Modified Sidereal Filtering and Stacking
Three sets of results are shown: original,
modified sidereal filtering, and modified
sidereal filtering + stacking. In each case
we have shown the east, north, and vertical
positions separately.
The noise characteristics of the original 1Hz GPS components are dramatically
different, with the east being the best and
the vertical the worst. While the high
frequency noise component in th east and
north components is similar, the low
frequency noise is much higher in the north
component.
There are also large signals in the north
component that appear unrelated to ground
motion, particular at MIDA and CRBT. The
poor high-rate position precision at MIDA is
apparently due to a tree (see photo). At
CRBT, the high-frequency oscillations are
related to metal surfaces ~ 20 meters away
(see photo).
While geodesists have
primarily concerned themselves with
multipath due to the ground and monument,
these surfaces produce very long-period
oscillations. Far reflectors cause shortperiod oscillations that negatively impact
our ability to resolve seismic displacements
that have significant energy at the same
frequencies. Below we have plotted the 1Hz positions corrupted by multipath at ~20
meters (fence) and real seismic
observations from the Denali Earthquake.
1-Hz GPS positions can be improved by
“sidereal filtering” and stacking. The idea of
sidereal filtering is generally attributed to
Genrich and Bock [1992]. They suggested
that since some of the error sources in
high-rate GPS analyses are related to
satellite-receiver geometry and this
geometry repeats at approximately the
sidereal period (23 h 56 m 4s), the position
estimates on days before and after the day
of interest could be used to model these
errors.
In an antenna phase center study, Seeber
et al. [1997] noted that satellite orbits were
inconsistent with the expected sidereal
repeat time. Choi et al. [2004] confirmed
this result and showed how it impacts highrate GPS positioning precision. For these
data, we use the modified sidereal filtering
approach.
We can see immediately that the odd
behavior at MIDA is significantly improved,
indicating that whatever is causing the
position degradation repeats. Note also the
improvement at CRBT ~1000 seconds
before the earthquake. We see some
degradation at POMM. We have confirmed
that at POMM a different satellite is being
reflected by a far surface – and thus POMM
requires a different repeat period than we
used for the rest of the sites.
The remaining errors appear to be
“common-mode.” Note for instance the
common signal that appears ~1500
seconds after the earthquake in the north
component in the modified sidereal filtering
estimates. This is not ground motion. We
used a technique introduced by Wdowinski
et al. [1997] – also known as stacking – to
remove these common-mode errors. A
time-varying empirical correction is
calculated by estimating (and averaging)
positions at sites unaffected by the
earthquake. We used sites in southern
California to determine our stack and
subtracted them from positions that had
been modified sidereal filtered.
The signal we saw at 1500 seconds is now
significantly reduced. Likewise, and more
importantly for the Parkfield earthquake, a
common-mode signal ~200 seconds before
the earthquake is reduced, making 1-Hz
positions more valuable for seismic source
studies.