Discrimination of P-Wave Interval
in Time-Quefrency Analysis
for Proximity Microseismic Doublets
Koji Nagano
Muroran Institute of Technology
Muroran, Hokkaido, 050-8585, Japan
nagano@mmm.muroran-it.ac.jp
What we want to know
Geothermal fracture reservoir
Cloud
Fine structures
Flow paths
in geothermal reservoir
Soultz in France
2
Proximity microseismic doublets
• Similar waveforms
• Interval between events is short, <1s.
3
Accurate location in proximity MS doublets
microseismic doublets with long interval
different velocity model
1st event
long
interval
2nd event
proximity microseismic doublets
More precise
than doublets with long interval
4
Relative location
P-wave interval
Relative location
The relative location estimated
based on the interval is much
precise than that calculated from
the each sources.
Fine structure
of fracture reservoir
5
Cepstrum analysis for proximity MS doublets
• Cepstrum analysis is used to detect interval
6
Cepstrum
y(t )  x(t )  rx(t  T )
Interval
T
Y ( f )  X ( f )[1  r exp( j 2fT )]
Y( f )  X ( f )
2
2
1  r
2
 2r cos  2 fT 
logY ( f )  log X ( f )  log1  r 2  2r cos2fT 
2
2


C (q)  F 1 log X  f   F 1 log1  r 2  2r cos2fT 
2
7
Two cepstrum peaks
• Which is the P-wave interval in the two
cepstrum peaks ?
P
S
P?
S?
8
quefrency
- Window function suppresses
data after the onset of the
2nd S-wave.
- I shorten the window function.
- When the window function
suppresses the 2nd S-wave,
S-waves lose similarity
and the S-wave peak decreases.
cepstrum
Time-quefrency analysis
- Cepstrum-quefrency graph
is used to detect the interval.
cepstrum
Terminal of window
9
quefrency
Contour plot and cepstrum graph
quefrency
Contour plot:
To discriminate the P-wave peak
from the S-wave peak
identification of the cepstrum peaks
- continuity of the peak,
- comparison of the peak width
- exclusion of artifacts
cepstrum
Terminal of window
- low resolution in quefrency
Cepstrum graph:
- precise detection of quefrency
quefrency
- difficult discrimination from artifacts
10
4 check points in contour plot
P-wave interval peak
S
cepstrum
quefrency
(1) starts more early.
The window function suppresses the 2nd S-wave.
The 1st and 2nd P-waves are isolated.
(2) is more stable.
The S-wave peak decreases because the S-wave loses similarity
(3) is lower.
The P-wave is smaller than the S-wave
(4) is narrower.
P
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Terminal of window
Soultz geothermal field
15089 MS events
were located during
hydraulic injection in
1993.
The data were
monitored at 4 stations
Data length was 1.6 s.
Sampling frequency was
5000 Hz.
Proximity MS doublets
were 230
12
Typical result of the time-quefrency analysis
quefrency
Early start
Stable, low, and narrow peak
Some artifacts are visible
cepstrum
Terminal of window
13
quefrency
9 events show P-wave interval peak
quefrency
quefrency
The P-wave interval should be detected at 4 stations
to determine relative location.
Terminal of window
quefrency
quefrency
Terminal of window
Terminal of window
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Terminal of window
Relative location
The P-wave intervals in the Proximity MS doublets
are compared among the 4 stations.
Moriya 2003 showed 4752
relative locations of MS
doublets with long interval.
We will examine my relative
locations and his data.
15
Conclusions
• Proximity MS doublets are a good tool to estimate fine
structures of a geothermal reservoir.
• Time-quefrency analysis can provide the P-wave interval
between the proximity MS doublets.
• 4 check points are indicated to discriminate the P-wave
interval in a contour plot of the time-quefrency analysis.
• I have estimated relative locations of 9 events recorded
in Soultz geothermal field.
16
Cepstrum and auto-correlation
18
Rotation of coordinates
3 component seismic detector was used.
3D particle motion associated with
seismic waves was measured.
Data in the direction of the P-wave polarization
is analyzed in the time-quefrency analysis.
The data is larger than that in the other directions
We have clear P-wave peak in the contour plot
when the data in the direction of the P-wave
polarization is analyzed in the time-quefrency
analysis.
19
A result of the rotation
X-Y-Z
P-wave polarization is
estimated in the data at
the onset of the P-wave
P-S1-S2
S1: the maximum variance on S-wave plane
S2: P and S1 are perpendicular
20