EKI_IP

extending EKI_geophysics_2020 to induced polarization. Prepared for paper submission.

Tso, C.-H.M., M. Iglesias, A.Binley (2023) Ensemble Kalman Inversion of Induced Polarization Data. Geophysical Journal International

Code citation: Michael Tso, & Marco Iglesias. (2023). Example scripts for ensemble Kalman inversion of induced polarization data (v1.0.0). Zenodo. https://doi.org/10.5281/zenodo.8256493

In particular, we use the above approach first for DC resistivity, then fixed the mean DC resistivity and invert for phase angles only.

Getting started

Download cR2 here and put cR2.exe in each of the <project> subfolders. You will need to install Wine to run it in a Linux-like system.

You can find each of the subfolders as a self-contained use case.

Use case

Each of these are referred as <project> directories below.

• Surf_IP2: surface synthetic example with 1/2 inclusions, not used in paper
• Surf50m_IP: surface synthetic example with 1/2 inclusions, a longer survey line than the previous case
• 2D_Pow: Pow catchment surface example (from Mejus thesis 2014)
• PRB_iso: 2D cross-borehole for imaging permeable reactive barrier (Slater and Binley 2006 Geophysics), synthetic and field data versions
• Drigg_iso: not used in paper
• arb3layers_IP: 3 layers synthetic model with pinch-out

See more detailed description of each case in the paper. Note some cases have not been included in the paper.

Order of appearance in Paper:

Figure #	folder
2	surf50m_IP
3	arb3layers_IP
4	LS2_arb3layers_IP
5	LS4_arb3layers_IP_separate
6	LS2_arb3layers_uniform
7	LS4_arb3layers_IP
9	2D_Pow_HEC
10	PRBsyn_iso
11	PRB_iso
12	PRBnoise_syn_iso

Unlike the others, Fig. 6 and 7 uses a non-informative prior distribution (i.e. prior ranges of zones overlap).

All examples uses an ensemble size of 300 samples, with the exception of 2D_Pow (100).

All use cases uses 1 level-set function to estimate 2 or 3 zones, unless otherwise specified. LS2* uses two level sets function for the 3 zone problem, while LS4 estimates four zones.

Creating your own use cases

Follow these steps:

1. Make sure you can run the problem in cR2 as forward problem (put it in inv/fwd). ResIPy is a python package that you may find useful
2. Copy the folder to the . Copy minimal input files to /template
3. Double check lines in EKI.m that it is reading the right data files. Add noise if needed.
4. Change prior ranges in Set_Prior*.m

Major difference from the DC resistivity version:

• Not much! except it uses the code cR2 rather than R2 for forward modelling and SCI
• Note that in EKI, we first perform a resistvity-only (fixing phase angles as zeros, because they are small) inversion, and then a separate phase angle-only (fixing resistivity as mean from the previous step) inversion (in constrat to a joint resistivity/phase angle inversion in EKI)

U size of R2 grid

• Un{1,1}=RN; %size(EKI_grid) x 1
• Un{1,2}=L_means; %n_fields x1, tempo = Un{1,2} by the end of Inversion.m
• Un{1,3}=L_per_x; %zeros
• Un{1,4}=L_per_y; %zeros
• Un{1,5}=fields_means; %n_fields x1

physical.m: remove change to take away log conversions for IP

For DC resisitvity, the values are log-transformed. For IP field, we are working with negative phase angles, so we add negative sign in write_R2_sigma.m

Plotting results

• You can simply run plot_tiled.m to plot the EKI resultant images. Note it will need a recent version of MATLAB. Note dialog boxes will pop up to ask you which vtk file to plot. To plot EKI results, you need to choose forward_model.vtk. To plot SCI results, choose inv/f001_res.vtk. Then simply choose the variable to plot.
• You can use plot_prior.m to plot some realizations of the prior model.

plotting (update, because I only had MATLAB R2018)

• The main plotting script is plot_subplots.m, which relies on subplots
• There will be dropdown boxes asking for mesh files for true/SCI/EKI. Note that for the EKI bits, we only care about the mesh and the data is read separately. I think they should be in this order forward_dat.vtk, inv/f001_res.vtk, forward_dat.vtk, forward_dat.vtk
• And then there will be dropdowns for fields to plot in each subplot. You can probably figure out what matches what. Feel free to change the script as you see fit.
• I was originally using plot_tiled.m as my plotting script but I stopped becauses I did not have MATLAB R2019+ at that time. You will probably find it to be easier to use since it supports tiled layout (but you have to adopt it yourself).

Troubleshoot

• solution converge immediately: most likely data used for synthetic generation is used for inversion. Check whether you are using protocol.dat (field data) or cR2_forward.dat (synthetic data) in the get_R2_data() lines in EKI.m
• Solution not updating and/or only 1 sigma_mean value (instead of 2 or 3). Double in cR2.in, num_region=0 and file path is resistivity.dat. Otherwise your updated field is not wirtten!
• Duouble check forward_model.dat. Make sure domain is not cropped in template R2 forward run.
• Make sure <project>/protocol.dat has data and not just survey data (i.e. column 6 and 7 are present). If not, run cp inv/protocol.dat . at <project>.
• Make sure you are in the right <project> directories!
• The line system('wine64 ../../cR2.exe'); in Tools/Inversion.m may need to change to system('wine ../../cR2.exe'); depending on your wine version.
• The codes are developed for Linux/Mac desktops or HPC (see myjob.com for an example job submission script. Modify the MATLAB script accordingly to run on Windows (and you won't need Wine to run cR2.exe if you do so).