Ver.1 (May 2005)
Hypocenter Calculation Software GAD (Geiger's method with Adaptive Damping)
By
K. Nishi Ph.D.
(Silver Expert JICA Indonesia)
1. Characteristics of GAD
1) Geiger's method is applied to the arrival time of P
and/or S waves to get the focal elements. The normal
equation is solved using damped least squares with
adaptive damping. The damping constant is adjusted
according to the results of previous iteration, so
that stable solutions become possible.
2) The usage is simple.
3) The valid for a maximum of 6 horizontally-layered media.
4) The minimum required number of data is 4 (including S
wave arrival).
2. Calculations
1) The coordinate system is Cartesian. East, north and
downward directions are positive (+ sign).
2) The location near the station for which arrival time P
is the fastest is assigned as the 1st approximation
by default.
3) Iteration terminates when the correction becomes less
than 0.001km or 0.001sec. And it also terminates
when the number of iterations exceed 50. These
conditions are changeable by the parameters of
dx,dy,dz,dt and maxiteration in the Geiger subroutine.
4) The following 3 files are necessary for calculation.
a) A file for the station code and cooridinates:
station.dat
b) A file for velocity structure:
velocity.dat
c) A file for arrival time data:
arrival.dat
A file for results, Results.dat, is created by the
program automatically.
3. Station file (station.dat)
Line 1: number of station
Line 2- : station code (3 characters)
x,y and z coordinates.
* notice: downward is positive.
Example of station.dat
4 (i2)
PUS 0.850 0.225 -2.625 (a3,1x,3f10.3)
KLA -2.036 0.628 -1.918
DEL 1.291 -2.117 -1.487
PLA -1.648 -4.762 -1.276
4. Velocity structure file (velocity.dat)
All data should be written after 15 columus.
Line 1: Number of layer
Line 2: Z coordinate of discontinuity.
In case the number of layer is one,
this line is skipped by the program.
But a blank line should exist.
Line 3: The values of P wave velocity are written
in f8.3 format for every layer.
Line 4: The values of S wave velocity are written
in f8.3 format for every layer.
Example of velocity.dat
nzLayer : 2 (15x,i4)
zLayer : 0.0 (15x,5f8.3)
VpL(nzLayer+1): 2.8 3.9 (15x,6f8.3)
VsL(nzLayer+1): 1.556 2.167 (15x,6f8.3)
5. Arrival time data file (arrival.dat)
Arrival data of a station are written in one line.
Event is separated by a blank line.
End of data is expressed by "999999999".
1-10 column: YYMMDDHHmm
11 column: blank or ","
12-14 column: station code (3 characters)
15 column: blank or ","
16-21 column: P time in f6.3 format.
If data does not exist "99.990" is written.
22 column: blank or ","
23 column: polarization of p wave. "+" or "-" or blank is
written
24 column: blank or ","
25 column: If onset of P is clear "I" otherwise "E".
26 column: blank or ","
27-32 column: S time in f6.3 format.
If data does not exist "99.990" is written.
33 column: blank or ","
34 column: If onset of S is clear "I" otherwise "E".
Example of arrival.dat
9101180048,PLA,53.690,-,I,99.990,I
9101180048,KLA,53.060,-,I,99.990,I
9101180048,DEL,53.110,-,I,99.990,I
9101180048,PUS,52.940,+,I,53.810,I
9101180049,PUS, 7.860,-,I, 8.150,I
9101180049,KLA, 8.130,-,I,99.990,I
9101180049,DEL, 8.480,-,I,99.990,I
9101180049,PLA, 9.160,+,I,99.990,I
9999999999
6. Results of calculation (Results.dat)
"Results.dat" obtained by the calculation using example files of
station.dat, velocity.dat and arrival.dat is shown in the following.
Results.dat
----------------------------------------------------------------------------
--------------
nst : 4
Station List
PUS .850 .225 -2.625
KLA -2.036 .628 -1.918
DEL 1.291 -2.117 -1.487
PLA -1.648 -4.762 -1.276
nZLayer: 2
zLayer : .000
Vp : 2.800 3.900
Vs : 1.556 2.167
Hypocenter
Date 91 1 18 Time 0:48
Focal Element Probable Error
X .294 .308
Y .604 .426
Z .250 .399
T 51.947 .127
Travel time residual rms= .037sec.
ST P S Cal (Obs-Cal)
PUS 52.940 52.975 -.035
KLA 53.060 53.036 .024
DEL 53.110 53.065 .045
PLA 53.690 53.729 -.039
PUS 53.810 53.798 .012
Date 91 1 18 Time 0:49
Focal Element Probable Error
X -.363 .080
Y -.114 .109
Z -3.018 .271
T 7.364 .049
Travel time residual rms= .036sec.
ST P S Cal (Obs-Cal)
PUS 7.860 7.835 .025
KLA 8.130 8.127 .003
DEL 8.480 8.441 .039
PLA 9.160 9.196 -.036
PUS 8.150 8.212 -.062
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Good luck !
