Leibniz Institute forApplied Geophysics

Spectral Inversion of SIP field data using pyGIMLi/BERTThomas Günther1, Tina Martin2, Carsten Rücker3

1Leibniz Institute for Applied Geophysics (LIAG), Hannover, Germany; 2Federal Institute for Geosciences and Natural Resources (BGR), Berlin,Germany; 3University of Technology Berlin, Germany

Motivation

No freely available tools for handling SIP dataI (laboratory) spectra: fitting, EM removalI processing large amounts of field dataI testing out different approachesI reproducible scientific workflowsI producing publication-ready figuresExample: slag heap lab and field measurements

Framework pyGIMLi

Geophysical Inversion and Modelling LibraryI free and easy-to-learn language PythonI fast C++ linear algebra kernelI flexible inversion and regularizationI data manager classes for easy scriptingI submodule for SIP spectra (frequency domain)http://www.pygimli.org

pyBERT

Boundless Electrical Resistivity TomographyI efficient triple-grid approach (Günther et al., 2006)I based on finite element calculationI inversion on triangle mesh (Martin&Günther, 2013)I customizable inversion and regularizationI submodule for SIP field data (so far only FD)https://gitlab.com/resistivity-net/bert

Example of spectra handlingfrom pygimli.physics import SIPsip = SIP(‘example.txt’)sip.showData(norm=True, KramersKronig=True)sip.removeEM(epsilon=True)sip.fitColeCole()sip.showAll(savePDF=True)

36.0

36.2

36.4

36.6

36.8

37.0

37.2

ρ [

Ωm

]

a)

measured

corrected

Cole-Cole fit0

5

10

15

20

25

30

-φ [

mra

d]

b)

measured

corrected

Cole-Cole fit

10-2 10-1 100 101 102 103 104 105

f [Hz]

26.9

27.0

27.1

27.2

27.3

27.4

27.5

27.6

27.7

27.8

σ′ [

mS/m

]

c)

corrected

Cole-Cole fit

10-2 10-1 100 101 102 103 104 105

f [Hz]

0.00

0.05

0.10

0.15

0.20

0.25

0.30

σ′′ [

mS/m

]

d)

corrected

Cole-Cole fit

Fig. 1: Example slag-sand mix (Hupfer et al., 2015).

Spectral field data inversion

I no assumption of specific model (e.g.Cole-Cole)I fully-spectral approach: simultaneous inversion of

all frequency data (Günther & Martin, 2016)I constraints along space and frequency axes

Synthetic slag heap model (Günther & Martin, 2016)

0 10 20 30 40x in m

−10

−8

−6

−4

−2

0

z in

m

topsoil

slag1 slag2

bedrock

Region ρ [Ωm] m [mV/V] τ [s] c [-]topsoil 100 0.001 0.001 0.25bedrock 500 0.001 0.001 0.25slag 1 200 0.8 0.1 0.5slag 2 200 0.7 1.0 0.5

Cole-Cole model:

ρ∗ = ρ

[1− m

(1− 1

1 + (ıωτ )c

)]

Fig. 2: Synthetic slag heap model with properties: resistivity ρ,chargeability m, time constant τ and relaxation exponent c.

0 10 20 30 40x in m

8

4

0

f = 156 mHz

0 10 20 30 40x in m

8

4

0

f = 1.25 Hz

8

4

0

f = 10 Hz

8

4

0

f = 80 Hz

100 131 171 224 292 382 500

ρ in Ωm

0 42 83 125 167 208 250

φ in mrad

Fig. 3: Resistivity (left) and phase (right) inversion results.

50

100

200

ρ in Ω

m

P=(12.0,-3.0) r=205 m=0.74, t=0.068 c=0.43P=(23.0,-3.0) r=140 m=0.58, t=0.640 c=0.48P=(30.0,-2.0) r=141 m=0.73, t=2.562 c=0.39

100 101 102 103

f in Hz

0

50

100

150

200

250

φ in m

rad

Fig. 4: Example sprectra fits (points see Fig. 3).

0 10 20 30 4012

10

8

6

4

2

0

m

x in mz in m

0 10 20 30 4012

10

8

6

4

2

0

τ in s

x in mz in m

0 10 20 30 4012

10

8

6

4

2

0

c

x in mz in m

0 0.25 0.50 0.75 1.0

0.030 0.095 0.30 0.95 3.0

0 0.12 0.25 0.38 0.50

Fig. 5: Distribution of fitted Cole-Cole parameters.

SIP field data example: slag heap (Günther & Martin, 2016)

Aim: mineral content in historical slag heapsI dipole-dipole survey with 40 electrodes and a=1 mI SIP256C device, separated current/potential rodsI 14 frequencies f =0.2-1000 Hz⇒ 4.5h meas. time

Fig. 6: Example resistivity (left) and phase (right) spectrum fora single current injection.

Fig. 7: Resistivity (left) and phase (right) pseudosections forthe smallest frequency.

0 10 20 30 40x in m

8

4

0

f = 156 mHz

0 10 20 30 40x in m

8

4

0

f = 312 mHz

8

4

0

f = 625 mHz

8

4

0

f = 1.25 Hz

8

4

0

f = 2.5 Hz

8

4

0

f = 5 Hz

8

4

0

f = 10 Hz

8

4

0

f = 20 Hz

8

4

0

f = 40 Hz

8

4

0

f = 80 Hz

8

4

0

f = 125 Hz

A BC

50 73 108 158 232 341 500

ρ in Ωm

50 100 150 200

φ in mrad

Fig. 8: Inversion result for f ≤125 Hz.

50

100

200

400

800

ρ in Ω

m

A (sim)B (sim)C (sim)

A (ind)B (ind)C (ind)

100 101 102 103

f in Hz

0

50

100

150

200

250

300

φ in m

rad

Fig. 9: Example fits of resistivity(top) & phase (bottom) spectra.

ρ [Ωm] m [-] τ [s] c [-]A ρ 531 0.70 0.89 0.52B ρ 696 0.35 0.15 0.69C ρ 284 0.91 0.70 0.52A φ 0.79 3.72 0.32B φ 0.75 2.35 0.24C φ 0.78 4.51 0.41

0 10 20 30 4012

10

8

6

4

2

0

m

x in mz in m

0 10 20 30 4012

10

8

6

4

2

0

τ in s

x in mz in m

0 10 20 30 4012

10

8

6

4

2

0

c

x in mz in m

0 0.25 0.50 0.75 1.0

0.030 0.095 0.30 0.95 3.0

0 0.12 0.25 0.38 0.50

Fig. 10: Cole-Cole parameter distribution.

I resistive heap with heavilypolarizable slag at the bottom

I m and τ (lower f end) from both ρand φ alone, c less well resolved

I contents ≈10-20% and grainsizes of cm-dm according toresults of Hupfer et al. (2015)

Example script for field datafrom pybert.SIP import SIPdata

sip = SIPdata(’example.res’)sip.generateSpectraPDF(maxdist=20)sip.generateDataPDF(kmax=50000)sip.removeEMTerms(Pelton=True)sip.invertSingleFrequency(f=0.625)sip.invertSimultaneous(maxF=200)sip.fitColeColeModel(show=True)

Conclusions & Outlook

I simultaneous inversion of spectral IP dataI retrieving relevant spectral parameters m, τI easy-to-handle open-source tools pyGIMLi/BERTI continuous improvement and documentationI extension to spectral time-domain IPI help improve and join the community!

ReferencesGünther & Martin (2016): Spectral two-dimensional inversion offrequency-domain induced polarisation data from a mining slag heap. J. ofApplied Geophysics, doi:10.1016/j.jappgeo.2016.01.008.Hupfer et al. (2015): Polarization effects of unconsolidated sulphide-sandmixtures. J. of Applied Geophysics, doi:10.1016/j.jappgeo.2015.12.003.Martin & Günther (2013): Complex Resistivity Tomography (CRT) forfungus detection on standing oak trees. European J. of Forest Research,132(5), 765-776, doi:10.1007/s10342-013-0711-4.Günther et al. (2006): 3-D modeling and inversion of DC resistivity dataincorporating topography - Part II: Inversion. - Geophys. J. Int. 166, 506-517

http://www.liag-hannover.de thomas.guenther@liag-hannover.de

http://www.pygimli.orghttps://gitlab.com/resistivity-net/bert