Method and Display

The original fk-analysis is restricted to short time windows and cannot be applied to the whole time window of the seismogram. To study the development of slowness and backazimuth over a period of time in the seismograms, a sliding-window fk-analysis and an effective display technique called 'fk-movies' have been developed in this study and are used for the study of P$^d$P phases.
For the sliding-window fk-analysis a short time window of constant width is shifted along the seismogram with a constant step size and a standard fk-analysis is performed for every time window. The results of the fk-analysis, i.e. the slowness and backazimuth of the power maximum and the information on the coherency of the signal for each time window, are stored.
To obtain the best possible results in the fk-analysis, a suitable time window and step size must be chosen. The time window must be wide enough to completely include all phases travelling over the array with different slownesses. In shorter time windows, not all components of the signal can be analysed and the fk-analysis becomes less accurate. Windows which are too large contain more incoherent noise, which disturbs the exact determination of slowness and backazimuth. Particularly, the coherency of the signal decays. Additionally, the time resolution of the method decreases. The window width is defined by the dominant period of the signal and its travel time over the array. This travel time depends on the slowness of the studied phase.
For YKA data a window width of 4 s and a step size of 1 s is used to detect the P$^d$P phases. Therefore, every second of the seismogram is sampled by 4 different time windows.
The sliding-window fk-analysis allows the search of P$^d$P phases for numerous time windows, and not only in time windows where the underside reflections from discontinuities are expected.
The results of the sliding-window fk-analysis are displayed as fk-movies. These movies are used to detect P$^d$P and provide a good overview how slowness and backazimuth change when different phases arrive at the array.
fk-movies of resolution tests and events used for this study can be seen at:


http://www.uni-geophys.gwdg.de/~srost/fk-movies.htm .


The resolution tests show the capability of the method to detect small signals buried in noise and to resolve small slowness and backazimuth differences. Additionally, the results of the sliding-window fk-analysis for some events recorded at YKA are shown. Some snapshots of the sliding-window fk-analysis shown at the web-page are discussed in the next section.