method for determining this RMS value used by HYPOSAT is extensively documented
(Schweitzer, 1997).
The method used by the LEVR algorithm is summarized as follows.
A.
The Point of Closest Approach.
Seismic theory for signals with a linear source moving at supersonic speed through the
earth implies that the first arrival at a given seismic station will come, to a good
approximation, from the Point of Closest Approach (POCA) of the source to the station.
The POCA is the intersection of the trajectory with a perpendicular from the station to the
line defined by the entry and exit points of the linear source, as diagrammed in Figure 1.
The first arrival signal source is offset slightly from this intersection (POCA) by the angle
of the MACH cone produced by the supersonic transit.
In practice, the effect of the cone
angle is negligible at the expected velocities and can be ignored.
The galactic viral
velocity for trapped materials is about 250 km/s.
In cases where the point of closest
approach lies outside of the Earth, the first arrival signal source is the closer of the entry
or the exit point.
Referring to Figure 1, the arrival time at any station is determined as the sum of the
source entry time, the time-of-flight from entry to POCA for that station, and the seismic
travel time from the POCA to the station.
The model assumes a spherical earth.
Two
additional second order corrections were manually included in the final fitting of the
event of November 1993: an elevation correction for the individual seismic stations, and
a source correction for signals originating in oceanic rather than continental crust.
B. The Test of Hypotheses
The test for fit to a linear source consists of constructing a hypothetical source as defined
by an entry, exit, and speed.
The POCA for each station in the event window is
calculated and the POCA-to-station travel times are obtained.
A range of speeds from
100 to 800 km/sec in 50 km/sec steps is used to calculate the time-of-flight, and a set of
predicted arrival times is determined.
Each station is then taken in turn as the reference station, and its arrival time subtracted
11
11

from the arrival times of all the others to produce an array of travel time differences,
t.
A similar
t array is created for the observed arrivals using the same reference stations,
and the two arrays are differenced to produce an array of residuals.
Next the residuals are
sorted and the lowest N residuals are used to calculate the total RMS error, where N is an
input parameter
7.
The residual, source geometry, velocity, and reference station are
returned for the linear source with the lowest RMS.
LEVR repeats this process for all "acceptable" linear sources with entry and exit points
located on a global 0.1x0.1 degree grid.
(A linear source was not considered "acceptable"
for a given geometry for a set of reports if the signal received by a station from its POCA
would require passage of the signal through the Earth's core, i.e. if there is core
shadowing.)

#### You've reached the end of your free preview.

Want to read all 24 pages?

- Spring '14
- DanielKevles
- Quark, Strange quark, Quark star, strange matter