Improved precision of delay times determined through cross correlation achieved by out-member averaging

The estimation of differential time delays between similar but noisy time series by cross-correlation is an important component of many data processing applications. In many cases, delays are determined for every pair of time series drawn from a large set of them. For instance, modern earthquake location techniques utilize the differential delays between all P waves (or S waves) observed at a common station, sets that could have thousands of members (one for each earthquake pair). We show that the variance of delay time estimates can be reduced by a factor of 2 to 4 through a process we term out-member averaging. It utilizes an estimate of the delay time constructed by adding together the delays between each member of the pair and a third time series. In addition to decreasing the variance of the estimates, thus potentially improving the accuracy of earthquake locations by a factor of 2–4, it also demonstrates that data from an earthquake can contribute to the location process, even when insufficient data are available to locate that particular earthquake.