Downloaded 10/14/14 to 50.244.108.113. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
Double difference method for locating microseismic events from a single well
Xiao Tian*, Jie Zhang, Wei Zhang, University of Science and Technology of China (USTC)
Summary
The double difference (DD) inversion method has long
been applied for locating a cluster of earthquakes, using
data recorded at surface seismic stations. We implement a
particular DD method for locating a cluster of microseismic
events with data from a single well. We assume a 1-D
velocity model and a vertical monitoring well, thus
projecting all events to a 2D profile. Event azimuth
solutions are determined from separate analysis of initial P
wave polarizations. Synthetic tests suggest that a DD
method using data from a single well can constrain event
depth better than a localization method based on absolute
traveltimes. Our input data includes the difference between
events of P or S traveltimes (like the traditional DD
method). However, the inversion results seem sensitive to
initial event locations, and the lateral location resolution is
poor. When we also include the S-P traveltime differences
for each event into the inversion, the lateral resolution
improves. In addition, this reduces the dependence on the
initial guess for the event locations and the velocity model.
Introduction
Microseismic monitoring, since the initial idea in the 1970s
and its commercialization around 2000, has proven to be a
vital tool for understanding underground processes
(Warpinski et al., 2009). It plays an important role in
hydraulic monitoring, water-flooding, and many other
production methods.
Microseismic location methods
include, for example, grid searches and migration-based
imaging methods (Rodi et al., 2006; Reshetnikov et al.,
2010).
Several factors affect the accuracy of the
determined locations; such as uncertainty in the velocity
model and uncertainty in traveltime picks.
In earthquake seismology, the double difference (DD)
inversion method has been developed to reduce the effect
of a poorly known velocity model (Waldhauser and
Ellsworth, 2000). It requires arrival time picks from
multiple events and infers accurate relative locations for the
group. One assumption is that the hypocenter separation
between two earthquakes is small, with respect to the
distance between the event and the recording station. The
hypocenter separation should also be small with respect to
the scale length of the velocity heterogeneities. Zhang et al.
(2006) propose a DD tomography method using both
absolute and relative arrival times for surface data.
Recently, the DD method has been used to determine
microseismic locations (Fernando et al., 2013). DD
methods have the advantages of a high precision of relative
© 2014 SEG
SEG Denver 2014 Annual Meeting
arrival times by using a cross-correlation method.
Obtaining the absolute event locations using a grid search
method is always the first step. The second step is to
compute cross-correlations to obtain the relative arrival
times between any pair of two events. Finally, the DD
method is used to obtain highly accurate relative event
locations. However, the assumptions for DD break if the
event cluster distribution is larger than the distance to
(Mukhtarov et al., 2012). Li et al. (2012) developed an
extended DD tomographic method using an anisotropic
tomography. In this study, we explore the issues associated
with monitoring microseismic events using an improved
microseismic DD method (including the S-P traveltime
differences) for data from a single well.
Theory
1.
Traditional double-difference method
The traditional DD method is an earthquake location
method, and it is developed for obtaining the relative
location of hypocenters (Waldhauser and Ellsworth, 2000).
The relationship between event locations and traveltimes is
highly nonlinear. After using a truncated Taylor expansion
to linearize this relationship, the residuals are linearly
related to the perturbations of parameters. We combine all
event pairs for all receivers to form a system of linear
equations of the following form：
(1)
G pp m  d ,
Where Gpp is the sensitivity matrix containing the partial
derivatives of P-wave differential arrival times with respect
to the model parameters. This matrix has dimensions:
n(n-1)/2*mr*3n, (where n is the event numbers, mr is the
receiver numbers). The dimension of the d vector is n(n1)/2*mr , and Δm is a vector of length 3n, containing the
changes of location parameters (Δx, Δz, Δτ).
There are several issues when we apply DD on data
recorded in a single well. If we attempt to locate an event
recorded by one station, by fitting the relative arrival times
of two events. The event locations could be on a series of
concentric circles with the radius at the distance between
source and receiver (see Figure 1b). If we attempt to locate
an event recorded by three stations, by fitting the relative
arrival times of two events. There are three sets of such
concentric circles (isochronous surfaces). The true events’
locations must be at the intersection of the three circles. If
the distance between the array and the events’ true
locations increases, the curvature of the concentric circles
intersection will decrease. This results in an increasing
uncertainty of the horizontal absolute locations. This
problem is eliminated when we use more then one well.
DOI http://dx.doi.org/10.1190/segam2014-1246.1
Page 2193
while the traditional DD method has a high vertical
resolution.
-3
Only use absolute data
x 10
80
14
100
12
a)
Depth(m)
120
b)
10
140
8
160
6
180
Figure 1: Single well monitoring geometry, green triangles indicate
the receivers and the red stars indicate the sources. a) Two events
recorded by only one receiver, the event locations could be on
concentric circles. b) Two events recorded by 3 receivers, the
events are located at the intersection of the concentric circles.
4
200
220
2
240
0
50
100
150
200
250
300
Distance(m)
350
400
450
-4
Only use DD method
x 10
60
We propose to include the P- and S-wave differential
arrival time between for each event. This has several
advantages. Firstly, the P- and S-wave differential arrival
time adds information on the absolute event’s locations.
Secondly, the P- and S-wave differential arrival eliminates
the dependency on the unknown event origin times. The
differential arrival times can be added into equation (1), we
find the following system of linear equations:
 G pp 
.


 Gss   m    d 
G p  Gs 


(2)
Where Gss is the sensitivity matrix containing the partial
derivatives of S-wave differential arrival times with respect
to
the
model
parameters
(with
dimensions:
n(n-1)/2*mr*3n). And Gp-Gs is the sensitivity matrix
containing the partial derivatives of P- and S-wave
differential arrival times with respect to the model
parameters (with dimensions n*mr).
80
2.5
100
2
120
Depth(m)
2.
Microseismic double-difference method
The traditional DD method (Waldhauser and Ellsworth,
2000) utilizes the relative P-wave or/and S-wave traveltime
information. Zhang and Thurber (2006) proposed the DD
tomography method by adding the absolute arrival times.
140
1.5
160
1
180
200
0.5
220
240
0
50
The location with absolute arrival times has the drawback
that the uncertainty of the vertical location is higher than in
horizontal location (Zimmer, et al. 2011). We compare the
accuracy of a conventional absolute localization method
(Geiger, 1910) and the traditional DD method by plotting
the traveltime misfits of both methods (see Figure 2). In
the DD misfit figure, we let the distance between two
events be a constant and each grid point represents the
average residual. At the minimum residual we find the
optimum location for the two events. Figure 2 shows that
the absolute location method has a bad vertical resolution
© 2014 SEG
SEG Denver 2014 Annual Meeting
150
200
250
300
Distance(m)
350
400
450
500
550
Figure 3 shows the geometry of our monitoring system
with a single well. We design a four layer horizontal
velocity model, where the second layer is a low velocity
layer. There are 10 receivers in the borehole with 15 meter
receiver spacing, and there are 4 sources. The dataset of
traveltimes from each event to each receiver is computed
using a ray tracing code.
0
50
100
The vertical and horizontal location uncertainty
100
Figure 2: Top panel; the traveltime residuals of the absolute
location method; Bottom panel; the residuals of the traditional DD
method. Red points indicate the true locations and green triangles
indicate the receivers.
Depth (m)
Downloaded 10/14/14 to 50.244.108.113. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
Double difference method for locating microseismic events from a single well
Vp=5770m/s
Vs=3331m/s H= 80m
Vp=4640m/s
Vs=2679m/s H=60m
150
Vp=5750m/s Vs3320m/s H=80m
200
250
Vp=6000m/s
Vs=3464m/s H=130m
300
350
0
100
200
300
400
Radial Distance(m)
500
600
Figure 3: Velocity model and acquisition geometry with 4 test
events (red stars) and a shallow geophone array with 10 receivers
(green triangles).
DOI http://dx.doi.org/10.1190/segam2014-1246.1
Page 2194
We use the traditional DD method to determine the
locations. Figure 4a and 4b shows that we retrieve the
vertical position well, but do not find the correct horizontal
position. In order to understand this result, lets take the
first receiver as an example: As shown in Figure 4c and 4d,
for each receiver the calculated arrival times using the
determined locations are similar to the calculated arrival
times using the true locations. We compare the relative
arrival times for any pair of two events; they approximate
overlap.
-6
175
2.6
initial data
inversion results
true data
170
inversion results
162
175
160
170
158
165
initial data
156
160
inversion results
true data
155
154
150
152
145
150
390
395
400
405
410
415
rms/ms
400
410
420
430
440
450
460
b)
165
165
160
160
155
2
155
390
170
2.2
160
380
a)
inversion results
rms with different iterations
x 10
2.4
165
155
1.8
1.6
150
150
1.4
150
1.2
145
145
340
1
140
360
370
380
390
400
410
420
0.8
0
430
5
10
a)
15
iterations
20
25
30
-3
0.0805
4
inversion results
true data
0.08
Receiver 1: the arrival times between any two events
x 10
inversion results
true data
3
350
360
370
380
c)
390
400
410
145
380
400
420
440
460
480
500
d)
Figure 5: Location results with different initial event locations: a)
the initial event center is same as with the true values; b), c) and d)
the initial event center is far away from the true value.
b)
Receiver 1: the arrival times for 4 events
0.0795
2
relative arrival times/s
0.079
arrival times/m
Downloaded 10/14/14 to 50.244.108.113. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
Double difference method for locating microseismic events from a single well
0.0785
0.078
0.0775
0.077
DD method tests in different microseismic monitoring
scenarios
1
0
-1
-2
0.0765
-3
0.076
0.0755
1
1.5
2
2.5
events
3
3.5
4
c)
-4
1
1.5
2
2.5
3
3.5
4
Any two events
4.5
5
5.5
6
d)
Figure 4: a) the located events with traditional DD method, include
the true locations (blue plus), initial event locations (green stars)
and the determined locations (red circles). Note that in the vertical
direction we have better location accuracy than on the horizontal
direction; b) RMS misfit as a function of iteration; c) the arrival
times for 4 events at the first receiver, the red line indicates the
inversion results and the blue dotted line indicates the true values;
d) the relative arrival times for any pair of two events.
The initial location of the center of the event cluster
Figure 5 demonstrates that the center value of the initial
event location is very important. We can obtain better
location results when the center of the initial event location
is close to the correct value. Table 1 shows the center of
the event cluster before and after event localization.
Model
true data
(a) model
(b) model
(c) model
(d) model
Before location
X/m
Z /m
400.000
155.000
400.000
155.000
450.000
170.000
357.500
155.000
467.500
155.000
After location
X /m
Z /m
400.000
155.000
400.029
154.948
159.005
450.604
374.924
152.971
454.186
159.301
We design a few different microseismic monitoring
scenarios; including two kinds of geophone arrays and four
groups of events (see Figure 6). From the results of
determining locations, we can conclude that if the event
depth is deeper than the receivers, the location accuracy
will deteriorate.
1.
Adding the differential S-P arrival times
In tests presented in Figure 6, it is obvious that the
traditional DD method has the weaknesses that it relies
heavily on an initial event location. In an attempt to
mitigate this weakness, we use the microseismic DD
location method with the addition of the differential S-P
arrival times.
Figure 7 show that this improved
microseismic DD method can obtain better accurate
locations than traditional DD method in both horizontal and
vertical directions.
2.
The effect of noise and velocity model uncertainty
Field data always contains noise, such as the arrival time
picking errors and receiver interferences. In order to
simulate the picking errors, we add a random noise level of
about 0.2 ms to the relative arrival times, and add a random
noise level of about 2 ms to the absolute arrival times
(Figure 8a). In addition, we test the consequence of an
inaccurate velocity model (Figure 8b). Results shows that
our improved microseismic DD method can perform well
in the presence of noise and velocity model inaccuraties.
Table 1: Location results with different initial events centers.
© 2014 SEG
SEG Denver 2014 Annual Meeting
DOI http://dx.doi.org/10.1190/segam2014-1246.1
Page 2195
Double difference method for locating microseismic events from a single well
y
165
160
160
155
100
Vp=4640m/s
Vs=2679m/s H=60m
155
150
Depth/m
150
150
Vp=5750m/s Vs3320m/s
H=80m
200
250
300
145
380
5
10
15
440
460
480
145
380
500
30
35
40
420
440
460
480
500
b)
45
175
a)
initial data
inversion results
true data
170
ray path
inversion results
7.5
inversion results
rms/ms
160
true data
-4
rms with different iterations
6.5
initial data
170
100
x 10
7
165
175
80
120
400
Figure 7: The located events before (b) and after (a) adding the
differential S-P travel times. Note the results are good even if the
initial event center is far away from the true value.
20
25
horizontal /m
60
420
a)
Vp=6000m/s
Vs=3464m/s H=130m
0
400
6
165
155
160
150
5
155
145
4.5
150
140
360
5.5
4 events
140
160
180
200
220
240
370
380
390
400
410
420
0
50
100
150
200
250
300
350
400
450
140
360
4
430
145
370
380
390
400
410
420
2
4
6
430
8
10
12
iterations
14
16
18
20
velocity model
175
265
0
initial data
inversion results
true data
ray path
50
170
true velocity
velocity perturbation
50
100
165
100
0
a)
260
150
160
150
depth/m
Downloaded 10/14/14 to 50.244.108.113. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
receivers 1
receivers 2
events 1
events 2
events 3
events 4
Vp=5770m/s
Vs=3331m/s
H= 80m
50
170
165
0
255
155
200
250
200
150
250
initial data
250
true data
300
0
50
100
150
200
250
300
350
400
450
60
240
380
385
390
395
400
405
140
360
410
415
380
390
400
410
420
430
400
4200
4400
4600
4800
5000 5200 5400
velocity/m/s
5600
5800
6000
6200
b)
Figure 8: The located events with the microseismic DD method; a)
the velocity model is accuracy, and add the random noise to arrival
times; b) the located events with the inaccurate velocity model and
correct arrival times.
initial data
inversion results
175
true data
100
350
370
420
180
80
300
145
inversion results
245
170
120
165
140
160
160
155
180
145
220
240
Conclusions
150
200
0
50
100
150
200
250
300
350
400
140
380
385
390
395
400
405
410
415
420
165
60
80
160
100
120
155
140
160
150
180
initial data
200
inversion results
145
true data
220
240
0
50
100
150
200
250
300
350
400
450
140
380
385
390
395
400
405
410
415
420
425
b)
Figure 6: a) Different observation systems; blue triangles indicates
10 receivers with a 10m interval and green triangles indicates 12
receivers with a 15m interval. The receiver 1 is for the event 2,3
and 4, while the receiver 2 is for event 1. b) The ray paths and the
results of determining the locations using the traditional DD
method, for the four models.
© 2014 SEG
SEG Denver 2014 Annual Meeting
We test the feasibility of using the traditional DD method
to locate microseismic events from a single well. It has
high resolution in the vertical direction compared to
absolute location methods. Nevertheless, the initial event
locations have strong influence on the localization results.
In order to solve this problem we add the differential S-P
arrival times. Numerical experiments show that the
microseismic DD method can provide a better location
results. In addition, the method is able to handle noise and
velocity model inaccuracies.
Acknowledgements
We appreciate the support from GeoTomo, allowing us to
use MiVu software package to perform this study.
DOI http://dx.doi.org/10.1190/segam2014-1246.1
Page 2196
Downloaded 10/14/14 to 50.244.108.113. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/
http://dx.doi.org/10.1190/segam2014-1246.1
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
Castellanos, F., and M. V. D. Baan, 2013, Microseismic event locations using the double -difference
algorithm: Focus.
Geiger, L., 1910, Herdbestimming bei Erdbeben aus den Ankunftszeiten, K. Ges Wiss: Gött, 4, 331–349.
Li, J., H. Zhang, W. Rodi, and M. N. Toksöz, 2012, Microseismicity location and simultaneous
anisotropic tomography with differential traveltimes and differential back azimuths: 82nd Annual
International Meeting, SEG, Expanded Abstracts, doi: 10.1190/segam2012-1382.1.
Mukhtarov, T., A. Pinnacle , 2012, Uncertainty space for microseismic event locations using a double
difference algorithm: Geoconvention Vision.
Reshetnikov, A., S. Buske, and S. A. Shapiro, 2010, Seismic imaging using microseismic events: Results
from the San Andreas Fault System at SAFOD: Journal of Geophysical Research: Solid Earth, 115,
no. B12.
Rodi, W., 2006, Grid-search event location with non-Gaussian error models: Physics of the Earth and
Planetary Interiors, 158, no. 1, 55–66, http://dx.doi.org/10.1016/j.pepi.2006.03.010.
Waldhauser, F., and W. L. Ellsworth, 2000, A double -difference earthquake location algorithm: Method
and application to the northern Hayward fault: California : Bulletin of the Seismological Society of
America, 90, no. 6, 1353–1368, http://dx.doi.org/10.1785/0120000006.
Warpinski, N., 2009, Microseismic monitoring: Inside and out: Journal of Petroleum Technology, 61, no.
11, 80–85, http://dx.doi.org/10.2118/118537-JPT.
Zhang, H. J., and C. Thurber, 2003, Double-difference tomography: The method and its application to the
Hayward fault, California : Bulletin of the Seismological Society of America, 93, no. 5, 1875–1889,
http://dx.doi.org/10.1785/0120020190.
Zimmer, U., 2011, Microseismic design studies: Geophysics, 76, no. 6, WC17–WC25,
http://dx.doi.org/10.1190/geo2011-0004.1.
© 2014 SEG
SEG Denver 2014 Annual Meeting
DOI http://dx.doi.org/10.1190/segam2014-1246.1
Page 2197