def test_tesseroid_vs_spherical_shell():
"gravmag.tesseroid equal analytical solution of spherical shell to 0.1%"
density = 1000.
top = 1000
bottom = 0
model = TesseroidMesh((0, 360, -90, 90, top, bottom), (1, 6, 12))
model.addprop('density', density*np.ones(model.size))
h = 10000
lon, lat, height = gridder.regular((0, model.dims[0], 0, model.dims[1]),
(10, 10), z=h)
funcs = ['potential', 'gx', 'gy', 'gz', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz',
'gzz']
shellvalues = calc_shell_effect(h, top, bottom, density)
for f in funcs:
shell = shellvalues[f]
tess = getattr(tesseroid, f)(lon, lat, height, model)
diff = np.abs(shell - tess)
# gz gy and the off-diagonal gradients should be zero so I can't
# calculate a relative error (in %).
# To do that, I'll use the gz and gzz shell values to calculate the
# percentage.
if f in 'gx gy'.split():
shell = shellvalues['gz']
elif f in 'gxy gxz gyz'.split():
shell = shellvalues['gzz']
diff = 100*diff/np.abs(shell)
assert diff.max() < 0.1, "diff > 0.1% for {}: {}".format(
f, diff.max())
def test_numba_vs_python():
"gravmag.tesseroid numba and pure python implementations give same result"
model = TesseroidMesh((0, 1, 0, 2, 1000, 0), (2, 2, 1))
model.addprop('density', -200*np.ones(model.size))
lon, lat, height = gridder.regular((0, 1, 0, 2), (20, 20), z=250e3)
for f in 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split():
func = getattr(tesseroid, f)
py = func(lon, lat, height, model, engine='numpy')
nb = func(lon, lat, height, model, engine='numba')
assert_allclose(nb, py, err_msg="Mismatch for {}".format(f))
def test_numba_vs_python():
"gravmag.tesseroid numba and pure python implementations give same result"
model = TesseroidMesh((0, 1, 0, 2, 1000, 0), (2, 2, 1))
model.addprop('density', -200 * np.ones(model.size))
lon, lat, height = gridder.regular((0, 1, 0, 2), (20, 20), z=250e3)
for f in 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split():
func = getattr(tesseroid, f)
py = func(lon, lat, height, model, engine='numpy')
nb = func(lon, lat, height, model, engine='numba')
assert_allclose(nb, py, err_msg="Mismatch for {}".format(f))
def test_serial_vs_parallel():
"gravmag.tesseroid serial and parallel execution give same result"
model = TesseroidMesh((-1, 1.5, -2, 2, 0, -10e3), (3, 2, 1))
model.addprop('density', 500*np.ones(model.size))
lon, lat, height = gridder.regular((-1, 1.5, -2, 2), (15, 21), z=150e3)
njobs = 3
for f in 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split():
func = getattr(tesseroid, f)
serial = func(lon, lat, height, model, njobs=1)
parallel = func(lon, lat, height, model, njobs=njobs)
assert_allclose(serial, parallel, err_msg="Mismatch for {}".format(f))
def test_thick_shell():
def density_linear(height):
r = height + MEAN_EARTH_RADIUS
return a * r + b
# Spherical shell model with a Tesseroid Mesh
top, bottom = 0, -35000
density_1, density_2 = 2670, 3300
a = -(density_2 - density_1) / abs(bottom)
b = (density_2 - density_1) / abs(bottom) * MEAN_EARTH_RADIUS + 2670
model = TesseroidMesh((0, 360, -90, 90, top, bottom), (1, 6, 12))
model.addprop("density", [density_linear for i in range(model.size)])
# Computation grids
shape = (10, 10)
grids = {
"pole": gridder.regular((89, 90, 0, 1), shape, z=2e3),
"equator": gridder.regular((0, 1, 0, 1), shape, z=2e3),
"260km": gridder.regular((89, 90, 0, 1), shape, z=260e3),
"30deg": gridder.regular((60, 90, 0, 30), shape, z=2e3)
}
fields = 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split()
for field in fields:
for grid in grids.keys():
msg = "Failed linear density test for thick shell while \
computing {} on {} grid".format(field, grid)
lats, lons, heights = grids[grid]
analytical = shell_linear_density(heights[0], top, bottom, a, b)
result = getattr(tesseroid, field)(lons, lats, heights, model)
diff = np.abs(result - analytical[field])
# gz gy and the off-diagonal gradients should be zero so I can't
# calculate a relative error (in %).
# To do that, I'll use the gz and gzz shell values to calculate the
# percentage.
if field in 'potential gz gxx gyy gzz'.split():
diff /= np.abs(analytical[field])
elif field in 'gx gy'.split():
diff /= np.abs(analytical['gz'])
elif field in "gxy gxz gyz".split():
diff /= np.abs(analytical['gzz'])
diff = 100 * np.max(diff)
assert diff < 1e-1, msg
def test_thick_shell():
def density_exponential(height):
r = height + MEAN_EARTH_RADIUS
return a * np.exp(-(r - deltah) / b) + c
# Spherical shell model with a Tesseroid Mesh
top, bottom = 0, -35000
density_1, density_2 = 2670, 3300
b = 850.
a = (density_2 - density_1) / (np.exp((abs(top - bottom)) / b) - 1)
c = density_1 - a
deltah = MEAN_EARTH_RADIUS
model = TesseroidMesh((0, 360, -90, 90, top, bottom), (1, 6, 12))
model.addprop("density", [density_exponential for i in range(model.size)])
# Computation grids
shape = (10, 10)
grid = gridder.regular((60, 90, 0, 30), shape, z=2e3)
fields = 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split()
for field in fields:
msg = "Failed linear density test for thin shell while \
computing {} on {} grid".format(field, grid)
lats, lons, heights = grid[:]
analytical = shell_exponential_density(heights[0], top, bottom, a, b,
c, deltah)
result = getattr(tesseroid, field)(lons, lats, heights, model)
diff = np.abs(result - analytical[field])
# gz gy and the off-diagonal gradients should be zero so I can't
# calculate a relative error (in %).
# To do that, I'll use the gz and gzz shell values to calculate the
# percentage.
if field in 'potential gz gxx gyy gzz'.split():
diff /= np.abs(analytical[field])
elif field in 'gx gy'.split():
diff /= np.abs(analytical['gz'])
elif field in "gxy gxz gyz".split():
diff /= np.abs(analytical['gzz'])
diff = 100 * np.max(diff)
assert diff < 1e-1, msg