def main():
gravfile = 'Data/gmm3_120_sha.tab'
topofile = 'Data/MarsTopo719.shape'
densityfile = 'Data/dichotomy_359.sh'
model_name = [
'dwcold', 'dwhot_modif', 'dwhot_stairs', 'DWTh2Ref1', 'DWTh2Ref2',
'eh70cold', '"eh70hot', 'Gudkova'
]
spec = 'Data/Mars-reference-interior-models/model_'
interior_file = [spec + name for name in model_name]
lmax_calc = 90
lmax = lmax_calc * 4
potcoefs, lmaxp, header = pyshtools.shio.shread(gravfile,
header=True,
lmax=lmax)
potential = pyshtools.SHCoeffs.from_array(potcoefs)
potential.r_ref = float(header[0]) * 1.e3
potential.gm = float(header[1]) * 1.e9
potential.mass = potential.gm / float(pyshtools.constant.grav_constant)
print('Gravity file = {:s}'.format(gravfile))
print('Lmax of potential coefficients = {:d}'.format(lmaxp))
print('Reference radius (km) = {:f}'.format(potential.r_ref / 1.e3))
print('GM = {:e}\n'.format(potential.gm))
topo = pyshtools.SHCoeffs.from_file(topofile, lmax=lmax)
topo.r0 = topo.coeffs[0, 0, 0]
print('Topography file = {:s}'.format(topofile))
print('Lmax of topography coefficients = {:d}'.format(topo.lmax))
print('Reference radius (km) = {:f}\n'.format(topo.r0 / 1.e3))
density = pyshtools.SHCoeffs.from_file(densityfile, lmax=lmax)
print('Lmax of density coefficients = {:d}\n'.format(density.lmax))
lat_insight = 4.43
lon_insight = 135.84
filter = 1
half = 50
nmax = 7
lmax_hydro = 15
t0_sigma = 5. # maximum difference between minimum crustal thickness
omega = float(pyshtools.constant.omega_mars)
d_lith = 150.e3
t0 = 1.e3 # minimum crustal thickness
model = 3 # identifier for the interior reference model
# --- read 1D reference interior model ---
print('=== Reading model {:s} ==='.format(model_name[model]))
with open(interior_file[model], 'r') as f:
lines = f.readlines()
print(lines[0].strip())
data = lines[1].split()
if float(data[2]) != 1:
raise RuntimeError('Program not capable of reading polynomial ' +
'files')
num = int(lines[2].split()[0])
crust_index = int(lines[2].split()[3])
mantle_index = int(lines[2].split()[3])
radius = np.zeros(num)
rho = np.zeros(num)
for i in range(0, num):
data = lines[i + 3].split()
radius[i] = float(data[0])
rho[i] = float(data[1])
r0_model = radius[num - 1]
print('Surface radius of model (km) = {:f}'.format(r0_model / 1.e3))
for i in range(0, num):
if radius[i] <= (r0_model - d_lith) and \
radius[i+1] > (r0_model - d_lith):
if radius[i] == (r0_model - d_lith):
i_lith = i
elif (r0_model - d_lith) - radius[i] <= radius[i+1] -\
(r0_model - d_lith):
i_lith = i
else:
i_lith = i + 1
break
n = num - 1
rho[n] = 0. # the density above the surface is zero
rho_mantle = rho[crust_index - 1]
print('Mantle density (kg/m3) = {:f}'.format(rho_mantle))
print('Assumed depth of lithosphere (km) = {:f}'.format(d_lith / 1.e3))
print('Actual depth of lithosphere in discretized model (km) = {:f}'.
format((r0_model - radius[i_lith]) / 1.e3))
# --- Compute gravity contribution from hydrostatic density interfaces ---
if False:
# compute values for a planet that is completely fluid
hlm_fluid, clm_fluid, mass_model = \
HydrostaticShape(radius, rho, omega, potential.gm, potential.r_ref,
finiteamplitude=True)
print('--- Hydrostatic potential coefficients for a fluid planet ---')
print('c20 = {:e}\nc40 = {:e}'.format(clm_fluid.coeffs[0, 2, 0],
clm_fluid.coeffs[0, 4, 0]))
print('--- Hydrostatic relief of surface for a fluid planet ---')
print('h20 = {:e}\nh40 = {:e}'.format(hlm_fluid[n].coeffs[0, 2, 0],
hlm_fluid[n].coeffs[0, 4, 0]))
hlm, clm_hydro, mass_model = \
HydrostaticShapeLith(radius, rho, i_lith, potential, omega,
lmax_hydro, finiteamplitude=False)
print('Total mass of model (kg) = {:e}'.format(mass_model))
print('% of J2 arising from beneath lithosphere = {:f}'.format(
clm_hydro.coeffs[0, 2, 0] / potential.coeffs[0, 2, 0] * 100.))
potential.coeffs[:, :lmax_hydro+1, :lmax_hydro+1] -= \
clm_hydro.coeffs[:, :lmax_hydro+1, :lmax_hydro+1]
# --- Constant density model ---
rho_c = 2900.
print('-- Constant density model --\nrho_c = {:f}'.format(rho_c))
tmin = 1.e9
thickave = 44.e3 # initial guess of average crustal thickness
while abs(tmin - t0) > t0_sigma:
# iterate to fit assumed minimum crustal thickness
moho = pyMoho.pyMoho(potential,
topo,
lmax,
rho_c,
rho_mantle,
thickave,
filter_type=filter,
half=half,
lmax_calc=lmax_calc,
nmax=nmax,
quiet=True)
thick_grid = (topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2')
print('Average crustal thickness (km) = {:f}'.format(thickave / 1.e3))
print('Crustal thickness at InSight landing sites (km) = {:f}'.format(
(topo.pad(lmax) - moho.pad(lmax)).expand(lat=lat_insight,
lon=lon_insight) / 1.e3))
tmin = thick_grid.data.min()
tmax = thick_grid.data.max()
print('Minimum thickness (km) = {:e}'.format(tmin / 1.e3))
print('Maximum thickness (km) = {:e}'.format(tmax / 1.e3))
thickave += t0 - tmin
thick_grid.plot(show=False, fname='Thick-Mars-1.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Mars-1.png')
# --- Model with variable density ---
rho_south = 2900.
rho_north = 2900.
porosity = 0.0
print('-- Variable density model ---\n' +
'rho_south = {:f}\n'.format(rho_south) +
'rho_north = {:f}'.format(rho_north))
density = density * (rho_north - rho_south)
density.coeffs[0, 0, 0] += rho_south
tmin = 1.e9
thickave = 44.e3 # initial guess of average crustal thickness
while abs(tmin - t0) > t0_sigma:
# iterate to fit assumed minimum crustal thickness
moho = pyMoho.pyMohoRho(potential,
topo,
density,
porosity,
lmax,
rho_mantle,
thickave,
filter_type=filter,
half=half,
lmax_calc=lmax_calc,
quiet=True,
nmax=nmax)
thick_grid = (topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2')
print('Average crustal thickness (km) = {:e}'.format(thickave / 1.e3))
print('Crustal thickness at InSight landing sites (km) = {:e}'.format(
(topo.pad(lmax) - moho.pad(lmax)).expand(lat=lat_insight,
lon=lon_insight) / 1.e3))
tmin = thick_grid.data.min()
tmax = thick_grid.data.max()
print('Minimum thickness (km) = {:e}'.format(tmin / 1.e3))
print('Maximum thickness (km) = {:e}'.format(tmax / 1.e3))
thickave += t0 - tmin
thick_grid.plot(show=False, fname='Thick-Mars-2.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Mars-2.png')
def main():
gravfile = 'Data/gmm3_120_sha.tab'
topofile = 'Data/MarsTopo719.shape'
densityfile = 'Data/dichotomy_359.sh'
model_name = ['DWThot', 'DWThotCrust1', 'DWThotCrust1r', 'EH45Tcold',
'EH45TcoldCrust1', 'EH45TcoldCrust1r', 'EH45ThotCrust2',
'EH45ThotCrust2r', 'LFAK', 'SANAK', 'TAYAK', 'DWAK',
'ZG_DW']
spec = 'Data/Mars-reference-interior-models/Smrekar/'
interior_file = [spec + name + '.deck' for name in model_name]
lmax_calc = 90
lmax = lmax_calc * 4
potential = pyshtools.SHGravCoeffs.from_file(gravfile, header_units='km')
print('Gravity file = {:s}'.format(gravfile))
print('Lmax of potential coefficients = {:d}'.format(potential.lmax))
print('Reference radius (km) = {:f}'.format(potential.r0 / 1.e3))
print('GM = {:e}\n'.format(potential.gm))
topo = pyshtools.SHCoeffs.from_file(topofile, lmax=lmax)
topo.r0 = topo.coeffs[0, 0, 0]
print('Topography file = {:s}'.format(topofile))
print('Lmax of topography coefficients = {:d}'.format(topo.lmax))
print('Reference radius (km) = {:f}\n'.format(topo.r0 / 1.e3))
density = pyshtools.SHCoeffs.from_file(densityfile, lmax=lmax)
print('Lmax of density coefficients = {:d}\n'.format(density.lmax))
lat_insight = 4.502384
lon_insight = 135.623447
filter = 1
half = 50
nmax = 7
lmax_hydro = 15
t0_sigma = 5. # maximum difference between minimum crustal thickness
omega = pyshtools.constant.omega_mars.value
d_lith = 150.e3
d_sigma = 45.e3
t0 = 1.e3 # minimum crustal thickness
model = 10 # identifier for the interior reference model
# --- read 1D reference interior model ---
with open(interior_file[model], 'r') as f:
lines = f.readlines()
print(lines[0].strip())
data = lines[1].split()
if float(data[2]) != 1:
raise RuntimeError('Program not capable of reading polynomial ' +
'files')
num_file = int(lines[2].split()[0])
crust_index_file = int(lines[2].split()[3])
core_index_file = int(lines[2].split()[2])
i_crust_file = crust_index_file - 1
i_core_file = core_index_file - 1
radius = np.zeros(num_file)
rho = np.zeros(num_file)
num = 0
for i in range(0, num_file-1):
data = lines[i+3].split()
rb = float(data[0])
rhob = float(data[1])
data = lines[i+4].split()
rt = float(data[0])
rhot = float(data[1])
if rb == rt:
if i == i_core_file:
i_core = num
if i == i_crust_file:
i_crust = num
else:
radius[num] = rb
rho[num] = (rhot + rhob) / 2.
num += 1
radius[num] = rt
rho[num] = 0. # the density above the surface is zero
num += 1
n = num - 1
radius = radius[:n+1]
rho = rho[:n+1]
r0_model = radius[n]
print('Surface radius of model (km) = {:f}'.format(r0_model / 1.e3))
for i in range(0, n+1):
if radius[i] <= (r0_model - d_lith) and \
radius[i+1] > (r0_model - d_lith):
if radius[i] == (r0_model - d_lith):
i_lith = i
elif (r0_model - d_lith) - radius[i] <= radius[i+1] -\
(r0_model - d_lith):
i_lith = i
else:
i_lith = i + 1
break
rho_mantle = rho[i_crust-1]
rho_core = rho[i_core-1]
print('Mantle density (kg/m3) = {:f}'.format(rho_mantle))
print('Mantle radius (km) = {:f}'.format(radius[i_crust]/1.e3))
print('Core density (kg/m3) = {:f}'.format(rho_core))
print('Core radius (km) = {:f}'.format(radius[i_core]/1.e3))
print('Assumed depth of lithosphere (km) = {:f}'.format(d_lith / 1.e3))
print('Actual depth of lithosphere in discretized model (km) = {:f}'
.format((r0_model - radius[i_lith]) / 1.e3))
# --- Compute gravity contribution from hydrostatic density interfaces ---
thickave = 44.e3 # initial guess of average crustal thickness
r_sigma = topo.r0 - thickave
rho_c = 2900.
if True:
# compute values for a planet that is completely fluid
hlm_fluid, clm_fluid, mass_model = \
HydrostaticShape(radius, rho, omega, potential.gm, potential.r0)
print('--- Hydrostatic potential coefficients for a fluid planet ---')
print('c20 = {:e}\nc40 = {:e}'.format(clm_fluid.coeffs[0, 2, 0],
clm_fluid.coeffs[0, 4, 0]))
print('--- Hydrostatic relief of surface for a fluid planet ---')
print('h20 = {:e}\nh40 = {:e}'.format(hlm_fluid[n].coeffs[0, 2, 0],
hlm_fluid[n].coeffs[0, 4, 0]))
hlm, clm_hydro, mass_model = \
HydrostaticShapeLith(radius, rho, i_lith, potential, topo, rho_c,
r_sigma, omega, lmax_hydro)
print('Total mass of model (kg) = {:e}'.format(mass_model))
print('% of J2 arising from beneath lithosphere = {:f}'
.format(clm_hydro.coeffs[0, 2, 0]/potential.coeffs[0, 2, 0] * 100.))
potential.coeffs[:, :lmax_hydro+1, :lmax_hydro+1] -= \
clm_hydro.coeffs[:, :lmax_hydro+1, :lmax_hydro+1]
# --- Constant density model ---
rho_c = 2900.
print('-- Constant density model --\nrho_c = {:f}'.format(rho_c))
tmin = 1.e9
thickave = 44.e3 # initial guess of average crustal thickness
while abs(tmin - t0) > t0_sigma:
# iterate to fit assumed minimum crustal thickness
moho = pyMoho.pyMoho(potential, topo, lmax, rho_c, rho_mantle,
thickave, filter_type=filter, half=half,
lmax_calc=lmax_calc, nmax=nmax, quiet=True)
thick_grid = (topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2')
print('Average crustal thickness (km) = {:f}'.format(thickave / 1.e3))
print('Crustal thickness at InSight landing sites (km) = {:f}'
.format((topo.pad(lmax) - moho.pad(lmax))
.expand(lat=lat_insight, lon=lon_insight) / 1.e3))
tmin = thick_grid.min()
tmax = thick_grid.max()
print('Minimum thickness (km) = {:e}'.format(tmin / 1.e3))
print('Maximum thickness (km) = {:e}'.format(tmax / 1.e3))
thickave += t0 - tmin
thick_grid.plot(show=False, fname='Thick-Mars-1.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Mars-1.png')
# --- Model with variable density ---
rho_south = 2900.
rho_north = 2900.
porosity = 0.0
print('-- Variable density model ---\n' +
'rho_south = {:f}\n'.format(rho_south) +
'rho_north = {:f}'.format(rho_north))
density = density * (rho_north - rho_south)
density.coeffs[0, 0, 0] += rho_south
tmin = 1.e9
thickave = 44.e3 # initial guess of average crustal thickness
while abs(tmin - t0) > t0_sigma:
# iterate to fit assumed minimum crustal thickness
moho = pyMoho.pyMohoRho(potential, topo, density, porosity, lmax,
rho_mantle, thickave, filter_type=filter,
half=half, lmax_calc=lmax_calc, quiet=True,
nmax=nmax)
thick_grid = (topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2')
print('Average crustal thickness (km) = {:e}'.format(thickave / 1.e3))
print('Crustal thickness at InSight landing sites (km) = {:e}'
.format((topo.pad(lmax) - moho.pad(lmax))
.expand(lat=lat_insight, lon=lon_insight) / 1.e3))
tmin = thick_grid.data.min()
tmax = thick_grid.data.max()
print('Minimum thickness (km) = {:e}'.format(tmin / 1.e3))
print('Maximum thickness (km) = {:e}'.format(tmax / 1.e3))
thickave += t0 - tmin
thick_grid.plot(show=False, fname='Thick-Mars-2.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Mars-2.png')
def main():
lmax = 900
lmax_calc = 600
gravfile = 'Data/JGGRAIL_900C11A_SHA.TAB'
topofile = 'Data/LOLA1500p.sh'
densityfile = 'Data/density_no_mare_n3000_f3050_719.sh'
potcoefs, lmaxp, header = pyshtools.shio.shread(gravfile,
header=True,
lmax=lmax)
pot = pyshtools.SHCoeffs.from_array(potcoefs)
pot.r_ref = float(header[0]) * 1.e3
pot.gm = float(header[1]) * 1.e9
pot.mass = pot.gm / float(pyshtools.constant.grav_constant)
print('Gravity file = {:s}'.format(gravfile))
print('Lmax of potential coefficients = {:d}'.format(lmaxp))
print('Reference radius (m) = {:e}'.format(pot.r_ref))
print('GM = {:e}\n'.format(pot.gm))
topo = pyshtools.SHCoeffs.from_file(topofile, lmax=lmax)
topo.r0 = topo.coeffs[0, 0, 0]
print('Topography file = {:s}'.format(topofile))
print('Lmax of topography coefficients = {:d}'.format(topo.lmax))
print('Reference radius (m) = {:e}\n'.format(topo.r0))
density = pyshtools.SHCoeffs.from_file(densityfile, lmax=lmax)
rho_c = density.coeffs[0, 0, 0]
print('Average grain density of crust (kg/m3) = {:e}'.format(rho_c))
print('Lmax of density coefficients = {:d}\n'.format(density.lmax))
a_12_14_lat = -3.3450
a_12_14_long = -20.450
# These parameters correspond to model 1 of Wieczorek et al. (2013).
thickave = 34.e3
porosity = 0.12
rho_m = 3220.0
filter = 1
half = 80
# Constant density model
rho_c = rho_c * (1. - 0.12) # assumed constant density
moho = pyMoho.pyMoho(pot,
topo,
lmax,
rho_c,
rho_m,
thickave,
filter_type=filter,
half=half,
lmax_calc=lmax_calc,
quiet=False)
thick_grid = (topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2')
thick_grid.plot(show=False, fname='Thick-Moon-1.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Moon-1.png')
print('Crustal thickness at Apollo 12/14 landing sites (km) = {:e}'.format(
(topo.pad(lmax) - moho.pad(lmax)).expand(lat=a_12_14_lat,
lon=a_12_14_long) / 1.e3))
# Model with variable density
moho = pyMoho.pyMohoRho(pot,
topo,
density,
porosity,
lmax,
rho_m,
thickave,
filter_type=filter,
half=half,
lmax_calc=lmax_calc,
quiet=False)
thick_grid = (topo - moho.pad(topo.lmax)).expand(grid='DH2')
thick_grid.plot(show=False, fname='Thick-Moon-2.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Moon-2.png')
print('Crustal thickness at Apollo 12/14 landing sites (km) = {:e}'.format(
(topo - moho.pad(topo.lmax)).expand(lat=a_12_14_lat,
lon=a_12_14_long) / 1.e3))
def main():
lmax = 900 # determines spatial resolution of grids
lmax_calc = 600 # maximum degree to use in calculations
gravfile = 'Data/JGGRAIL_900C11A_SHA.TAB'
topofile = 'Data/LOLA1500p.sh'
densityfile = 'Data/density_no_mare_n3000_f3050_719.sh'
pot = pyshtools.SHGravCoeffs.from_file(gravfile, header_units='km')
print('Gravity file = {:s}'.format(gravfile))
print('Lmax of potential coefficients = {:d}'.format(pot.lmax))
print('Reference radius (m) = {:e}'.format(pot.r0))
print('GM = {:e}\n'.format(pot.gm))
topo = pyshtools.SHCoeffs.from_file(topofile, lmax=lmax)
topo.r0 = topo.coeffs[0, 0, 0]
print('Topography file = {:s}'.format(topofile))
print('Lmax of topography coefficients = {:d}'.format(topo.lmax))
print('Reference radius (m) = {:e}\n'.format(topo.r0))
density = pyshtools.SHCoeffs.from_file(densityfile, lmax=lmax)
rho_c0 = density.coeffs[0, 0, 0] # average grain density
print('Average grain density of crust (kg/m3) = {:e}'.format(rho_c0))
print('Lmax of density coefficients = {:d}\n'.format(density.lmax))
a_12_14_lat = -3.3450
a_12_14_long = -20.450
# These parameters correspond to model 1 of Wieczorek et al. (2013).
thickave = 34.e3
porosity = 0.12
rho_m = 3220.0
filter = 1
half = 80
print('Average thickness of the crust (km) = {:e}'.format(thickave / 1.e3))
print('Porosity (%)= {:e}'.format(porosity * 100))
print('Mantle density (kg/m3)= {:e}'.format(rho_m))
# Constant density model
print('\n=== Constant density crust ===')
rho_c = rho_c0 * (1. - porosity) # assumed constant density
print('Bulk density of the crust(kg/m3)= {:e}'.format(rho_c * 100))
moho = pyMoho.pyMoho(pot,
topo,
lmax,
rho_c,
rho_m,
thickave,
filter_type=filter,
half=half,
lmax_calc=lmax_calc,
quiet=False,
delta_max=25.)
thick_grid = (topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2')
thick_grid.plot(show=False, fname='Thick-Moon-1.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Moon-1.png')
print('Crustal thickness at Apollo 12/14 landing sites (km) = {:e}'.format(
(topo.pad(lmax) - moho.pad(lmax)).expand(lat=a_12_14_lat,
lon=a_12_14_long) / 1.e3))
# Model with variable density
print('\n=== Variable density crust ===')
moho = pyMoho.pyMohoRho(pot,
topo,
density,
porosity,
lmax,
rho_m,
thickave,
filter_type=filter,
half=half,
lmax_calc=lmax_calc,
quiet=False,
delta_max=25.)
thick_grid = (topo - moho.pad(topo.lmax)).expand(grid='DH2')
thick_grid.plot(show=False, fname='Thick-Moon-2.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Moon-2.png')
print('Crustal thickness at Apollo 12/14 landing sites (km) = {:e}'.format(
(topo - moho.pad(topo.lmax)).expand(lat=a_12_14_lat,
lon=a_12_14_long) / 1.e3))
def main():
gravfile = 'Data/gmm3_120_sha.tab'
topofile = 'Data/MarsTopo719.shape'
densityfile = 'Data/dichotomy_359.sh'
model_name = [
'DWThot', 'DWThotCrust1', 'DWThotCrust1r', 'EH45Tcold',
'EH45TcoldCrust1', 'EH45TcoldCrust1r', 'EH45ThotCrust2',
'EH45ThotCrust2r', 'LFAK', 'SANAK', 'TAYAK', 'DWAK', 'ZG_DW'
]
spec = 'Data/Mars-reference-interior-models/Smrekar/'
interior_file = [spec + name + '.deck' for name in model_name]
lmax_calc = 90
lmax = lmax_calc * 4
potential = pyshtools.SHGravCoeffs.from_file(gravfile, header_units='km')
print('Gravity file = {:s}'.format(gravfile))
print('Lmax of potential coefficients = {:d}'.format(potential.lmax))
print('Reference radius (km) = {:f}'.format(potential.r0 / 1.e3))
print('GM = {:e}\n'.format(potential.gm))
topo = pyshtools.SHCoeffs.from_file(topofile, lmax=lmax)
topo.r0 = topo.coeffs[0, 0, 0]
print('Topography file = {:s}'.format(topofile))
print('Lmax of topography coefficients = {:d}'.format(topo.lmax))
print('Reference radius (km) = {:f}\n'.format(topo.r0 / 1.e3))
density = pyshtools.SHCoeffs.from_file(densityfile, lmax=lmax)
print('Lmax of density coefficients = {:d}\n'.format(density.lmax))
lat_insight = 4.502384
lon_insight = 135.623447
filter = 1
half = 50
nmax = 7
lmax_hydro = 15
t0_sigma = 5. # maximum difference between minimum crustal thickness
omega = pyshtools.constant.omega_mars.value
d_lith = 150.e3
d_sigma = 45.e3
t0 = 1.e3 # minimum crustal thickness
model = 10 # identifier for the interior reference model
# --- read 1D reference interior model ---
radius, rho, i_crust, i_core, i_lith = ReadRefModel(interior_file[model],
depth=d_lith,
quiet=False)
rho_mantle = rho[i_crust - 1]
rho_core = rho[i_core - 1]
n = len(radius) - 1
r0_model = radius[n]
# --- Compute gravity contribution from hydrostatic density interfaces ---
thickave = 44.e3 # initial guess of average crustal thickness
r_sigma = topo.r0 - thickave
rho_c = 2900.
if True:
# compute values for a planet that is completely fluid
hlm_fluid, clm_fluid, mass_model = \
HydrostaticShape(radius, rho, omega, potential.gm, potential.r0)
print('--- Hydrostatic potential coefficients for a fluid planet ---')
print('c20 = {:e}\nc40 = {:e}'.format(clm_fluid.coeffs[0, 2, 0],
clm_fluid.coeffs[0, 4, 0]))
print('--- Hydrostatic relief of surface for a fluid planet ---')
print('h20 = {:e}\nh40 = {:e}'.format(hlm_fluid[n].coeffs[0, 2, 0],
hlm_fluid[n].coeffs[0, 4, 0]))
hlm, clm_hydro, mass_model = \
HydrostaticShapeLith(radius, rho, i_lith, potential, topo, rho_c,
r_sigma, omega, lmax_hydro)
print('Total mass of model (kg) = {:e}'.format(mass_model))
print('% of J2 arising from beneath lithosphere = {:f}'.format(
clm_hydro.coeffs[0, 2, 0] / potential.coeffs[0, 2, 0] * 100.))
potential.coeffs[:, :lmax_hydro+1, :lmax_hydro+1] -= \
clm_hydro.coeffs[:, :lmax_hydro+1, :lmax_hydro+1]
# --- Constant density model ---
rho_c = 2900.
print('-- Constant density model --\nrho_c = {:f}'.format(rho_c))
tmin = 1.e9
thickave = 44.e3 # initial guess of average crustal thickness
while abs(tmin - t0) > t0_sigma:
# iterate to fit assumed minimum crustal thickness
moho = pyMoho.pyMoho(potential,
topo,
lmax,
rho_c,
rho_mantle,
thickave,
filter_type=filter,
half=half,
lmax_calc=lmax_calc,
nmax=nmax,
quiet=True)
thick_grid = (topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2')
print('Average crustal thickness (km) = {:f}'.format(thickave / 1.e3))
print('Crustal thickness at InSight landing sites (km) = {:f}'.format(
(topo.pad(lmax) - moho.pad(lmax)).expand(lat=lat_insight,
lon=lon_insight) / 1.e3))
tmin = thick_grid.min()
tmax = thick_grid.max()
print('Minimum thickness (km) = {:e}'.format(tmin / 1.e3))
print('Maximum thickness (km) = {:e}'.format(tmax / 1.e3))
thickave += t0 - tmin
thick_grid.plot(show=False, fname='Thick-Mars-1.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Mars-1.png')
# --- Model with variable density ---
rho_south = 2900.
rho_north = 2900.
porosity = 0.0
print('-- Variable density model ---\n' +
'rho_south = {:f}\n'.format(rho_south) +
'rho_north = {:f}'.format(rho_north))
density = density * (rho_north - rho_south)
density.coeffs[0, 0, 0] += rho_south
tmin = 1.e9
thickave = 44.e3 # initial guess of average crustal thickness
while abs(tmin - t0) > t0_sigma:
# iterate to fit assumed minimum crustal thickness
moho = pyMoho.pyMohoRho(potential,
topo,
density,
porosity,
lmax,
rho_mantle,
thickave,
filter_type=filter,
half=half,
lmax_calc=lmax_calc,
quiet=True,
nmax=nmax)
thick_grid = (topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2')
print('Average crustal thickness (km) = {:e}'.format(thickave / 1.e3))
print('Crustal thickness at InSight landing sites (km) = {:e}'.format(
(topo.pad(lmax) - moho.pad(lmax)).expand(lat=lat_insight,
lon=lon_insight) / 1.e3))
tmin = thick_grid.data.min()
tmax = thick_grid.data.max()
print('Minimum thickness (km) = {:e}'.format(tmin / 1.e3))
print('Maximum thickness (km) = {:e}'.format(tmax / 1.e3))
thickave += t0 - tmin
thick_grid.plot(show=False, fname='Thick-Mars-2.png')
moho.plot_spectrum(show=False, fname='Moho-spectrum-Mars-2.png')