def load_love_numbers(LMAX, LOVE_NUMBERS=0, REFERENCE='CF'):
"""
Reads PREM load Love numbers for the range of spherical harmonic degrees
and applies isomorphic parameters
Arguments
---------
LMAX: maximum spherical harmonic degree
Keyword arguments
-----------------
LOVE_NUMBERS: Load Love numbers dataset
0: Han and Wahr (1995) values from PREM
1: Gegout (2005) values from PREM
2: Wang et al. (2012) values from PREM
REFERENCE: Reference frame for calculating degree 1 love numbers
CF: Center of Surface Figure (default)
CM: Center of Mass of Earth System
CE: Center of Mass of Solid Earth
Returns
-------
kl: Love number of Gravitational Potential
hl: Love number of Vertical Displacement
ll: Love number of Horizontal Displacement
"""
#-- load love numbers file
if (LOVE_NUMBERS == 0):
#-- PREM outputs from Han and Wahr (1995)
#-- https://doi.org/10.1111/j.1365-246X.1995.tb01819.x
love_numbers_file = utilities.get_data_path(['data', 'love_numbers'])
header = 2
columns = ['l', 'hl', 'kl', 'll']
elif (LOVE_NUMBERS == 1):
#-- PREM outputs from Gegout (2005)
#-- http://gemini.gsfc.nasa.gov/aplo/
love_numbers_file = utilities.get_data_path(
['data', 'Load_Love2_CE.dat'])
header = 3
columns = ['l', 'hl', 'll', 'kl']
elif (LOVE_NUMBERS == 2):
#-- PREM outputs from Wang et al. (2012)
#-- https://doi.org/10.1016/j.cageo.2012.06.022
love_numbers_file = utilities.get_data_path(
['data', 'PREM-LLNs-truncated.dat'])
header = 1
columns = ['l', 'hl', 'll', 'kl', 'nl', 'nk']
#-- LMAX of load love numbers from Han and Wahr (1995) is 696.
#-- from Wahr (2007) linearly interpolating kl works
#-- however, as we are linearly extrapolating out, do not make
#-- LMAX too much larger than 696
#-- read arrays of kl, hl, and ll Love Numbers
hl, kl, ll = read_love_numbers(love_numbers_file,
LMAX=LMAX,
HEADER=header,
COLUMNS=columns,
REFERENCE=REFERENCE,
FORMAT='tuple')
#-- return a tuple of load love numbers
return (hl, kl, ll)
def test_point_masses(NPTS):
# create spatial grid
dlon, dlat = (1.0, 1.0)
lat = np.arange(90.0 - dlat / 2.0, -90.0 - dlat / 2.0, -dlat)
lon = np.arange(-180.0 + dlon / 2.0, 180.0 + dlon / 2.0, dlon)
gridlon, gridlat = np.meshgrid(lon, lat)
nlat, nlon = np.shape(gridlon)
# parameterize point masses
LAT = lat[0] - dlat * np.random.randint(0, nlat, size=NPTS)
LON = lon[0] + dlon * np.random.randint(0, nlon, size=NPTS)
MASS = 100.0 - 200.0 * np.random.randn(NPTS)
# create test gridded field
data = np.zeros((nlat, nlon))
for i in range(NPTS):
indy, indx = np.nonzero((gridlat == LAT[i]) & (gridlon == LON[i]))
data[indy, indx] += MASS[i]
# path to load Love numbers file
love_numbers_file = get_data_path(['data', 'love_numbers'])
# read load Love numbers
hl, kl, ll = read_love_numbers(love_numbers_file)
# calculate harmonics and degree amplitudes for each case
grid_Ylms = gen_stokes(data, lon, lat, LMAX=60, UNITS=2, LOVE=(hl, kl, ll))
grid_Ylms.amplitude()
point_Ylms = gen_point_load(MASS,
LON,
LAT,
LMAX=60,
UNITS=2,
LOVE=(hl, kl, ll))
point_Ylms.amplitude()
# check that harmonic data is equal to machine precision
difference_Ylms = grid_Ylms.copy()
difference_Ylms.subtract(point_Ylms)
harmonic_eps = np.finfo(np.float32).eps
assert np.all(np.abs(difference_Ylms.clm) < harmonic_eps)
# verify that the degree amplitudes are within tolerance
assert np.all(np.abs(grid_Ylms.amp - point_Ylms.amp) < harmonic_eps)