Jökull - 01.01.2014, Side 15

Reviewed research article
Improved precision of delay times determined through cross
correlation achieved by out-member averaging
William Menke1 and Hannah Menke2
1 Lamont-Doherty Earth Observatory of Columbia University, Palisades, New York, USA
2 Department of Earth Science and Engineering, Imperial College, London, UK
Abstract — 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.
Remembering Sigurður Thorlacius Rögnvaldsson
(1964–1999)
This paper is dedicated to the late Dr. Sigurður Rögn-
valdsson, a bright young seismologist who died trag-
ically fifteen years ago in an automobile accident.
Siggi’s 1994 Ph.D. Thesis, Microearthquakes in South
Iceland, was seminal in the development of mod-
ern high-precision earthquake location techniques.
His method’s subsequent integration into a computer-
ized earthquake location system in the South Iceland
Lowland (SIL) seismographic network dramatically
demonstrated its advantages. The fidelity of location
achieved was remarkable, allowing even very small
earthquakes to be correlated with specific geological
faults. Central to the method was the use of cross-
correlation to make very precise measurements of the
differential arrival times of P and S waves. Siggi’s
work was at the onset of what is now recognized as
a period of revolutionary advance in earthquake lo-
cation methodology, during which time the accuracy
of earthquake locations improved by more than an or-
der of magnitude. Siggi’s insight has proved long-
lasting, for cross-correlations are still at the heart of
the double-difference method, the current state-of-the-
art earthquake location technique.
Siggi made an extended visit to the Lamont-
Doherty Earth Observatory in 1993, during which
time he lodged at our home and collaborated with
one of us (WM) on use of polarization data (also de-
termined via cross-correlation) in tomographic inver-
sion. Much of our own interest in and enthusiasm for
the subject of signal-processing stems from the many
lively discussions that we had during those months.
We remember his visit – and his life - with gratitude.
INTRODUCTION
A radical improvement in earthquake location
methodology occurred in the 1990’s, when the grow-
ing ubiquity of digital recording drove a fundamental
change in the underlying type of data. Older loca-
tions methods used arrival time data of P and S waves,
picked by eye off paper records (Klein, 1978). The
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