# Seismogram Rearrangement as a Perspective Basis for Defining New Attributes
## 2 Materials and Methods
### Attributes Based Directly on EFs/SFs  
The original seismogram looks identical to its parsed version. Nevertheless, the latter one provides additional degree of freedom for manipulations with the waveform, just because it is segmented. There is no need at once to go up to rearrangement to get the R-envelope, but to apply more simple operations on EFs/SFs to attain some attributes. One idea is simply to shift the EFs along the \(t\)-axis and overlap them to coincide their inflection points (Figure 5a,b). The same picture could be attained with the SFs, but with the SFs, one should use all of them to create a proper picture, while with the EFs, it is possible to get the contours of the final picture with a sample of limited size. At last, the EFs is a more natural form of earthquake acting, as is said above, reflecting the very basic form of change in the seismogram--the 'push-pull' action, more closely to the pattern in which an earthquake acts on structures. On the other hand, the SFs are slightly artificially separated, to give additional room for manipulations. It is not difficult to comprehend the picture resulting from overlapping of all or from a considerable number of EFs. The pretty entangled mesh of overlapped EFs can show a certain average picture but is very blurred. More transparency is attained by introducing, let us call it, the structural axis of the EF, as explained in Figure 5a,c. This axis connects three characteristic points of an EF: both peaks and zero crossing (the inflection point). Note that the term 'inflection point' refers to the function, which would formally describe the actual EF. All these are point-like, pretty local features, so the structural axis form highly depends on the shape of EF, which is very variable. A more adequate feature would be the slope (tangent) through the inflection point (where the EF crosses the \(t\)-axis) (see Figures 6a and 7). Notice the difference between ascending (blue lines) and descending (red lines) tangents, which shows a kind of statistical asymmetry of SFs. It determines the maximum change of mechanical variables acting in the site. It has something to do with the transfer of earthquake force to structures. Let us remember the simple thing that when one says 'earthquake,' it is thought of as seismic effects in the site, not in the hypocenter. The said tangent, although the most characteristic of all tangents along the EF function, does not reflect well this energy transfer, particularly in the case of complex EF shape (Figure 6). This tangent is also a local feature, standing in the middle of the complex shape of the EF, but it is still a peripheral description of force transfer from seismic waves to the structure. Figure 5: (**a**) Graphical explanation of the idea of EF structural axis: the two-segment line connecting the peaks and \(t\)-axis crossing skeletonizes entangled shape of EF. (**b**) Already two overlapped EFs, whose inflection points coincide, indicate what would look like a picture of tens of EFs. (**c**) Overlapped structural axes make the representation on (**b**) much more transparent. Different EFs are represented by dark red and green solid lines in (**a**) to distinguish them in (**b**), and their structural axes in (**c**). In order to take the shape of the EF into consideration, which actually carries the influence, it is more proper to speak of energy transfer since the EF shape itself shows the energy distribution contained in it. There, one can define the instantaneous energy transfer carried by a single EF. In other words, it is the instantaneous average power, as the energy contained within the EF divided by its duration \(\Delta t\):  
\[p_{\Delta}=\frac{1}{\Delta t}\int\limits_{\Delta t}EFdt=\frac{1}{\Delta t}\int \limits_{\Delta t}ef(t)dt \tag{25}\]  
where the label \(EF\) symbolically designates the function describing the EF shape (see (9)). Of course, it is a rough measure of energy transfer. It is well known from dynamics that the inertial forces and impulse loads depend on d/dt (Figure 6).