ERT field data with topography

Simple example of data measured over a slagdump demonstrating:

• 2D inversion with topography

• geometric factor generation

• topography effect

import numpy as np
import pygimli as pg

from pygimli.physics.ert import ERTManager, createGeometricFactors

Get some example data with topography

data = pg.getExampleFile('ert/slagdump.ohm', load=True, verbose=True)
print(data)

Out:

/tmp/gimli-org/example-data/ert/slagdump.ohm
Data: Sensors: 38 data: 222, nonzero entries: ['a', 'b', 'm', 'n', 'r', 'valid']

The data file does not contain geometric factors (token field ‘k’), so we create them based on the given topography.

data['k'] = createGeometricFactors(data, numerical=True)

We initialize the ERTManager for further steps and eventually inversion.

ert = ERTManager(sr=False, useBert=True, verbose=True, debug=False)

It might be interesting to see the topography effect, i.e the ratio between the numerically computed geometry factor and the analytical formula

k0 = createGeometricFactors(data)
ert.showData(data, vals=k0/data['k'], label='Topography effect')

Out:

((<matplotlib.axes._subplots.AxesSubplot object at 0x7f988a8b5940>, <matplotlib.colorbar.Colorbar object at 0x7f988a687cc0>), None)

The data container has no apparent resistivities (token field ‘rhoa’) yet. We can let the Manager fix this later for us (as we now have the ‘k’ field), or we do it manually.

ert.checkData(data)
print(data)

Out:

Data: Sensors: 38 data: 222, nonzero entries: ['a', 'b', 'k', 'm', 'n', 'r', 'rhoa', 'valid']

The data container does not necessarily contain data errors data errors (token field ‘err’), requiring us to enter data errors. We can let the manager guess some defaults for us automaticly or set them manually

data['err'] = ert.estimateError(data, absoluteError=0.001, relativeError=0.03)
# or manually:
# data['err'] = data_errors  # somehow

Now the data have all necessary fields (‘rhoa’, ‘err’ and ‘k’) so we can run the inversion. The inversion mesh will be created with some optional values for the parametric mesh generation.

mod = ert.invert(data, lam=10,
                 paraDX=0.3, paraMaxCellSize=10, paraDepth=20, quality=33.6)

Out:

fop: <pygimli.physics.ert.ert.ERTModelling object at 0x7f98b60330a0>
Data transformation: <pygimli.core._pygimli_.RTransLogLU object at 0x7f98b6a541f0>
Model transformation: <pygimli.core._pygimli_.RTransLog object at 0x7f98b6a54110>
min/max (data): 6.07/33.48
min/max (error): 3.00%/3.02%
min/max (start model): 10.65/10.65
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
inv.iter 2 ... chi² = 1.79 (dPhi = 81.55%) lam: 10.0
--------------------------------------------------------------------------------
inv.iter 3 ... chi² = 1.15 (dPhi = 13.02%) lam: 10.0
--------------------------------------------------------------------------------
inv.iter 4 ... chi² = 1.11 (dPhi = 0.68%) lam: 10.0
################################################################################
#                 Abort criteria reached: dPhi = 0.68 (< 2.0%)                 #
################################################################################

We can view the resulting model in the usual way.

ert.showResultAndFit()
# np.testing.assert_approx_equal(ert.inv.chi2(), 1.10883, significant=3)

Out:

<Figure size 640x480 with 6 Axes>

Or just plot the model only.

ert.showModel(mod)

Out:

(<matplotlib.axes._subplots.AxesSubplot object at 0x7f98b517af28>, <matplotlib.colorbar.Colorbar object at 0x7f98b6df4470>)