The data were first converted from the original format into a format suitable for processing with the available seismic software. Next, it was sorted into time and station order by groups of one year. A sample of the sorted data shown in Figure shows earthquakes, noisy traces, and dead zones. The noisy traces are probably caused by water-wave action at stations located on small islands. For example, trace 16 in Figure is from the station located at Rarotonga, on the Cook Islands. The missing data is caused by stations not in operation, data lost at tape changes, or data removed in the original cleaning process.
To separate the response of the earth to gravitational waves from the seismic background, high amplitude earthquake events need to be removed from the data. I was fortunate to have data with instrument spikes and much other non-seismic noise manually removed. To remove the earthquake noise, a program scanned each station's data for the maximum value, then if this maximum value was above a given threshold, the samples recorded one hour before and five hours after were zeroed. After zeroing, the station's samples were once again searched for the maximum value, and if that maximum value was again above the threshold, the zeroing and searching process was repeated until the maximum amplitude was below the threshold. Figure shows that the large earthquakes were removed, but smaller events are still present. Notice that the noisy traces also had some zeroed zones. If the maximum value considered to be an earthquake event is lowered, more data are removed, and much of the signal may be lost.
This earthquake removal process could be improved by changing the mute time according to the strength of the earthquake, or by removing the earthquakes according to the tables of earthquake events that are available. The process used has the advantage of simplicity. Many small spikes still remain in the records. These spikes could have been removed by a median filter.
To attempt to produce a sharp response in frequency to any signals in the data and to further suppress noise and enhance weak signal, the data were gained. In the gained examples, a 160 minute, or 480 sample sliding gain window was used. Zeroed data were ignored by this gain to avoid undesirable effects near the ends of zeroed zones. As seen in Figure , the traces are better equalized, but spikes remain.
The data for each station were tapered around the zones zeroed by the previous processes with simple cosine tapers. The length of the taper was 25 hours, or 4500 samples. This taper length was used to keep the effects of the truncation away from the frequency range of interest. Before tapering, small groups of non-zero samples were removed, and during tapering, small groups of zeros were ignored to prevent excessive overlapping of the tapers. While this process eliminates much of the data, it also should avoid creating noise in the spectra. Figure shows an example of this process.
Two different attempts at detecting gravitational wave excitations were done. The first attempt was to correct the data for the rotation of the earth with respect to fixed directions in space, and then produce three spectra corresponding to three perpendicular directions in space. The second attempt was to correct for the rotation of the earth, then calculate the spectra for both polarities in many directions.
The first method would have provided some indication of direction, but the signal strength would have had to be high to detect an event. This method had the advantage of being fast. The second method, that of examining many directions, would allow a more reliable measure of directional consistency. The results shown here are from the second method. The second method is slow since it calculates spectra for 84 directions and two polarities for each direction. The polarization could have been used to determine the consistency in direction of a signal in time. For binary systems, a constant direction and polarization is expected.
The directions scanned for possible gravitational waves are shown in the grid displayed in Figure . Only one hemisphere was examined, since the excitation caused by a gravitational wave in one direction is the same as the excitation caused by a wave moving in the opposite direction. The numbers shown in Figure correspond to the trace numbers shown in Figure and the other directional spectra. The center of the figure is north.
Figure 11 Imaging positions.
The instrument response was not removed from the data since it is expected to be constant between stations at the frequencies of interest. Removing the response also increases the energy at low frequencies making the data unbalanced and difficult to display.
Ideally, the response of a gravitational wave would be a spike in frequency on the spectra. This spike will be smoothed somewhat by the earth's orbit about the sun, but it will be a small change at the low frequencies considered here. The frequency increment corresponding to the Fourier transform of a data sequence of a year is Hz. For signals with one-hour periods, the frequency change from the earth's orbital velocity is Hz. For 10 hour periods, the change is Hz. This smear of the response is likely to be small compared to the effects of the earth's response and to the muting, gaining, and tapering of the time series to remove noise.