Inversion by equal logarithmic wavelength intervals

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Aniket19061990
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Joined: Sun Jan 24, 2021 11:11 am

Inversion by equal logarithmic wavelength intervals

Post by Aniket19061990 »

Hello.
In DINVER, is it possible to view the input dispersion curve in phase velocity-wavelength domain (logarithmic)? And more importantly, is it possible to sample it at equal log wavelength intervals prior to inversion?
I am asking this because as per Socco & Strobbia (2004), a uniform sampling in frequency domain corresponds to a coarser sampling in wavelength domain at lower frequencies (longer wavelengths) (Figure attached).
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Re: Inversion by equal logarithmic wavelength intervals

Post by admin »

Hi,

This is the common pitfall of most of the dispersion plots you can find in the literature, even nowadays. There are so many dispersion plots with a linear scale where the curve is almost unreadable at low frequency. USE LOG scales for plotting variable quantities vs. frequency or period. They are equivalent on a log scale which stops the debate between period or frequency among geophysicists and seismologists.

I give you an example plotted with regular sampling on a log scale and a second one with regular sampling on a frequency scale. For both, I show the velocity vs. frequency plot on the left and the velocity vs. wavelength on the right. Effectively, for the regular sampling in frequency, all samples are aggregated in the shallowest part.

.page file can be viewed with figue. .pdf is the same file. With figue, you can change the axis scale yourself.

A regular sampling on a log scale is definitively a good choice. A regular sampling in wavelength is not advised. You will have a lot of samples at long wavelength like a regular sampling in period. Wavelength is proportional to period. A regular sampling on a log(wavelength) might be better than log(frequency) as it include a small correction in case of strong velocity variation. But in most cases, the effort is not worth it.

Best regards,

Marc
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