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##############################################################################
#
# Copyright (c) 2012-2018 by The University of Queensland
# http://www.uq.edu.au
#
# Primary Business: Queensland, Australia
# Licensed under the Apache License, version 2.0
# http://www.apache.org/licenses/LICENSE-2.0
#
# Development until 2012 by Earth Systems Science Computational Center (ESSCC)
# Development 2012-2013 by School of Earth Sciences
# Development from 2014 by Centre for Geoscience Computing (GeoComp)
#
##############################################################################
from __future__ import division, print_function
"""
Advanced 3D gravity/magnetic joint inversion example without using any
inversion drivers
"""
__copyright__="""Copyright (c) 2012-2018 by The University of Queensland
http://www.uq.edu.au
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Apache License, version 2.0
http://www.apache.org/licenses/LICENSE-2.0"""
__url__="https://launchpad.net/escript-finley"
# Import required modules
import numpy as np
from esys.downunder import *
from esys.escript import unitsSI as U
from esys.escript import *
from esys.weipa import *
# Set parameters
MAGNETIC_DATASET = 'data/MagneticSmall.nc'
MAG_UNITS = U.Nano * U.V * U.sec / (U.m**2)
GRAVITY_DATASET = 'data/GravitySmall.nc'
GRAV_UNITS = 1e-6 * U.m/(U.sec**2)
# background magnetic field components (B_East, B_North, B_Vertical)
B_b = [2201.*U.Nano*U.Tesla, 31232.*U.Nano*U.Tesla, -41405.*U.Nano*U.Tesla]
thickness = 40. * U.km # below surface
l_air = 6. * U.km # above surface
n_cells_v = 25 # number of cells in vertical direction
# apply 20% padding
PAD_X = 0.2
PAD_Y = 0.2
MU_GRAVITY = 10.
MU_MAGNETIC = 0.1
COORDINATES=WGS84ReferenceSystem()
def work():
# read data:
source_g=NetCdfData(NetCdfData.GRAVITY, GRAVITY_DATASET, scale_factor=GRAV_UNITS, reference_system=COORDINATES)
source_m=NetCdfData(NetCdfData.MAGNETIC, MAGNETIC_DATASET, scale_factor=MAG_UNITS, reference_system=COORDINATES)
# create domain:
db=DomainBuilder(dim=3, reference_system=COORDINATES)
db.addSource(source_g)
db.addSource(source_m)
db.setVerticalExtents(depth=thickness, air_layer=l_air, num_cells=n_cells_v)
db.setFractionalPadding(pad_x=PAD_X, pad_y=PAD_Y)
db.fixDensityBelow(depth=thickness)
db.fixSusceptibilityBelow(depth=thickness)
dom=db.getDomain()
DIM=dom.getDim()
# create mappings with standard parameters
rho_mapping=DensityMapping(dom)
k_mapping=SusceptibilityMapping(dom)
# create regularization with two level set functions:
reg_mask=Data(0.,(2,), Solution(dom))
reg_mask[0] = db.getSetDensityMask() # mask for locations where m[0]~rho is known
reg_mask[1] = db.getSetSusceptibilityMask() # mask for locations where m[0]~k is known
regularization=Regularization(dom, numLevelSets=2,
w1=np.ones((2,DIM)), # consider gradient terms
wc=[[0,1],[0,0]], # and cross-gradient term
coordinates=COORDINATES,
location_of_set_m=reg_mask)
# create forward model for gravity
# get data with deviation
g,sigma_g=db.getGravitySurveys()[0]
# turn the scalars into vectors (vertical direction)
d=kronecker(DIM)[DIM-1]
w=safeDiv(1., sigma_g)
gravity_model=GravityModel(dom, w*d, g*d, coordinates=COORDINATES)
gravity_model.rescaleWeights(rho_scale=rho_mapping.getTypicalDerivative())
# create forward model for magnetic
d=normalize(np.array(B_b)) # direction of measurement
B,sigma_B=db.getMagneticSurveys()[0]
w=safeDiv(1., sigma_B)
magnetic_model=MagneticModel(dom, w*d, B*d, B_b, coordinates=COORDINATES)
# or
# magnetic_model=SelfDemagnetizationModel(dom, w*d, B*d, B_b, coordinates=COORDINATES)
magnetic_model.rescaleWeights(k_scale=k_mapping.getTypicalDerivative())
# finally we can set up the cost function:
cf=InversionCostFunction(regularization,
((rho_mapping,0), (k_mapping, 1)),
((gravity_model,0), (magnetic_model,1)) )
cf.setTradeOffFactorsModels([MU_GRAVITY, MU_MAGNETIC])
# sun solver:
solver=MinimizerLBFGS()
solver.setCostFunction(cf)
solver.setTolerance(1e-4)
solver.setMaxIterations(50)
solver.run(Data(0.,(2,),Solution(dom)))
m=solver.getResult()
density, susceptibility = cf.getProperties(m)
# write everything to file:
saveSilo("result_gravmag.silo",
density=density, susceptability=susceptibility,
g_data=g, sigma_g=sigma_g, B_data=B, sigma_B=sigma_B)
saveVTK("result_gravmag.vtu",
density=density, susceptability=susceptibility,
g_data=g, sigma_g=sigma_g, B_data=B, sigma_B=sigma_B)
print("All done. Have a nice day!")
if 'NetCdfData' in dir():
work()
else:
print("This example requires scipy's netcdf support which does not appear to be installed.")
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