## 2 Materials and Methods
### R/RQ-Envelope--Bigraph, Equivalence, or Complement? While the graphical appearances of the bigraph and the R-envelope might seem different, they are deeply equivalent. Figure 10: Turning out the seismogram into the sequence of SFs is the basis for creating the R\({}_{\text{Q}}\)-envelope and the bigraph. All subsequent operations can be gathered into a transform of the seismogram, yielding a result composed of R\({}_{\text{Q}}\) and BG. The bigraph obviously does not contain any information about time, as opposed to the R-envelope, either drawn over original SFs or over approximated SF(A)s: both contain data about durations of SFs. Therefore, the R-envelope is over-equivalent to bigraph and, hence, not truly equivalent. On the other hand, in depicting the R\({}_{\text{Q}}\)-envelope, having all SF(A)s reduced to their maximum amplitudes (as samples) and equidistantly positioned along the abscissa, one can disregard the time and assign samples by integers, designating earlier positions of SFs in the rearranged seismogram. Because of that, one simply puts a random sequence on integers along the abscissa. As can be seen on Figure 9, each vertical pair of integers indicates the mapping (displacement) span, e.g., in the 6 th column, one sees numbers 20 and 6, which means that the mapping span is 20 \(-\) 6 = 14, etc. By placing the regular indexing, or just identifying the linear address of a number along the abscissa (i.e., its position), one implicitly depicts the respective bigraph. In other words, the bigraph is contained (hidden) within these two strings of integers. This means that the diagram of the R\({}_{\text{Q}}\)-envelope contains its (equivalent) bigraph. This is a plain bigraph in which nodes and edges do not have weights. This still does not mean that the R\({}_{\text{Q}}\)-envelope and respective diagram are fully equivalent since the R\({}_{\text{Q}}\)-envelope contains maximum amplitudes of SFs, or SF(A)s, the only residual from the seismogram in the R\({}_{\text{Q}}\)-envelope. If one considers the weighted instead of the plain bigraph, where the weights of nodes represent maximum amplitudes of SFs, or SF(A)s, then a complete equivalence between the R\({}_{\text{Q}}\)-envelope and respective bigraph is attained. In brief, the simple bigraph is a 2D structure, while the weighted bigraph is a 3D structure. The claimed equivalence still seems suspicious since there are two very different mathematical objects to compare: one continuous (R\({}_{\text{Q}}\)-envelope), and another truly discrete (bigraph). The point is that the R\({}_{\text{Q}}\)-envelope is seemingly continuous since it is not a monotonic curve but a polygonal line whose nodes are maximum amplitudes of SF(A)s. A polygonal line is composed of linear segments, and each segment is completely determined by its nodes, i.e., the coordinates of each point along a segment are determined by the coordinates of its ends (nodes). In other words, a polygonal line does not contain more information than the nodes that it is drawn through. Therefore, the R\({}_{\text{Q}}\)-envelope is actually a string of numbers, the same as those assigned to the nodes of the bigraph, where the polygonal line is drawn only for better visual grasping of the relationships between nodes, which is a representation adapted to the vision of humans. Variability in the R/R\({}_{\text{Q}}\)-Envelope and the Bigraph  
In general, the variability of an entity (a system) depends on the number of elements it contains and their ability to mutually combine to form various resulting structures. This can be seen in earthquakes, particularly if one considers the waveform as a combination of SFs, which can be combined in different ways to yield different combinations. One of these combinations is the considered seismogram itself, and another one is its ordered version. Obviously, the inner variability of the considered seismogram is higher in its original form than in its ordered counterpart.