## 4 Discussion
**R\({}_{\rm Q}\) as invariant and redundancy in seismogram--**The form of the R\({}_{\rm Q}\) and convergence in its ensemble apparently suggest the existence of a kind of invariant. Moreover, they suggest redundancy in seismograms as well since all seismograms addressed in this paper show very close similarity between their R\({}_{\rm Q}\)s. This means that each seismogram contains plenty of redundant information. It is well known that the alternating fluctuation along the waveform is the main cause of redundancy through strong local correlation of alternating amplitudes. In this regard, an important fact should be underlined: the R\({}_{\rm Q}\) is the result of the ordering of SFs by peak amplitudes. This means that in the ordering procedure, all local correlative interrelations that provide seismogram redundancy are disrupted. Then, one would expect redundancy to decrease, but it is increased. The explanation of this paradox is simple: the ordering means putting the most similar SFs one next to the other (which are now closer by peak amplitude), which now means the appearance of additional correlation. This is an interesting effect and deserves further analysis. **Equivalence of R-envelope and bigraph--**This issue has been discussed extensively so far. Here, we will add just a few essential remarks. Instead of the term 'equivalence', it might be more appropriate to qualify the R-envelope and bigraph as complementary characteristics, although their equivalence cannot be disputed. The R- and R\({}_{\rm Q}\)-envelopes contain information on maximum amplitudes of SFs, giving the amplitude content of the seismogram waveform. If one assumes regular indexing along the abscissa, then the complete information about the mapping structure is lost. However, if one adds positional indexing, then the complete mapping is known, and, actually, the complete bigraph is given below the abscissa (Figures 8 and 9). Thus, the R- or R\({}_{\rm Q}\)-envelope with positional indexing contains the complete bigraph. On the other hand, the bigraph, without any additions, directly by its structure, by nodes and mesh of edges, reflects the general structure of the seismogram but without data about maximum amplitudes. This is for the case of a simple bigraph with no weights in nodes and edges. In brief, one can say that the bigraph is more internal, while the R/R\({}_{\rm Q}\)-envelope is a more external representation of the seismogram. **Main part of the seismogram--**There is an additional distinction in the previous concept. The main part of a seismogram is the one containing significant SFs, i.e., all SFs that are large, which mostly cause significant seismic effects on the built environment. An ordering operation gathers these SFs together, whatever their disposition throughout the seismogram, so that the ordered seismogram is a monotonic object where SFs gradually increase or decrease, depending on the ordering convention (starting from the largest or from the smallest SF). The main part of the rearranged seismogram contains the SFs that are the most important for seismic effects (magnitude, delivered energy, inflicted damage, influence on structures, etc.). The long decreasing tail of the ordered seismogram stemsfrom the tail, which is of secondary influence and significance. Therefore, the ordering makes more explicit the issue of what part of the tail is to be recorded or where to terminate its recording prior to it sinking into seismic noise. One should be careful when considering the main part of the seismogram. The rearrangement operation gathers all the prominent SFs in one place, sometimes from different areas of the seismogram, so it may produce the impression that they act together. In addition, the SFs are gathered one-sided, positive, negative, or both, with the seismogram rectified.