Filtering

All short-period stations of YKA are equipped with the same seismometer type recording ground velocity. Consequently, the instrument responses of all stations are the same and a deconvolution of the instrument response function is not necessary.
Despite the good noise conditions at YKA, frequency filtering is essential, especially for smaller events. Several filters have been tested to obtain the best choice between noise reduction and the sharpness of the filtered signals. The different spectral compositions of P and PP were taken into consideration during the selection of the filter. PP travels through the asthenosphere at the reflection point on the upgoing and downgoing path. The asthenosphere is characterized by a small Q-factor and high frequencies are suppressed strongly. Therefore, the PP spectrum contains less high frequencies and is shifted to longer periods.
A causal 4th-order Butterworth band-pass filter with cut-off frequencies of 0.5 Hz and 1.4 Hz was selected. A causal filter was applied to avoid misinterpretation of sidelobes at negative times produced by the acausal filters. Sidelobes might influence the differential travel times used for the computation of the depth of the reflector or might interfere with the underside reflections from shallow discontinuities (e.g. Moho).
Figure 5.1a) shows the results of a causal and an acausal band-pass filter applied to a pulse. The filter described above was used. The wavelet of the acausal filtered trace shows sidelobes several seconds before the original onset. Figure 5.1b) shows the selected filter applied to a seismogram from YKA. The filtered trace (top) shows less noise and sharper onsets of the phases P and PP.

Figure 5.1: a) Effect of causal and acausal filters on a pulse. The filter used was a 4th-order band-pass filter with cut-off frequencies of 0.5 Hz and 1.4 Hz. The acausal filter produces sidelobes at times before the original onset (negative times). These sidelobes begin $\sim$6 s before the main pulse. The causal filter does not produce these sidelobes.
b) 4th-order band-pass with cut-off frequencies of 0.5 Hz and 1.4 Hz applied to a YKA seismogram. The bottom trace is the unfiltered trace and the top trace is the filtered trace. The P and PP arrivals are marked. The noise reduction is clearly noticeable.

The seismograms were processed to remove the mean values from all traces due to offsets between stations, to remove trends within the traces and to remove spikes. All these effects are produced by instrumental errors and can be removed without changing the information content of the seismograms significantly.
Other methods of processing like restitution and deconvolution have not been applied to the data. The restitution of the data with the instrument-response offers the possibility to use lower frequencies of the signal than with unrestituted data. Restitution does not help for the YKA data to detect P$^d$P. For periods longer than $\sim$3 s, the differential travel times between the stations are too short compared to the period of the waves. The wavelength becomes larger than the array aperture and array processing methods are no longer practicable.
The deconvolution of the traces with the PP- or P-wavelet is used to amplify the amplitudes of phases with similar waveforms. Additionally, the deconvolution can be used to remove the source mechanism from the seismograms to produce stacks of several different events. The deconvolution turned out to be unstable for such short time windows necessary to isolate the P or PP wavelets in short period data.