IEEE Signal Processing - March 2018 - 107

seismic emission tomography (SET) semblance function was
proposed [10] to combat the complex radiation pattern, which
may cause false detection and degrade the localization result. The
approach uses maximum-likelihood (ML) in the frequency
domain to detect microseismic events, as well as estimate the
source mechanism parameters by maximizing the generalized semblance functional over source coordinates and source
parameters. The ML result not only improves the detectability of microseismic events and reliable estimation of the source
mechanism of events with SNR of less than one, it also helps
in determining parameters of complex microseismic origins in
the presence of various incoherent noise sources. As an added
benefit, the method also overcomes the detection of false events
in incorrect locations for more complex focal mechanisms, previously observed with SET during the presence of high SNR.
To determine the source mechanism and seismic moment,
we can use either full waveform inversion or ray amplitude
inversion. In both cases, we must compute the spatial derivatives of the Green's function matrix. The derivative matrix G
represents the response of the medium, i.e., the velocity and
density model between the receivers and the source, to the
force couple M ij (1 # i, j # 3) in the moment tensor matrix
M. The observed amplitudes of waveforms in particle displacement d can be related to the derivative of the Green's
function G by

There are two principal challenges to the use of semblance
in passive seismic monitoring:
1) Very low signal amplitude below the noise level results in
low semblance because the semblance of noise is low.
2) The signal radiated by a shear source, or even by a tensile
source, is not spatially coherent and varies across the
sphere with the take-off angle, because microseismic events
have generally complex radiation patterns.
The first challenge is generally difficult to overcome as the
semblance of true events decreases with SNR and the exponentially growing total events count and information obtained from
the monitoring. Initially, semblance in microseismic monitoring was used by [6] to test the limits of detectability of isotropic sources, such as underground explosions (perforations).
However, later use [19] of semblance to detect microseismic
events encountered the aforementioned second challenge-
the radiation pattern of microseismic events. The radiation
pattern of a typical shear event results in severe reduction of
semblance and affects the value of semblance much more than
propagation effects (geometrical spreading/attenuation) [34].
The use of signal envelopes [19] overcame this challenge, but
this methodology lowers the SNR on stacked traces, especially
for weaker events [36]. High semblance for real microseismic
events can be preserved if the amplitudes used for computation are corrected by a source mechanism, i.e., the amplitudes
are corrected by the radiation pattern of the inverted source
mechanism before the semblance computation [34].
Practically, not only the magnitude of the event but also the radiation pattern could greatly affect the detection results. A method based on a statistically optimal functional that generalizes the

20,000

d = G ) m,

(9)

where ) denotes convolution. The source mechanism is represented by a vectorized moment tensor m with six components

Top View of the Dense Array

10,000

5,000

1
2

-5,000

-10,000

5
6

-15,000

0
5,
00
0
10
,0
00
15
,0
00

00
-1 0
0,
00
-5 0
,0
00

-20,000

-1
5,

Time (s)

y (m)

15,000

x (m)

2,000

4,000

6,000

x (m)

8,000

10,000

(a)

15,000
12,500
10,000
7,500
5,000
y (m)
2,500

(b)

Figure 9. (a) The top view of the surface sensor array with the located event indicated by a red star. (b) The 3-D view of the picks (°) from the 2-D sensor
array with the fitted hyperbolic surface in red, which is used to determine the event location.
IEEE Signal Processing Magazine

March 2018

107

Table of Contents for the Digital Edition of IEEE Signal Processing - March 2018