Exploration of the Event Echo hypothesis

William C. Treurniet, May, 2006

The GCP project evaluates the likelihood that the globally distributed random event generators, or EGGs (ElectroGaiaGrams), respond to events that are meaningful to humans. The evidence that this occurs is persuasive, although the magnitude of the effect varies widely. The usual measure for detecting a signal in the noise is the Stouffer-Z score, a cumulative statistic which can be assigned a probability that it occurred by chance.

It is typically assumed that the EGG response distribution is perturbed for a period of time after the event, and that is the end of it. However, by analogy with seismic activity, there could be aftershocks following the main event, and this possibility is explored here. The assumption is made that the aftershocks will appear as echoes of the main event. That is, the main event will trigger a change in activity in some measured variable, and the form of this change will be observed again and again for a period of time.

A number of events were selected for examination from the list of formal predictions on the GCP website. To qualify, an event had to be localized in time so that the corresponding EGG activity could be specified unambiguously. Thus, calamitous events such as bombings or accidents were appropriate, whereas extended events such as the Pope's visit to Israel were not. The following intervals around six events were chosen for this report.

Event Time Information (UTC)

 Dataset name  Start time  Stop time  Event onset time
 Sept11  2001-09-10 12:46:00  2001-09-13 12:46:00  2001-09-11 12:46:00
 BaghdadBridge  2005-08-30 07:30:00  2005-09-02 07:30:00  2005-08-31 07:30:00
 AlgeriaQuake  2003-05-20 17:45:00  2003-05-23 17:45:00  2003-05-21 17:45:00
 IndianTsunami  2004-12-25 00:29:00  2004-12-28 00:29:00  2004-12-26 00:29:00
 QuakePakistan  2005-10-07 03:50:40  2005-10-10 03:50:40  2005-10-08 03:50:40
 MadridAttack  2004-03-10 06:00:00  2004-03-13 06:00:00  2004-03-11 06:00:00

The variable employed in this report is the second-by-second variance of EGG activity. The data was processed with an exponential filter having the form y(t)= (1-alpha)*y(t-1)+alpha*x(t), where t is the time index, y is the filtered data, x is the unfiltered data, and alpha= .001. The event signature was defined as the 4-hour segment of filtered data beginning at the time of event onset. The signature was cross-correlated with the filtered variance beginning 24 hours before event onset, and extending to 48 hours after event onset. Finally, the array of correlation coefficients was processed using a 65536 point FFT window to identify periodicities in the array of correlations. Large peaks in the power spectrum obtained from the FFT indicate the occurrence of event echoes. The FFT window spanned approximately 18 hours of data, so the lowest frequency of interest has a period of about 9 hours. The following list shows the hours-per-cycle corresponding to the first 12 bins of the power spectrum shown in the figures that follow.

 Freq bin  1  2  3  4  5  6  7  8  9  10  11  12
Hours/cycle   0  18.20  9.10  6.07  4.55  3.64  3.03  2.60  2.28  2.02  1.82  1.65

To guard against over-interpretation of the results, corresponding pseudo EGG data (PED) was obtained from the GCP website and analyzed identically. These analyses show the results that can be expected from completely random data.

The following links present the results obtained from the six data sets. The upper graphs on each page show the correlation arrays spanning 72 hours for both the real and pseudo data. Note that the position of the event onset is marked by a correlation of 1.0. The lower graphs show the power spectrum of one 18-hour frame immediately before the event, and the spectra of three successive overlapping frames after the event. The post-event frames overlap by one-half window length or approximately 9 hours.

At the bottom of each set of graphs are controls of an audio player which enable you to listen to a sonification of the power spectrum data. Three chords are produced per dataset, and each chord is composed of three frequencies translated from the three largest peaks in each post-event frame. All chord components have equal amplitude.


Main Results

The accompanying graphs show that event echoes do occur, but not in all cases. The Sept11 and BaghdadBridge analyses strongly indicate the presence of echoes in the first frame after the event, with magnitudes about twice as large as peaks in the later frames. Curiously, the IndianTsunami analysis shows similar strong echoes delayed until the third frame, more than 18 hours after the main event. The magnitudes of the peaks well exceed the magnitudes found in more than 20 pseudo datasets analyzed thus far. The AlgeriaQuake, QuakePakistan, and MadridAttack datasets show smaller spectral peaks that might indicate the presence of weaker echoes. However, since the magnitudes are well within the range of those found in analyses of pseudo data and pre-event frames, it is safer to interpret these peaks as random occurrences.

These results are interesting but not conclusive. Further work is required to permit proper statistical analysis of the evidence for event echoes. In the meantime, the presence of large spectral peaks immediately following selected events is additional support for the hypothesis that the EGGs respond to significant events. Further, the responses may have more complex dynamics than previously thought.