Usage

The fdip package holds some functions for importing, modelling and inverting tomographic spectral IP data measured in the frequency domain, based upon pyGIMLi. Single-frequency modelling and inversion is completely included in pyGIMLi, so this repository adds up for exploiting the spectral information.

Main entry is the class FDIP, to be imported by

from fdip import FDIP

It can be initialized empty or directly with a data file

pro = TDIP("datafile.ohm")

Valid formats are:

• ERT scheme set accompagnied by .RHOA/.PHIA files
• Radic RES file from SIP256C or D
• MPT DAS-1
• single files holding individual frequencies

You can also create an empty instance and use pro.load(filename).

As a result, the instance holds an ERT data file pro.dataand matrices of apparent resistivity pro.RHOA) and phase ( pro.PHIA).

You can add other files by pro.addData(filename)

If electrode positions (e.g. elevations) are not contained in the data file, they can be specified by FDIP(..., electrodes=) or set by p2.setElectrodePositions(xh). Both triggers a numerical computation of geometric factors and recomputation of apparent resistivity.

Preprocessing

Most important preprocessing tool is pro.filter(). It works either along the data sequence axis (like data.remove()) or along the time axis and removes complete data (including all gates) or gates (for all data). Important keywords are

nr=[], # list of numbers
fmin=0, fmax=1e9, # minimum/maximum frequency
kmax=1e6, # maximum geometric factor
forward=False, # keep only forward measurements
electrode=None, ab=None, mn=None, # electrodes (combinations)

If you don't want to remove the whole data point, but only disregard some erroneous data (like outliers), you can mask these using .mask() with the keywords

rhomin=0, rhomax=9e99, # min/max app res.
phimin=-9e99, phimax=9e99 # min/max app. phase

You can also mask the whole decay by filter(..., mask=True) in order to not to loose the apparent resistivity information.

The function .removeEpsilon() tries to get rid of high-frequency effects by fitting a constant permittivity (imaginary part proportional to f) to the highest frequency data.

Synthetic modelling

You can generate synthetic data assuming a Cole-Cole model by using

pro.simulate(mesh, rhovec, mvec, tauvec, cvec)

where rhovec, mvec, tauvec, cvec are vectors pointing into the different regions of the mesh. See notebook on synthetic modelling in example directory.

Visualization

.showDataSpectrum() shows the spectra for specific electrode combinations. .generateSpectraPDF() generates a multi-page PDF of frequency spectra, one for every AB combination, so that you can get an overview on the spectral behaviour. A single spectrum can be obtained by .getDataSpectrum() providing a SIPSpectrum instance from the pygimli.physics.SIP module.

All data for a specific frequency can be shown by .showSingleFrequencyData specifying a number (int) or a frequency (float). You can also show the data of all frequencies at the same time by .showAllFrequencyData. A bit more overview is obtained by putting these into a multi-page pdf using .generateDataPDF() and browse through the frequencies.

Inversion

Data for a single frequency can be obtained by pro.singleFrequencyData(), also specifying either the number or a value. This can then be treated with the ERTIPManager of pyGIMLi's ERT module, completely independent of FDIP. However, you can also do the same with pro.singleInversion(). This triggers an ERTIPManager, to which you can pass all options.

pro.showSingleResult shows the result of this inversion.

To invert all frequencies sequentially, use pro.individualInversion(), The better option is to invert them simultaneously by pro.simultaneousInversion(), which in turn calls pro.simultaneousRestivityInversion() and pro.simultaneousPhaseInversion() (the latter will be replaced by a fully complex constrained inversion). Class instances can be accessed by pro.ERT, pro.invIP

There is also a special inversion into Debye models for every cell using pro.invertDebye() which treats everything in the Debye (exponential Decay) space.

Postprocessing

As a result of apparent chargeability inversion, you have a matrix of resistivities pro.RES and phases pro.PHI for every model cell, matching the inversion mesh pro.pd.

.showModelSpectrum() plots the inverted spectrum for a certain position (and showModelSpectra for a list of them), whereas .getModelSpectrum() returns a pyGIMLi SIP Spectrum class instance which then can be further analysed.

.fitAllRhoPhi() fits both resistivity and phase, whereas .fitAllPhi() fits only phases

As a result, you obtain a Cole-Cole model for every cell, whose parameter can be show with showColeColeParameters. After inversion, you can save the results by saveResults() and load them later by loadResults(), so that you can do postprocessing independent of inversion by

pro = FDIP(filename)
pro.loadResults()
...

saveFigures() saves all created figures under a filename consisting of the data file and the type of the figure.

Working in 3D

While visualization is designed for 2D profiles, numerical computations should work in 3D as well, provided a 3D mesh is created for the ERT manager.

Conversion to TD

convertToTD() converts the whole data set to a time-domain instance TDIP through Debye decomposition (package TDIP required).