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 # 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():
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 calc_crust(mantlefile, # filename for mantle profile input
fnam_out_model, # Output file name for thickness map
gravfile='Data/gmm3_120_sha.tab',
topofile='Data/MarsTopo719.shape',
densityfile='Data/dichotomy_359.sh',
fnam_out_plot=None, # Output file name for plot of map
t0=1.e3, # minimum crustal thickness
d_lith=300.e3 # Lithosphere thickness
):
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)
# --- read 1D reference interior model ---
print('=== Reading model {:s} ==='.format(mantlefile))
with open(mantlefile, 'r') as f:
lines = f.readlines()
ncomments = 4 # Remove initial four lines in AxiSEM files
nlines = len(lines)
nlayer = nlines - ncomments
radius = np.zeros(nlayer)
rho = np.zeros(nlayer)
vp = np.zeros(nlayer)
vs = np.zeros(nlayer)
lines = lines[::-1]
crust_index = nlayer - 6
for i in range(0, nlayer):
data = lines[i].split()
radius[i] = float(data[0])
rho[i] = float(data[1])
vp[i] = float(data[2])
vs[i] = float(data[3])
# Q = float(data[4])
# if (Q in (500, 600)) and Q_last not in (500, 600):
# crust_index = i
# Q_last = Q
# Correct the sub-Moho parameters
radius[-8] = radius[-7]
# Calculate crustal density
mass_crust = 0
for i in range(crust_index, nlayer-1):
vol_layer = (radius[i+1] - radius[i]) * 1e3 * 4 * np.pi
mass_crust += rho[i] * vol_layer
vol_crust = (radius[-1] - radius[crust_index]) * 1e3 * 4 * np.pi
rho_c = mass_crust / vol_crust
print('Crustal density: = {:8.1f}'.format(rho_c))
r0_model = radius[nlayer-1]
print('Surface radius of model (km) = {:8.1f}'.format(r0_model / 1.e3))
# Find layer at bottom of lithosphere
for i in range(0, nlayer):
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 = nlayer - 1
rho[n] = 0. # the density above the surface is zero
rho_mantle = rho[crust_index-1]
print('Mantle density (kg/m3) = {:8.1f}'.format(rho_mantle))
print('Assumed depth of lithosphere (km) = {:6.1f}'.format(d_lith / 1.e3))
print('Actual depth of lithosphere in discretized model (km) = {:6.1f}'
.format((r0_model - radius[i_lith]) / 1.e3))
# initial guess of average crustal thickness
thickave = r0_model - radius[crust_index]
print('Crustal thickness (km) = {:5.1f}'.format(thickave / 1e3))
print('Moho layer: {:d}'.format(crust_index))
# --- Compute gravity contribution from hydrostatic density interfaces ---
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 ---
print('-- Constant density model --\nrho_c = {:f}'.format(rho_c))
tmin = 1.e9
converged = False
while not converged:
# 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 = topo.pad(lmax) - moho.pad(lmax)
print('Average crustal thickness (km) = {:6.2f}'.format(thickave /
1.e3))
thick_insight = thick.expand(lat=lat_insight, lon=lon_insight)
print('Crustal thickness at InSight landing sites (km) = {:6.2f}'
.format(thick_insight / 1.e3))
thick_grid = thick.expand(grid='DH2')
tmin = thick_grid.data.min()
tmax = thick_grid.data.max()
print('Minimum thickness (km) = {:6.2f}'.format(tmin / 1.e3))
print('Maximum thickness (km) = {:6.2f}'.format(tmax / 1.e3))
if tmin - t0 < - t0_sigma:
thickave += t0 - tmin
else:
converged = True
if fnam_out_plot:
thick_grid.plot(show=False, fname=fnam_out_plot,
vmin=0.0, vmax=120.e3)
# Write Model to disk
# lmax_out = 17 # 89
# topo_grid = (topo.pad(lmax)).expand(grid='DH2', lmax=lmax_out)
# moho_grid = (moho.pad(lmax)).expand(grid='DH2', lmax=lmax_out)
# lats = topo_grid._lats()
# lons = topo_grid._lons()
lats = np.arange(-87.5, 90., 5.)
lons = np.arange(0, 360, 5)
# Apply tapered anti-aliasing filter to SH before transformation
lmax_filter = 36 # 17
order = 2
lvals = np.zeros_like(topo.coeffs)
for i in range(0, lvals.shape[1]):
for j in range(0, lvals.shape[2]):
l = np.max([i, j])
lvals[:, i, j] = np.exp(-2. * np.pi * l ** order /
(2. * lmax_filter) ** order)
topo.coeffs *= lvals
lvals = np.zeros_like(moho.coeffs)
for i in range(0, lvals.shape[1]):
for j in range(0, lvals.shape[2]):
l = np.max([i, j])
lvals[:, i, j] = np.exp(-2. * np.pi * l ** order /
(2. * lmax_filter) ** order)
moho.coeffs *= lvals
#moho.plot_spectrum(show=False, fname='%s.png' % fnam_out_model)
lats_grid, lons_grid = np.meshgrid(lats, lons)
topo_grid = (topo).expand(lat=lats_grid, lon=lons_grid)
moho_grid = (moho).expand(lat=lats_grid, lon=lons_grid)
moho.expand(grid='DH2').plot(show=False, fname='%s_moho.png' % fnam_out_model)
topo.expand(grid='DH2').plot(show=False, fname='%s_topo.png' % fnam_out_model)
(topo.pad(lmax) - moho.pad(lmax)).expand(grid='DH2').plot(show=False,
fname='%s_thick.png' % fnam_out_model)
with h5py.File(fnam_out_model, 'w') as f:
print('Writing to %s' % fnam_out_model)
grp_crust = f.create_group('crust')
grp_crust.create_dataset('moho', data=moho_grid.data)
grp_crust.create_dataset('topo', data=topo_grid.data)
grp_crust.create_dataset('latitudes', data=lats)
grp_crust.create_dataset('longitudes', data=lons)
grp_mantle = f.create_group('mantle')
grp_mantle.create_dataset('radius', data=radius)
grp_mantle.create_dataset('rho', data=rho)
grp_mantle.create_dataset('vp', data=vp)
grp_mantle.create_dataset('vs', data=vs)
grp_status = f.create_group('status')
grp_status.create_dataset('thickness_insight', data=thick_insight)
grp_status.create_dataset('thickness_average_pycrust', data=thickave)
grp_status.create_dataset('thickness_average_input',
data=r0_model - radius[crust_index])
grp_status.create_dataset('thickness_lithosphere', data=d_lith)
grp_status.create_dataset('thickness_minimum', data=tmin)
grp_status.create_dataset('thickness_maximum', data=tmax)
grp_status.create_dataset('rho_crust', data=rho_c)
grp_status.create_dataset('rho_mantle', data=rho_mantle)
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')