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Automatic Event Detection on Noisy Microseismograms Fangyu Li*, Jamie Rich, and Kurt J. Marfurt, The University of Oklahoma;
Huailai Zhou, Chengdu University of Technology;
Summary
Accurate automatic seismic event identification is a
fundamental problem for passive microseismic monitoring.
Simply stated, more accurate picks provide more accurate
location of microseismic events. This paper introduces a
new approach carrying out precise seismic event
determination based on high-order statistics (HOS). Short
term kurtosis to long term kurtosis ratio (S/L-Kurt) is a
simple, accurate and fast event identification method. By
measuring kurtosis, we are able to identify the transition
from Gaussian to non-Gaussian behavior that coincides
with the onset of the microseismic event in the presence of
noise. We test the reliability and robustness of the proposed
algorithm on synthetic and real field data and find our
method provides accurate picks even in noisy
microseismograms. The simplicity of the proposed method
makes it an attractive candidate for the analysis of huge
seismic data sets.
Introduction
Microseismic tremors are low amplitude events that are key
to understanding slow-slip earthquakes, incipient volcanic
activity, and hydraulic fracturing. In all three cases, the
seismic records register different kinds of waves
originating from a certain unknown source locations within
the subsurface of the earth. The location and moments of
such events can be determined by measuring the of the
arrival time, polarization, and amplitude of compressional
(P-wave), transverse (S-wave), and surface waves (Raleigh,
Love waves).
In microseismic analysis of hydraulic fracturing, accurate
and reliable picking of the first (P-wave) arrival is of
paramount importance. The arrival of a compressional
wave or P-wave, which has the largest propagation
velocity, denotes the onset of a seismic event. This arrival
can provide important geophysical and seismological
information, and is predominantly used for acoustic/seismic
source location, different types of signal frequency
analysis, mechanism determination, structure description,
seismicity designation, and hazard assessment. etc.
Traditionaly, reliable and accurate signal onset
determination is done by visual human analyst inspection.
However, during applications of passive seismic
monitoring, microseismic datasets may consist of tens of
hundreds of thousands of seismic traces, even though the
vast majority may be discarded after found to contain no
useful information. (Maxwell and Urbancic, 2001). With
the increase in the number of monitoring wells, the number
of stages in a given well, and simultaneous, sequential, or
zipper stimulation of multiple wells from the same or near
by pads, the increase in the amount of continuous data has
increased dramatically, thereby motivating the development
of reliable, automated seismic event picking algorithms. In
addition to consistency and ability to process large datasets,
automated procedures are key to real-time event location
applications that may influence completion decisions made
for subsequent stages.
In the last three decades, several automatic data processing
algorithms for determining individual P-wave arrival time
have been developed, based on characteristic function (CF)
(Allen, 1978), crossing of the threshold level of singal
average energy (Akram, 2011), ratio of short-term average
to long-term average (STA/LTA) (Baer and Kradolfer,
1987; Munro, 2004; Chen and Stewart, 2005), modified
energy ratio (MER) (Han et al, 2010), seismic wave
polarity assumption (Jurkevic, 1988), neural network (Zhao
and Takano, 1999; Gentili and Michelini, 2006), wavelet
transform (WT) (Anant and Dowla, 1997), high-order
statistics (HOS) (Saragiotis et al, 2002), and hybrid HOS
and WT (Saragiotis et al, 1999). However, despite their
sophistication, these methods can be overly sensitive to
noise, perform better in some locations than others, and
often require human intervention.
In this paper, we developed a new method involving the
computation of kurtosis, the fourth zero-lag cumulant
parameter. The proposed short term kurtosis to long term
kurtosis ratio (S/L-Kurt) method takes into account the
non-Gaussian nature of the P-wave in order to overcome
the above mentioned drawbacks. Though our proposed
algorithm is based on HOS, which in general has high
computational complexity, it is straightforward, simple to
implement and computationally tractable given current
field computer capabilities. Experimental results of
synthetic and field data show a promising performance both
on accuracy and robustness in the presence of noise.
Mathematical Background
Statistics describe the patterns of a collection of data. There
are four basic statistic moments: the mean value (first
statistical moment), the standard deviation (second
statistical moment), skewness (third statistical moment) and
kurtosis (fourth statistical moment). Theoretically, any
order statistic moment can be used, but the computational
complexity increases with the order.
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Automatic Seismic Event Detection on Microseimograms
For dataset1 2, , , NX X X , the mean value is defined as
1
N
iiX
mean XN
, (1)
The standard deviation as
2
2 1( )
1
N
iiX X
stdN
, (2)
And the skewness (a measure of the lack of symmetry) as
3
1
3
( )
( 1)
N
iiX X
skewnessN
. (3)
The skewness for a normal distribution is zero; any
symmetric data should have skewness near zero.
Kurtosis is the measure of “peakedness” or heaviness of the
tails in the distribution of the sequence, and is defined as
4
1
4
( )3
( 1)
N
iiX X
kurtosisN
.
(4)
The kurtosis value will be high for anomalous outliers
indicating non-Gaussian signals (such as seismic events)
and can be viewed as the measure of Gaussianity.
Figure 1: A field microseismogram (Top) and normalized
distribution densities (Bottom). Before the seismic event, the data in the red box is noisy and exhibits an almost Gaussian distribution
(red dotted curve). In contrast the data in the black box containing
the P-wave event exhibits a distribution that is non-Gaussian, and more peaked than the reference Gaussian distribution given by the
red dotted curve.
Figure 1 shows different distribution densities of the
microseismograms with and without a seismic event.
Before the seismic event (within the red window), the
microseismogram exhibits an almost Gaussian distribution
with the value of kurtosis=0.7056. In the presence of the
seismic event (within the black window) the distribution is
non-Gaussian with the value of kurtosis=14.1312 giving a
more peaked distribution in Figure 1. In this example
kurtosis establishes an effective statistical test in
identifying signals having a non-Gaussian distribution. In
contrast, the skewness value doesn’t change as much as the
kurtosis, with both distributions appearing quite
symmetrical in Figure 1.
The S/L-Kurt Algorithm
Kurtosis is a measure of the signal’s Gaussianity. In order
to estimate the kurtosis value at each time sample, we
employ a sliding window. The choice of the length of the
window function is a fundamental problem. If the window
is not long enough, the background noise may show many
windows to be non-Gaussian characteristic. If the window
is too long, the non-Gaussian statics will be swamped in the
Gaussian statistics of the preceding and following noise and
not differentiate the seismic event.
Inspired by the STA/LTA method, we propose to utilize the
ratio of short term kurtosis (STK) and long term kurtosis
(LTK) to determine the onset of non- Gaussianity of the
seismograms. Let ls and ll be the length of short and long-
term window, respectively. Then the kurtosis of the short
and long-term windows preceding the time index j are
4
4
( )
( 1)
j
i ji j ls
j
j
X XSTK
ls
,
(5)
where,
2
2( )
,1
j j
i j ii j ls i j ls
j j
X X XX
ls ls
,
and 4
4
( )
( 1)
j
i ji j ll
j
j
X XLTK
ll
,
(6)
where,
2
2( )
,1
j j
i j ii j ll i j ll
j j
X X XX
ll ll
.
Finally, we define:
/j
j
j
STKS L Kurt ratio
LTK
,
where, is a small value added to the denominator to
avoid division by zero.
The S/L-Kurt detects an increase of STK compared to the
preceding LTK, derived by proper windowing of the
seismic trace. When the S/L-Kurt exceeds an empirically
set threshold, an event is detected.
Synthetic Examples
In this section, we use synthetic examples and compare our
new algorithm to the well known STA/LTA algorithm to
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Automatic Seismic Event Detection on Microseimograms
show its effectiveness. Our synthetic microseismic events
consists of two exponetially decaying sine waves, denoting
P-wave and S-wave arrivals.
Figure 2 demonstrates noise-free and very noisy situations,
and indicates that S/L-Kurt is more robust than the
STA/LTA method. Figure 3 addresses the situation where
for reasons of attenuation or moment tensor that the P-
wave is weaker than S-wave; the proposed method still
works well.
Figure 2: Synthetic microseismic event picking example. (Left) noise-free microseismogram with STA/LTA and S/L-Kurt result; (Right) 0 dB
noisy microseismogram with STA/LTA and S/L-Kurt result. It is clear that S/L-Kurt method is more robust.
Figure 3: Synthetic example. (Left) microseismogram with stronger P-wave onset and S/L-Kurt, STK, LTK results; those with stronger S-wave onset are on the (Right). S/L-Kurt method recognizes both seismic events, but the other two statistical attributes only detect the stronger one. (In
order to distinguish them, STK and LTK are normalized into [0 0.5], while S/L-Kurt is normalized into [0 1].)
The methods based on average or standard deviation are
actually responsive to the change of energy. Therefore, they
are effective in the noise free situation, but perform poorly
when the signal-noise ratio (SNR) is low.
In contrast, the S/L-Kurt method is based on Gaussianity
detection. The background noise is often assumed to
Gaussian random noise. In principal, the strength of the
Gaussian noise does not change the non-Gaussianity of the
seismic event up to and perhaps beyond the 0 dB level. We
hypothesize that this is why the S/L-Kurt scheme is more
robust in the presence of noise than methods based on other
principles.
In addition, Figure 3 displays the difference between S/L-
Kurt and kurtosis in sliding windows. Both LTK and STK
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Automatic Seismic Event Detection on Microseimograms
are biased towards identification of the stronger event, such
that in the right part of the Figure 3, they recognize the S-
wave event rather than P-wave event. In contrast, the S/L-
Kurt method recognizes both seismic events.
Field data Examples
Before hydraulic fracturing, the perforation shots are used
to determine the orientation of geophones. Since the
perforation data have a relatively high SNR, we first apply
the proposed method on a perforation shot record. Figure 4
shows that the proposed method can not only accurately
identify the seismic P-wave onset, but also the two
subsequent S-wave arrivals.
Figure 4: Perforation shot example. (Top) Perforation shot; (Bottom) Normalized S/L-Kurt, STK and LTK results. (STK and
LTK are normalized into [0 0.5], while S/L-Kurt into [0 1].)
Figure 5: Field data example with strong P-wave. (Top) Micro-seismic record; (Bottom) Normalized S/L-Kurt, STK and LTK
results. (STK and LTK are normalized into [0 0.5], while S/L-Kurt
into [0 1].)
Figure 6: Field data example with strong S-wave. (Top) Micro-
seismic record; (Bottom) Normalized S/L-Kurt, STK and LTK results. (STK and LTK are normalized into [0 0.5], while S/L-Kurt
into [0 1].)
Figures 5 and 6 demonstrate the field microseismic data
application results. Regardless of whethere the P-wave or
S-wave is stronger, S/L-Kurt can detect both arrivals. A
simple threshold segmentation step can help us pick an
accurate seismic event first break.
Conclusion
We have developed a seismic event indentification
algorithm based on HOS. The proposed S/L-Kurt method
provides reliable and accurate seismic event identification
on both synthetic and field data examples in the presence
of 0 dB Gaussian noise. The examples shown indicate that
the method can detect not only the P-wave arrival but also
both S-wave arrivals.
Acknowledgments
We express our gratitude to the industry sponsors of the
Attribute-Assisted Seismic Processing and Interpretation
(AASPI) Consortium for their financial support. The field
seismograms were provided by Devon Energy. Also thanks
to the National Natural Science Foundation of China
(seismic multi-wave fields characteristics analysis of the
thin interbedded reservoirs, Grant No. 41204091).
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http://dx.doi.org/10.1190/segam2014-1605.1 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2014 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES
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