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_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_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_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_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_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 anomaly_calculation(x, y, w, t, rho):
from fatiando import utils
from fatiando.mesher import Prism
from fatiando.gravmag import prism
ny, nx = np.shape(x)
prismas = []
for i in xrange(ny-1):
for j in xrange(nx-1):
prisma = Prism(y[i][j], y[i+1][j+1], x[i][j], x[i+1][j+1], t,
t + (w[i][j] + w[i+1][j] + w[i][j+1] + w[i+1][j+1])/4.)
prismas.append(prisma)
gz = -prism.gz(y.ravel(),x.ravel(),np.zeros(nx*ny),prismas,dens=rho)
gz = utils.mgal2si(np.reshape(gz,(ny,nx)))
return gz
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)
from fatiando.vis import mpl, myv
# Make a model
bounds = [-5000, 5000, -5000, 5000, 0, 5000]
model = [
Prism(-1500, -500, -1500, -500, 500, 1500, {'density': 1000}),
Prism(500, 1500, 1000, 2000, 500, 1500, {'density': 1000})]
# Generate some data from the model
shape = (100, 100)
area = bounds[0:4]
xp, yp, zp = gridder.regular(area, shape, z=-1)
# Add a constant baselevel
baselevel = 10
# Convert the data from mGal to SI because Euler and FFT derivation require
# data in SI
gz = utils.mgal2si(prism.gz(xp, yp, zp, model)) + baselevel
xderiv = transform.derivx(xp, yp, gz, shape)
yderiv = transform.derivy(xp, yp, gz, shape)
zderiv = transform.derivz(xp, yp, gz, shape)
mpl.figure()
titles = ['Gravity anomaly', 'x derivative', 'y derivative', 'z derivative']
for i, f in enumerate([gz, xderiv, yderiv, zderiv]):
mpl.subplot(2, 2, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
mpl.contourf(yp, xp, f, shape, 50)
mpl.colorbar()
mpl.m2km()
mpl.show()
"""
GravMag: Calculating the derivatives of the gravity anomaly using FFT
"""
from fatiando import mesher, gridder, utils
from fatiando.gravmag import prism, transform
from fatiando.vis import mpl
model = [mesher.Prism(-1000, 1000, -1000, 1000, 0, 2000, {'density': 100})]
area = (-5000, 5000, -5000, 5000)
shape = (51, 51)
z0 = -500
xp, yp, zp = gridder.regular(area, shape, z=z0)
gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.001)
# Need to convert gz to SI units so that the result can be converted to Eotvos
gxz = utils.si2eotvos(transform.derivx(xp, yp, utils.mgal2si(gz), shape))
gyz = utils.si2eotvos(transform.derivy(xp, yp, utils.mgal2si(gz), shape))
gzz = utils.si2eotvos(transform.derivz(xp, yp, utils.mgal2si(gz), shape))
gxz_true = prism.gxz(xp, yp, zp, model)
gyz_true = prism.gyz(xp, yp, zp, model)
gzz_true = prism.gzz(xp, yp, zp, model)
mpl.figure()
mpl.title("Original gravity anomaly")
mpl.axis('scaled')
mpl.contourf(xp, yp, gz, shape, 15)
mpl.colorbar(shrink=0.7)
mpl.m2km()
mpl.figure(figsize=(14, 10))
# Make a model
bounds = [-5000, 5000, -5000, 5000, 0, 5000]
model = [
Prism(-1500, -500, -1500, -500, 500, 1500, {'density': 1000}),
Prism(500, 1500, 1000, 2000, 500, 1500, {'density': 1000})
]
# Generate some data from the model
shape = (100, 100)
area = bounds[0:4]
xp, yp, zp = gridder.regular(area, shape, z=-1)
# Add a constant baselevel
baselevel = 10
# Convert the data from mGal to SI because Euler and FFT derivation require
# data in SI
gz = utils.mgal2si(prism.gz(xp, yp, zp, model)) + baselevel
xderiv = transform.derivx(xp, yp, gz, shape)
yderiv = transform.derivy(xp, yp, gz, shape)
zderiv = transform.derivz(xp, yp, gz, shape)
mpl.figure()
titles = ['Gravity anomaly', 'x derivative', 'y derivative', 'z derivative']
for i, f in enumerate([gz, xderiv, yderiv, zderiv]):
mpl.subplot(2, 2, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
mpl.contourf(yp, xp, f, shape, 50)
mpl.colorbar()
mpl.m2km()
mpl.show()
"""
GravMag: Calculating the derivatives of the gravity anomaly using FFT
"""
from fatiando import mesher, gridder, utils, gravmag
from fatiando.vis import mpl
prisms = [mesher.Prism(-1000,1000,-1000,1000,0,2000,{'density':100})]
area = (-5000, 5000, -5000, 5000)
shape = (51, 51)
z0 = -500
xp, yp, zp = gridder.regular(area, shape, z=z0)
gz = utils.contaminate(gravmag.prism.gz(xp, yp, zp, prisms), 0.001)
# Need to convert gz to SI units so that the result can be converted to Eotvos
gxz = utils.si2eotvos(
gravmag.fourier.derivx(xp, yp, utils.mgal2si(gz), shape))
gyz = utils.si2eotvos(
gravmag.fourier.derivy(xp, yp, utils.mgal2si(gz), shape))
gzz = utils.si2eotvos(
gravmag.fourier.derivz(xp, yp, utils.mgal2si(gz), shape))
gxz_true = gravmag.prism.gxz(xp, yp, zp, prisms)
gyz_true = gravmag.prism.gyz(xp, yp, zp, prisms)
gzz_true = gravmag.prism.gzz(xp, yp, zp, prisms)
mpl.figure()
mpl.title("Original gravity anomaly")
mpl.axis('scaled')
mpl.contourf(xp, yp, gz, shape, 15)
mpl.colorbar(shrink=0.7)
mpl.m2km()
"""
GravMag: Calculating the derivatives of the gravity anomaly using FFT
"""
from fatiando import mesher, gridder, utils, gravmag
from fatiando.vis import mpl
prisms = [mesher.Prism(-1000, 1000, -1000, 1000, 0, 2000, {'density': 100})]
area = (-5000, 5000, -5000, 5000)
shape = (51, 51)
z0 = -500
xp, yp, zp = gridder.regular(area, shape, z=z0)
gz = utils.contaminate(gravmag.prism.gz(xp, yp, zp, prisms), 0.001)
# Need to convert gz to SI units so that the result can be converted to Eotvos
gxz = utils.si2eotvos(gravmag.fourier.derivx(xp, yp, utils.mgal2si(gz), shape))
gyz = utils.si2eotvos(gravmag.fourier.derivy(xp, yp, utils.mgal2si(gz), shape))
gzz = utils.si2eotvos(gravmag.fourier.derivz(xp, yp, utils.mgal2si(gz), shape))
gxz_true = gravmag.prism.gxz(xp, yp, zp, prisms)
gyz_true = gravmag.prism.gyz(xp, yp, zp, prisms)
gzz_true = gravmag.prism.gzz(xp, yp, zp, prisms)
mpl.figure()
mpl.title("Original gravity anomaly")
mpl.axis('scaled')
mpl.contourf(xp, yp, gz, shape, 15)
mpl.colorbar(shrink=0.7)
mpl.m2km()
mpl.figure(figsize=(14, 10))
mpl.subplots_adjust(top=0.95, left=0.05, right=0.95)
"""
GravMag: Calculating the derivatives of the gravity anomaly using FFT
"""
from fatiando import mesher, gridder, utils
from fatiando.gravmag import prism, fourier
from fatiando.vis import mpl
model = [mesher.Prism(-1000,1000,-1000,1000,0,2000,{'density':100})]
area = (-5000, 5000, -5000, 5000)
shape = (51, 51)
z0 = -500
xp, yp, zp = gridder.regular(area, shape, z=z0)
gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.001)
# Need to convert gz to SI units so that the result can be converted to Eotvos
gxz = utils.si2eotvos(fourier.derivx(xp, yp, utils.mgal2si(gz), shape))
gyz = utils.si2eotvos(fourier.derivy(xp, yp, utils.mgal2si(gz), shape))
gzz = utils.si2eotvos(fourier.derivz(xp, yp, utils.mgal2si(gz), shape))
gxz_true = prism.gxz(xp, yp, zp, model)
gyz_true = prism.gyz(xp, yp, zp, model)
gzz_true = prism.gzz(xp, yp, zp, model)
mpl.figure()
mpl.title("Original gravity anomaly")
mpl.axis('scaled')
mpl.contourf(xp, yp, gz, shape, 15)
mpl.colorbar(shrink=0.7)
mpl.m2km()
mpl.figure(figsize=(14,10))