Hi Marc,

Posting here as per your advice.

I hope this email finds you well. I have been a Geopsy user for quite some time now but only restricted to HVSR processing. I am now exploring how to invert fundamental mode rayleigh wave ellipticity since I am soon to work on glacial ice thickness estimates and would like to have a go at HVTFA. With this, I just want to ask a couple of questions or clarifications rather regarding the entire process to produce a 1D shear velocity profile, particularly in max2curve and some of the script. Figures here will probably be incorrect (test data) but for the sake of visualization, I have included them here.

1. After loading the .max file into max2curve, the curve at the right window is essentially the fundamental mode Rayleigh wave ellipticity forward model I believe?

2. From here, we pick either left flank, right flank (or a combination), or the entire curve itself and save it as a multi-column file. Or do we just resample the existing curve into the left or right flanks such that the standard deviations are not lost? Here is the right flank as an example:

3. Say we proceeded with the picked right flank, load the curve into Dinver.

4. The resulting output of ellipticity (colored lines) are the numerical forward models fitting the experimental forward model?

5. And to extract the best fitting forward model after saving the report file, the script to use is:

gpdcreport name.report -best 1 | gpell -abs

I guess ultimately, I would like to produce something similar to the output of Knapmeyer-Endrun et al. (2017) https://link.springer.com/article/10.10 ... 016-0300-1:

I feel like I have been stuck in this process and would be really thankful for your inputs and comments regarding HVTFA.

Thank you so much for your time!

Best regards,

Leandro Aque

## HVTFA - ellipticity inversions

### Re: HVTFA - ellipticity inversions

Hi Leandro,

Numbers correspond to your numbered points.

1. The results of HVTFA depends upon the criteria used to selected events (max2curve -h TFA for a list of filters). One of the simplest filter is '-tfaNppm' (maximum number of peaks on the vertical component per minute and frequency). If you increase this number the obtained curve should tends to the H/V computed in the classical way (with combination of horizontal components 'Total horizontal energy'). With a more selective condition, you should tends to the Rayleigh ellipticity curve. The good choice is case-dependent, usually lower for deeper sites.

2. I prefer to keep the standard deviation.

3. Dinver is now processing the angular ellipticity (atan(H/V)) instead of the plain ellipticity. In you image it is still with plain ellipticity. I guess this is an old release.

4. They should fit the experimental data... in your case, they don't.

5. If you invert the ellipticity curve alone, without any information about Vs, there is a trade-off between depth and velocity a bit like in the classical formula Vs/4H=f0. The curve, compared to f0 only, does not help so much to solve the ambiguity. Hobiger et al. (2013) shows this clearly on various examples. If you have MASW data to invert with, it is fine even if it provides only the high frequency dispersion curve. Re-reading quickly Knapmeyer et al (2017), I understood that they processed only numerical simulations.I'm unsure you can obtained similare results with experimental data.

Back on your case, how many layers did you use? Did you try to increase the number of layers? If stuck , you can eventually send me the picked curve. I can play with Dinver to check if an acceptable fit can obtained.

Numbers correspond to your numbered points.

1. The results of HVTFA depends upon the criteria used to selected events (max2curve -h TFA for a list of filters). One of the simplest filter is '-tfaNppm' (maximum number of peaks on the vertical component per minute and frequency). If you increase this number the obtained curve should tends to the H/V computed in the classical way (with combination of horizontal components 'Total horizontal energy'). With a more selective condition, you should tends to the Rayleigh ellipticity curve. The good choice is case-dependent, usually lower for deeper sites.

2. I prefer to keep the standard deviation.

3. Dinver is now processing the angular ellipticity (atan(H/V)) instead of the plain ellipticity. In you image it is still with plain ellipticity. I guess this is an old release.

4. They should fit the experimental data... in your case, they don't.

5. If you invert the ellipticity curve alone, without any information about Vs, there is a trade-off between depth and velocity a bit like in the classical formula Vs/4H=f0. The curve, compared to f0 only, does not help so much to solve the ambiguity. Hobiger et al. (2013) shows this clearly on various examples. If you have MASW data to invert with, it is fine even if it provides only the high frequency dispersion curve. Re-reading quickly Knapmeyer et al (2017), I understood that they processed only numerical simulations.I'm unsure you can obtained similare results with experimental data.

Back on your case, how many layers did you use? Did you try to increase the number of layers? If stuck , you can eventually send me the picked curve. I can play with Dinver to check if an acceptable fit can obtained.

### Re: HVTFA - ellipticity inversions

Hi Marc,

What should be the column designations when importing ellipticity I obtained from the old max2curve if I wanted to use the newer dinver version?

I have tried the default but am getting larger misfits as compared to the older version.

In the newer version I am getting as high as 10 whereas the older version, never larger than 0.5. Thank you!

What should be the column designations when importing ellipticity I obtained from the old max2curve if I wanted to use the newer dinver version?

I have tried the default but am getting larger misfits as compared to the older version.

In the newer version I am getting as high as 10 whereas the older version, never larger than 0.5. Thank you!

### Re: HVTFA - ellipticity inversions

If the number are coming from

*max2curve*, you have to change the column headers. Values are not in degrees. You have to select 'Ellipticity (H/V)' for the mean values. For the error, I'm not so sure. It should be 'H/V stddev (approx)' or 'H/V*stddev (approx)'. Try both and compare with the plot of*max2curve*.. What's best?### Re: HVTFA - ellipticity inversions

Hi Marc,

Would this be correct?

Upon import, I changed the columns as you have suggested to 'Ellipticity (H/V)' for the mean values and 'H/V stddev (approx)' for the error. I also changed the curve value from 'Singed' to 'Absolute'.

The ellipticity I got after inversion is this: With ellipticity angle (deg) as the y-axis

With very low misfit as well (quite happy with it actually)

The error bars though look very large

Please let me know your thoughts. Thank you!

Cheers

Would this be correct?

Upon import, I changed the columns as you have suggested to 'Ellipticity (H/V)' for the mean values and 'H/V stddev (approx)' for the error. I also changed the curve value from 'Singed' to 'Absolute'.

The ellipticity I got after inversion is this: With ellipticity angle (deg) as the y-axis

With very low misfit as well (quite happy with it actually)

The error bars though look very large

Please let me know your thoughts. Thank you!

Cheers