My PhD Thesis, PDF 3MB - Stanford University

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The amplitude decay method is simple and direct. However, amplitudes are easily contaminated by many factors such as scattering, geometric spreading, source and receiver coupling, radiation patterns and transmission/reflection losses; therefore, it is very difficult to obtain reliable attenuation estimates from the amplitude decay method. The pulse broadening and spectral ratio methods are more reliable, because they are not sensitive to transmission/reflection losses and far-field geometrical spreading. However, a precise and robust measurement of pulse broadening is difficult for field data, and the spectral ratio method needs a precise reference signal to calculate the ratio (this reference signal may not be available for attenuation tomography). We need to seek other approaches that are more suitable for attenuation estimation, especially for attenuation tomography. Chapter 4 presents a new approach, the centroid frequency shift method, for seismic attenuation estimation. In most natural materials, the high frequency components of a seismic signal are attenuated more rapidly than the low frequency components as the wave propagates. As a result, the centroid of the signal's spectrum experiences a downshift during propagation. This phenomenon has been observed in VSP data (Hauge, 1981). I have observed the frequency downshift in crosswell data. In general, the frequency shift in crosswell data is greater than the VSP data, because crosswell data have broader frequency band. Under the assumption of a frequency-independent Q model, we can derive a simple formula that relates the frequency shift to the Q-value, showing that the frequency downshift is proportional to a path integral through the attenuation distribution. This relationship is appropriate for tomographic reconstruction of the attenuation distribution. In Chapter 4, I successfully applied the frequency shift method to crosswell attenuation tomography for - 21 -
oth synthetic data and field data. The forward modeling method developed in Chapter 3 is used to calculate the synthetic data. The frequency shift method is applicable in any seismic survey geometry where the signal bandwidth is broad enough and the attenuation is high enough to cause noticeable losses of high frequencies during propagation. Crosswell seismic profiling uses broad band high frequency sources, and therefore is especially suitable for the centroid frequency shift method. 1.3 ACOUSTIC ATTENUATION LOGGING Many efforts have been made to estimate seismic attenuation from full waveform sonic logs. Existing methods include amplitude decay, spectral ratio, and full waveform inversion (e.g., Cheng, et al., 1982; Paillet and Cheng, 1991, Page 138). Since accuracy and robustness are still problems, the acoustic attenuation logging has not been used in the industry for routine interpretation as of now. More research work is needed. Acoustic full waveform logs seem to be another type of data suitable for applying the frequency shift method to estimate attenuation, because of the high frequency source with relatively broad bandwidth. I have also observed clear frequency shift in acoustic logs. In Chapter 5, I propose the use of the frequency shift method for attenuation estimation from acoustic logs. In order to understand the attenuation properties of P waves in complex boreholes and provide a guide to in situ measurement, I used the generalized reflection and transmission coefficients method (Chapter 2; Chen, et al., 1996) to simulate waves in - 22 -
Page 1 and 2: SEISMOGRAM SYNTHESIS IN COMPLEX BOR
Page 3 and 4: I certify that I have read this dis
Page 5 and 6: developed in this thesis do not hav
Page 7 and 8: Finally, I would like to thank my w
Page 9 and 10: 2.4.2 Cased borehole 2.4.3 Borehole
Page 11 and 12: 6.4.3 Attenuation estimation from t
Page 13 and 14: 3.4b Seismograms calculated using t
Page 15 and 16: List of Tables 2.1 Model parameters
Page 17 and 18: Seismogram synthesis can help us un
Page 19 and 20: calculate the wave fields (e.g., St
Page 21: modeling techniques to crosswell se
Page 25 and 26: simultaneously determine both phase
Page 27 and 28: to measure formation properties fro
Page 29 and 30: x ( r , z ) are used. Since there
Page 31 and 32: normalized Hankel functions of n th
Page 33 and 34: (1 ) ?u r ( r ) (1 ) ? ( r )
Page 35 and 36: Figure 2.2 Pictorial explanation of
Page 37 and 38: Figure 2.3 Pictorial explanation of
Page 39 and 40: (1 ) (1 ) ( 1) (1 ) (1 ) ? ( r )
Page 41 and 42: imaginary angular frequency I also
Page 43 and 44: Figure 2.4 (a) Seismogram calculate
Page 45 and 46: Figure 2.5 (a) Seismograms calculat
Page 47 and 48: Table 2.3a Model parameters of a si
Page 49 and 50: profiling. Chen et al. (1994) gave
Page 51 and 52: Figure 2.7 (a) Configuration of the
Page 53 and 54: Figure 2.8a An invaded zone model u
Page 55 and 56: Two special examples for single bor
Page 57 and 58: measurement technique: seismic atte
Page 59 and 60: Let us start with the elastodynamic
Page 61 and 62: Substituting equation (3.2) into eq
Page 63 and 64: where { E pq with ( j) ( r ; l , n
Page 65 and 66: different dimensions. Moreover, R
Page 67 and 68: 3.4 GENERALIZED REFLECTION AND TRAN
Page 69 and 70: 3.6 DETERMINATION OF EIGEN FUNCTION
Page 71 and 72: Eigenvalues ( n ( j ) ) 2 and ( n
Page 73 and 74:
peak frequency 1KHz. Figures 3.4b g
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Figure 3.4b A common source gather
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3.5b). Figure 3.5a shows the synthe
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(a) Synthetic full waveform sonic l
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(a) Seismograms. The peak frequency
Page 83 and 84:
3.9 CONCLUSIONS A semi-analytical a
Page 85 and 86:
Seismic wave attenuation includes i
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Under this model, the high frequenc
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the amplitude. In this study, I con
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and the variance to be 2 S 0 (
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o dl 18 ( f S f R ) / B 2 - 92 -
Page 95 and 96:
Spectrum Shape Figure 4.3a A boxcar
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decreases from 370 Hz to 280 Hz ove
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Here, the index i represents the it
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comparison. We can see that the tom
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Figure 4.7 Synthetic test on 2-D at
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Figure 4.8 The data picked from the
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profile curves within the tomograms
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Figure 4.10 The attenuation and vel
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Chapter 5 Acoustic Attenuation Logg
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decreases with the increasing offse
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Assume that the intrinsic attenuati
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2 i 0 ( f f ) i 2 R ( f ) df i
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Figure 5.3b Micro-seismograms calcu
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This simulation shows the central f
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Figure 5.5b Micro-seismograms recor
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Figure 5.8 Centroid frequency picks
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p 1 log [ z i 1 z i log [ ] R ( f
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spreading. To understand how the in
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5.9b, in fact, shows the velocity s
Page 133 and 134:
The generalized reflection and tran
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eflection and transmission (R/T) co
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where, signs "+" and "-" refer to o
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Therefore, equation (6.5) is a disp
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[ ?v n ( ), ?v p , ?v s ] [ v n
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tested for three typical radially l
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Figure 6.2 A plot of the function d
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6.4.3 Attenuation Estimation from t
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References Aki, K, and Richards, P.
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Parker, K., Lerner, R. & Waag, R.,
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A-2 ELASTODYNAMIC EQUATION IN TERMS
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? (1 ) (1 ) ( 1) (1 ) ( r , k , )
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where, ( j ) k 2 ( j) e 32 ( j )
Page 159 and 160:
( j ) ( j ) ( j ) ( j) ( j ) ( j) E
Page 161 and 162:
- 160 -
Page 163 and 164:
( j) E 31 ( j) E 32 ( j) E 33 ( j)
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or rewrite it as ( j ) D 11 D 21 (
Page 167 and 168:
Appendix C Relationships between th
Page 169:
a dl 12 ( f f ) / B o S R ray 2 C
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