1. Development of crosshole GPR data full-waveform inversion and a real data test at the Boise Hydrogeophysics Research Site
Good morning and thank you for the introduction of my talk. Welcome to my presentation about the…
X. Yang, A. Klotzsche, G.A. Meles,
H. Vereecken, J. van der Kruk

2. Application to real Data – Boise: Overview
The survey was conducted at the Boise Hydrogeophysical Research Site in the US. The area is about 9 by 16 meters large and dominated by water-saturated braided river deposits. 40 transmitters are located in the left and 311 receivers in the right borehole. The table shows some parameter of the GPR setup. (a) The location of BHRS is close to the Boise River. The red box indicates the location point of the boreholes, where C5 and C6 (red line) are used for the crosshole GPR profile. (b) A simplified acquisition setup of the experimental data set acquired at the BHRS. Transmitter and receiver locations are indicated by TRN with crosses and REC with circles, respectively. The unit boundaries (dashed red lines) were determined based on borehole porosity logs. (Adapted from Ernst et al. (2007b))
(NEXT)
A noise-filtered and windowed radar section for the central receiver and every third transmitter is shown to the right…
Although 311 receivers were used to measure the data, initial inversion [6] only used 77 receiver locations.
The traces are much more complicated at least partially due to the water-filled boreholes -> I therefore use a longer source wavelet to try to compensate these effects. In any case it may be hard to reconstruct these traces with what ever approach I choose… (NEXT) DISCUSSS!!!!!!!!!!!!!!!

3. Comparison of inversion results
77 receivers
311 receivers
(a)
(c)
(e)
(g)
(i)
(b)
(d)
(f)
(h)
(j)
(a, b) show the eps and sig ray-based tomography results, respectively. Scalar, vector, simultaneous and dense simultaneous and FWI inversion results are shown in (c, d; e, f; g, h and i, j), respectively. Transmitter and receivers are indicated by crosses and circles, respectively. Note that, the ray-based results are used as the start model of the FWI methods and the logarithmical scale of the conductivity images.

4. Comparison of normalized gradients
77 receivers
311 receivers
(a)
(c)
(e)
(g)
(i)
(b)
(d)
(f)
(h)
(j)
We introduce here normalized permittivity and conductivity gradients by dividing with the number of sources times the number of receivers. The new normalization of the gradients enable the comparison between different source-receiver setups and more general perturbation factors. (a, b) show the and remain gradients obtained by the ray-based tomography, respectively. Scalar, vector, simultaneous and dense simultaneous and remain gradients obtained by the FWI at the last iteration shown in (c, d; e, f; g, h and i, j), respectively. Note that, (a, b) show the gradient for the permittivity and conductivity, respectively, after one iteration of the FWI to illustrate the misfit between the ray-based inversion result and the observed data. Transmitter and receivers are indicated by crosses and circles, respectively.

5. (a) shows the observed GPR data
(a) shows the observed GPR data. (b) shows the synthetic data based on ray-based tomography results which are shown in Fig. 3 (a, b). (c) shows the synthetic data based on scalar FWI results which are shown in Fig. 3 (c, d). (d) shows the synthetic data based on dense simultaneous FWI results which are shown in Fig. 3 (i, j) with their true amplitude. Note that only 9 transmitters were chosen with equal intervals from the 40 transmitters.

6. Compare with porosity log data
Permittivity dense simultaneous FWI result at the last iteration number, which taking samples close to the borehole C5 and C6 (indicated by the dashed white lines) converted to porosity value were compared to Neutron-Neutron porosity log data acquired in borehole C5 and C6.

7. Compare with conductivity log data
Conductivity dense simultaneous FWI result at the last iteration number, which taking samples close to the borehole C5 and C6 (indicated by the dashed black lines) compared to capacitive conductivity log data acquired in borehole C5 and C6. Note the logarithmic conductivity scale for FWI result and the different scaling of the lower and upper horizontal axes for the logging data and FWI results.

8. Conclusion This work give a overview of FWI.
It is important to include the vector character of electromagnetic wave and to use a simultaneous update scheme
New normalized gradients been introduced which do not depend on the number of sources and receivers and enable more general perturbation factors.
The inversion results have been compared with logging data.
A simple wavenumber filter has been estimated.

9. Full-waveform inversion of GPR data in
frequency-domain
Good morning and thank you for the introduction of my talk. Welcome to my presentation about the…
X. Yang, J. van der Kruk, J. Bikowski, P. Kumbhar, H. Vereecken, G.A. Meles

10. Frequency domain full-waveform inversion
Forward
Use frequency-domain finite-difference (FDFD) method.
Use MPI and MUMPS to get a parallel version code and can directly run on the supercomputer.
Inversion
Use Gauss-Newton method which means we need to calculate approximate Hessian matrix.
Use parabolic approach to get the optimized step length.
We are already have the frequency domain FWI code. The forward part use FDFD method which is very mature and stable. We also parallel the code use MPI technique and use direct solver to let the code working on our supercomputer in Juelich. For the inversion part we use Gauss-Newton method which means we need to calculate approximate Hessian matrix. And we also use parabolic approach to get the optimized step length. Comparing to time domain FWI use these technique making the inversion more efficiency.

11. Full waveform inversion of two small pipes
Time domain
Frequency domain
Gradient approach
Conjugate gradient
Gauss-Newton
Steplength Calculation
Linear
Parabolic
Number forward model cells
290
467
Cell size (m)
0.04
0.033
Time/frequency sampling
Time sampling: 85 ps using 2355 timesteps
7 frequencies:
150, 200, 250, 300, 350, 400, 450 MHz.
Forward model calculation time for all times/frequencies
22.5 s
24 s
Here is a table show the detail of the different between two methods. I will give the first synthetic model to compare them.

12. Full waveform inversion of two small pipes

13. Full waveform inversion of two small pipes

14. Full waveform inversion of two small pipes

15. Full waveform inversion of two small pipes

16. Full waveform inversion of two small pipes
Time domain FWI
Frequency domain FWI
CPU Time
56 min
24.5 min
Memory
400MB
1GB
Number of Iterations 40
10 per frequency
Start value Cost function
6.4e-7
2.3e-13
Final value Cost function
3.8e-8
1.7e-18
Forward calculation times needed per iteration 4 6
Total forward models calculations
160 60

17. Preliminary results for two crosses with high contrast

18. Preliminary results for two crosses with high contrast

19. Preliminary results for two crosses with high contrast
(TE mode)

20. Preliminary results for two crosses with high contrast
(TE mode)
(TM mode)

21. Summary
Achieve full waveform inversion in frequency domain and got preliminary results.
Vectorial full wave field
Gauss-Newton method
Compared with time domain FWI frequency domain FWI has several advantages.
Select optimum frequencies
faster
Use different cost functions (e.g. log)
Disadvantage
Large memory requirement

22. Thank you for your attention!