Constraining Relative Timing Between Stations Recorded On Analog Seismograms

With modern day technologies such as GPS timing, we often take for granted the synchronization of data across stations and networks. However, this was not the case in the era of analog recording on paper seismograms. During this era, it was usually the case that each instrument had its own clock. Each of these were independent of all other clocks in the sense of being set independently, drifting independently, and being reset independently. As such the relative timing of analog data between stations is quite uncertain.

To better constrain relative timing error in digitized analog records, the inherent symmetry of ambient noise correlations can be utilized. Most analog seismograms span 24 hours and are not necessarily changed over at the same time; as a result, ambient noise correlations must be computed for time windows spanning less than 24 hours. When relative timing offsets are introduced to the time series from which noise correlations are computed, the entire structure will shift towards either the positive or negative time lag. This effectively moves the center of symmetry to the time lag indicating relative timing error (e.g., a center of symmetry at -2.5s would indicate a 2.5s relative timing offset, and a center of symmetry at 0s would indicate no relative timing offset). In order to find this center of symmetry, noise correlations are folded at different time lags (MIDDLE) and strength of symmetry is inferred from a cross-correlation value for the two sides (BOTTOM).

TOP: Noise correlation function, with associated envelope function and local maxima. MIDDLE: Noise correlation function with amplitudes on both sides normalized. BOTTOM: Correlation coefficients (inferred symmetry) of sides across different time lags. Time lag associated with maximal correlation as title of plot.

Before use with digitized analog timeseries, this approach was applied to modern data with known accurate relative timing for verification of efficacy. It was found that extremely non-uniform distribution of noise sources combined with the limit of 24 hours for the time window could lead to extremely one-sided noise correlations without easily identifiable symmetry. In these cases, relative time offset was not reliably identified, and as such, attention should be paid to noise distributions in areas where this method is applied. In cases with more uniform distribution of noise the uncertainty of the relative time offset inferred by this method was less than 1/5 of a second. However, it should be noted that while not comparable to modern timing uncertainties, having an uncertainty of 0.2s for digitized analog records is not insignificant.