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Improve sensor orientation using both drop-ball and microseismic events
Yuanhang Huo*, Wei Zhang, Jie Zhang, University of Science and Technology of China (USTC)
Summary
The event locations are essential quantities in microseismic
monitoring for mapping hydraulic fractures. For downhole
monitoring, the accuracy of the event locations depends on
the accuracy of the P-wave polarization angle, which
consequently depends on the accuracy of sensor orientation.
Sensor orientation angle is generally determined by known
location events such as perforation or drop-ball event,
which is characterized by low signal-to-noise ratio (SNR).
The accuracy of sensor orientation can be verified by the
waveform coherence for various events after applying
sensor orientation. In this study, we develop a new method
utilizing both perforation/drop-ball event and high SNR
microseismic events at unknown locations to derive
orientation angles. In this approach, the waveform
coherence of unknown events is directly used in the
determination of sensor orientation angle. We use both
synthetic data and real data to demonstrate the feasibility
and reliability of the new method, which is more accurate
than the traditional approach using drop-ball event alone.
Introduction
Microseismic monitoring is an efficient technique for
mapping hydraulic fractures. Event locations can provide
information about the geometry and development of the
hydraulic fractures for evaluating the stimulation. For
downhole monitoring with a single monitoring well, the
location procedure usually consists of two steps: the first
step locates events in a 2D vertical plane, the second step
projects the 2D locations to 3D by P-wave polarization
angle, which represents the back-azimuth of the event. But
the direction of the horizontal components of the threecomponents seismic sensors in downhole are usually
unknown and random orientated, which needs a sensor
orientation approach to correct to the right direction. The
error of the sensor orientation angle will directly propagate
to the derived P-wave polarization angle, which may cause
less coherent waveform of the events and large error in
calculation of event azimuth.
Sensor orientation can be done by performing a
polarization analysis to derive P-wave propagation
direction, then the difference between P-wave propagation
direction and geometry direction from event to sensor
indicates the rotation angle, which can be applied to rotate
three-component traces to the correct orientation. Becquey
and Dubesset (1990) developed a method with polarization
analysis to derive three-component sensor orientation in a
deviated observation well. Unlike processing geophones
deployed in land, Nakamura et al. (1987) adopted air-gun
© 2016 SEG
SEG International Exposition and 87th Annual Meeting
shots to determine the location and orientation of OBS
stations. Besides, Di Siena et al. (1984) proposed a power
maximization approach to obtain the azimuthal orientation
of three-component geophones in a vertical observation
well, which consists on maximizing the signal energy of the
first P-wave arrival by orientation on a particular axis.
Utilizing SH wave, Michaels (2001) applied a technique
based on principal component analysis to acquire the sensor
orientation relative to the source polarization direction.
Differently from the common approaches calculating
orientation of every sensor directly, Zeng and McMechan
(2006) used traces cross-correlation to infer relative
rotation angles among all sensors in borehole arrays.
However, we do not know the true rotation angles of the
sensors for real data. The derived rotation angle is affected
by noise and contains error. To investigate the accuracy of
the rotation angle, we can apply rotation on the data and
check the coherence of the waveform along the sensor
array. If the rotation angle is correct, we expect the
maximum coherency of the waveform to be observed.
However, if the data does not show strong coherence, the
rotation angle may contain error, but there is no solution to
improve it. The error of the rotation angle generally comes
from noise. Surface orientation shots may show good SNR
but may not be available in all the projects. For those cases
without surface orientation shots, we have to use
perforation shots or ball-drop events to obtain the
orientation angles. The low SNR of those events, especially
drop-ball event data, may cause large error in the calculated
rotation angles.
In this study, we introduce the constraint of waveform
consistency of unknown events into the calculation of
orientation angles and develop a new method for
orientation utilizing both perforation/drop-ball event and
high SNR microseismic events of unknown locations. Since
we can generally always find some microseismic events
with high SNR, the accuracy of the new method should be
higher than the traditional approach using perforation or
drop-ball event due to the higher SNR of those events.
Theory
In our method, we first scan all the data to find several high
SNR events even though we are not aware of their locations.
We utilize these events to maximize the waveform
consistency between adjacent sensors to compute relative
rotation angles between sensors. After rotations with those
relative angles, all the sensors are orientated to the same
direction with an absolute rotation angle. This absolute
rotation angle can be obtained by comparing the
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Improve sensor orientation using drop-ball and microseismic events
polarization angle of each sensor to the geometry angle of
the drop-ball event in the least-squares sense.
(a) Determination of relative orientation
A rotation of the vector, composed of the two horizontal
components (X and Y), can be described by a rotation
matrix in two dimensions under the assumption that all
vertical components are parallel to the casing of the vertical
borehole. The rotation matrix is
 X rot  cos  sin    X ori 
(1)
 Y    sin  cos    Y  ,
  ori 
 rot  
where X ori and Yori are original components,  denotes
the rotation angle (counter-clockwise is positive), X rot and
Yrot are rotated components.
Our method relies on the fact that the waveform misfit
reaches a global minimum for two aligned sensors, while
larger misfit implies little similarity. Because we just invert
one independent angle every time, ensuring no rankdeficient and ill-conditioned problems, the objective
function can be imposed without regularization terms in a
quite simple form
(2)
 (m) || Pref  Prot (m) ||2 ,
(b) Determination of absolute orientation
After relative rotations of all other sensors with respect to
the reference sensor, the absolute orientation of reference
one can be determined with the algorithm described in this
section.
The polarization within a time window is estimated as
following. The terms of covariance matrix are evaluated as
PP T
1 N
S jk 
  pij pik ,
(6)
N
N i 1
where P is the data matrix in given time window, pij is
the ith sample of component j and N is the number of
samples (Jurkevics, 1988). In addition, the estimation of
principal axes involves computing the eigenvalues
( 1 , 2 , 3 ) and eigenvectors ( u1 , u2 , u3 ), which are
nontrivial solutions to
(7)
( S   2 I )u  0 ,
where I is the 3×3 identity matrix and 0 is a column
vector of zeros.
The azimuth of P-wave propagation can be calculated from
u
(8)
Azimuth  tan 1 ( x1 ) ,
u y1
where m is the relative rotation angle, Pref is observed
where ux1 and u y1 are the X and Y direction cosines of
waveform data for the sensor we choose as the reference
sensor and Prot is rotated waveform data for adjacent
sensor with respect to the reference one. Since the vertical
component is not affected by rotation transform, we only
take into account the horizontal components from several
unknown microseismic events and define Pref as
eigenvector u1 corresponding to the largest eigenvalue.
Pref  ( Px11 Px12 ... Pxl1 , Py11 Py12 ... Pyl1 , Px21 Px22 ... Pxl2 ,
Py21 Py22 ... Pyl2 , ... ... , Pxk1 Pxk2 ... Pxlk , Pyk1 Pyk2 ... Pylk )
lated in the least-squares sense to minimize
  Az
, (3)
and Y components associated with the kth event,
respectively.
We can get the rotation angle by utilizing Gauss-Newton
method to minimize  (m) and solve the norm equation
(4)
J (m) m   F (m) ,
where
1
 Prot
(m)  Pref1 


2
P (m)  Pref2 
.
(5)
F (m)=  rot



 2 k  l

2 k  l
 Prot (m)  Pref 
2
M
i 1
where Pxlk and Pylk denote the lth sample point data of X
© 2016 SEG
SEG International Exposition and 87th Annual Meeting
The absolute orientation of it, Azleast  squares , can be calcu-
i
 Azleast  squares  ,
(9)
where M denotes the number of sensors and Azi represents
the calculation result of ith sensor.
Synthetic example
To prove the feasibility and reliability of the above
approach, we apply it to synthetic data generated with
General Reflection and Transmission Method (GRTM) for
a homogeneous layered model (Zhang et al., 2003).
The acquisition geometry consists of twelve threecomponent sensors from the depth of 1350 m to 1625 m,
with an interval of 25 m. Eight microseismic events are
located in different positions and the drop-ball event is
located at (800 m, 100 m, 1400 m), the depth within
between sensors (Figure 1). For the homogeneous isotropic
model, P wave velocity is 3000 m/s and ratio of Vp/Vs is
equal to 1.7.
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Improve sensor orientation using drop-ball and microseismic events
(a)
(b)
Figure 1: Acquisition geometry with 12 sensors (green triangle), 8
microseismic events (red asterisk) and 1 drop-ball event (blue
asterisk).
We use random rotation angles (Table 1) to rotate the
synthetic waveforms to model the situation that the
orientation of every sensor is unknown and distributed
randomly.
(a)
Figure 3: (a) Waveforms of X and Y components after orientation
correction with traditional approach in Event 8. (b) Waveform of X
and Y components after orientation correction with traditional
approach in drop-ball event.
(a)
(b)
Figure 2: (a) Waveforms of X and Y components with 5%
Gaussian noise added after forward rotations in Event 8. (b)
Waveforms of X and Y components with the same level noise
added after forward rotations in drop-ball event.
Random noise of the same level is added to both events and
drop-ball event. Figure 2a shows the horizontal components
(X and Y) of P-wave waveform for Event 8 (800m, 500m,
1500m) and Figure 2b is for the drop-ball event. It should
be noted that the drop-ball event has lower amplitude. The
same noise level roughly corresponds to 5% Gaussian noise
for Event 8 while 20% Gaussian noise for the drop-ball
event. Figure 2a and Figure 2b are scaled separately for
better visualization.
We use all the 8 events to calculate 11 relative rotation
© 2016 SEG
SEG International Exposition and 87th Annual Meeting
(b)
Figure 4: (a) Waveforms of X and Y components after orientation
correction with our method in Event 8. (b) Waveforms of X and Y
components after orientation correction with our method in dropball event.
angles with our developed method. Using the sixth sensor
as the reference one, other 11 sensors are rotated towards
the reference sensor using corresponding relative angles.
Then the absolute orientation is estimated using all the
sensors in the least-squares sense. Figure 3a and Figure 3b
show the orientated X and Y components of Event 8 and
drop-ball event using orientation angles from the
conventional approach; while Figure 4a and Figure 4b are
corresponding results by using our new method. The higher
level of coherence of the waveform by the new method at
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Improve sensor orientation using drop-ball and microseismic events
Sensor 7 and 8 and 9 is obvious, which indicates the higher
accuracy of the derived rotation angle by the new method.
Table 1 shows the comparison between the results by our
method and the ones obtained using the traditional
approach with the drop-ball event alone, which shows more
accurate and reliable results of the new method
quantitatively.
Sensors
Number
True
Orientation
Angle (°)
1
2
3
4
5
6
7
8
9
10
11
12
-5
100
-50
20
30
-35
-20
55
-90
10
-79
-100
Conventional
Technique (°)
Angle
Error
Our
Method (°)
Angle
Error
-6
102
-47
21
35
-37
-24
56
-91
16
-77
-97
-5.0
100.1
-49.9
20.3
30.1
-35.0
-20.0
55.3
-89.8
10.1
-79.1
-99.9
-1
2
3
1
5
-2
-4
1
-1
6
2
3
0
0.1
0.1
0.3
0.1
0
0
0.3
0.2
0.1
-0.1
0.1
Table 1: Comparison between orientations obtained with our
method and the estimated ones with conventional technique.
ensure better waveform similarity after applying sensor
orientation. Synthetic examples and real data suggest that
our approach can provide more accurate and reliable results
than the conventional one.
(a)
(b)
Figure 5: (a) Raw data. (b) Rotated data with our new approach.
(a)
(b)
Real data example
We test our method in a real data example, where two
microseismic events with unknown locations and high SNR
are selected to calculate the relative orientation angles and
one drop-ball event is applied to determine absolute
orientation of the first sensor using the algorithm in this
paper. The calculated orientation angles are shown in Table
2 for both methods, which have a difference from 0.6° to
10.3°. Figure 5a shows raw data of a microseismic event
and its rotated traces using the orientation angles obtained
with our new method are in Figure 5b. We can see a high
coherence between adjacent sensor pairs. Figure 6 shows
the distribution of event azimuth from the 12 sensors for
this event after orientation correction by the two methods.
Obviously, the event azimuths in Figure 6b are more
concentrated and have a smaller variance, implying our
method superior performance than the traditional method.
Conclusions
We develop a new method for determining the orientations
of sensors deployed in the vertical observation well, taking
into account both unknown microseismic events and dropball event together. Due to constraining the waveform
coherence between adjacent sensor pairs, accuracy of
relative angles calculated can be improved. Compared with
the orientation angles obtained with drop-ball event alone,
our new approach can derive the orientation angle that can
© 2016 SEG
SEG International Exposition and 87th Annual Meeting
Figure 6: Event azimuth (cross symbol) (a) after orientation
correction with conventional technique; (b) after orientation
correction with our method.
Sensor
Number
Conventional (°)
Our Method (°)
Sensor
Number
Conventional (°)
Our Method (°)
1
2
3
4
5
6
87
90.0
-35
-44.9
124
-127.8
45
43.5
49
42
23
26.2
7
8
9
10
11
12
21
14.5
-16
-12.0
29
32.3
146
156.3
-103
-103.6
-36
-27.0
Table 2: Comparison of orientation angles obtained with
conventional technique and our method.
Acknowledgements
We appreciate the support of GeoTomo, allowing us to use
the MiVu software package to perform this study.
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EDITED REFERENCES
Note: This reference list is a copyedited version of the reference list submitted by the author. Reference lists for the 2016
SEG Technical Program Expanded Abstracts have been copyedited 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.
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© 2016 SEG
SEG International Exposition and 87th Annual Meeting
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