principles and applications of microearthquake networks

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3.4. Everit Prncessitig 67
7’ - ~
7; 7.1
+T -pb1+2
Fig. 18. (a) Schematic graph showing a P-wave onset and a portion of the coda of an
earthquake. The modified signal amplitude Y(k) is plotted against time f, where k is a
counting index. (b) The characteristic function f (k) described by Anderson (1978) in which
Y(k) is transformed to a set of blips. See text for explanation.
of the onset. But assigning a relative weight is subjective and often ambiguous.
Crampin and Fyfe (1974) and Stewart (1977) assigned equal
weights to all the first P-arrival times regardless of their onset qualitq.
Allen (1978) assigned relative weights to the first P-arrival times empirically
by using (1) the background level just before the onsets;(2) the first
difference in signal amplitude at the onset times, and (3) the peak amplitudes
of the first three peaks after the onsets. Anderson (1978) did not
assign relative weights to the first P-arrival times, but discussed an objective
method to estimate the accuracy of first P-arrival times. The standard
deviation of the arrival time ot was computed by
(3.19)
where u, is the standard deviation of the noise, and g is the slope of the
line between the threshold crossing and the first maximum amplitude.
Although Anderson cited some problems with this approach, the theoretical
foundation exists and could be developed further (see, e.g., Torrieri,
1972).
Shirai and Tokuhiro (1979) used a log-likelihood ratio function to time P-