IEEE Signal Processing - March 2018 - 103

stacked in the patches as an input for semblance computation,
and S-wave amplitudes of seismic waves can be made for tenbut this is difficult to achieve with a star-like array.
sile sources (e.g., [7]). Note that information about relative
A matched filter is perhaps the most common signal proamplitudes and polarities needs to be obtained from diverse
cessing tool for effective signal detection because it maximizes
spatial angles [38] to invert the source mechanism, adding
the output SNR in the presence of additive noise. The discretecomplexity to the signal processing as will be discussed in the
time impulse response of the matched filter is a time-reversed
section "Source Mechanism-Based Detection, Localization,
version of a known template signal, or wavelet, and the operaand Moment Tensor Estimation."
tion of matched filtering is equivalent to cross correlation. By
A reservoir stimulation, such as hydraulic fracturing, is accorrelating the template with a received trace, the value of the
companied with induced seismicity resulting from a reactivation
correlation peak can be used as a likelihood
of an already existing fracture or creation of
indicator for the presence of the template in
new fractures. Locations of microseismic
The most significant
the trace, and the peak location gives the
events are used to map the geometry: the
challenge in surface
time offset in the trace.
direction of fracture propagation, fracture
In seismology, matched filtering analysis
microseismic monitoring
length, and height. The observed seismic(MFA)
was originally applied in studies of
ity contains additional information-the
is the difficulty of directly
repeating
earthquakes, which exhibit high
source mechanisms. The injection of the
observing P- and S-wave
resemblance in waveforms, focal mechafluid and creation of fractures that can store
signals.
nism, and location. In microseismic monitorlarge volumes of incompressible proppant
ing, events induced by hydraulic fracturing
particles suggest that seismicity induced by
have similar features as repeating earthquakes, so MFA, which
hydraulic fracturing may have a volumetric component. Thereuses a strong signal template to detect similar weaker events, is
fore, it is important to determine if the induced seismic events
a prevalent approach [12].
are shear or tensile. Another important parameter characterWhen the MFA requirement of having a template is not met
izing microseismic events is size, which is usually measured
due to high noise on a surface array or low magnitude of the
by a magnitude or, better, by a seismic moment, representing a
microseismicity, cross correlation is still a very useful operation
total energy released by the microseismic event [8]. The corfor detecting and locating similar events across the channels of
rect source mechanisms allow us to accurately interpret the dean array. Mathematically, MFA and cross correlation are nearly
termined seismic moments, i.e., for shear events, moments are
the same. However, in MFA, a known template waveform is
proportional to sizes of fractured planes (assuming a constant
correlated against a continuous data stream to detect occurstress drop), while for volumetric events, moments represent the
rences of that waveform, whereas cross correlation is usually
amount of volumetric change. Thus, a complete source mechaapplied to measure similarities across different channels.
nism characterization is crucial for correct interpretation of the
One can pick a signal segment in a channel and regard it
interaction between microseismicity and hydraulic fracturing
as the reference template to detect correlated signals on other
and interpretation of microseismicity.
channels using cross correlation. If the presence of a reference template is detected on many other channels, we could
Microseismic signal detection and
regard it as a good candidate of detected events. However, in
enhancement in a sensor array
practice, the pairwise cross correlation of many low SNR sigTwo important steps in microseismic monitoring are detecnals gives only low SNR cross correlation functions (CCFs).
tion and characterization of microseismic events in data sets
Among a variety of techniques developed for this issue, stacking
that might contain a large number of weak events. Automated
the CCF in phase over all of the channels and, if necessary, over
detection, and enhancement is challenging for events with
different components of a 3C sensor is a simple and effective
complex waveforms, small magnitudes, and low SNR. In addisolution. In general,
tion, the number of induced microseismic events exponentially
increases with lower SNR. This property is summarized in the
3
N
empirically observed Gutenberg-Richter law resulting from
s [x] = 1 / / c i, j [x - t i],
(1)
3N j = 1 i = 1
the fractal nature of fracture distribution [21]. Although recent
studies indicate this law, commonly observed in natural earthquakes, does not strictly extend to induced seismicity because
of the limited volume [13], [37], it is still observed that, for any
event of a magnitude M w, there is at least a tenfold increase of
events with magnitudes M w - 1. Therefore, any method that
enables us to detect weaker events will significantly increase
the number of detected events, which can then be used for
characterizing fractures resulting from injected fluids. The
geometry of a large sensor array can be optimized to enhance
the low SNR signals from weaker events. For example, a monitoring array consisting of 2-D subarray patches can use signals

where c i, j [x] = (h r, j * x i, j) [x], and h r, j and x i, j are the template
and received signal for the ith channel, reference channel r, and
jth component. In addition, t i is the travel time from the reference
event location to the ith receiver, which can be determined by the
moveout of the parent event (i.e., a strong reference event).
Equivalently, the stacking in (1) is along the moveout of the
reference events [12]. If the location of the microseismic events
significantly deviates from the parent event, it is not satisfactory
to shift the CCFs according to the moveout of the parent events.
In addition, the moveout of the parent event is usually determined

IEEE Signal Processing Magazine

March 2018

103

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