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_pelgrav_prism_interp():
"PELGravity can interpolate data from a prism"
model = [Prism(-300, 300, -500, 500, 100, 600, {'density': 400})]
shape = (40, 40)
n = shape[0]*shape[1]
area = [-2000, 2000, -2000, 2000]
x, y, z = gridder.scatter(area, n, z=-100, seed=42)
data = prism.gz(x, y, z, model)
layer = PointGrid(area, 100, shape)
windows = (20, 20)
degree = 1
eql = (PELGravity(x, y, z, data, layer, windows, degree)
+ 5e-22*PELSmoothness(layer, windows, degree))
eql.fit()
layer.addprop('density', eql.estimate_)
assert_allclose(eql[0].predicted(), data, rtol=0.01)
xp, yp, zp = gridder.regular(area, shape, z=-100)
true = prism.gz(xp, yp, zp, model)
calc = sphere.gz(xp, yp, zp, layer)
assert_allclose(calc, true, atol=0.001, rtol=0.05)
# Make synthetic data
props = {'density': 1000}
model = [mesher.Prism(-500, 500, -1000, 1000, 500, 4000, props)]
shape = (50, 50)
x, y, z = gridder.regular([-5000, 5000, -5000, 5000], shape, z=0)
gz = utils.contaminate(prism.gz(x, y, z, model), 0.1, seed=0)
# Setup the layer
layer = mesher.PointGrid([-5000, 5000, -5000, 5000], 200, (100, 100))
# Estimate the density using the PEL (it is faster and more memory efficient
# than the traditional equivalent layer).
windows = (20, 20)
degree = 1
misfit = PELGravity(x, y, z, gz, layer, windows, degree)
# Apply a smoothness constraint to the borders of the equivalent layer windows
# to avoid gaps in the physical property distribution
solver = misfit + 1e-18 * PELSmoothness(layer, windows, degree)
solver.fit()
# Add the estimated density distribution to the layer object for plotting and
# forward modeling
layer.addprop('density', solver.estimate_)
residuals = solver[0].residuals()
print("Residuals:")
print("mean:", residuals.mean())
print("stddev:", residuals.std())
# Now I can forward model the layer at a greater height and check against the
# true solution of the prism
gz_true = prism.gz(x, y, z - 500, model)
gz_up = sphere.gz(x, y, z - 500, layer)
mpl.figure(figsize=(14, 4))
# 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(prism.tf(x, y, z, model, inc, dec), 5, seed=0)
# Setup the layer
layer = mesher.PointGrid([-5000, 5000, -5000, 5000], 200, (100, 100))
# Estimate the density using the PEL (it is faster and more memory efficient
# than the traditional equivalent layer).
windows = (20, 20)
degree = 1
misfit = PELTotalField(x, y, z, tf, inc, dec, layer, windows, degree)
regul = PELSmoothness(layer, windows, degree)
# Use an L-curve analysis to find the best regularization parameter
solver = LCurve(misfit, regul, [10 ** i for i in range(-20, -10)]).fit()
layer.addprop('magnetization', solver.estimate_)
residuals = solver.residuals()
print "Residuals:"
print "mean:", residuals.mean()
print "stddev:", residuals.std()
# Now I can forward model the layer at the south pole and 500 m above the
# original data. Check against the true solution of the prism
tfpole = prism.tf(x, y, z - 500, model, -90, 0)
tfreduced = sphere.tf(x, y, z - 500, layer, -90, 0)
mpl.figure()
mpl.suptitle('L-curve')