Hi Luigi,
It takes a little while but my answer won't be so short.
Old release 2.5.0
First, I try with 2.5.0, an old one, even older than yours. Effectively the minimum misfit that I reach is around 0.8, lower than what you got with 3.3.4. But... if you look at the fit of the dispersion curve it is rather bad (
fig_250-01.png).
If you look into the log of each run, you may see a lot of warnings of this type:
Code: Select all
** Warning ** : probably a missing peak, bad initial sampling
This warning is issued when computing a theoretical ellipticity peak, if the obtained peak is outside the user frequency range. The frequency sampling and its range is defined by merging all samples from all target curves (dispersion and eventually ellipticity). For efficiency, it is better to have the same sample set for all curves: computing an ellipticity value requires the Rayleigh dispersion value at the same frequency. Before running anything it is always better to resample all curves in the same way (e.g. 50 samples on a log scale). If a curve is not available over the complete range, invalid samples are added, these frequencies will not be considered for the misfit computation. When including the peak frequency in the target list, you have to add extra samples at low frequency. For instance, if the dispersion curve is available from 2 to 20 Hz and the observed peak is at 1 Hz, you have to resample from at least 0.5 Hz. If deep ground structures are produced by the parameterization, the warning may still appear. In your case I resample everything from 0.1 to 25 Hz with 50 log samples. The warning is visible a few times at the beginning and then disappears as long as the inversion focuses on the area of interest.
I could see that you generated 300 models using Monte-Carlo before starting NA. This is not really useful and only a few is necessary. I'm used to 50 random models to initiate the inversion process.
Release 3.3.5
If I create a new run with your exact target and parameterization, I get a minimum misfit of 9.47 after 10000 models, which is a very high misfit. If I resample the targets as specified here above, I get a minimum misfit of 2.40, which is a little better but not that good.
fig_335-01.png shows that the ellipticity target appears only on the signed ellipticity plot. If the ellipticity curves comes from a single station processing, it is only an absolute value of the ellipticity and the sign is unknown. In this case we add extra data that the ellipticity is positive which is probably false.
The next step is to set the correct type to the ellipticity curve. In
fig_335-02.png, you have to change "Signed" to "Absolute". The misfit drops to 0.85 and the results are shown in
fig_335-03.png. There is a strange feature around the ellipticity peak.
fig_335_04.png shows the signed and absolute values of the ellipticity for the best model, zoomed around the peak. The signed curve must be smooth. The absolute ellipticity on a log scale may have singular points produced by the absolute value. The values between 0.9 and 1 Hz are the plain ellipticity values instead of the angular ellipticity. atan(-1.1)=-47.7 deg, the correct angular ellipticity at that frequency. That's a bug encountered while inverting for the peak frequency. This artefact disappears if the peak frequency is deactivated in the target list. Refined values computed for getting the exact peak frequency are not properly transformed to angular ellipticity. This is now fixed for the next releases (3.3.6-preview under preparation).
Release 3.3.6-preview
The same inversion is now restarted with a fix for the above ellipticity bug. The best misfit is 0.95 after 10000 models. I did not try to improve it by running any further.
fig_336-01.png shows the results. The ellipticity curve is rather well matched and the peak is at 1 Hz as expected, but the dispersion curve is absolutely not recovered. This tends to be closer to what we obtained with 2.5.0.
The dispersion curve has no standard deviation while it is the case for other sub-targets. When there is no uncertainty estimation on a curve, the misfit is computed using relative values (slowness difference normalized by the experimental slowness). Hence a misfit of 0.1 is an average adjustment at 10%. I suggest here to manually add a 10% uncertainty on the dispersion curve. In the curve table, select all valid rows (the entire row by clicking on the row numbers), modify Stddev column to 1.1. Modification in one cell applies to the whole selection after pressing "Enter". The misfit now drops to 0.78 (see
fig_336-02.png). It gets better and even it starts to be acceptable. By adding uncertainties, we change the way misfit is normalized (by stddev instead experimental slowness) and it gives more weight to the dispersion sub-target compared to the previous cases.
We can see for the Vs profiles close to the surface that collection of models directly starts with the best ones. The distribution looks like sharply cut at 150 m/s. This limit comes from the parameterization itself. Before proceeding to other tries, we must set the lower limits to something more adequate. Effectively, the minimum phase velocity is at 146 m/s, Vs can be lower. Initial tries must leave parameters with the largest possible range. Let's move all Vs minima to 50 m/s (even in the half-space).
I obtained a minimum misfit of 0.8 after 30000 models. Results are shown in
fig_336-03.png. Vs profiles are now better sampled. In the same time, all layers are now concentrated above 50 m, while the previous case spans down to 100 m. The shallow part is now better investigated.
The dispersion curve is bending towards an increase at high frequency. This kind of shape can be the signature of a low velocity zone (LVZ) prohibited for default parameterizations. Let's relax this condition for the second layer: Vs1 can be lower than Vs0. I obtained a minimum misfit of 0.51 after 30000 models. The results are shown in
fig_336-04.png. High frequency par of the dispersion curve is fine and the ellipticity as well. Lower frequency part of the dispersion would still require a better fit. Profiles are constrained by the targets to a maximum depth of 40 m. An additional layer would probably provide an expected degree of freedom. I force it to be between 40 and 200 m to explore the deeper part.
I get 0.40 as a minimum misfit after generating 30000 models (
fig_336-05.png). The lower frequency part of the dispersion curves is a bit improved. The Vp profiles indicate a maximum penetration depth of 60 m. This limit is not reached for Vs due to a missing degree of freedom.
I added one more layer from 80 to 200 m to reach a misfit of 0.36 after the generation of 60000 models (6 layers and 16 parameters,
fig_336-06.png). That's much better: the deeper part of the Vs profile is now correctly explored, providing a maximum depth around 150 m.
Now at least two details should raise your attention:
- There is effectively a small peak in the ellipticity at 1 Hz but there is another one much larger between 0.3 and 0.6 Hz. Is it supported by your experimental data?
- Vp profiles look very well constrained in the first 40 m. This is unusual. It might be induced by a biased ellipticity curve. You did not specify if it comes from a classical H/V measurement or from a more sophisticated processing aimed at extracting pure Rayleigh waves: HVTFA (NERIES project) or Raydec (Hobiger et al. 2009, to be included soon in geopsy). In classical H/V, Love and body waves can modify the amplitude of the curve, which is not taken into account by dinver modelling, based only on Rayleigh waves.
To stay on the safe side, we can re-run the inversion with the same parameterization without the ellipticity curve. We keep only the ellipticity peak. The minimum misfit is much lower as expected (0.09) with only 20000 models generated (
fig_336-07.png). Vp profiles are now unconstrained which is more usual. The obtained ellipticities are almost parallel to the experimental one but at a much lower level. The Love contribution could easily explain this difference. Again, the peak at 1 Hz appears as a secondary peak compared to another one between 0.3 and 0.6 Hz. Is it supported by your data? If not a more gradient-like profile should be considered in the deep part (from 50 to 200 m).