Haar

In the sections above synthetic seismograms are compared with observed ones with a strong focus on amplitudes. To quantify effects of finite sources and viscoelasticity on waveforms without the ascendance of amplitudes a different approach must be made. In this section normalized envelopes are use to study the pure influence on waveforms. The normalized envelope Y of a seismogram X is defined as:

Y(t) = abs(X(t) +j∗hilbert(X(t))

max(abs(X(t) +j_∗hilbert(X(t))).

In this definitionjis the unit imaginary number andhilbertrepresents the Hilbert trans-

form of the time seriesX. From a practical point of view the envelope of a timeseries

is an unsigned lowpass of the original signal. The normalization erases any influence from the amplitude in order to ease recognition of similarities in the waveforms. Nev- ertheless relative amplitudes within the trace are kept, allowing for example analysis of amplitude ratio of P to S-waves or relative amplitudes within the coda. It is instructive to carry out the comparison of envelopes in different frequency ranges to study similar- ities in the low frequency part achievable already with point source approximations, the improvements in the higher frequency part by more complex simulations as well as the influence of viscoelasticity which is also intrinsically frequency dependent. Observed seismograms are corrected for receiver response before individual filters are applied. On the following pages comparisons of normalized envelopes are presented for an as- sortment of stations. The individual plots are arranged in a similar way as the ones used for the seismogram comparisons of the previous subsection. Results from point and finite sources are facing each other in left and right columns, whereas elastic and viscoelastic simulations appear in the top and bottom row, respectively. For each simula- tion type envelope comparisons were carried out in a range of periods from 0.8 seconds which is associated with the highest achievable frequency in these simulations to 3.6 seconds in 8 equally spaced steps. For each period range a low pass with appropriate cut-off frequency is applied to observed and synthetic traces. The following paragraphs outline main results for the stations chosen.

Station BNS Comparing the relative amplitudes of P and S-waves at station BNS

(Bensberg) in figure 6.28 reveals a quite complex behavior. Whereas for the highest frequencies this ratio is better matched by the point source simulations the opposite holds true for the range of other frequencies. Analyzing the match in P-wave amplitudes for the finite source simulations reveals a clear improvement with increasing period. For the point source simulations the opposite is the case. Long period P-wave amplitudes appear herein strongly overrated. The overall characteristics of the frequency dependent envelopes reveal a much smoother picture for the finite source simulations. As expected considering the location of station Bensberg on solid rock the effect of viscoelastic attenuation does not appear significantly. However, it is visible within the coda.

Station GMA Envelope comparison at station GMA (Gut Margaretenhöhe) located

Figure 6.28: Normalized envelopes of East-West component seismograms at station BNS (Bensberg). Traces are low pass filtered with a cut-off period ranging from 0.8 sec- onds to 3.6 seconds. Observed data is plotted in black against synthetics (red) achieved with different simulation settings as indicated.

a quite good match for the simplemost simulations. This fit can not be improved signif- icantly by increased complexity in the simulations. In fact, relative amplitudes of early arrivals and coda waves reveal overrated damping for this station. As station GMA is lo- cated atop the thickest sediment accumulation of the stations available it becomes clear that the assumed uniform quality factor of 50 for the complete sedimental structure is too high. Whereas for most of the stations located on thinner sediment layers the am- plitude ratio between early arrivals and late arrivals, which are affected more strongly by attenuation is improved, for this station the opposite is the case. Envelopes shown in figure 6.29 support the assumption that a depth dependent quality factor could improve the overall fit of the seismograms.

Station MIL Figure 6.30 shows a comparison of envelopes at the basin station MIL

(Millendorf), located at an epicentral distance of 28 km. It clearly demonstrates im- provements in waveform fitting achieved with the use of finite source modeling. Whereas the point source simulations result in a sharp peak at about 7 seconds simulation time, envelopes derived from finite source simulations show a much broader distribution of energy. This observation holds for the whole frequency range covered in this investiga- tion. However, it is also notable that incorporation of viscoelasticity does not improve the relation of peak and coda amplitudes, in fact it has negative impact on that param- eter. Due to the above mentioned normalized nature of the envelopes shown here this feature can be recognized quite clearly. Again the observation emphasize a more de- tailed attenuation model for the sedimentary structure.

Station PES At station PES (Pesch), located at a epicentral distance of 26 km on sed-

iments, improvements achieved by the usage of finite source and viscoelasticity is re- markably clear. Figure 6.31 illustrates the improved reproduction of observed envelopes for the different simulation settings over a range of dominant frequencies. Comparing the results columnwise in order to focus on the attenuation effect demonstrates improved ratio between amplitudes observed in the coda and on earlier arrivals. This opposite be- havior to the above discussed results for station GMA favors a depth dependent attenu- ation model alike the velocity model used in this study. The mentioned amplitude ratio and therefore the envelope could be kept for stations placed above smaller sediment thickness and at the same time the coda for stations on deeper parts of the sedimental basin are improved. The overall shape of the envelopes, especially the first part is mod- eled better by the finite source simulations. Combining both complexities leads to an accurate fit in relative amplitudes of different onsets.

In figure 6.32 the improvements in terms of envelopes at station PES with increasing complexity of the simulation are illustrated for the highest frequencies contained in the simulations. Clearly it can be seen how the fit in terms of envelope shape improves with the incorporation of the finite source model. Furthermore with additional viscoelastic attenuation the relative amplitudes of individual peaks coincide.

Figure 6.29: Normalized envelopes of East-West component seismograms at station GMA (Gut Margaretenhöhe). traces are low pass filtered with a cut-off period ranging from 0.8 seconds to 3.6 seconds. Observed data is plotted in black against synthetics (red) achieved with different simulation settings as indicated.

Figure 6.30: Normalized envelopes of East-West component seismograms at station MIL (Millendorf). Traces are low pass filtered with a cut-off period ranging from 0.8 seconds to 3.6 seconds. Observed data is plotted in black against synthetics (red) achieved with different simulation settings as indicated.

Figure 6.31: Normalized envelopes of East-West component seismograms at station PES (Pesch). Traces are low pass filtered with a cut-off period ranging from 0.8 seconds to 3.6 seconds. Observed data is plotted in black against synthetics (red) achieved with different simulation settings as indicated.

PE

FV

FE

PV

Figure 6.32: Envelopes of synthetic (red) and observed (black) seismograms low pass filtered with 0.8 s cut-off period at station PES. Synthetics result from simulations with point source and elastic model (PE), point source and viscoelastic model (PV) finite source and elastic model (FE), finite source and viscoelastic model (FV). Introduction of complexities into the simulation setting results in an improved agreement of envelopes.