12
L. Dong
Fig. 1.5 Diagram of real-time acquisition and processing of the multiple monitoring data (Revised
from [9, 10, 22, 28, 29]).
where M W is the moment magnitude. N is the cumulative number of a seismic
event in the magnitude range (M ±M). a and b are empirical constants. The b value
is an important parameter to measure the regional seismicity level and to describe the
proportional relationship for numbers of large magnitude events and small magnitude
events in the area.
(2) The Hurst exponent can be calculated by rescaled range analysis (R/S analysis)
[31, 32]. For a time series of the moment magnitude for microseismic events,
M = M 1 , M 2 , …, M n , R/S analysis method is described as follows:
M A =
1
t
t
i=1
M i
(1.7)
Y i = M i − M A , i = 1, 2, . . . , t
(1.8)
Z i =
t
i=1
Y i , i = 1, 2, . . . , t
(1.9)
R m = max(Z 1 , Z 2 , . . . , Z t ) − min(Z 1 , Z 2 , . . . , Z t )
(1.10)
S m =
1
t
t
i=1
(M i − M A )
2
, i = 1, 2, . . . , t
(1.11)
L. Dong
Fig. 1.5 Diagram of real-time acquisition and processing of the multiple monitoring data (Revised
from [9, 10, 22, 28, 29]).
where M W is the moment magnitude. N is the cumulative number of a seismic
event in the magnitude range (M ±M). a and b are empirical constants. The b value
is an important parameter to measure the regional seismicity level and to describe the
proportional relationship for numbers of large magnitude events and small magnitude
events in the area.
(2) The Hurst exponent can be calculated by rescaled range analysis (R/S analysis)
[31, 32]. For a time series of the moment magnitude for microseismic events,
M = M 1 , M 2 , …, M n , R/S analysis method is described as follows:
M A =
1
t
t
i=1
M i
(1.7)
Y i = M i − M A , i = 1, 2, . . . , t
(1.8)
Z i =
t
i=1
Y i , i = 1, 2, . . . , t
(1.9)
R m = max(Z 1 , Z 2 , . . . , Z t ) − min(Z 1 , Z 2 , . . . , Z t )
(1.10)
S m =
1
t
t
i=1
(M i − M A )
2
, i = 1, 2, . . . , t
(1.11)