.nr LL 6.5i
.nr VS 24
.SH
Troff table with MS macros
.ND
.EQ
delim $$
.EN
.XS
.XE
.\".ID
.PP
The analysis of travel time anomalies is undertaken in the form
of perturbations on
the tau function, $ tau (p) $, which is related to the travel time
$T(p)$ by the Legendre transformation (Goldstein, 1964, section 8.1)
.EQ (1)
tau (p) ~=~ T(p) ^ - ^ p DELTA (p)
.EN
where $p$ is the slowness parameter given by Bendorff's relation
.EQ (2)
p ~=~ {delta T(p)} over {delta DELTA (p)} ~~.
.EN
The negative derivative of the tau function recovers the epicentral distance
at a particular slowness,
.EQ (3)
DELTA (p) ~=~ - ^ {delta tau (p)} over {delta p} ~~.
.EN
At a fixed slowness $p$ and corresponding epicentral distance $ DELTA (p) $ ,
a perturbation in $ tau (p) $ is equivalent to a perturbation in the
travel time of the particular ray path.
as deviations from $ tau sub 0 (p) $.
.SH
DATA
.PP
The travel times of seismic P-waves from the
.UL Bulletin
.UL of
.UL the
.UL International
.UL Seismological
.UL Centre
(ISC) provided the basic data set.  Over 1.25
million ray paths, for the periods February 1971 through December 1974,
January 1978 through January 1981, and April 1981 through October 1981, in
the epicentral distance interval of 10 to 100 degrees and source depths less
than 70km were compiled.  Selection of only shallow focus events minimizes
the scatter in the data associated with increasing variations in the
hypocentral parameters of deeper earthquakes.  No attention is given to the
ISC phase identification.  Instead, the travel times are compared to the
Jeffreys-Bullen (1940) P-wave table and considered a direct arrival if
the residual is within 50 seconds (a 60 second window would include
occasional 1 minute reading errors).
.nr VS 12
.TS
center, box;
cfB s s s
cfB s s s
c|c|c|c
n|n|n|n.
TABLE 1
Modified Jordan Regionalization
_
Region	Fractional Area	Paths	Percent of Total
_
1	0.13	46184	0.037
2	0.34	246091	0.195
3	0.13	111012	0.088
4	0.19	468728	0.372
5	0.10	221407	0.176
6	0.07	55810	0.044
7	0.04	110523	0.088
_
Total	1.000	1259755	1.000
.TE
.nr VS 24
The development of this database proved to be
the most time consuming phase of the processing, with typical
runs of 75 cpu minutes per ISC month
of data on the LBL-NMC VAX 11/780 computer.