ERT field data with topography

Simple example of data measured over a slagdump demonstrating:

• 2D inversion with topography

• geometric factor generation

• topography effect

import pygimli as pg
from pygimli.physics import ert

Get some example data with topography, typically by a call like data = ert.load(“filename.dat”) that supports various file formats

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

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'] = ert.createGeometricFactors(data, numerical=True)

We initialize the ERTManager for further steps and eventually inversion.

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

(<Axes: >, <matplotlib.colorbar.Colorbar object at 0x2acd276d0>)

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.

mgr.checkData(data)
print(data)

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, absoluteUError=5e-5, relativeError=0.03)
# or manually:
# data['err'] = data_errors  # somehow
ert.show(data, data['err']*100)

(<Axes: >, <matplotlib.colorbar.Colorbar object at 0x17f6de620>)

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 = mgr.invert(data, lam=10, verbose=True,
                 paraDX=0.3, paraMaxCellSize=10, paraDepth=20, quality=33.6)

mgr.showResult()

fop: <pygimli.physics.ert.ertModelling.ERTModelling object at 0x17f6fd3a0>
Data transformation: <pygimli.core._pygimli_.RTransLogLU object at 0x17f6fc180>
Model transformation: <pygimli.core._pygimli_.RTransLog object at 0x17f6fd940>
min/max (data): 6.07/33.48
min/max (error): 3.02%/4.11%
min/max (start model): 10.65/10.65
--------------------------------------------------------------------------------
inv.iter 0 ... chi² =  198.15
--------------------------------------------------------------------------------
inv.iter 1 ... chi² =   16.19 (dPhi = 90.28%) lam: 10.0
--------------------------------------------------------------------------------
inv.iter 2 ... chi² =    1.58 (dPhi = 80.45%) lam: 10.0
--------------------------------------------------------------------------------
inv.iter 3 ... chi² =    1.01 (dPhi = 11.84%) lam: 10.0
--------------------------------------------------------------------------------
inv.iter 4 ... chi² =    0.98 (dPhi = 0.53%) lam: 10.0


################################################################################
#                  Abort criterion reached: chi² <= 1 (0.98)                   #
################################################################################

(<Axes: >, <matplotlib.colorbar.Colorbar object at 0x2b811b730>)

We can view the resulting model in the usual way.

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

<Figure size 1100x600 with 6 Axes>

Or just plot the model only using your own options.

mgr.showResult(mod, cMin=5, cMax=30, cMap="Spectral_r", logScale=True)

(<Axes: >, <matplotlib.colorbar.Colorbar object at 0x2bc14c5b0>)