def test_eqlayer_polereduce():
"EQLTotalField can reduce data to the pole"
# Use remanent magnetization
sinc, sdec = -70, 30
model = [Prism(-100, 100, -500, 500, 0, 100,
{'magnetization': utils.ang2vec(5, sinc, sdec)})]
inc, dec = -60, -15
shape = (50, 50)
area = [-2000, 2000, -2000, 2000]
x, y, z = gridder.regular(area, shape, z=-100)
data = prism.tf(x, y, z, model, inc, dec)
true = prism.tf(x, y, z, model, -90, 0, pmag=utils.ang2vec(5, -90, 0))
layer = PointGrid(area, 200, shape)
eql = (EQLTotalField(x, y, z, data, inc, dec, layer, sinc, sdec)
+ 1e-24*Damping(layer.size))
eql.fit()
assert_allclose(eql[0].predicted(), data, rtol=0.01)
layer.addprop('magnetization',
utils.ang2vec(eql.estimate_, inc=-90, dec=0))
calc = sphere.tf(x, y, z, layer, inc=-90, dec=0)
assert_allclose(calc, true, atol=10, rtol=0.05)
def test_ignore_none_and_missing_properties():
'gravmag.prism ignores None and prisms without the required property'
inc, dec = 50, -30
model = [None,
Prism(-6000, -2000, 2000, 4000, 0, 3000,
{'density': 1000,
'magnetization': utils.ang2vec(10, inc, dec)}),
Prism(2000, 6000, 2000, 4000, 0, 1000,
{'magnetization': utils.ang2vec(15, inc, dec)}),
None,
Prism(-6000, -2000, -4000, -2000, 500, 2000,
{'density': -1000})]
area = [-10000, 10000, -5000, 5000]
x, y, z = gridder.regular(area, (101, 51), z=-1)
for mod in [prism, _prism_numpy]:
# Test gravity functions
funcs = ['potential', 'gx', 'gy', 'gz',
'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
for f in funcs:
combined = getattr(mod, f)(x, y, z, model)
separate = getattr(mod, f)(x, y, z, [model[1], model[4]])
precision = 10
assert_almost(separate, combined, precision, 'Field = %s' % (f))
# Test magnetic functions
funcs = ['tf', 'bx', 'by', 'bz']
for f in funcs:
mag_only = [model[1], model[2]]
if f == 'tf':
combined = getattr(mod, f)(x, y, z, model, inc, dec)
separate = getattr(mod, f)(x, y, z, mag_only, inc, dec)
else:
combined = getattr(mod, f)(x, y, z, model)
separate = getattr(mod, f)(x, y, z, mag_only)
precision = 10
assert_almost(separate, combined, precision, 'Field = %s' % (f))
def test_pel_polereduce():
"PELTotalField can reduce data to the pole"
# Use remanent magnetization
sinc, sdec = -70, 30
model = [Prism(-100, 100, -500, 500, 0, 100,
{'magnetization': utils.ang2vec(5, sinc, sdec)})]
inc, dec = -60, -15
shape = (40, 40)
area = [-2000, 2000, -2000, 2000]
x, y, z = gridder.regular(area, shape, z=-100)
data = prism.tf(x, y, z, model, inc, dec)
true = prism.tf(x, y, z, model, -90, 0, pmag=utils.ang2vec(5, -90, 0))
layer = PointGrid(area, 100, shape)
windows = (20, 20)
degree = 3
pel = PELTotalField(x, y, z, data, inc, dec, layer, windows, degree,
sinc, sdec)
eql = pel + 1e-25*PELSmoothness(layer, windows, degree)
eql.fit()
assert_array_almost_equal(eql[0].predicted(), data, decimal=1)
layer.addprop('magnetization',
utils.ang2vec(eql.estimate_, inc=-90, dec=0))
calc = sphere.tf(x, y, z, layer, inc=-90, dec=0)
assert_allclose(calc, true, atol=10, rtol=0.05)
def test_upcontinue():
"gravmag.transform upward continuation matches analytical solution"
model = [Prism(-1000, 1000, -500, 500, 0, 1000,
{'density': 1000,
'magnetization': utils.ang2vec(5, 20, -30)})]
shape = (100, 100)
inc, dec = -10, 15
x, y, z = gridder.regular([-5000, 5000, -5000, 5000], shape, z=-500)
dz = 10
fields = 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split()
accuracy = [0.002, 0.2, 0.2, 0.3, 2, 2, 4, 4, 4, 6]
for f, atol in zip(fields, accuracy):
func = getattr(prism, f)
data = func(x, y, z, model)
analytical = func(x, y, z + dz, model)
up = transform.upcontinue(x, y, data, shape, dz)
diff = np.abs(up - analytical)
check = diff <= atol
assert np.all(check), \
'Failed for {} (mismatch {:.2f}%)'.format(
f, 100*(check.size - check.sum())/check.size)
data = prism.tf(x, y, z, model, inc, dec)
analytical = prism.tf(x, y, z + dz, model, inc, dec)
up = transform.upcontinue(x, y, data, shape, dz)
diff = np.abs(up - analytical)
check = diff <= 15
assert np.all(check), \
'Failed for tf (mismatch {:.2f}%)'.format(
100*(check.size - check.sum())/check.size)
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_fails_if_bad_pad_operation():
'gridder.pad_array fails if given a bad padding array operation option'
p = 'foo'
shape = (100, 100)
x, y, z = gridder.regular((-1000., 1000., -1000., 1000.), shape, z=-150)
g = z.reshape(shape)
assert_raises(ValueError, gridder.pad_array, g, padtype=p)
def test_radial_average_spectrum_distances():
shape = (201, 201)
area = (-100, 100, -100, 100)
x, y = gridder.regular(area, shape)
x, y = x.reshape(shape), y.reshape(shape)
x, y = np.fft.ifftshift(x), np.fft.ifftshift(y)
distances = np.sqrt(x**2 + y**2)
k, radial_distances = transform.radial_average_spectrum(x, y, distances)
npt.assert_allclose(k[2:], radial_distances[2:], rtol=0.1) # doesn't fail
def setup():
global model, xp, yp, zp, inc, dec
inc, dec = -30, 50
reg_field = np.array(utils.dircos(inc, dec))
model = [
Sphere(500, 0, 1000, 1000,
{'density': -1., 'magnetization': utils.ang2vec(-2, inc, dec)}),
Sphere(-1000, 0, 700, 700,
{'density': 2., 'magnetization': utils.ang2vec(5, 25, -10)})]
xp, yp, zp = gridder.regular([-2000, 2000, -2000, 2000], (50, 50), z=-1)
def test_upcontinue_warning():
"gravmag.transform upward continuation raises warning if height <= 0"
model = [Prism(-1000, 1000, -500, 500, 0, 1000, {'density': 1000})]
shape = (100, 100)
x, y, z = gridder.regular([-5000, 5000, -5000, 5000], shape, z=-500)
data = prism.gz(x, y, z, model)
with pytest.warns(UserWarning):
up = transform.upcontinue(x, y, data, shape, height=0)
with pytest.warns(UserWarning):
up = transform.upcontinue(x, y, data, shape, height=-100)
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_fails_if_npd_lessthan_arraydim():
'gridder.pad_array raises error if given npad is less than array length'
shape = (101, 172)
x, y, z = gridder.regular((-5000., 5000., -5000., 5000.), shape, z=-150)
g = z.reshape(shape)
npdt = (128, 128)
assert_raises(ValueError, gridder.pad_array, g, npd=npdt)
prng = RandomState(12345)
g = prng.rand(20)
npdt = 16
assert_raises(ValueError, gridder.pad_array, g, npd=npdt)
def test_detect_invalid_tesseroid_dimensions():
"gravmag.tesseroid raises error when tesseroids with bad dimensions"
props = dict(density=2000)
model = [Tesseroid(0, -10, 4, 5, 1000, 0, props),
Tesseroid(-10, 0, 5, 4, 1000, 0, props),
Tesseroid(-10, 0, 5, 4, 0, 1000, props)]
lon, lat, height = gridder.regular((-20, 20, -20, 20), (50, 50), z=250e3)
for f in 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split():
func = getattr(tesseroid, f)
for t in model:
raises(AssertionError, func, lon, lat, height, [t])
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_fails_if_npd_incorrect_dimension():
'gridder.pad_array raises error if given improper dimension on npadding'
s = (101, 172)
x, y, z = gridder.regular((-5000., 5000., -5000., 5000.), s, z=-150)
g = z.reshape(s)
npdt = 128
assert_raises(ValueError, gridder.pad_array, g, npd=npdt)
npdt = (128, 256, 142)
assert_raises(ValueError, gridder.pad_array, g, npd=npdt)
prng = RandomState(12345)
g = prng.rand(50)
assert_raises(ValueError, gridder.pad_array, g, npd=npdt)
def test_derivatives_uneven_shape():
"gravmag.transform FFT derivatives work if grid spacing is uneven"
model = [Prism(-1000, 1000, -500, 500, 0, 2000, {'density': 100})]
shape = (150, 300)
x, y, z = gridder.regular([-10000, 10000, -10000, 10000], shape, z=-100)
grav = utils.mgal2si(prism.gz(x, y, z, model))
analytical = prism.gzz(x, y, z, model)
calculated = utils.si2eotvos(transform.derivz(x, y, grav, shape,
method='fft'))
diff = _trim(np.abs(analytical - calculated), shape)
assert np.all(diff <= 0.005*np.abs(analytical).max()), \
"Failed for gzz"
def test_tilt_analytical_derivatives():
"gravmag.transform tilt returns same values given analytical derivatives"
model = [Prism(-100, 100, -100, 100, 0, 100, {'density': 1000})]
shape = (400, 400)
x, y, z = gridder.regular([-10000, 10000, -10000, 10000], shape, z=-100)
data = utils.mgal2si(prism.gz(x, y, z, model))
dx = utils.eotvos2si(prism.gxz(x, y, z, model))
dy = utils.eotvos2si(prism.gyz(x, y, z, model))
dz = utils.eotvos2si(prism.gzz(x, y, z, model))
tilt_analytical = transform.tilt(x, y, data, shape, dx, dy, dz)
tilt_numerical = transform.tilt(x, y, data, shape)
npt.assert_allclose(tilt_numerical, tilt_analytical, rtol=0.10)
def test_tilt_sane_values():
"gravmag.transform tilt returns sane values, between -90 and 90 degrees"
inc, dec = 90, 0
mag = utils.ang2vec(200, inc, dec)
model = [Prism(-500, 500, -500, 500, 0, 2000, {'magnetization': mag})]
shape = (300, 300)
x, y, z = gridder.regular([-10000, 10000, -10000, 10000], shape, z=-100)
data = prism.tf(x, y, z, model, inc, dec)
tilt = np.degrees(transform.tilt(x, y, data, shape))
assert tilt.max() < 90, \
"Maximum tilt greater than 90: {}".format(tilt.max())
assert tilt.min > -90, \
"Minimum tilt less than -90: {}".format(tilt.min())
def test_fails_if_shape_mismatch():
'gravmag.tesseroid fails if given computation points with different shapes'
model = [Tesseroid(0, 1, 0, 1, 1000, -20000, {'density': 2670})]
area = [-2, 2, -2, 2]
shape = (51, 51)
lon, lat, h = gridder.regular(area, shape, z=100000)
for f in 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split():
func = getattr(tesseroid, f)
raises(AssertionError, func, lon[:-2], lat, h, model)
raises(AssertionError, func, lon, lat[:-2], h, model)
raises(AssertionError, func, lon, lat, h[:-2], model)
raises(AssertionError, func, lon[:-5], lat, h[:-2], model)
def test_overwrite_density():
"gravmag.tesseroid uses given density instead of tesseroid property"
model = [Tesseroid(0, 1, 0, 1, 1000, -20000, {'density': 2670})]
density = -1000
other = [Tesseroid(0, 1, 0, 1, 1000, -20000, {'density': density})]
area = [-2, 2, -2, 2]
shape = (51, 51)
lon, lat, h = gridder.regular(area, shape, z=250000)
funcs = ['potential', 'gx', 'gy', 'gz', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz',
'gzz']
for f in funcs:
correct = getattr(tesseroid, f)(lon, lat, h, other)
effect = getattr(tesseroid, f)(lon, lat, h, model, dens=density)
assert_array_almost_equal(correct, effect, 9, 'Failed %s' % (f))
def test_null_tesseroid():
"gravmag.tesseroid ignores tesseroids with 0 volume"
props = dict(density=2000)
model = [Tesseroid(-10, 0, 4, 5, 1000.1, 1000.1, props),
Tesseroid(-10, 0, 4, 5, 1000.001, 1000, props),
Tesseroid(-10, 0, 3.999999999, 4, 1000, 0, props),
Tesseroid(-10, -9.9999999999, 4, 5, 1000, 0, props),
Tesseroid(5, 10, -10, -5, 2000.5, 0, props)]
lon, lat, height = gridder.regular((-20, 20, -20, 20), (50, 50), z=250e3)
for f in 'potential gx gy gz gxx gxy gxz gyy gyz gzz'.split():
func = getattr(tesseroid, f)
f1 = func(lon, lat, height, model)
f2 = func(lon, lat, height, [model[-1]])
assert_allclose(f1, f2, err_msg="Mismatch for {}".format(f))
def test_gx_derivatives():
"gravmag.transform FFT 1st derivatives of gx against analytical solutions"
model = [Prism(-1000, 1000, -500, 500, 0, 2000, {'density': 100})]
shape = (300, 300)
x, y, z = gridder.regular([-10000, 10000, -10000, 10000], shape, z=-100)
derivatives = 'x y z'.split()
grav = utils.mgal2si(prism.gx(x, y, z, model))
for deriv in derivatives:
analytical = getattr(prism, 'gx{}'.format(deriv))(x, y, z, model)
calculated = utils.si2eotvos(
getattr(transform, 'deriv' + deriv)(x, y, grav, shape,
method='fft'))
diff = _trim(np.abs(analytical - calculated), shape)
assert np.all(diff <= 0.005*np.abs(analytical).max()), \
"Failed for gx{}".format(deriv)
def setup():
global model, x, y, z, inc, dec, struct_ind, field, xderiv, yderiv, \
zderiv, base, pos
inc, dec = -30, 50
pos = np.array([1000, 1000, 200])
model = Sphere(pos[0], pos[1], pos[2], 1,
{'magnetization': utils.ang2vec(10000, inc, dec)})
struct_ind = 3
shape = (128, 128)
x, y, z = gridder.regular((0, 3000, 0, 3000), shape, z=-1)
base = 10
field = utils.nt2si(sphere.tf(x, y, z, [model], inc, dec)) + base
xderiv = fourier.derivx(x, y, field, shape)
yderiv = fourier.derivy(x, y, field, shape)
zderiv = fourier.derivz(x, y, field, shape)
def test_pad_and_unpad_equal_2d():
'gridder.pad_array and subsequent .unpad_array gives original array: 2D'
shape = (100, 101)
x, y, z = gridder.regular((-5000., 5000., -5000., 5000.), shape, z=-150)
# rosenbrock: (a-x)^2 + b(y-x^2)^2 a=1 b=100 usually
X = x.reshape(shape)
Y = y.reshape(shape)
xy = [x, y]
gz = scipy.optimize.rosen([Y/100000., X/100000.])
pads = ['mean', 'edge', 'lintaper', 'reflection', 'oddreflection',
'oddreflectiontaper', '0']
for p in pads:
gpad, nps = gridder.pad_array(gz, padtype=p)
gunpad = gridder.unpad_array(gpad, nps)
assert_almost(gunpad, gz)
def test_laplace_from_potential():
"gravmag.transform 2nd derivatives of potential obey the Laplace equation"
model = [Prism(-1000, 1000, -500, 500, 0, 2000, {'density': 200})]
shape = (300, 300)
x, y, z = gridder.regular([-10000, 10000, -10000, 10000], shape, z=-100)
potential = prism.potential(x, y, z, model)
gxx = utils.si2eotvos(transform.derivx(x, y, potential, shape, order=2,
method='fft'))
gyy = utils.si2eotvos(transform.derivy(x, y, potential, shape, order=2,
method='fft'))
gzz = utils.si2eotvos(transform.derivz(x, y, potential, shape, order=2))
laplace = _trim(gxx + gyy + gzz, shape)
assert np.all(np.abs(laplace) <= 1e-10), \
"Max: {} Mean: {} STD: {}".format(
laplace.max(), laplace.mean(), laplace.std())
def setup():
global model, x, y, z, inc, dec, struct_ind, field, xderiv, yderiv, zderiv, base, pos
inc, dec = -30, 50
pos = np.array([1000, 1200, 200])
model = Sphere(pos[0], pos[1], pos[2], 1, {"magnetization": utils.ang2vec(10000, inc, dec)})
struct_ind = 3
shape = (200, 200)
x, y, z = gridder.regular((0, 3000, 0, 3000), shape, z=-100)
base = 10
field = sphere.tf(x, y, z, [model], inc, dec) + base
# Use finite difference derivatives so that these tests don't depend on the
# performance of the FFT derivatives.
xderiv = (sphere.tf(x + 1, y, z, [model], inc, dec) - sphere.tf(x - 1, y, z, [model], inc, dec)) / 2
yderiv = (sphere.tf(x, y + 1, z, [model], inc, dec) - sphere.tf(x, y - 1, z, [model], inc, dec)) / 2
zderiv = (sphere.tf(x, y, z + 1, [model], inc, dec) - sphere.tf(x, y, z - 1, [model], inc, dec)) / 2
def test_horizontal_derivatives_fd():
"gravmag.transform 1st xy derivatives by finite diff against analytical"
model = [Prism(-1000, 1000, -500, 500, 0, 2000, {'density': 100})]
shape = (300, 300)
x, y, z = gridder.regular([-5000, 5000, -5000, 5000], shape, z=-200)
derivatives = 'x y'.split()
grav = utils.mgal2si(prism.gz(x, y, z, model))
for deriv in derivatives:
analytical = getattr(prism, 'g{}z'.format(deriv))(x, y, z, model)
func = getattr(transform, 'deriv' + deriv)
calculated = utils.si2eotvos(func(x, y, grav, shape, method='fd'))
diff = np.abs(analytical - calculated)
assert np.all(diff <= 0.005*np.abs(analytical).max()), \
"Failed for g{}. Max: {} Mean: {} STD: {}".format(
deriv, diff.max(), diff.mean(), diff.std())
def test_coordinatevec_padding_2d():
'gridder.padcoords accurately pads coordinate vector in 2D'
shape = (101, 172)
x, y, z = gridder.regular((-5000., 5000., -5000., 5000.), shape, z=-150)
gz = np.zeros(shape)
xy = []
xy.append(x)
xy.append(y)
gpad, nps = gridder.pad_array(gz)
N = gridder.pad_coords(xy, gz.shape, nps)
Yp = N[1].reshape(gpad.shape)
Xp = N[0].reshape(gpad.shape)
assert_equal(N[0].reshape(gpad.shape).shape, gpad.shape)
assert_almost(Yp[nps[0][0]:-nps[0][1], nps[1][0]:-nps[1][1]].ravel(), y)
assert_almost(Xp[nps[0][0]:-nps[0][1], nps[1][0]:-nps[1][1]].ravel(), x)
def test_pole_reduce():
"gravmag.transform pole reduction matches analytical solution"
# Use remanent magnetization
sinc, sdec = -70, 30
model = [Prism(-100, 100, -500, 500, 0, 100,
{'density': 1000,
'magnetization': utils.ang2vec(5, sinc, sdec)})]
# Use low latitudes to make sure that there are no problems with FFT
# instability.
inc, dec = -60, -15
shape = (50, 50)
x, y, z = gridder.regular([-2000, 2000, -2000, 2000], shape, z=-100)
data = prism.tf(x, y, z, model, inc, dec)
pole = transform.reduce_to_pole(x, y, data, shape, inc, dec, sinc, sdec)
pole_true = prism.tf(x, y, z, model, -90, 0, pmag=utils.ang2vec(5, -90, 0))
npt.assert_allclose(pole, pole_true, atol=10, rtol=0.01)
def test_second_derivatives():
"gravmag.transform FFT second derivatives against analytical solutions"
model = [Prism(-1000, 1000, -500, 500, 0, 2000, {'density': -200})]
shape = (300, 300)
x, y, z = gridder.regular([-10000, 10000, -10000, 10000], shape, z=-100)
derivatives = 'xx yy zz'.split()
pot = prism.potential(x, y, z, model)
for deriv in derivatives:
analytical = getattr(prism, 'g{}'.format(deriv))(x, y, z, model)
calculated = utils.si2eotvos(
getattr(transform, 'deriv' + deriv[0])(x, y, pot, shape, order=2,
method='fft'))
diff = _trim(np.abs(analytical - calculated), shape)
assert np.all(diff <= 0.005*np.abs(analytical).max()), \
"Failed for g{}. Max: {} Mean: {} STD: {}".format(
deriv, diff.max(), diff.mean(), diff.std())
def test_second_horizontal_derivatives_fd():
"gravmag.transform 2nd xy derivatives by finite diff against analytical"
model = [Prism(-1000, 1000, -500, 500, 0, 2000, {'density': 100})]
shape = (300, 300)
x, y, z = gridder.regular([-10000, 10000, -10000, 10000], shape, z=-500)
derivatives = 'xx yy'.split()
grav = prism.potential(x, y, z, model)
for deriv in derivatives:
analytical = getattr(prism, 'g{}'.format(deriv))(x, y, z, model)
func = getattr(transform, 'deriv' + deriv[0])
calculated = utils.si2eotvos(func(x, y, grav, shape, method='fd',
order=2))
diff = np.abs(analytical - calculated)
assert np.all(diff/np.abs(analytical).max() <= 0.01), \
"Failed for g{}. Max: {} Mean: {} STD: {}".format(
deriv, diff.max(), diff.mean(), diff.std())
mpl.subplot(2, 1, 1)
mpl.axis('scaled')
mpl.title('Density (mass)')
mpl.pcolor(grid.y, grid.x, grid.props['density'], grid.shape)
mpl.colorbar()
mpl.subplot(2, 1, 2)
mpl.axis('scaled')
mpl.title('Magnetization intensity (dipole moment)')
mpl.pcolor(grid.y, grid.x, utils.vecnorm(grid.props['magnetization']),
grid.shape)
mpl.colorbar()
mpl.show()
# Now do some calculations with the grid
shape = (100, 100)
x, y, z = gridder.regular(grid.area, shape, z=0)
gz = sphere.gz(x, y, z, grid)
tf = sphere.tf(x, y, z, grid, inc, dec)
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.axis('scaled')
mpl.title('Gravity anomaly')
mpl.contourf(y, x, gz, shape, 30)
mpl.colorbar()
mpl.subplot(2, 1, 2)
mpl.axis('scaled')
mpl.title('Magnetic total field anomaly')
mpl.contourf(y, x, tf, shape, 30)
mpl.colorbar()
mpl.show()
"""
GravMag: Use the Polynomial Equivalent Layer to reduce a magnetic total field
anomaly to the pole
"""
from fatiando import gravmag, gridder, utils, mesher
from fatiando.vis import mpl
# Make synthetic data
inc, dec = -60, 23
props = {'magnetization': 10}
model = [mesher.Prism(-500, 500, -1000, 1000, 500, 4000, props)]
shape = (50, 50)
x, y, z = gridder.regular([-5000, 5000, -5000, 5000], shape, z=-150)
tf = utils.contaminate(gravmag.prism.tf(x, y, z, model, inc, dec), 5)
# Setup the layer
grid = mesher.PointGrid([-5000, 5000, -5000, 5000], 200, (100, 100))
# Wrape the data
data = [gravmag.eqlayer.TotalField(x, y, z, tf, inc, dec)]
# Calculate the magnetization intensity
# PEL returns the matrices it computes so that you can re-calculate with
# different smoothness and damping at very low cost
intensity, matrices = gravmag.eqlayer.pel(data,
grid, (20, 20),
degree=1,
smoothness=10.**-2)
grid.addprop('magnetization', intensity)
# Compute the predicted data and the residuals
predicted = gravmag.sphere.tf(x, y, z, grid, inc, dec)
residuals = tf - predicted
print "Residuals:"
print "mean:", residuals.mean()
"""
Meshing: Generate a 3D prism model of the topography
"""
from fatiando import gridder, utils, mesher
from fatiando.vis import myv
area = (-150, 150, -300, 300)
shape = (100, 50)
x, y = gridder.regular(area, shape)
height = (-80 * utils.gaussian2d(x, y, 100, 200, x0=-50, y0=-100, angle=-60) +
100 * utils.gaussian2d(x, y, 50, 100, x0=80, y0=170))
nodes = (x, y, -1 * height) # -1 is to convert height to z coordinate
reference = 0 # z coordinate of the reference surface
relief = mesher.PrismRelief(reference, gridder.spacing(area, shape), nodes)
relief.addprop('density', (2670 for i in xrange(relief.size)))
myv.figure()
myv.prisms(relief, prop='density', edges=False)
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds, opacity=0.2)
myv.wall_north(axes.axes.bounds)
myv.show()
plt.legend()
p12x = [p1[0], p2[0]]
p12y = [p1[1], p2[1]]
plt.plot(p12x, p12y, c='red')
p12v = plt.scatter(p12x, p12y, c='red')
txt = ['p1', 'p2']
for i in range(len(p12x)):
plt.annotate(txt[i], (p12x[i], p12y[i]), c='red')
plt.xlabel('x (m)')
plt.ylabel('y (m)')
prl = 60
# shape = shape (max(xp)-min(xp))/
# shape = (115,115)
xint_scipy, yint_scipy = gridder.regular(
(min(xp) - prl, max(xp) + prl, min(yp) - prl, max(yp) + prl), shape=shape)
#%% Solution 1
# extrapolate False and fill with 0 before derivative - mask them later on
U_int_scipy = gridder.interp_at(xp,
yp,
U,
xint_scipy,
yint_scipy,
algorithm='cubic',
extrapolate=False)
InterpData = np.array([xint_scipy, yint_scipy, U_int_scipy]).T
where_are_NaNs = np.isnan(InterpData)
InterpData[where_are_NaNs] = 0.0074
xint_scipy, yint_scipy, U_int_scipy = InterpData.T
def load_surfer(fname, dtype='float64'):
"""
Read data from a Surfer ASCII grid file.
Surfer is a contouring, griding and surface mapping software
from GoldenSoftware. The names and logos for Surfer and Golden
Software are registered trademarks of Golden Software, Inc.
http://www.goldensoftware.com/products/surfer
Parameters:
* fname : str
Name of the Surfer grid file
* dtype : numpy dtype object or string
The type of variable used for the data. Default is numpy.float64. Use
numpy.float32 if the data are large and precision is not an issue.
Returns:
* data : dict
The data in a dictionary with some metadata:
* ``'file'`` : string
The name of the original data file
* ``'shape'`` : tuple
(nx, ny), the number of grid points in x (North) and y (East)
* ``'area'`` : tuple
(x1, x2, y1, y2), the spacial limits of the grid.
* ``'x'`` : 1d-array
Value of the North-South coordinate of each grid point.
* ``'y'`` : 1d-array
Value of the East-West coordinate of each grid point.
* ``'data'`` : 1d-array
Values of the field in each grid point. Field can be for example
topography, gravity anomaly, etc. If any field values are >=
1.70141e+38 (Surfers way of marking NaN values), the array will be
masked at those values (i.e., ``'data'`` will be a numpy masked
array).
"""
# Surfer ASCII grid structure
# DSAA Surfer ASCII GRD ID
# nCols nRows number of columns and rows
# xMin xMax X min max
# yMin yMax Y min max
# zMin zMax Z min max
# z11 z21 z31 ... List of Z values
with open(fname) as input_file:
# DSAA is a Surfer ASCII GRD ID (discard it for now)
input_file.readline()
# Read the number of columns (ny) and rows (nx)
ny, nx = [int(s) for s in input_file.readline().split()]
shape = (nx, ny)
# Our x points North, so the first thing we read is y, not x.
ymin, ymax = [float(s) for s in input_file.readline().split()]
xmin, xmax = [float(s) for s in input_file.readline().split()]
area = (xmin, xmax, ymin, ymax)
dmin, dmax = [float(s) for s in input_file.readline().split()]
field = np.fromiter(
(float(s) for line in input_file for s in line.split()),
dtype=dtype)
nans = field >= 1.70141e+38
if np.any(nans):
field = np.ma.masked_where(nans, field)
err_msg = "{} of data ({}) doesn't match one from file ({})."
assert np.allclose(dmin, field.min()), err_msg.format(
'Min', dmin, field.min())
assert np.allclose(dmax, field.max()), err_msg.format(
'Max', dmax, field.max())
x, y = gridder.regular(area, shape)
data = dict(file=fname, shape=shape, area=area, data=field, x=x, y=y)
return data
-------------
You can create the (x, y, z) coordinate arrays for regular grids using
:func:`fatiando.gridder.regular`.
"""
from __future__ import print_function
from fatiando import gridder
import matplotlib.pyplot as plt
# Define the area of the grid in meters: [x1, x2, y1, y2]
area = [0, 10e3, -5e3, 5e3]
# The shape is the number of points in the grid: (nx, ny)
shape = (5, 9)
x, y = gridder.regular(area, shape)
# x and y are 1d arrays with the coordinates of each point in the grid
print('x =', x)
print('y =', y)
# Optionally, you can generate a 3rd array with constant z values
# (remember that z is positive downward)
x, y, z = gridder.regular(area, shape, z=-150)
print('z =', z)
plt.figure(figsize=(6, 5))
plt.title('Regular grid')
# In Fatiando, x is North and y is East.
# So we should plot x in the vertical axis and y in horizontal.
plt.plot(y, x, 'ok')
area = (-2, 2, -2, 2)
x, y = gridder.scatter(area, n=200, seed=0)
# And calculate 2D Gaussians on these points as sample data
def data(x, y):
return (utils.gaussian2d(x, y, -0.6, -1) -
utils.gaussian2d(x, y, 1.5, 1.5))
z = data(x, y)
shape = (100, 100)
# First, we need to know the real data at the grid points
grdx, grdy = gridder.regular(area, shape)
grdz = data(grdx, grdy)
mpl.figure()
mpl.subplot(2, 2, 1)
mpl.axis('scaled')
mpl.title("True grid data")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the default interpolation (cubic)
grdx, grdy, grdz = gridder.interp(x, y, z, shape)
mpl.subplot(2, 2, 2)
mpl.axis('scaled')
mpl.title("Interpolated using cubic minimum-curvature")
"""
Gridding: Cut a section from a grid
"""
from fatiando import gridder, utils
from fatiando.vis import mpl
# Generate some synthetic data on a regular grid
x, y = gridder.regular((-10, 10, -10, 10), (100, 100))
# Using a 2D Gaussian
z = utils.gaussian2d(x, y, 1, 1)
subarea = [-2, 2, -3, 3]
subx, suby, subscalar = gridder.cut(x, y, [z], subarea)
mpl.figure(figsize=(12, 5))
mpl.subplot(1, 2, 1)
mpl.title("Whole grid")
mpl.axis('scaled')
mpl.pcolor(x, y, z, (100, 100))
mpl.square(subarea, 'k', linewidth=2, label='Cut this region')
mpl.legend(loc='lower left')
mpl.subplot(1, 2, 2)
mpl.title("Cut grid")
mpl.axis('scaled')
mpl.pcolor(subx, suby, subscalar[0], (40, 60), interp=True)
mpl.show()
"""
Meshing: Make and plot a tesseroid mesh with topography
"""
from fatiando import gridder, utils, mesher
from fatiando.vis import myv
w, e = -2, 2
s, n = -2, 2
bounds = (w, e, s, n, 500000, 0)
x, y = gridder.regular((w, e, s, n), (50, 50))
height = (250000 +
-100000 * utils.gaussian2d(x, y, 1, 5, x0=-1, y0=-1, angle=-60) +
250000 * utils.gaussian2d(x, y, 1, 1, x0=0.8, y0=1.7))
mesh = mesher.TesseroidMesh(bounds, (20, 50, 50))
mesh.carvetopo(x, y, height)
scene = myv.figure(zdown=False)
myv.tesseroids(mesh)
myv.earth(opacity=0.3)
myv.continents()
scene.scene.camera.position = [
21592740.078245595, 22628783.944262519, -28903782.916664094
]
scene.scene.camera.focal_point = [
5405474.2152075395, -1711034.715136874, 2155879.3486608281
]
scene.scene.camera.view_angle = 1.6492674416639987
scene.scene.camera.view_up = [
0.91713422625547714, -0.1284658947859818, 0.37730799740742887
being generally inferior to an inversion result.
Here we'll show how the Generalized Inverse imaging method can be used on some
synthetic data. We'll plot the final result as slices across the x, y, z axis.
"""
from __future__ import division
from fatiando import gridder, mesher
from fatiando.gravmag import prism, imaging
from fatiando.vis.mpl import square
import matplotlib.pyplot as plt
import numpy as np
# Make some synthetic gravity data from a simple prism model
model = [mesher.Prism(-1000, 1000, -3000, 3000, 0, 2000, {'density': 800})]
shape = (25, 25)
xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=-10)
data = prism.gz(xp, yp, zp, model)
# Run the Generalized Inverse
mesh = imaging.geninv(xp, yp, zp, data, shape, zmin=0, zmax=5000, nlayers=25)
# Plot the results
fig = plt.figure()
X, Y = xp.reshape(shape) / 1000, yp.reshape(shape) / 1000
image = mesh.props['density'].reshape(mesh.shape)
# First plot the original gravity data
ax = plt.subplot(2, 2, 1)
ax.set_title('Gravity data (mGal)')
ax.set_aspect('equal')
log.info("Fetching CRUST2.0 model")
archive = io.fetch_crust2()
log.info("Converting to tesseroids")
model = io.crust2_to_tesseroids(archive)
log.info(' model size: %d' % (len(model)))
# Plot the tesseroid model
myv.figure(zdown=False)
myv.tesseroids(model, 'density')
myv.continents(linewidth=3)
myv.show()
# Make the computation grid
area = (-180, 180, -80, 80)
shape = (100, 100)
lons, lats, heights = gridder.regular(area, shape, z=250000)
# Divide the model into nproc slices and calculate them in parallel
log.info('Calculating...')
def calculate(chunk):
return gravmag.tesseroid.gz(lons, lats, heights, chunk)
def split(model, nproc):
chunksize = len(model) / nproc
for i in xrange(nproc - 1):
yield model[i * chunksize:(i + 1) * chunksize]
yield model[(nproc - 1) * chunksize:]
sediments["bottom"] = sediments_top - sediments["thickness"]
# Create Tesseroids model of the sediments layer
# ----------------------------------------------
bottom, top = sediments["bottom"].copy(), sediments["top"].copy()
top[nans] = 0
bottom[nans] = 0
basin = TesseroidModel(sediments['area'], top, bottom, sediments['shape'])
# Create computation grid at 10km above the spheroid
# --------------------------------------------------
shape = (79, 81)
area = (-40.8, -33., 287, 295.)
lat, lon, height = gridder.regular(area, shape, z=10e3)
grid = {'lat': lat,
'lon': lon,
'height': height,
'shape': shape,
'area': area}
# Common variables between computations
# -------------------------------------
# Define density values for the top and the bottom of the sediment layer
density_top, density_bottom = -412, -275
# Define top and bottom variables as the maximum and minimum sediments'
# height and depth, respectively
top, bottom = basin.top[~nans].max(), basin.bottom[~nans].min()
print("Top of sediments: {} \nBottom of sediments: {}".format(top, bottom))
p1, p2 = p
rot = 60
origin = (max(xp), min(yp))
point_torotate = np.array([xp, yp])
xp_r, yp_r = MALM_pm.rotate_60(origin,
point_torotate,
angle_deg=rot,
showfig=False)
Xs = xp_r - min(xp_r)
Ys = yp_r - min(yp_r)
prl = 60
# shape = shape (max(xp)-min(xp))/
shape = (150, 150)
xint_scipy, yint_scipy = gridder.regular(
(min(Xs) - prl, max(Xs) + prl, min(Ys) - prl, max(Ys) + prl), shape=shape)
#%% ------------------------------- MALM DATA real
MainPath = r'E:\Padova\Software\SourceInversion\Potential_field_imaging\dEXP_imaging\examples_in_prep\\'
# os.chdir(MainPath)
## --------- read MALM measured data file (with electrode positions) --------- ##
# RealData = np.loadtxt("./1_Data_2_plot/to_plot.dat",skiprows=0,delimiter='\t')
out = MALM_pm.load_MALM_Porto_real(MainPath + '/malm_models/',
MainPath +
'./malm_models/XYObs_real_f_m3.txt',
shape=(100, 100),
radius=200,
rcor=10,
rot=0,
showfig=False)
import sys
from matplotlib import pyplot
import numpy
from fatiando.mesher.dd import Square
from fatiando.seismic import epicenter, traveltime
from fatiando import vis, utils, inversion, gridder, ui
import cPickle as pickle
with open('dados.pickle') as f:
recs, src, ttr, error = pickle.load(f)
area = (0, 100000, 0, 100000)
vp, vs = 2000, 1000
shape = (50, 50)
xs, ys = gridder.regular(area, shape)
goals = epicenter.mapgoal(xs, ys, ttr, recs, vp, vs)
pyplot.figure()
ax = pyplot.subplot(1, 1, 1)
pyplot.axis('scaled')
pyplot.suptitle("Escolha a estimativa inicial")
vis.map.contourf(xs, ys, goals, shape, 30)
vis.map.points(recs, '^r')
vis.map.points(src, '*y')
inicial = ui.picker.points(area, ax, marker='*', color='k')[0]
solver = inversion.gradient.newton(initial=inicial)
result = epicenter.flat_earth(ttr, recs, vp, vs, solver)
estimate, residuals = result
predicted = ttr - residuals
""" Vis: Plot a map using the Mercator map projection and pseudo-color """ from fatiando import gridder, utils, vis # Generate some data to plot area = (-20, 40, 20, 80) shape = (100, 100) lon, lat = gridder.regular(area, shape) data = utils.gaussian2d(lon, lat, 10, 20, 10, 60, angle=45) # Now get a basemap to plot with some projection bm = vis.mpl.basemap(area, 'merc') # And now plot everything passing the basemap to the plotting functions vis.mpl.figure(figsize=(5, 8)) vis.mpl.pcolor(lon, lat, data, shape, basemap=bm) vis.mpl.colorbar() bm.drawcoastlines() bm.drawmapboundary() bm.drawcountries() vis.mpl.draw_geolines(area, 10, 10, bm) vis.mpl.show()
"""
GravMag: Forward modeling of the gravity anomaly using tesseroids in parallel
using ``multiprocessing``
"""
import time
from multiprocessing import Pool
from fatiando import gravmag, gridder, utils
from fatiando.mesher import Tesseroid
from fatiando.vis import mpl, myv
# Make a "crust" model with some thinker crust and variable density
marea = (-70, 70, -70, 70)
mshape = (200, 200)
mlons, mlats = gridder.regular(marea, mshape)
dlon, dlat = gridder.spacing(marea, mshape)
depths = (30000 + 70000 * utils.gaussian2d(mlons, mlats, 10, 10, -20, -20) +
20000 * utils.gaussian2d(mlons, mlats, 5, 5, 20, 20))
densities = (2700 + 500 * utils.gaussian2d(mlons, mlats, 40, 40, -20, -20) +
-300 * utils.gaussian2d(mlons, mlats, 20, 20, 20, 20))
model = [
Tesseroid(lon - 0.5 * dlon,
lon + 0.5 * dlon,
lat - 0.5 * dlat,
lat + 0.5 * dlat,
0,
-depth,
props={'density': density})
for lon, lat, depth, density in zip(mlons, mlats, depths, densities)
]
# Plot the tesseroid model
GravMag: Upward continuation of noisy gz data
"""
from fatiando import mesher, gridder, utils
from fatiando.gravmag import prism, transform
from fatiando.vis import mpl
import numpy as np
model = [
mesher.Prism(-3000, -2000, -3000, -2000, 500, 2000, {'density': 1000}),
mesher.Prism(-1000, 1000, -1000, 1000, 0, 2000, {'density': -800}),
mesher.Prism(1000, 3000, 2000, 3000, 0, 1000, {'density': 900})
]
area = (-5000, 5000, -5000, 5000)
shape = (50, 50)
z0 = -100
x, y, z = gridder.regular(area, shape, z=z0)
gz = utils.contaminate(prism.gz(x, y, z, model), 0.5, seed=0)
height = 1000 # How much higher to go
gzcontf = transform.upcontinue(x, y, gz, shape, height)
# Compute the true value at the new height for comparison
gztrue = prism.gz(x, y, z - height, model)
args = dict(shape=shape, levels=20, cmap=mpl.cm.RdBu_r)
fig, axes = mpl.subplots(1, 3, figsize=(12, 3.5))
axes = axes.ravel()
mpl.sca(axes[0])
mpl.title("Original")
mpl.axis('scaled')
mpl.contourf(x, y, gz, **args)
"""
from fatiando.mesher import Prism
from fatiando import gridder, utils
from fatiando.gravmag import prism, transform
from fatiando.gravmag.euler import Classic
from fatiando.vis import mpl, myv
# The regional field
inc, dec = -45, 0
# Make a model
bounds = [-5000, 5000, -5000, 5000, 0, 5000]
model = [Prism(-1500, -500, -500, 500, 1000, 2000, {'magnetization': 2})]
# Generate some data from the model
shape = (200, 200)
area = bounds[0:4]
xp, yp, zp = gridder.regular(area, shape, z=-1)
# Add a constant baselevel
baselevel = 10
# Convert from nanoTesla to Tesla because euler and derivatives require things
# in SI
tf = (utils.nt2si(prism.tf(xp, yp, zp, model, inc, dec)) + baselevel)
# Calculate the derivatives using FFT
xderiv = transform.derivx(xp, yp, tf, shape)
yderiv = transform.derivy(xp, yp, tf, shape)
zderiv = transform.derivz(xp, yp, tf, shape)
mpl.figure()
titles = ['Total field', 'x derivative', 'y derivative', 'z derivative']
for i, f in enumerate([tf, xderiv, yderiv, zderiv]):
mpl.subplot(2, 2, i + 1)
mpl.title(titles[i])
"""
GravMag: 3D imaging using the migration method on synthetic gravity data
(simple model)
"""
from fatiando import gridder, mesher, gravmag
from fatiando.vis import mpl, myv
# Make some synthetic gravity data from a simple prism model
prisms = [mesher.Prism(-1000, 1000, -2000, 2000, 2000, 4000, {'density': 500})]
shape = (50, 50)
xp, yp, zp = gridder.regular((-10000, 10000, -10000, 10000), shape, z=-10)
gz = gravmag.prism.gz(xp, yp, zp, prisms)
# Plot the data
mpl.figure()
mpl.axis('scaled')
mpl.contourf(yp, xp, gz, shape, 30)
mpl.colorbar()
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
mpl.m2km()
mpl.show()
mesh = gravmag.imaging.migrate(xp, yp, zp, gz, 0, 10000, (25, 25, 25))
# Plot the results
myv.figure()
myv.prisms(prisms, 'density', style='wireframe', linewidth=2)
myv.prisms(mesh, 'density', edges=False)
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds)
"""
Meshing: Make and plot a 3D prism mesh with topography
"""
from fatiando import gridder, utils, mesher
from fatiando.vis import myv
x1, x2 = -100, 100
y1, y2 = -200, 200
bounds = (x1, x2, y1, y2, -200, 0)
x, y = gridder.regular((x1, x2, y1, y2), (50, 50))
height = (100 +
-50 * utils.gaussian2d(x, y, 100, 200, x0=-50, y0=-100, angle=-60) +
100 * utils.gaussian2d(x, y, 50, 100, x0=80, y0=170))
mesh = mesher.PrismMesh(bounds, (20, 40, 20))
mesh.carvetopo(x, y, height)
myv.figure()
myv.prisms(mesh)
myv.axes(myv.outline(bounds), fmt='%.0f')
myv.wall_north(bounds)
myv.show()
for key in cdir:
if case == key and i == cdir.get(key):
return 10
return 0
# The test cases as string list
cases = ['above', 'below', 'north', 'south', 'east', 'west']
# Create reference model
bounds = (0, 3, 0, 3, 0, 3)
shape = (3, 3, 3)
shapegz = (10, 10)
for testcase in cases:
mref = PrismMesh(bounds, shape)
mesh = mref.copy()
mref.addprop('density', [fill(i, testcase) for i in xrange(mref.size)])
# Calculate reference gravity field
xp, yp, zp = gridder.regular(bounds[:4], shapegz, z=-1)
gzref = prism.gz(xp, yp, zp, mref)
# Initiate harvest
hgref = [harvester.Gz(xp, yp, zp, gzref)]
loc = [[1.5, 1.5, 1.5, {'density': 10}]]
seeds = harvester.sow(loc, mesh)
# est0 should be incorrect and thus fail wilst est1 should yield the
# same geometry as mref
est0, pred0 = harvester.harvest(hgref, seeds, mesh, compactness=0.1,
threshold=0.001, restrict=[testcase])
est1, pred1 = harvester.harvest(hgref, seeds, mesh, compactness=0.1,
threshold=0.001)
res0 = mesh.copy()
res0.addprop('density', est0['density'])
res1 = mesh.copy()
res1.addprop('density', est1['density'])