def setUp(self):
# Mesh
N = 100
mesh = TensorMesh([N])
# Survey design parameters
nk = 30
jk = np.linspace(1.0, 59.0, nk)
p = -0.25
q = 0.25
# Physics
def g(k):
return np.exp(p * jk[k] * mesh.vectorCCx) * np.cos(
np.pi * q * jk[k] * mesh.vectorCCx)
G = np.empty((nk, mesh.nC))
for i in range(nk):
G[i, :] = g(i)
self.G = G
# Creating the true model
true_model = np.zeros(mesh.nC)
true_model[mesh.vectorCCx > 0.3] = 1.0
true_model[mesh.vectorCCx > 0.45] = -0.5
true_model[mesh.vectorCCx > 0.6] = 0
self.true_model = true_model
# Create a SimPEG simulation
model_map = IdentityMap(mesh)
sim = simulation.LinearSimulation(mesh, G=G, model_map=model_map)
# Create a SimPEG data object
relative_error = 0.1
noise_floor = 1e-4
data_obj = sim.make_synthetic_data(true_model,
relative_error=relative_error,
noise_floor=noise_floor,
add_noise=True)
dmis = data_misfit.L2DataMisfit(simulation=sim, data=data_obj)
self.dmis = dmis
# Test for joint misfits
n_misfits = 5
multipliers = np.random.randn(n_misfits)**2
multipliers /= np.sum(multipliers)
self.multipliers = multipliers
dmiscombo = dmis
for i, mult in enumerate(multipliers):
dmiscombo += mult * dmis
self.dmiscombo = dmiscombo
# Test for a regularization term
reg = Tikhonov(mesh=mesh)
self.reg = reg
# Test a mix combo
self.beta = 10.
self.mixcombo = self.dmis + self.beta * self.reg
def get_problem_survey(self):
survey_obj = survey.LinearSurvey()
simulation_obj = simulation.LinearSimulation(
survey=survey_obj,
mesh=self.mesh_prop,
model_map=maps.IdentityMap(),
G=self.G,
)
return survey_obj, simulation_obj
fig = plt.figure(figsize=(8, 5))
ax = fig.add_subplot(111)
for i in range(G.shape[0]):
ax.plot(G[i, :])
ax.set_title("Columns of matrix G")
#############################################
# Defining the Simulation
# -----------------------
#
# The simulation defines the relationship between the model parameters and
# predicted data.
#
sim = simulation.LinearSimulation(mesh, G=G, model_map=model_map)
#############################################
# Predict Synthetic Data
# ----------------------
#
# Here, we use the true model to create synthetic data which we will subsequently
# invert.
#
# Standard deviation of Gaussian noise being added
std = 0.02
np.random.seed(1)
# Create a SimPEG data object
data_obj = sim.make_synthetic_data(true_model, noise_floor=std, add_noise=True)
def get_simulation(self):
lin_simulation = simulation.LinearSimulation(
self.mesh, G=self.G, model_map=maps.IdentityMap(self.mesh)
)
return lin_simulation
max_iter=1000,
n_init=100,
init_params="kmeans",
random_state=None,
warm_start=False,
verbose=0,
verbose_interval=10,
)
clfnomapping = clfnomapping.fit(model2d)
wires = maps.Wires(("m1", mesh.nC), ("m2", mesh.nC))
relatrive_error = 0.01
noise_floor = 0.0
prob1 = simulation.LinearSimulation(mesh, G=G, model_map=wires.m1)
survey1 = prob1.make_synthetic_data(m,
relative_error=relatrive_error,
noise_floor=noise_floor,
add_noise=True)
prob2 = simulation.LinearSimulation(mesh, G=G, model_map=wires.m2)
survey2 = prob2.make_synthetic_data(m,
relative_error=relatrive_error,
noise_floor=noise_floor,
add_noise=True)
dmis1 = data_misfit.L2DataMisfit(simulation=prob1, data=survey1)
dmis2 = data_misfit.L2DataMisfit(simulation=prob2, data=survey2)
dmis = dmis1 + dmis2
minit = np.zeros_like(m)
# True model
mtrue = np.zeros(mesh.nC)
mtrue[mesh.cell_centers_x > 0.2] = 1.0
mtrue[mesh.cell_centers_x > 0.35] = 0.0
t = (mesh.cell_centers_x - 0.65) / 0.25
indx = np.abs(t) < 1
mtrue[indx] = -(((1 - t**2.0)**2.0)[indx])
mtrue = np.zeros(mesh.nC)
mtrue[mesh.cell_centers_x > 0.3] = 1.0
mtrue[mesh.cell_centers_x > 0.45] = -0.5
mtrue[mesh.cell_centers_x > 0.6] = 0
# SimPEG problem and survey
prob = simulation.LinearSimulation(mesh, G=G, model_map=maps.IdentityMap())
std = 0.01
survey = prob.make_synthetic_data(mtrue, relative_error=std, add_noise=True)
# Setup the inverse problem
reg = regularization.Tikhonov(mesh, alpha_s=1.0, alpha_x=1.0)
dmis = data_misfit.L2DataMisfit(data=survey, simulation=prob)
opt = optimization.ProjectedGNCG(maxIter=10, maxIterCG=50, tolCG=1e-4)
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt)
directiveslist = [
directives.BetaEstimate_ByEig(beta0_ratio=1e-5),
directives.BetaSchedule(coolingFactor=10.0, coolingRate=2),
directives.TargetMisfit(),
]
inv = inversion.BaseInversion(invProb, directiveList=directiveslist)