Wave Modeling, Tomography, Geostatistics and Edge Detection

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Wave Modeling, Tomography, Geostatistics and Edge
Detection

• Youli Quan

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Modeling Waves in a Borehole
First Topic
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Modeling Waves in a Borehole

• Borehole models
• Mathematical description
• Examples
• Conclusions

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Modeling Waves in a Borehole

• Borehole models
• Mathematical description
• Examples
• Conclusions

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BOREHOLE RELATED SEISMIC MEASUREMENTS
Fluid-filled borehole
Fluid-filled borehole
Vertical seismic profiling
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Single borehole profiling
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Cross- borehole profiling
Sonic logging
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Source
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Modeling Waves in a Borehole

• Borehole models
• Mathematical description
• Examples
• Conclusions

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Modeling Waves in a Borehole

• Borehole models
• Mathematical description
• Examples
• Conclusions

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REFLECTION DUE TO AN OUTER-CYLINDRICAL FORMATION
Model
Borehole
Vp3 km/s Vs1.8 km/s
Vp1.9 km/s Vs1.4 km/s
x x x x x x x x x x
Receivers
150 m
10 m
Formation I
Formation II
Source
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100 m
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Seismograms (fo 800 Hz)
150
source - receiver offset (m)
10
100
150
10
50
Time (ms)
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A SYNTHETIC CROSSWELL SURVEY
Cased borehole
30 m
30 m
x x x x x x x x x x x x x x x
o o o o o o o o o o o o o o o
100
Vp5 km/s Vs2.9 km/s
Formation
100 m
S-R offset (m)
Vs3.3 km/s
Vp5.8 km/s
0
10
30
0
20
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Receivers
Sources
Time (ms)
(a) Model. There is a fault in the formation
(b) A common receiver gather
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Modeling Waves in a Borehole

• Borehole models
• Mathematical description
• Examples
• Conclusions

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• A new wave modeling method based on the
  generalized R/T coefficients is developed for
  complex borehole simulations.
• This method is efficient, robust, and accurate.
  It has been applied to sonic logging, crosswell
  profiling, and single borehole profiling.

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Second Topic
Attenuation Tomography
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Waveform and Attenuation
Higher frequency Waveform
Lower Absorption
Lower frequency Waveform
Acoustic Sources
Higher Absorption
Acoustic Receivers
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Measure Attenuation from Waveform
Incident Wave S(f)
Transmitted Wave R(f)S(f)H(f)
Medium Response H(f)
H
(
f
)

exp

-
f
a
dl

ò
o
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SYNTHETIC EXAMPLE ON ATTENUATION
TOMOGRAPHY Crosswell geometry, RT method for
modeling
(a) Original model
(b) Reconstruction
Receivers
Sources
x x x x x x x x x x x x
o o o o o o o o o o o o o o
Vf5 kft/s Qf20
Vp11.8 kft/s Vs6.9 kft/s Qp30
100 ft
Vp12 kft/s Vs7 kft/s Qp60
70 ft
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Third Topic
Geostatistics
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Geostatistics

• Introduction
• Variogram
• Kriging

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Geostatistics

• Introduction
• Variogram
• Kriging

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• Geostatistics is the study of phenomena that
• fluctuate in space.

• It offers tools aimed at understanding and
• modeling spatial variability.

• These tools include histogram, covariance,
• variogram, kriging, simulation, and etc.

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Geostatistics

• Introduction
• Variogram
• Kriging

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Experimental Models
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Theoretical Models
Exponential Model
Spherical Model
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Geostatistics

• Introduction
• Variogram
• Kriging

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Kriging is a linear estimator with following
features

• Weighting factors are solved based on the
  selected variogram.
• It has minimum variance of the estimation errors.
• The estimation is unbiased.
• Estimated values has the same statistical
  properties as given data

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