Discrimination of P-Wave Interval in Time-Quefrency Analysis

for Proximity Microseismic Doublets

Koji NaganoMuroran Institute of Technology

Muroran, Hokkaido, 050-8585, Japannagano@mmm.muroran-it.ac.jp

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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

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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

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Terminal of window

cep

stru

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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

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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

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Terminal of window

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Terminal of window

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Terminal of window

que

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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