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Discrimination of P-Wave Interval in Time-Quefrency Analysis
for Proximity Microseismic Doublets
Koji NaganoMuroran Institute of Technology
Muroran, Hokkaido, 050-8585, [email protected]
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What we want to know
Fine structuresFlow pathsin geothermal reservoir
Cloud
Soultz in France
Geothermal fracture reservoir
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Proximity microseismic doublets
• Similar waveforms• Interval between events is short, <1s.
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Accurate location in proximity MS doublets
microseismic doublets with long interval
long interval
different velocity model
proximity microseismic doublets
More precise than doublets with long interval
1st event 2nd event
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Relative location
P-wave interval
Relative location
Fine structureof fracture reservoir
The relative location estimated based on the interval is much precise than that calculated from the each sources.
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Cepstrum analysis for proximity MS doublets
• Cepstrum analysis is used to detect interval
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Cepstrum
)()()( Ttrxtxty
)]2exp(1)[()( fTjrfXfY
2 2 2( ) ( ) 1 2 cos 2Y f X f r r fT
fTrrfXfY 2cos21log)(log)(log 222
fTrrFfXFqC 2cos21loglog)( 2121
T
Interval
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Two cepstrum peaks
• Which is the P-wave interval in the two cepstrum peaks ?
P
S
P ? S ?
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Time-quefrency analysis
- 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.
cep
stru
m
quefrency
que
fre
ncy
Terminal of window
- Cepstrum-quefrency graph is used to detect the interval.
cep
stru
m
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Contour plot and cepstrum graph
Contour plot: To discriminate the P-wave peak from the S-wave peakidentification of the cepstrum peaks - continuity of the peak, - comparison of the peak width - exclusion of artifacts
- low resolution in quefrency
Cepstrum graph: - precise detection of quefrency
- difficult discrimination from artifacts
que
fre
ncy
Terminal of window
cep
stru
m
quefrency
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4 check points in contour plotP-wave interval peak
(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
S
que
fre
ncy
Terminal of window
cep
stru
m
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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
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Typical result of the time-quefrency analysis
Early startStable, low, and narrow peak
Some artifacts are visible
que
fre
ncy
Terminal of window
cep
stru
m
quefrency
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9 events show P-wave interval peak
The P-wave interval should be detected at 4 stations to determine relative location.
que
fre
ncy
Terminal of window
que
fre
ncy
Terminal of window
que
fre
ncy
Terminal of window
que
fre
ncy
Terminal of window
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Relative locationThe 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.
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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.
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Cepstrum and auto-correlation
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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.
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A result of the rotation
X-Y-Z P-S1-S2
S1: the maximum variance on S-wave planeS2: P and S1 are perpendicular
P-wave polarization is estimated in the data at the onset of the P-wave