# Four-point sensitivities#

In this example, we illustrate how to visualize the sensitivities of four-point arrays. You can easily loop over the plotting command to create something like: https://www.youtube.com/watch?v=lt1qV-2d5Ps

import numpy as np
import matplotlib.pyplot as plt
import pygimli as pg
import pygimli.meshtools as mt
from pygimli.physics import ert

We start by creating a ERT data container with three four-point arrays.

scheme = pg.DataContainerERT()

nelecs = 10
pos = np.zeros((nelecs, 2))
pos[:, 0] = np.linspace(5, 25, nelecs)
scheme.setSensorPositions(pos)

measurements = np.array((
[0, 3, 6, 9],  # Dipole-Dipole
[0, 9, 3, 6],  # Wenner
[0, 9, 4, 5]   # Schlumberger
))

for i, elec in enumerate("abmn"):
scheme[elec] = measurements[:,i]

scheme["k"] = ert.createGeometricFactors(scheme)

Now we set up a 2D mesh.

world = mt.createWorld(start=[0, 0], end=[30, -10], worldMarker=True)
for pos in scheme.sensorPositions():
world.createNode(pos)

mesh = mt.createMesh(world, area=.05, quality=33, marker=1)

As a last step we invoke the ERT manager and calculate the Jacobian for a homogeneous half-space.

fop = ert.ERTModelling()
fop.setData(scheme)
fop.setMesh(mesh)

model = np.ones(mesh.cellCount())
fop.createJacobian(model)

Final visualization

def getABMN(scheme, idx):
""" Get coordinates of four-point cfg with id `idx` from DataContainerERT
`scheme`."""
coords = {}
for elec in "abmn":
elec_id = int(scheme(elec)[idx])
elec_pos = scheme.sensorPosition(elec_id)
coords[elec] = elec_pos.x(), elec_pos.y()
return coords

def plotABMN(ax, scheme, idx):
""" Visualize four-point configuration on given axes. """
coords = getABMN(scheme, idx)
for elec in coords:
x, y = coords[elec]
if elec in "ab":
color = "red"
else:
color = "blue"
ax.plot(x, y, marker=".", color=color, ms=10)
ax.annotate(elec.upper(), xy=(x, y), ha="center", fontsize=10, bbox=dict(
boxstyle="round", fc=(0.8, 0.8, 0.8), ec=color), xytext=(0, 20),
textcoords='offset points', arrowprops=dict(
arrowstyle="wedge, tail_width=.5", fc=color, ec=color,
patchA=None, alpha=0.75))
ax.plot(coords["a"][0],)

labels = ["Dipole-Dipole", "Wenner", "Schlumberger"]
fig, ax = plt.subplots(scheme.size(), 1, sharex=True, figsize=(6,8))

for i, sens in enumerate(fop.jacobian()):
# Label in lower-left corner
ax[i].text(.01, .15, labels[i], horizontalalignment='left',
verticalalignment='top', transform=ax[i].transAxes, fontsize=12,
fontweight="bold")

# Electrode annotations
plotABMN(ax[i], scheme, i)

# Log-scaled and normalized sensitivity
normsens = pg.utils.logDropTol(sens/mesh.cellSizes(), 8e-4)
normsens /= np.max(normsens)
pg.show(mesh, normsens, cMap="RdGy_r", ax=ax[i], orientation="vertical",
label="Normalized\nsensitivity", nLevs=3, cMin=-1, cMax=1)

fig.tight_layout()

Gallery generated by Sphinx-Gallery