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)