def plot_subsurface_01():
"""
Create a basic graben geology using recursive procedural API
:return: nothing (but plot the result)
"""
z0, L, NL = 0.0, 10000.0, 30
h = L / NL
print("z0, L, nL, h =", z0, L, NL, h)
mesh = baseline_tensor_mesh(NL, h, centering='CCN')
survey = survey_gridded_locations(L, L, 20, 20, z0)
history = [Basement()]
history.append(StratigraphicLayer(history[-1]))
history.append(StratigraphicLayer(history[-1]))
history.append(PlanarFault(history[-1]))
history.append(PlanarFault(history[-1]))
# Basic stratigraphy
histpars = [3.0, 1900.0, 2.5, 2500.0, 2.0]
# Fault #1
histpars.extend([-4000.0, 0.0, 0.0, 0.940, 0.0, 0.342, -4200.0])
# Fault #2
histpars.extend([+4000.0, 0.0, 0.0, 0.940, 0.0, -0.342, 4200.0])
fwdmodel = DiscreteGravity(mesh, survey, history[0])
fwdmodel.gfunc = Basement()
fwdmodel.edgemask = profile_timer(fwdmodel.calc_gravity, h, [1.0])
for m, part_history in enumerate(history):
fwdmodel.gfunc = part_history
npars = np.sum([e.npars for e in history[:m + 1]])
profile_timer(fwdmodel.calc_gravity, h, histpars[:npars])
fwdmodel.fwd_data -= fwdmodel.edgemask * fwdmodel.voxmodel.mean()
fig = plt.figure(figsize=(12, 4))
ax1 = plt.subplot(121)
fwdmodel.plot_model_slice(ax=ax1)
ax2 = plt.subplot(122)
fwdmodel.plot_gravity(ax=ax2)
plt.show()
def initialize_geomodel(gconf): # pars, L, NL, foldhistory=False):
"""
Initialize a GeoModel instance and get it ready for sampling
:param pars: parameter vector (see top of file)
:return: GeoModel instance ready for sampling with riemann
"""
# Initialize a mesh for forward gravity calculation
L, NL = gconf.L, gconf.NL
z0, h = 0.0, L / NL
print("z0, L, nL, h =", z0, L, NL, h)
mesh = baseline_tensor_mesh(NL, h, centering='CCN')
survey = survey_gridded_locations(L, L, 20, 20, z0)
# Initialize a GeoHistory based on the parameters passed in
history = gconf.geohist()
# Initialize a DiscreteGravity forward model instance
fwdmodel = DiscreteGravity(mesh, survey, history.rockprops)
# Make some synthetic data based on this history and mesh
data0 = fwdmodel.calc_gravity(h)
np.random.seed(413)
sigdata = 0.05 * np.std(data0)
epsilon = sigdata * np.random.normal(size=data0.shape)
dsynth = data0 + epsilon
# Construct and return a GeoModel
mymodel = GeoModel(history, fwdmodel, dsynth, sigdata, alpha=2.5)
mymodel.stepsizes = gconf.stepsizes
return mymodel
def plot_subsurface_02():
"""
Create a basic graben geology using object-oriented API
:return: nothing (but plot the result)
"""
# Initialize basic grid parameters
z0, L, NL = 0.0, 10000.0, 30
h = L / NL
print("z0, L, nL, h =", z0, L, NL, h)
mesh = baseline_tensor_mesh(NL, h, centering='CCN')
survey = survey_gridded_locations(L, L, 20, 20, z0)
# Create the history
history = gen_two_fault_model_demo([
3.0, 1900.0, 2.5, 2500.0, 2.0, -4000.0, 0.0, +20.0, 0.0, -4200.0,
+4000.0, 0.0, -20.0, 0.0, +4200.0
])
# Add a final Fold event just for laughs
history.add_event(
FoldEvent([('nth', 'nph', vMFDist(th0=+0.0, ph0=0.0, kappa=100)),
('pitch', UniGaussianDist(mean=0.0, std=30.0)),
('phase', UniformDist(mean=0.0, width=360.0)),
('wavelength', UniGaussianDist(mean=3000.0, std=300.0)),
('amplitude', UniGaussianDist(mean=300.0, std=50.0))]))
print("history.pars =", history.serialize())
# Can also set parameters all at once -- good for running MCMC
history.set_to_prior_draw()
history.deserialize([
3.0, 1900.0, 2.5, 2500.0, 2.0, -4000.0, 0.0, +20.0, 0.0, -4200.0,
+4000.0, 0.0, -20.0, 0.0, +4200.0, -0.0, 0.0, 0.0, 0.0, 3000.0, 300.0
])
print("history.pars =", history.serialize())
print("history.prior =", history.logprior())
# Plot a cross-section
fwdmodel = DiscreteGravity(mesh, survey, history.event_list[0])
fwdmodel.gfunc = history.event_list[0].rockprops
fwdmodel.edgemask = profile_timer(fwdmodel.calc_gravity, h)
for m, event in enumerate(history.event_list):
print("current event:", event)
fwdmodel.gfunc = lambda r, h: np.array(event.rockprops(r, h))
profile_timer(fwdmodel.calc_gravity, h)
fwdmodel.fwd_data -= fwdmodel.edgemask * fwdmodel.voxmodel.mean()
fig = plt.figure(figsize=(12, 4))
ax1 = plt.subplot(121)
fwdmodel.plot_model_slice(ax=ax1)
ax2 = plt.subplot(122)
fwdmodel.plot_gravity(ax=ax2)
plt.show()
def plot_subsurface_02():
"""
Create a basic graben geology using object-oriented API
:return: nothing (but plot the result)
"""
# Initialize basic grid parameters
z0, L, NL = 0.0, 10000.0, 30
h = L / NL
print("z0, L, nL, h =", z0, L, NL, h)
mesh = baseline_tensor_mesh(NL, h, centering='CCN')
survey = survey_gridded_locations(L, L, 20, 20, z0)
# Create the history
history = GeoHistory()
history.add_event(BasementEvent(3.0))
history.add_event(StratLayerEvent(1900.0, 2.5))
history.add_event(StratLayerEvent(2500.0, 2.0))
history.add_event(PlanarFaultEvent(-4000.0, 0.0, +20.0, 0.0, -4200.0))
history.add_event(PlanarFaultEvent(+4000.0, 0.0, -20.0, 0.0, +4200.0))
print("history.pars =", history.serialize())
# Can also set parameters all at once -- good for running MCMC
history = GeoHistory()
history.add_event(BasementEvent())
history.add_event(StratLayerEvent())
history.add_event(StratLayerEvent())
history.add_event(PlanarFaultEvent())
history.add_event(PlanarFaultEvent())
history.deserialize([
3.0, 1900.0, 2.5, 2500.0, 2.0, -4000.0, 0.0, +20.0, 0.0, -4200.0,
+4000.0, 0.0, -20.0, 0.0, +4200.0
])
print("history.pars =", history.serialize())
# Plot a cross-section
fwdmodel = DiscreteGravity(mesh, survey, history.event_list[0])
fwdmodel.gfunc = BasementEvent(1.0).rockprops
fwdmodel.edgemask = profile_timer(fwdmodel.calc_gravity, h)
for m, event in enumerate(history.event_list):
print("current event:", event)
fwdmodel.gfunc = lambda r, h: np.array(event.rockprops(r, h))
profile_timer(fwdmodel.calc_gravity, h)
fwdmodel.fwd_data -= fwdmodel.edgemask * fwdmodel.voxmodel.mean()
fig = plt.figure(figsize=(12, 4))
ax1 = plt.subplot(121)
fwdmodel.plot_model_slice(ax=ax1)
ax2 = plt.subplot(122)
fwdmodel.plot_gravity(ax=ax2)
plt.show()
def gradtest():
"""
Testing ground for adding automatic gradients to GeoFuncs
:return: nothing (yet)
"""
# All the same setup as before
z0, L, NL = 0.0, 10000.0, 15
h = L / NL
print("z0, L, nL, h =", z0, L, NL, h)
mesh = baseline_tensor_mesh(NL, h, centering='CCN')
survey = survey_gridded_locations(L, L, 20, 20, z0)
history = [Basement()]
history.append(StratigraphicLayer(history[-1]))
history.append(StratigraphicLayer(history[-1]))
history.append(PlanarFault(history[-1]))
history.append(PlanarFault(history[-1]))
# Basic stratigraphy
histpars = [3.0, 1900.0, 2.5, 2500.0, 2.0]
# Fault #1
histpars.extend([-4000.0, 0.0, 0.0, 0.940, 0.0, 0.342, -4200.0])
# Fault #2
histpars.extend([+4000.0, 0.0, 0.0, 0.940, 0.0, -0.342, 4200.0])
# Forward model stuff
fwdmodel = DiscreteGravity(mesh, survey, history[0])
fwdmodel.gfunc = Basement()
fwdmodel.edgemask = profile_timer(fwdmodel.calc_gravity, h, [1.0])
# Test gradient of anti-aliasing function
x = np.linspace(-1, 1, 4001)
t0 = time.time()
g = [soft_if_then_piecewise_ifthen(xi, 0.0, 1.0, 1.0) for xi in x]
t1 = time.time()
g = soft_if_then_piecewise(x, np.zeros(x.shape), np.ones(x.shape), 1.0)
t2 = time.time()
g = soft_if_then_logjit(x, np.zeros(x.shape), np.ones(x.shape), 1.0)
t3 = time.time()
print("looped: {:.2e} sec".format(t1 - t0))
print("vector: {:.2e} sec".format(t2 - t1))
print("logistic: {:.2e} sec".format(t3 - t2))
# a vectorized way to take the 1-D derivative
logistic_jac = jacobian(soft_if_then_logjit)
dg = np.sum(logistic_jac(x, 0.0, 1.0, 1.0), axis=0)
fig = plt.figure()
plt.plot(x, g)
plt.plot(x, dg, ls='--')
plt.show()
# Go through the history event by event
for m, part_history in enumerate(history):
fwdmodel.gfunc = part_history
npars = np.sum([e.npars for e in history[:m + 1]])
profile_timer(fwdmodel.calc_gravity, h, histpars[:npars])
fwdmodel.fwd_data -= fwdmodel.edgemask * fwdmodel.voxmodel.mean()
fig = plt.figure(figsize=(12, 4))
ax1 = plt.subplot(121)
fwdmodel.plot_model_slice(ax=ax1)
ax2 = plt.subplot(122)
fwdmodel.plot_gravity(ax=ax2)
plt.show()
# Finite differences, hrngh
t0 = time.time()
dgfd = []
for i in range(len(histpars)):
hp1, hp2 = np.array(histpars), np.array(histpars)
dth = 1e-7 * max(1, histpars[i])
hp1[i] -= dth
vox1 = history[-1](fwdmodel.mesh.gridCC, h, hp1)
hp2[i] += dth
vox2 = history[-1](fwdmodel.mesh.gridCC, h, hp2)
dgfd.append((vox2 - vox1) / (2 * dth))
dgfd = np.array(dgfd).T
t1 = time.time()
print("dgfd ran in {:.3f} seconds".format(t1 - t0))
# Demonstrate an end-to-end derivative w/rt parameters
gfuncjac = profile_timer(jacobian, history[-1], 2)
gfuncjac = jit(gfuncjac)
jhistpars = jnp.array(histpars)
dg = profile_timer(gfuncjac, fwdmodel.mesh.gridCC, h, jhistpars)
print("dg.shape =", dg.shape)
for i in range(3):
dg = profile_timer(gfuncjac, fwdmodel.mesh.gridCC, h, jhistpars)
for dgi in dg.T:
fwdmodel.voxmodel = np.array(dgi)
print("voxmodel.mean, voxmodel.std =", fwdmodel.voxmodel.mean(),
fwdmodel.voxmodel.std())
print("voxmodel.isnan.sum() =", np.sum(np.isnan(fwdmodel.voxmodel)))
# fwdmodel.plot_model_slice()
# plt.show()
idx = (np.abs(dgfd) > 1e-9)
resids = 0.5 * (dgfd[idx] - dg[idx]) / (np.abs(dg[idx] + dgfd[idx]))
print("mean fractional derivative error: {:.3g} +/- {:.3g}".format(
resids.mean(), resids.std()))