A tool for designing digital filters for the Hankel and Fourier transforms in potential, diffusive, and wavefield modeling

Werthmüller, D., K. Key, and E. Slob, 2019, A tool for designing digital filters for the Hankel and Fourier transforms in potential, diffusive, and wavefield modeling: Geophysics, 84(2), F47-F56; DOI: 10.1190/geo2018-0069.1.

Manuscript for Geophysics paper

Directory contains the LaTeX source of the manuscript as well as the notebooks to reproduce all the figures.

History

1. First submitted 22/01/2018 to Geophysics for the Software & Algorithms Section. The stable release at the time of submission of empymod was Version 1.5.0 and of empyscripts was Version 0.2.0.

   • Re-submitted 22/02/2018. The stable release at the time of submission of empymod was Version 1.5.0 and of empyscripts was Version 0.3.0. There is no difference in the article between the first and the second submission. In the first submission only the file fdesign.py was submitted as source code to Geophysics. The second submission contains a zip-file with the current version of empymod and empyscripts as well as all the notebooks to reproduce the figures.

   • Re-submitted 12/03/2018. The only difference is that all binary files were replaced by plain ASCII files, due to restrictions by the SEG, and a routine to convert the ASCII files into the binary format was added.

2. Re-submitted 19/06/2018. The stable release at the time of submission of empymod was Version 1.7.1.

3. Final manuscript submitted 21/11/2018. The stable release at the time of submission of empymod was Version 1.8.1.

Instructions to reproduce the figures with the zip-file provided by the SEG

The piece of code related to the publication is fdesign.py, located in the folder notebooks/empymod/scripts in the zip-file or in the folder empymod/scripts on https://github.com/empymod/empymod.

• The zip-file provided by the SEG contains all files required to reproduce the figures of the article.
• Have a look at https://empymod.github.io for the latest version of empymod, further instructions, the manual, and many more examples and information.
• For a maintained version of the figures in the article see https://github.com/empymod/article-fdesign.

Requirements

Required are Python version 3.5 or higher and the modules NumPy and SciPy to use fdesign. To reproduce the figures with the provided notebooks the modules IPython, Jupyter, and matplotlib are required additionally.

If you are new to Python I recommend using a Python distribution, which will ensure that all dependencies are met, specifically properly compiled versions of NumPy and SciPy; I recommend using Anaconda, https://www.anaconda.com.

The required module empymod is included in the provided source code (folder in which this README resides). Have a look at https://empymod.github.io if you want to install the latest version of them.

Reproducing

Start Jupyter and navigate to the notebooks-folder. The notebooks to reproduce the figures in the article are:

1. 01-Figure_InversionCriterium.ipynb: Figure 1.
2. 02-03-04-Figure_ExampleDesign.ipynb: Figures 2, 3, and 4.
3. 05-06-Figure_KongKey.ipynb: Figures 5 and 6.
4. 07-08-Figure_Errors.ipynb: Figures 7 and 8.
5. 09-Figure_GPR.ipynb: Figure 9.
6. 10-11_Figure_GPR-f-t.ipynb: Figures 10 and 11.
7. A-GPR-create-data.ipynb: Creation of data for Figures 9-11 (see comments below).

Some comments regarding A-GPR-create-data.ipynb:

• If you want to reproduce the data for EMmod too, you will have to install EMmod as well (see http://software.seg.org/2015/0001).
• If you want to run the whole file, including the cell for EMmod, the whole script will take likely a day to run.
• The required data-zips are provided in the notebooks/data-directory on https://github.com/empymod/article-fdesign, so you can get them there instead of running A-GPR-create-data.ipynb in order to run 09-Figure_GPR.ipynb and 10-11-Figure_GPR-f-t.ipynb.

Other notebooks in the notebooks-folder:

8. AnalyticalTransformPairs.ipynb: Visual check of all theoretical transform pairs included in fdesign.
9. Errors-AllFilters.ipynb: Check the errors as in Figure 7 but for all filters included in empymod.
10. Example-using-empymod.ipynb: Create a filter using empymod or your own theoretical transform pairs.
11. Filter-wer2001.ipynb: Creation of the 2001 pt filter.
12. Filter-wer201-SineCosine.ipynb: Creation of a 201 pt Fourier filter.
13. Filter-wer201.ipynb: Creation of the 201 pt filter.
14. GPR-RPD.ipynb: Another error plot for the GPR result.

Maintained versions of the notebooks can be found on https://github.com/empymod/article-fdesign.

Note

The final edited version is © Society of Exploration Geophysicists SEG.