Page 323 - Rock Mechanics For Underground Mining

CHARACTERISATION OF SEISMIC EVENTS

Figure 10.26 Waveform of a seis-
mic event recorded on an ISS seis-
mic system with a triaxial accelerom-
eter as the ground motion sensor (after
Duplancic, 2001).

Although much more sophisticated and accurate methods are employed in practice,
for purposes of illustration a simple linear solution method for source location, among
several described by Gibowicz and Kijko (1994), is discussed here. The working
parameters are the travel times of seismic waves from an unknown source location to
several sensors of known location. The length, D i , of a seismic path from a source or
event hypocentre, h, at unknown location (x o , y o , z o ) to a geophone sensor i at known
location (x i , y i , z i )isgiven by
2
2 1/2
2
D i = [(x i − x o ) + (y i − y o ) + (z i − z o ) ] (10.93)
The seismic travel time, T i (h), between the unknown event hypocentre and the sensor
i is therefore given by

T i (h) = Ta i − T o = D i /C

or
D i = C(Ta i − T o ) (10.94)

where i = 1, n
n = number of sensors in the array
Ta i is the known arrival time of a wave at sensor i
T o is the unknown time of occurrence of the seismic event
C is the P- or S-wave velocity, assumed constant for the whole area.

Combining equations 10.93 and 10.94 yields
2
2
2 1/2
C(Ta i − T o ) = [(x i − x o ) + (y i − y o ) + (z i − z o ) ] (10.95)
There are four unknowns to be determined – the source time of the event, T o , and the
unknown coordinates (x o ,y o ,z o ) of the hypocentre, so that at least four simultaneous

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