass * (2 * l + 1) *\
((r0 / d)**l) / \
(4.0 * np.pi * d**2)
# expand to grid of h, divide by density map to derive initial moho relief
moho_grid3 = expand.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
moho_grid3 = np.divide(moho_grid3, rho_m - rho_grid)
# add degree-0 term to h, which gives moho relief (radius)
moho_c[0, 0, 0] = d
moho_grid3 = moho_grid3 + d
print('Maximum Crustal thickness (km) = ',
(topo_grid - moho_grid3).max() / 1.e3)
print('Minimum Crustal thickness (km) = ',
(topo_grid - moho_grid3).min() / 1.e3)
print('Average Crustal thickness (km) = ',
(topo_grid - moho_grid3).mean() / 1.e3)
# moho_c = gravmag.BAtoHilmDH(ba, moho_grid3, nmax, mass, r0,
# (rho_m - rho_c), lmax=lmax,
# filter_type=filter_type, filter_deg=half,
# lmax_calc=degmax)
moho_c = gravmag.BAtoHilmRhoHDH(ba,
moho_grid3,
rho_m - rho_grid,
nmax,
mass,
r0,
filter_type=filter_type,
filter_deg=half,
lmax=lmax,
lmax_calc=degmax)
moho_grid2 = expand.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
print('Delta (km) = ', abs(moho_grid3 - moho_grid2).max() / 1.e3)
temp_grid = topo_grid - moho_grid2
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
print('Average Crustal thickness (km) = ', temp_grid.mean() / 1.e3)
iter = 0
delta = 1.0e9
while delta > delta_max:
iter += 1
print('Iteration ', iter)
moho_grid = (moho_grid2 + moho_grid3) / 2.0
print("Delta (km) = ", abs(moho_grid - moho_grid2).max() / 1.e3)
temp_grid = topo_grid - moho_grid
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
print('Average Crustal thickness (km) = ', temp_grid.mean() / 1.e3)
moho_grid3 = moho_grid2
moho_grid2 = moho_grid
iter += 1
print('Iteration ', iter)
# moho_c = gravmag.BAtoHilmDH(ba, moho_grid2, nmax, mass, r0,
# rho_m - rho_c, lmax=lmax,
# filter_type=filter_type, filter_deg=half,
# lmax_calc=degmax)
moho_c = gravmag.BAtoHilmRhoHDH(ba,
moho_grid2,
rho_m - rho_grid,
nmax,
mass,
r0,
filter_type=filter_type,
filter_deg=half,
lmax=lmax,
lmax_calc=degmax)
moho_grid = expand.MakeGridDH(moho_c,
lmax=lmax,
sampling=2,
lmax_calc=degmax)
delta = abs(moho_grid - moho_grid2).max()
print('Delta (km) = ', delta / 1.e3)
temp_grid = topo_grid - moho_grid
print('Maximum Crustal thickness (km) = ', temp_grid.max() / 1.e3)
print('Minimum Crustal thickness (km) = ', temp_grid.min() / 1.e3)
print('Average Crustal thickness (km) = ', temp_grid.mean() / 1.e3)
moho_grid3 = moho_grid2
moho_grid2 = moho_grid
if temp_grid.max() > 100.e3:
print('Not converging')
exit(1)
temp_grid = temp_grid * 1e-3
# fig_map = plt.figure()
# im = plt.imshow(temp_grid,cmap='jet')
# fig_map.colorbar(im, orientation='horizontal')
# fig_map.savefig('InvCrustalThickness_test.png')
np.savetxt('CrustalThickness_Lambda80.out', temp_grid)