def load_grav_pygimli_cylinder():
#!/usr/bin/env python
# -*- coding: utf-8 -*-
r"""
Semianalytical Gravimetry and Geomagnetics in 2D
------------------------------------------------
Simple gravimetric and magnetostatic field caluculation using integration approach after :cite:`WonBev1987`.
"""
radius = 2.
depth = 5.
rho = 1000.0
x = np.arange(-20, 20, 1)
pnts = np.zeros((len(x), 2))
pnts[:, 0] = x
pos = [0, -depth]
fig, ax = pg.plt.subplots(nrows=3, ncols=1, figsize=(12, 8), sharex=True)
# Horizontal cylinder
circ = createCircle([0, -depth],
radius=radius,
marker=2,
area=0.1,
segments=32)
pg.show(circ, ax=ax[0], fillRegion=False)
ga = gradUCylinderHoriz(pnts, radius, rho, pos=pos)
gza = gradGZCylinderHoriz(pnts, radius, rho, pos=pos)
g, gz = solveGravimetry(circ, rho, pnts, complete=True)
plot(x, ax[1], ga, gza, ax[2], g, gz, legend=False)
# ax[0].set_ylim(bottom=-depth*2, top=1)
labels = ["Horizontal cylinder", "Half plate"]
for ax, label in zip(ax[:], labels):
ax.set_title(label)
ax.set_aspect("equal")
ax.set_xlim(left=x[0], right=x[-1])
ax.set_ylim(bottom=-depth * 2, top=1)
# pg.wait()
return ga, gza
def calcInvBlock(mesh, dens, out='gravInv'):
# extract block delta density
densBlock = pg.RVector(dens)
densMarker2 = dens[pg.find(mesh.cellMarker() == 2)[0]]
#densBlock[(mesh.cellMarker() == 1) | (mesh.cellMarker() == 3)] = densMarker2
densBlock[pg.find((mesh.cellMarker() == 1)
| (mesh.cellMarker() == 3))] = densMarker2
densBlock -= densMarker2
# define meausrement positions
gravPointsX = np.linspace(-20, 20, 41)
sensorPositions = np.vstack((gravPointsX, np.zeros(len(gravPointsX)))).T
# solve analytical
gz = solveGravimetry(mesh, densBlock, pnts=sensorPositions, complete=False)
# noisyfy
errAbs = 0.00001
dzerr = np.random.randn(len(sensorPositions)) * errAbs
gz = gz + dzerr
# createParamesh
paraMesh = pg.createGrid(x=np.linspace(-20, 20, 41),
y=np.linspace(-20, 0, 21))
# init Gravimetry manager (should do meshing, simulation and noisying)
Grav = Gravimetry(verbose=True)
model = Grav.invert(sensorPositions, gz, errAbs, verbose=1, mesh=paraMesh)
fig, ax = plt.subplots()
ax.plot(pg.x(sensorPositions), gz, label='gz')
ax.plot(pg.x(sensorPositions), Grav.inv.response(), label='response')
ax.legend()
ax.grid()
ax.set_xlabel('$x$ [m]')
ax.set_ylabel('$\partial u / \partial z$ [mGal]')
plt.show(block=False)
ax.figure.savefig(out, bbox_inches='tight')
return Grav, densBlock
def calcInvBlock(mesh, dens, out='gravInv'):
# extract block delta density
densBlock = pg.RVector(dens)
densMarker2 = dens[pg.find(mesh.cellMarker() == 2)[0]]
# densBlock[(mesh.cellMarker() == 1)|(mesh.cellMarker() == 3)] = densMarker2
densBlock[pg.find((mesh.cellMarker() == 1) | (mesh.cellMarker() == 3))] = \
densMarker2
densBlock -= densMarker2
# define meausrement positions
gravPointsX = np.linspace(-20, 20, 41)
sensorPositions = np.vstack((gravPointsX, np.zeros(len(gravPointsX)))).T
# solve analytical
gz = solveGravimetry(mesh, densBlock, pnts=sensorPositions, complete=False)
# noisyfy
errAbs = 0.00001
dzerr = np.random.randn(len(sensorPositions)) * errAbs
gz = gz + dzerr
# createParamesh
paraMesh = pg.createGrid(x=np.linspace(-20, 20, 41),
y=np.linspace(-20, 0, 21))
# init Gravimetry manager (should do meshing, simulation and noisying)
Grav = Gravimetry(verbose=True)
model = Grav.invert(sensorPositions, gz, errAbs, verbose=1, mesh=paraMesh)
fig, ax = plt.subplots()
ax.plot(pg.x(sensorPositions), gz, label='gz')
ax.plot(pg.x(sensorPositions), Grav.inv.response(), label='response')
ax.legend()
ax.grid()
ax.set_xlabel('$x$ [m]')
ax.set_ylabel('$\partial u / \partial z$ [mGal]')
plt.show(block=False)
ax.figure.savefig(out, bbox_inches='tight')
return Grav, densBlock
def simulateGravimetry(mesh, dDens):
gravPointsX = np.arange(-19, 19.1, 1)
gravPoints = np.vstack((gravPointsX, np.zeros(len(gravPointsX)))).T
solutionName = createCacheName('grav', mesh, times)
try:
#vel = pg.load(solutionName + '.bmat')
Gdg = np.load(solutionName + '.bmat.npy')
except Exception as e:
print(e)
print("Building .... ")
#Gdg, Gdgz = solveGravimetry(mesh, None, pnts=gravPoints, complete=True)
Gdg = solveGravimetry(mesh, None, pnts=gravPoints)
np.save(solutionName + '.bmat', Gdg)
#dz = Gdg.dot(dDens.transpose([1,0])).T
dz = np.zeros((len(dDens), len(gravPoints)))
for i in range(len(dDens)):
dzerr = np.random.randn(len(gravPoints)) * 0.01
dz[i] = Gdg.dot(dDens[i]) + dzerr
print(Gdg.shape, dDens.shape, dz.shape)
return gravPoints, dz
def simulateGravimetry(mesh, dDens):
gravPointsX = np.arange(-19, 19.1, 1)
gravPoints = np.vstack((gravPointsX, np.zeros(len(gravPointsX)))).T
solutionName = createCacheName('grav', mesh, times)
try:
#vel = pg.load(solutionName + '.bmat')
Gdg = np.load(solutionName + '.bmat.npy')
except Exception as e:
print(e)
print("Building .... ")
#Gdg, Gdgz = solveGravimetry(mesh, None, pnts=gravPoints, complete=True)
Gdg = solveGravimetry(mesh, None, pnts=gravPoints)
np.save(solutionName + '.bmat', Gdg)
#dz = Gdg.dot(dDens.transpose([1,0])).T
dz = np.zeros((len(dDens), len(gravPoints)))
for i in range(len(dDens)):
dzerr = np.random.randn(len(gravPoints)) * 0.01
dz[i] = Gdg.dot(dDens[i]) + dzerr
print(Gdg.shape, dDens.shape, dz.shape)
return gravPoints, dz
def load_grav_pygimli_plate():
# Half plate
thickness = 1
mesh = pg.createGrid(x=np.linspace(0, 5000),
y=[-depth - thickness / 2., -depth + thickness / 2.0])
pg.show(mesh, ax=ax[0, 1])
ga = gradUHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
gza = gradGZHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
g, gz = solveGravimetry(mesh, rho, pnts, complete=True)
plot(x, ax[1, 1], ga, gza, ax[2, 1], g, gz)
labels = ["Horizontal cylinder", "Half plate"]
for ax, label in zip(ax[0], labels):
ax.set_title(label)
ax.set_aspect("equal")
ax.set_xlim(left=x[0], right=x[-1])
ax.set_ylim(bottom=-depth * 2, top=1)
fig.tight_layout()
return g
x = np.arange(-20, 20.1, .5)
pnts = np.array([x, np.zeros(len(x))]).T
###############################################################################
# Analytical solution first
gz_a = gradUCylinderHoriz(pnts, radius, dRho, pos)[:, 1]
###############################################################################
# Integration for a 2D polygon after :cite:`WonBev1987`
circ = createCircle([0, -depth],
radius=radius,
marker=2,
area=0.1,
nSegments=16)
gz_p = solveGravimetry(circ, dRho, pnts, complete=False)
###############################################################################
# Integration for complete 2D mesh after :cite:`WonBev1987`
world = createWorld(start=[-20, 0], end=[20, -10], marker=1)
mesh = createMesh([world, circ])
dRhoC = pg.solver.parseMapToCellArray([[1, 0.0], [2, dRho]], mesh)
gc_m = solveGravimetry(mesh, dRhoC, pnts)
###############################################################################
# Finite Element solution for :math:`u`
world = createWorld(start=[-200, 200], end=[200, -200], marker=1)
# Add some nodes to the measurement points to increase the accuracy a bit
[world.createNode(x_, 0.0, 1) for x_ in x]
plc = world + circ
fig = pg.plt.figure(figsize=(8, 8))
ax = [fig.add_subplot(2, 2, i) for i in range(1, 5)]
# Horizontal cylinder
ga = gradUCylinderHoriz(pnts, radius, rho, pos=pos)
gza = gradGZCylinderHoriz(pnts, radius, rho, pos=pos)
circ = createCircle([0, -depth],
radius=radius,
marker=2,
area=0.1,
segments=32)
g, gz = solveGravimetry(circ, rho, pnts, complete=True)
plot(x, ax[0], ga, gza, ax[1], g, gz)
# Half plate
thickness = 0.1
# mesh = pg.createGrid(x=[-2,2], y=[-2,2], z=[-3,-7])
mesh = pg.createGrid(x=np.linspace(0, 5000, 2),
y=[-depth - thickness / 2.0, -depth + thickness / 2.0])
ga = gradUHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
gza = gradGZHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
g, gz = solveGravimetry(mesh, rho, pnts, complete=True)
a2.set_xlabel('$x$-coordinate [m]')
a2.legend(loc='best')
fig = pg.plt.figure(figsize=(8,8))
ax = [fig.add_subplot(2, 2, i) for i in range(1, 5)]
# Horizontal cylinder
ga = gradUCylinderHoriz(pnts, radius, rho, pos=pos)
gza = gradGZCylinderHoriz(pnts, radius, rho, pos=pos)
circ = createCircle([0, -depth], radius=radius, marker=2, area=0.1,
segments=32)
g, gz = solveGravimetry(circ, rho, pnts, complete=True)
plot(x, ax[0], ga, gza, ax[1], g, gz)
# Half plate
thickness = 0.1
# mesh = pg.createGrid(x=[-2,2], y=[-2,2], z=[-3,-7])
mesh = pg.createGrid(x=np.linspace(0, 5000, 2),
y=[-depth-thickness/2.0, -depth+thickness/2.0])
ga = gradUHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
gza = gradGZHalfPlateHoriz(pnts, thickness, rho, pos=[0, -depth])
g, gz = solveGravimetry(mesh, rho, pnts, complete=True)
depth = 5. # [m]
pos = [0., -depth]
dRho = 100
x = np.arange(-20, 20.1, .5)
pnts = np.array([x, np.zeros(len(x))]).T
###############################################################################
# Analytical solution first
gz_a = gradUCylinderHoriz(pnts, radius, dRho, pos)[:, 1]
###############################################################################
# Integration for a 2D polygon after :cite:`WonBev1987`
circ = createCircle([0, -depth], radius=radius, marker=2, area=0.1,
segments=16)
gz_p = solveGravimetry(circ, dRho, pnts, complete=False)
###############################################################################
# Integration for complete 2D mesh after :cite:`WonBev1987`
world = createWorld(start=[-20, 0], end=[20, -10], marker=1)
mesh = createMesh([world, circ])
dRhoC = pg.solver.parseMapToCellArray([[1, 0.0], [2, dRho]], mesh)
gc_m = solveGravimetry(mesh, dRhoC, pnts)
###############################################################################
# Finite Element solution for :math:`u`
world = createWorld(start=[-200, 200], end=[200, -200], marker=1)
# Add some nodes to the measurement points to increase the accuracy a bit
[world.createNode(x_, 0.0, 1) for x_ in x]
plc = mergePLC([world, circ])
radius = 2 # [m] depth = 5 # [m] x = np.arange(-20, 20.1, 1) pnts = np.array([x, np.zeros(len(x))]).T pos = [0, -depth] dRho = 100 ax1 = pg.plt.subplot(2,1,1) ax2 = pg.plt.subplot(2,1,2) # analytical first ax1.plot(x, gradUCylinderHoriz(pnts, radius, dRho, pos)[:,1], label='Analytical') # polygon circ = createCircle([0, -depth], radius=radius, marker=2, segments=16) ax1.plot(x, solveGravimetry(circ, dRho, pnts, complete=False), label='Poly') # complete cell based mesh world = createWorld(start=[-20, 0], end=[20, -10], marker=1) mesh = createMesh([world, circ]) dRhoC = pg.solver.parseMapToCellArray([[1, 0.0], [2, dRho]], mesh) ax1.plot(x, solveGravimetry(mesh, dRhoC, pnts), label='Mesh') pg.show([world, circ], axes=ax2) # Finite Element way world = createWorld(start=[-200, 200], end=[200, -200], marker=1) # add some nodes to the measurement points to increase accuracy a bit [world.createNode(x_,0.0, 1) for x_ in x] circ = createCircle([0, -depth], radius=radius, area=0.1, marker=2, segments=16)
