## Power resolving of arrays

Discuss here all technical and scientific questions about the processing of ambient vibrations for site characterization (H/V, Array methods,...)
Leonard
Posts: 8
Joined: Tue Jul 14, 2015 2:50 am

### Power resolving of arrays

Hi Marc and Geopsy users

Well let me first introduce myself to you, i am a student interested in the theory behind near surface geophysics mainly surface wave methods. Well i'm getting in touch with the microtremor methods but i know these are rarely used in engineering practice, in this field ReMi is the main method (At least in my country). Do you know about the resolution of the different methods to detect soil's layers? or a way to calculate for a specific array the min/max theoretical layer given a velocity profile ?.

My doubt rises when i began to note in a lot of Vs profiling reports, ReMi arrays with channel interval between 5-10m reporting thin layers as 1m. I think it's crazy because using simple Shannon- Nyquist Sampling Theorem this thick is lower than the Nyquist's wavenumber, but i'm not sure.

Best regards.

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Joined: Mon Aug 13, 2007 11:48 am
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### Re: Power resolving of arrays

Hi,

You are right, many many reports are providing Vs profiles without any indication of minimum and maximum depth of reliability, without talking of uncertainties. This is still the case nowadays even from a lot of experts and in the scientific literature.

About Shannon or Nyquist, it gives the minimum wavelength you can get without aliasing effect. Practically speaking, for cases with a well defined dispersion curve without mode ambiguities, the curve can be followed far above the Nyquist limit. You can clearly see the aliased curves (not to be confused with a higher mode) on a FK plot. In all other cases, the situation is sufficiently complex with higher modes and so on, and it is better to avoid useless artefacts: record with the appropriate sensor spacing according to Nyquist.

The usual rule of thumb is to consider 1/3 or 1/4 of wavelength for the depth of penetration. For instance, if you want to get information down to 1 m, you should have a wavelength from 3 to 4 m, hence with a spacing of 1.5 to 2 m it is OK. This is just an approximate rule of thumb. The best method is to check the true resolution limits with the inversion tool. What are the minimum and maximum depths beyond which you cannot properly resolve the Vs profile? Dinver can do that task by adding specific "uncertainty" layers on top and at the bottom. This is something to do systematically on all inverted profiles.

About ReMi with sensors along a single line, I'm still surprised to observe that 15 years after the paper from John Louie the method is still used. This is not a serious approach. The ambient vibrations may travels in all directions. The most robust solution to converge to the correct velocity is to record a few tens of minutes with an appropriate 2D array. In case of laterally incoming wave the results of ReMi are strongly biased. Moreover, the picking proposed by ReMi is strongly subjective. With the same refraction equipment, why not recording a L-shape array? It is not as good as a circle or a random distribution but better than just a line.