3D surface ERT inversion

Inversion of 3D surface ERT field data (the gallery).

We import the used pygimli library and toolboxes for mesh, plot and ERT.

import pygimli as pg
import pygimli.meshtools as mt
from pygimli.physics import ert
from pygimli.viewer import pv

We load the data file from the example repository. It represents a surface ERT array in a 14x9 electrode grid with a spacing of 2.5m (Günther, 2004). Data are measured using the dipole-dipole array in both x and y direction.

data = pg.getExampleData("ert/gallery3d.dat")
data["k"] = ert.geometricFactors(data, dim=3)
print(data)

Data: Sensors: 126 data: 753, nonzero entries: ['a', 'b', 'k', 'm', 'n', 'rhoa', 'valid']

For generating the mesh, we first create a piecewise-linear complex, i.e. the boxes for inversion region and background and mesh it then.

plc = mt.createParaMeshPLC3D(data, paraDepth=12, paraMaxCellSize=1,
                             surfaceMeshQuality=34)
print(plc)
mesh = mt.createMesh(plc, quality=1.3)
print(mesh)

Mesh: Nodes: 596 Cells: 0 Boundaries: 1157
Mesh: Nodes: 8349 Cells: 48320 Boundaries: 97997

We estimate an error using 2% relative error and an absolute error of 100uV at an assumed current of 100mA which is almost zero.

data["err"] = ert.estimateError(data, relativeError=0.02)
mgr = ert.ERTManager(data)
mgr.invert(mesh=mesh, verbose=True)

fop: <pygimli.physics.ert.ertModelling.ERTModelling object at 0x7fa029e3a630>
Data transformation: <pygimli.core._pygimli_.RTransLogLU object at 0x7fa029e3a5e0>
Model transformation: <pygimli.core._pygimli_.RTransLog object at 0x7fa029e3aae0>
min/max (data): 119/488
min/max (error): 2%/2%
min/max (start model): 257/257
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
inv.iter 1 ... chi² = 14.23 (dPhi = 91.71%) lam: 20
--------------------------------------------------------------------------------
inv.iter 2 ... chi² = 3.68 (dPhi = 53.87%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 3 ... chi² = 2.9 (dPhi = 8.39%) lam: 20.0
--------------------------------------------------------------------------------
inv.iter 4 ... chi² = 2.81 (dPhi = 0.58%) lam: 20.0
################################################################################
#                 Abort criteria reached: dPhi = 0.58 (< 2.0%)                 #
################################################################################

24563 [322.1916057678988,...,156.92883065080179]

We visualize the result by a resistivity threshold and a slice using pyVista

pd = mgr.paraDomain
pd["res"] = mgr.model
pl, _ = pg.show(pd, label="res", style="surface", cMap="Spectral_r", hold=True,
                filter={"threshold": dict(value=500, scalars="res")})
pv.drawMesh(pl, pd, label="res", style="surface", cMap="Spectral_r",
            filter={"slice": dict(normal=[-1, 0, 0], origin=[5, 15, -2])})
pl.camera_position = "yz"
pl.camera.azimuth = 20
pl.camera.elevation = 20
pl.camera.zoom(1.2)
_ = pl.show()

References

Günther, T. (2004): Inversion Methods and Resolution Analysis for the 2D/3D Reconstruction of Resistivity Structures from DC Measurements. PhD thesis, University of Mining and Technology, Freiberg, available on http://nbn-resolving.de/urn:nbn:de:swb:105-4152277.