The Horizontal to Vertical Spectral Ratio technique (HVSR) and the Nakamura technique (or the HVNR technique) are both tools to measure ground motion amplification. What is the difference between the inputs of the two?
Both techniques consider the ratio between the (smoothed) Fourier spectra of the horizontal and vertical components of ground motion at a single site. The HVNR technique as proposed by Y. Nakamura uses ambient noise recordings, while, probably, what you call the HVSR technique uses earthquake recordings (is is the often called "EQHVR"). NONE of them, according to the vast majority of the published literature,can provide directly the ground amplification, the only robust information they give is the fundamental frequency of the site (f0). The HVSR (or EQHVR) and HVNR provide different curves, and those curves are most often different from the true horizontal amplification HSR: EQHVR and HVNR are generally smaller than HSR. You can see a compilation of comparisons form many different sites in Haghshenas et al. (2008), but there are plenty of other, similar results.
Pierre-Yves Bard do you mean with "true horizontal amplification HSR" referred to theoretical transfer funciton of incident S waves?
By the way Anangsha Alammyan , Mr. Bard is the most significant scientist (authority in the field) about numerical and emprical site amplification issues. You can accept what he says :D
Hamdullah: thank you very much for your kind words, which I want to complement by a warning to Anangsha Alammyan: as said in latin, "errare humanum est", and everybody may be wrong. So never trust 100% of what you read, always check it !
Regarding your question Hamdullah, what I call "true HSR" is the true amplification of the site with respect to outcropping reference bedrock. If the site is perfectly 1D, then it should be equal to the theoretical 1D transfer function, IF you know perfectly the underground structure - which is rarely the case... It gets even more difficult in 2D or 3D cases. So if there is an outcropping bedrock nearby, the best estimate of HSR is the traditional average spectra ration H(site)/H(bedrock) - which requires to have a sufficient number of good quality instrumental recordings at both sites -. If there is no nearby outcropping bedrock, "true" HSR may be obtained with Generalized Inversion technique with a good control of the reference rock. Ground truth is observation...
Follwing Prof. Bard’s comments, HVSR based on earthquake recordings indeed underestimates the true horizontal S-wave amplifications in most cases, and the underestimation can be approximated by the vertical amplifications. Thus, there is a proposed method to use HVSR after corrections by generic vertical amplification spectra, in this way to estimate horizontal amplifications.
When noise is being used both are same, the cocept behind the two groups are different to justify the results.