def example():
"""
example that plots the power spectrum of Mars topography data
"""
# --- input data filename ---
infile = '../../ExampleDataFiles/MarsTopo719.shape'
coeffs, lmax = shtools.SHRead(infile, 719)
lmax = coeffs.shape[1] - 1
# --- plot grid ---
grid = shtools.MakeGridDH(coeffs, lmax, csphase=-1)
fig_map = plt.figure()
plt.imshow(grid)
# ---- compute spectrum ----
ls = np.arange(lmax + 1)
pspectrum = shtools.SHPowerSpectrum(coeffs)
pdensity = shtools.SHPowerSpectrumDensity(coeffs)
# ---- plot spectrum ----
fig_spectrum, ax = plt.subplots(1, 1)
ax.set_xscale('log')
ax.set_yscale('log')
ax.set_xlabel('degree l')
ax.grid(True, which='both')
ax.plot(ls[1:], pspectrum[1:], label='power per degree l')
ax.plot(ls[1:], pdensity[1:], label='power per degree l and order m')
ax.legend()
fig_map.savefig('SHCtopography_mars.png')
fig_spectrum.savefig('SHCspectrum_mars.png')
print('mars topography and spectrum saved')
def example():
print('---- SHrtoc example ----')
# --- input data filename ---
infile = '../../ExampleDataFiles/MarsTopo719.shape'
coeffs1, lmax = shtools.SHRead(infile, 719)
coeffs1 = coeffs1[:, :lmax + 1, :lmax + 1]
# --- convert to complex coefficients, fill negative order coefficients ---
coeffs2 = np.empty((2, lmax + 1, lmax + 1), dtype=np.complex)
coeffs2_buf = shtools.SHrtoc(coeffs1, convention=1, switchcs=0)
coeffs2[0, :, :].real = coeffs2_buf[0, :, :]
coeffs2[0, :, :].imag = coeffs2_buf[1, :, :]
coeffs2[1] = (coeffs2[0].conjugate() *
((-1)**np.arange(lmax + 1))[np.newaxis, :])
# --- compute and plot grid ---
grid1 = shtools.MakeGridDH(coeffs1, lmax, csphase=-1)
grid2 = shtools.MakeGridDHC(coeffs2, lmax, csphase=-1)
gridmin = min(grid1.min(), grid2.real.min())
gridmax = max(grid1.max(), grid2.real.max())
norm = plt.Normalize(gridmin, gridmax)
fig, axes = plt.subplots(1, 2)
im1 = axes[0].imshow(grid1, norm=norm)
axes[0].set_title('from real coefficients')
im2 = axes[1].imshow(grid2.real, norm=norm)
axes[1].set_title('from complex coefficients')
fig.tight_layout(pad=1)
fig.savefig('topography_mars.png')
print('mars topography plotted and saved to file')
def TimingAccuracyDH(sampling=1):
# ---- input parameters ----
maxdeg = 2800
ls = np.arange(maxdeg + 1)
beta = 1.5
print('Driscoll-Healy (real) sampling =', sampling)
# ---- create mask to filter out m<=l ----
mask = np.zeros((2, maxdeg + 1, maxdeg + 1), dtype=np.bool)
mask[0, 0, 0] = True
for l in ls:
mask[:, l, :l + 1] = True
mask[1, :, 0] = False
# ---- create Gaussian powerlaw coefficients ----
print('creating {:d} random coefficients'.format(2 * (maxdeg + 1) *
(maxdeg + 1)))
np.random.seed(0)
cilm = np.random.normal(loc=0., scale=1., size=(2, maxdeg + 1, maxdeg + 1))
old_power = shtools.SHPowerSpectrum(cilm)
new_power = 1. / (1. + ls)**beta # initialize degrees > 0 to power-law
cilm[:, :, :] *= np.sqrt(new_power / old_power)[None, :, None]
cilm[~mask] = 0.
# ---- time spherical harmonics transform for lmax set to increasing
# ---- powers of 2.
lmax = 2
print('lmax maxerror rms tinverse tforward')
while lmax <= maxdeg:
# trim coefficients to lmax
cilm_trim = cilm[:, :lmax + 1, :lmax + 1]
mask_trim = mask[:, :lmax + 1, :lmax + 1]
# synthesis / inverse
tstart = time.time()
grid = shtools.MakeGridDH(cilm_trim, sampling=sampling)
tend = time.time()
tinverse = tend - tstart
# analysis / forward
tstart = time.time()
cilm2_trim = shtools.SHExpandDH(grid, sampling=sampling)
tend = time.time()
tforward = tend - tstart
# compute error
err = np.abs(cilm_trim[mask_trim] - cilm2_trim[mask_trim]) / \
np.abs(cilm_trim[mask_trim])
maxerr = err.max()
rmserr = np.mean(err**2)
print('{:4d} {:1.2e} {:1.2e} {:1.1e}s {:1.1e}s'.format(
lmax, maxerr, rmserr, tinverse, tforward))
lmax = lmax * 2
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/jgmro_110b_sha.tab'
pot, lmaxp, header = shtools.SHReadH(gravfile, degmax, 2)
gm = header[1] * 1.e9
mass = gm / constant.grav_constant
r_grav = header[0] * 1.e3
print(r_grav, gm, mass, lmaxp)
topofile = '../../ExampleDataFiles/MarsTopo719.shape'
hlm, lmaxt = shtools.SHRead(topofile, 719)
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 = shtools.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 = shtools.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] = 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] = 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 = shtools.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 = shtools.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 = shtools.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 = shtools.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 = shtools.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')