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__copyright__ = "Copyright (c) 2020 by University of Queensland http://www.uq.edu.au"
__license__ = "Licensed under the Apache License, version 2.0 http://www.apache.org/licenses/LICENSE-2.0"
__credits__ = "Lutz Gross, Andrea Codd"
"""
Simple direct current resistivity code that uses class dcResistivityModel in dcModels.py
The domain is made using finley Brick creating a structured grid.
Inputs are
gridline spacing,
number of elements in the x, y, and z directions,
height of the data above ground,
background magnetic field,
and assumed susceptibility.
class dcModel(domain) sets up the PDE and domain
This example is for a model with conductivity = 1 apart from a small sphere centre c and radius R that has the assumed conductivity.
Sources are on the top of the domain, z=zmax.
The output from this code is a silo file containing conductivity and primary and secondary electric potential.
"""
# Import required modules
from esys.escript import *
from esys.finley import Brick
from esys.weipa import saveSilo
from esys.downunder.apps import DCResistivityModel
import numpy as np
# Set Parameters
dx = 6 # grid line spacing in [m]
NEx = 200 # number of nodes in the x direction
NEy = 200 # number of nodes in the y direction
NEz = 200 # number of nodes in the z direction
H0 = 600 # height [m] of transect above bottom of domain (will be locked to grid)
sig_p = 1. # primary conductivity
sig_2 = 100. # conductivity in ball
useAnalytic = True
POSx = 100
POSy = 70
NEGx = 100
NEGy = 110
POS_node = ( POSx*dx, POSy*dx, NEz*dx)
NEG_node = ( NEGx*dx, NEGy*dx, NEz*dx)
Lx = dx*NEx
Ly = dx*NEy
Lz = dx*NEz
print("domain dimensions = [%dm x %dm x %dm]"%(Lx,Ly,Lz))
print("grid = [%d x %d x %d]"%(NEx, NEy, NEz))
# Create domain with Dirac points
domain=Brick(n0=NEx, n1=NEy, n2=NEz, l0=Lx, l1=Ly, l2=Lz,
diracPoints= [POS_node, NEG_node], diracTags = ['e0','e1'])
# Define model using class dcresistivityModel3D
# Assumes zero Dirichlet BC at bottom left front corner
# Define conductivity
Z0=100 # vertical position of circle below transect [m]
c=[Lx/2.,Ly/2., H0-Z0] # circle center
R=50. # radius
x=domain.getX()
d=length(x-c)
sigma = Scalar(sig_p,ContinuousFunction(domain))
model=DCResistivityModel(domain,sigma0=sigma,useFastSolver = True)
print("ERT forward model created.")
print("background conductivity = %s"%(sigma))
print("positive charge %s at %s"%(1.0, POS_node))
print("negative charge %s at %s"%(1.0, NEG_node))
if useAnalytic:
print("half space solution as primary potential used.")
model.setPrimaryPotentialForHalfSpace(sources= [POS_node, NEG_node],
charges=[1.0, -1.0] )
print("primary potential set.")
else:
src=Scalar(0., DiracDeltaFunctions(domain))
src.setTaggedValue('e0', 1.0)
src.setTaggedValue('e1', -1.0)
print("source = %s"%src)
model.setPrimaryPotential(source=src)
print("primary potential set.")
sphereCond=sigma+(sig_2-sig_p)*whereNegative(d-R) # 0 for d>R and 1 for d<R
model.setConductivity(sphereCond)
saveSilo("dcAppExample",sigma=model.getConductivity(), u2=model.getSecondaryPotential(),up=model.getPrimaryPotential())
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