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
import pygimli as pg
from pygimli.meshtools import createCircle, createWorld, createMesh
from pygimli.physics.gravimetry import gradUCylinderHoriz, solveGravimetry
radius = 2. # [m]
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,
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)
linestyle='',
label=r'Won & Bevis: $\frac{\partial^2 u}{\partial z,z}$')
a1.set_xlabel('$x$-coordinate [m]')
a1.set_ylabel(r'$\frac{\partial u}{\partial (x,z)}$ [mGal]')
a1.legend(loc='best')
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
a2.plot(x, gz[:, 2], marker='o', linestyle='',
label=r'Won & Bevis: $\frac{\partial^2 u}{\partial z,z}$')
a1.set_xlabel('$x$-coordinate [m]')
a1.set_ylabel(r'$\frac{\partial u}{\partial (x,z)}$ [mGal]')
a1.legend(loc='best')
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])
import pygimli as pg
from pygimli.meshtools import createCircle, createWorld, createMesh, mergePLC
from pygimli.physics.gravimetry import gradUCylinderHoriz, solveGravimetry
radius = 2. # [m]
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)
###############################################################################
from pygimli.meshtools import * from pygimli.physics.gravimetry import gradUCylinderHoriz, solveGravimetry 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)