Note
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A single-frequency inversion (CR container)ΒΆ
Full processing of one frequency of one timestep of the data from Weigand and Kemna 2017 (Biogeosciences).
This example uses the CR container to load single-frequency data from a CRTomo-style volt.dat file.
imports
import os
import numpy as np
import crtomo
import reda
import reda.utils.geometric_factors as geom_facs
from reda.utils.fix_sign_with_K import fix_sign_with_K
import reda.importers.eit_fzj as eit_fzj
define an output directory for all files
output_directory = 'output_single_freq_inversion_CR'
cr = reda.CR()
cr.import_crtomo_data('data/volt.dat')
# this is a container measurement, we need to compute geometric factors using
# numerical modeling
# Note that this only works if CRMod is available
settings = {
'rho': 100,
'elem': 'data/elem.dat',
'elec': 'data/elec.dat',
'sink_node': '6467',
'2D': True,
}
k = geom_facs.compute_K_numerical(cr.data, settings)
cr.data = geom_facs.apply_K(cr.data, k)
fix_sign_with_K(cr.data)
print(cr.data.iloc[0:5])
SETTINGS
{'rho': 100, 'elem': 'data/elem.dat', 'elec': 'data/elec.dat', 'sink_node': '6467', '2D': True}
2D modeling
a b m n ... k rho_a sigma_a rho_a_complex
0 1 2 21 20 ... 9061.232484 46.166980 0.021661 40.270914+ 22.575286j
1 1 27 30 28 ... 1.529047 1282.753055 0.000780 1282.753033- 0.235647j
2 1 27 31 29 ... 1.596560 1298.674366 0.000770 1298.674241- 0.569899j
3 1 27 32 28 ... 0.689674 1336.160025 0.000748 1336.159970- 0.383912j
4 1 27 32 30 ... 1.256348 1380.042077 0.000725 1380.041984- 0.505736j
[5 rows x 15 columns]
apply correction factors, as described in Weigand and Kemna, 2017 BG
corr_facs_nor = np.loadtxt('data/corr_fac_avg_nor.dat')
corr_facs_rec = np.loadtxt('data/corr_fac_avg_rec.dat')
corr_facs = np.vstack((corr_facs_nor, corr_facs_rec))
cr.data, cfacs = eit_fzj.apply_correction_factors(cr.data, corr_facs)
apply some filters import IPython IPython.embed()
cr.filter('r < 0')
cr.filter('rho_a < 15 or rho_a > 35')
cr.filter('rpha < - 40 or rpha > 3')
cr.filter('rphadiff < -5 or rphadiff > 5')
cr.filter('k > 400')
cr.filter('rho_a < 0')
cr.filter('a == 12 or b == 12 or m == 12 or n == 12')
cr.filter('a == 13 or b == 13 or m == 13 or n == 13')
# NOTE: this is also a single-frequency filtering,
cr.print_data_journal()
cr.print_log()
--- Data Journal Start ---
2026-06-04 12:42:17.966710
A filter was applied with query "r < 0". In total 15 records were removed
A filter was applied with query "rho_a < 15 or rho_a > 35". In total 394 records were removed
A filter was applied with query "rpha < - 40 or rpha > 3". In total 159 records were removed
A filter was applied with query "rphadiff < -5 or rphadiff > 5". In total 82 records were removed
A filter was applied with query "k > 400". In total 224 records were removed
A filter was applied with query "rho_a < 0". In total 0 records were removed
A filter was applied with query "a == 12 or b == 12 or m == 12 or n == 12". In total 36 records were removed
A filter was applied with query "a == 13 or b == 13 or m == 13 or n == 13". In total 33 records were removed
--- Data Journal End ---
2026-06-04 12:42:17,486 - reda.containers.BaseContainer - INFO - Data sized changed from 1925 to 1910
2026-06-04 12:42:17,577 - reda.containers.BaseContainer - INFO - Data sized changed from 1910 to 1516
2026-06-04 12:42:17,649 - reda.containers.BaseContainer - INFO - Data sized changed from 1516 to 1357
2026-06-04 12:42:17,713 - reda.containers.BaseContainer - INFO - Data sized changed from 1357 to 1275
2026-06-04 12:42:17,773 - reda.containers.BaseContainer - INFO - Data sized changed from 1275 to 1051
2026-06-04 12:42:17,823 - reda.containers.BaseContainer - INFO - Data sized changed from 1051 to 1051
2026-06-04 12:42:17,873 - reda.containers.BaseContainer - INFO - Data sized changed from 1051 to 1015
2026-06-04 12:42:17,921 - reda.containers.BaseContainer - INFO - Data sized changed from 1015 to 982
export to volt.dat file note that this is not required for the subsequent code
with reda.CreateEnterDirectory(output_directory):
cr.export_crtomo('volt.dat', 'nor')
alternatively: directly create a tdman object that represents a single-frequency inversion with CRTomo
grid = crtomo.crt_grid('data/elem.dat', 'data/elec.dat')
tdman = cr.export_to_crtomo_td_manager(grid, norrec='nor')
# set inversion settings
tdman.crtomo_cfg['robust_inv'] = 'F'
tdman.crtomo_cfg['mag_abs'] = 0.012
tdman.crtomo_cfg['mag_rel'] = 0.5
tdman.crtomo_cfg['hom_bg'] = 'T'
tdman.crtomo_cfg['d2_5'] = 0
tdman.crtomo_cfg['fic_sink'] = 'T'
tdman.crtomo_cfg['fic_sink_node'] = 6467
# run the inversion, use the given output directory to store the CRTomo
# directory structure for later use
# only invert if the output directory does not exists
outdir = '{}/tomodir_inversion'.format(output_directory)
if not os.path.isdir(outdir):
tdman.invert(
catch_output=False,
output_directory=outdir,
)
else:
tdman.read_inversion_results(outdir)
print('Statistics of last iteration:')
print(tdman.inv_stats.iloc[-1])
This grid was sorted using CutMcK. The nodes were resorted!
Rectangular grid found
Attempting inversion in directory: output_single_freq_inversion_CR/tomodir_inversion
Using binary: /usr/bin/CRTomo_dev
Calling CRTomo
b' ######### CRTomo ############\nLicence:\nCopyright \xc2\xa9 1990-2017 Andreas Kemna <kemna@geo.uni-bonn.de>\nCopyright \xc2\xa9 2008-2017 CRTomo development team (see AUTHORS file)\nPermission is hereby granted, free of charge, to any person obtaining a copy of\nthis software and associated documentation files (the \xe2\x80\x9cSoftware\xe2\x80\x9d), to deal in\nthe Software without restriction, including without limitation the rights to\nuse, copy, modify, merge, publish, distribute, sublicense, and/or sell copies\nof the Software, and to permit persons to whom the Software is furnished to do\nso, subject to the following conditions:\n\nThe above copyright notice and this permission notice shall be included in all\ncopies or substantial portions of the Software.\n\nTHE SOFTWARE IS PROVIDED \xe2\x80\x9cAS IS\xe2\x80\x9d, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\nIMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\nFITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE\nAUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\nLIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\nOUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE\nSOFTWARE.\n \n \n Process_ID :: 5386\n OpenMP max threads: 2\n Version control of binary:\n Git-Branch master\n Commit-ID cb89ccd2c4341b9b08bbe7bb08f5aea0d60916ee\n Created Mon-Mar-25-14:34:56-2024\n Compiler \n OS GNU/Linux\n\nOS identification: Linux-OS\n writing inversion results into ../inv\n ## using complex error ellipses ##\n++ check 1\r++ check 2 done!\n\nFictious sink @ node 6467 31.000 -53.000\n\n + Taking error model\n\n+++ Found no presettings for lambda_0 (default)\n\n Saving lamba presettings -> crt.lamnull\n\n++ (CRI) Setting complex error ellipse\n\n\n\n2D without Dirichlet nodes setting k=1e-6\n OpenMP threads: 2( 2)\n\r \r Iteration 0, 0 : Calculating Potentials++ Starting Fit 68.04 \n\n\n\rWRITING STARTING MODEL\n\n\r \r Iteration 1, 0 : Calculating Sensitivities\nRegularization:: Triangular smooth\n C_m^ calculation time 0d/ 0h/ 0m/ 0s/ 0ms\n\r Iteration 1, 1 : Calculating 1st regularization parameter \r found lam_0 1536. \nlam_0:: 0.15E+04\r \r Iteration 1, 1 : Updating\r \r Iteration 1, 1 : Calculating Potentials -- Update Fit 1.168 \r \r Iteration 1, 2 : Updating\r \r Iteration 1, 2 : Calculating Potentials -- Update Fit 1.159 \r \r Iteration 1, 3 : Updating\r \r Iteration 1, 3 : Calculating Potentials -- Update Fit 1.134 \r \r Iteration 1, 4 : Updating\r \r Iteration 1, 4 : Calculating Potentials -- Update Fit 1.160 \r \r Iteration 1, 5 : Updating\r \r Iteration 1, 5 : Calculating Potentials -- Update Fit 34.06 \r \r Iteration 1, 5 : Updating\r \r Iteration 1, 5 : Calculating Potentials ++ Actual Fit 1.134 \n\n+++ Convergence check (CHI (old/new)) -5903. %\n\n\r \r Iteration 2, 0 : Calculating Sensitivities\r \r Iteration 2, 0 : Updating\r \r Iteration 2, 0 : Calculating Potentials -- Update Fit 0.9791 \r \r Iteration 2, 1 : Updating\r \r Iteration 2, 1 : Calculating Potentials -- Update Fit 1.000 \r \r Iteration 2, 2 : Updating\r \r Iteration 2, 2 : Calculating Potentials -- Update Fit 0.9879 \r \r Iteration 2, 3 : Updating\r \r Iteration 2, 3 : Calculating Potentials -- Update Fit 1.022 \r \r Iteration 2, 3 : Updating\r \r Iteration 2, 3 : Calculating Potentials ++ Actual Fit 1.000 \n\n+++ Convergence check (CHI (old/new)) -13.31 %\n\n\rMODEL ESTIMATE AFTER 2 ITERATIONS \n Iteration terminated: Min. CHI.\n CPU time: 0d/ 0h/ 1m/ 59s/ 38ms\n ***finished***\nNote: The following floating-point exceptions are signalling: IEEE_DIVIDE_BY_ZERO\nSTOP 0\n'
Inversion attempt finished
Attempting to import the results
Reading inversion results
is robust False
Info: res_m.diag not found: output_single_freq_inversion_CR/tomodir_inversion/inv/res_m.diag
/home/runner/work/crtomo_tools/crtomo_tools/examples/02_simple_inversion
Info: ata.diag not found: output_single_freq_inversion_CR/tomodir_inversion/inv/ata.diag
/home/runner/work/crtomo_tools/crtomo_tools/examples/02_simple_inversion
Statistics of last iteration:
iteration 2
main_iteration 2
it_type DC/IP
type main
dataRMS 1.0
magRMS 1.0
phaRMS 0.0
lambda 476.2
roughness 0.4061
cgsteps 62.0
nrdata 477.0
steplength 0.0
stepsize 61.68
l1ratio NaN
Name: 11, dtype: object
evolution of the inversion
fig = tdman.plot_inversion_evolution()
with reda.CreateEnterDirectory(output_directory):
fig.savefig('inversion_evolution.png')
# the statistics are stored in a data frame
print(tdman.inv_stats)
print(tdman.inv_stats.columns)
#############################
0
Empty DataFrame
Columns: [iteration, main_iteration, it_type, type, dataRMS, magRMS, phaRMS, lambda, roughness, cgsteps, nrdata, steplength, stepsize, l1ratio]
Index: []
#############################
1
iteration main_iteration it_type ... steplength stepsize l1ratio
1 1 1 DC/IP ... 1.0 7440.0 NaN
2 2 1 DC/IP ... 1.0 7370.0 NaN
3 3 1 DC/IP ... 1.0 7290.0 NaN
4 4 1 DC/IP ... 1.0 7200.0 NaN
5 5 1 DC/IP ... 0.5 3650.0 NaN
[5 rows x 14 columns]
#############################
2
iteration main_iteration it_type ... steplength stepsize l1ratio
7 0 2 DC/IP ... 1.0 61.0 NaN
8 1 2 DC/IP ... 1.0 61.7 NaN
9 2 2 DC/IP ... 1.0 61.3 NaN
10 3 2 DC/IP ... 0.5 30.8 NaN
[4 rows x 14 columns]
iteration main_iteration it_type ... steplength stepsize l1ratio
0 0 0 DC/IP ... NaN NaN NaN
1 1 1 DC/IP ... 1.0 7440.00 NaN
2 2 1 DC/IP ... 1.0 7370.00 NaN
3 3 1 DC/IP ... 1.0 7290.00 NaN
4 4 1 DC/IP ... 1.0 7200.00 NaN
5 5 1 DC/IP ... 0.5 3650.00 NaN
6 1 1 DC/IP ... 3.0 7293.00 NaN
7 0 2 DC/IP ... 1.0 61.00 NaN
8 1 2 DC/IP ... 1.0 61.70 NaN
9 2 2 DC/IP ... 1.0 61.30 NaN
10 3 2 DC/IP ... 0.5 30.80 NaN
11 2 2 DC/IP ... 0.0 61.68 NaN
[12 rows x 14 columns]
Index(['iteration', 'main_iteration', 'it_type', 'type', 'dataRMS', 'magRMS',
'phaRMS', 'lambda', 'roughness', 'cgsteps', 'nrdata', 'steplength',
'stepsize', 'l1ratio'],
dtype='object')
evolution of data misfits
fig = tdman.plot_eps_data()
fig = tdman.plot_eps_data_hist()
# eps data is found here:
tdman.eps_data
r = tdman.plot.plot_elements_to_ax(
tdman.a['inversion']['rmag'][-1],
plot_colorbar=True,
cmap_name='jet_r',
)
with reda.CreateEnterDirectory(output_directory):
r[0].savefig('rmag.png', bbox_inches='tight')
r = tdman.plot.plot_elements_to_ax(
tdman.a['inversion']['rpha'][-1],
plot_colorbar=True,
cmap_name='jet_r',
)
with reda.CreateEnterDirectory(output_directory):
r[0].savefig('rpha_last_it.png', bbox_inches='tight')
Total running time of the script: (2 minutes 3.811 seconds)