## 4 Discussion  
The primary intention of this paper was limited to only introducing the new concept and considering its features in the frame of seismogram interpretation, processing, and, finally, more effective clustering. Some quantitative and qualitative results are given, which contain assessments of issues of reduced variability and clustering. The exact verification of these issues, in addition to a comprehensive presentation of the many items in this paper, would lead to excessive volume; therefore, it is left for the next research. **Seismogram variability and issue of grouping--**An earthquake is a very complex random phenomenon, i.e., a very complex random entity with immense variability, which imposes difficulties in grouping (clustering) and database organization. Typically, grouping (clustering) criteria (parameters) usually include fault (focal mechanism), distance, magnitude, duration (D5-95(s)), Rjb (Joyner-Boore distance), Arias intensity, event name, station name, year, etc. [18]. These are general criteria whose generality confirms said difficulties. The fault mechanism could serve as a basic classification factor. However, earthquakes affect the surrounding areas, bringing propagation effects into seismograms recorded at certain sites. This is easily seen in, e.g., the PEER database, which is organized according to general criteria despite the fact that it is the result of tremendous accumulated experience and knowledge. In dealing with a database, one enters parameters for a certain group (class) and can work with any of the presented seismic events (i.e., earthquake), either in the form of its seismogram (time series) or its spectrum. Selecting an individual event from the database by its name is a trivial operation and not concerned with its organization. It is interesting to notice that the spectrum, as an ordered and more compact image of the seismogram with less variability, is only an entity added to the seismogram, but, as such, not a factor that can be used for database organization, i.e., not a factor but the object of grouping. The problem of clustering objects that are difficult to cluster is usually solved by converting one object into another using a mathematical operation called transform, mapping  
Figure 26: (from (top)–(down)) An example of a distant seismogram: SFs are labeled by positive integers, separately for positive (red) and negative (blue) SFs. For better legibility of SF indexing, same indices are given in bigger font size, while the others can be easily identified by enumerating ‘points’ (i.e., indices in small size font) between them. (next) Both R(\(\tau\)) envelopes, for positive and negative SFs. (next) Bigraph for positive SFs. (next) Bigraph for negative SFs. it from the original domain into the domain of the object's images, which are now easier to cluster. This paper proposes an approach to transforming a seismogram into a combination of an R\({}_{\rm Q}\)-envelope and bigraph, which, then, deserves the name transform. **More about the variability of R\({}_{\rm Q}\)-envelope and bigraph--**Previously, R\({}_{\rm Q}\) variability was thoroughly considered, and its measure was defined. It can serve as a distance in certain topological spaces, which is the basis for the criterion of clustering (grouping). The variability of the head and the tail in the R\({}_{\rm Q}\)-envelope is quite different (see Figure 14). For the shape of the R\({}_{\rm Q}\)-envelope, one can even speak of it as invariant. More precisely, the head of the R\({}_{\rm Q}\) is less invariant than the tail of the R\({}_{\rm Q}\) which is inherently invariant, so it is possible to divide the R\({}_{\rm Q}\) into two parts and consider their variability in different ways or even measure their variability according to different criteria. In a practical way, the issue of R\({}_{\rm Q}\) variability can be brought down to the head variability. As for bigraph variability, the measure of distance relies on primary and secondary bundles, angle, and number of edges per bundle.