NOAA/ OERD

### Results of Error Analysis for the T-Phase Locations

*T-K
Andy Lau *

The results are the 3 contour plots of the standard errors for Latitude,
Longitude, and Origin Time of the T-Phase locations. The error contours
are generated by the Monte Carlo Simulations. The random errors are normally
distributed with the mean=0 and standard deviation = 0.75 (from calibration).
The errors are added to the arrival times from 6 hydrophones for each grid
cell in the region. The standard errors for each cell are the results of
experiment repeated 100 times. For more detail. check out the full
report.

For all 3 figures below, weighted and unweighted results can be seen
by clicking the pictures. Cclick on the area inside the square marks
( the hydrophones ) for an enlarged view of the area.

Figure 1: The contour lines are in minutes, 1^{o}=60 minutes.

Figure 2: The contour lines are in minutes, 1^{o}=60 minutes.

^Figure 3: The contour lines are in seconds.^

For all 3 figures above, the simulations did not include the gulf of
Alaska. The area to the west of the Washington and Oregon coast lines are
blind spots for the hydrophones. The abrupt contours at between -50^{o}
&-40^{o }latitudes and -180^{o} longitude were caused
by the Islands of New Zealand and Chatham.

**Interpolation of the T-Phase Location Errors**

Figures 1 and 2 show the contours of standard errors in minutes for
latitudes and longitudes when computing the T-Phase event origins. For
example, if an event is located at 20^{o}N and 150^{o}W,
the standard errors for this position will be approximately 6 minutes in
latitude and 20 minutes in longitude, i.e., the ranges of the computed
location will be 20^{o}N +/- 6 minutes and 150^{o}W +/-
20 minutes. By the Empirical rule in statistics, these are the approximately
68% confidence intervals. For 95.5%, double the errors, e.g., 20^{o}N
+/- 2x(6 minutes). For 99.7%, triple the errors. Again this is assuming
the error distribution of arrival times is +/- 0.75 seconds.

**For other results and Discussion, check out the full
report.**

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