My PhD Thesis, PDF 3MB - Stanford University

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oreholes. Then, I applied the centroid frequency shift method to synthetic data for the attenuation estimation. After the synthetic test, I also applied the frequency shift method to field data for acoustic attenuation logging. Geometrical spreading is a very important property of waves. It is also very important for the attenuation estimation. When measuring intrinsic attenuation of the formation, we must correct for the geometrical spreading of the wave. For a monopole source in a simple borehole, the geometrical spreading factor is approximately 1/z for the P wave (Roever et al., 1974; Winbow, 1980). However, in general the geometrical spreading factor is frequency-dependent (Paillet and Cheng, p144, 1991; Quan, et al., 1994). In Chapter 5, I propose an empirical formula to describe the frequency-dependent geometrical spreading of the P wave in a borehole. With the forward modeling method developed in Chapter 2, I investigated the effect of complex invaded zones on the frequency-dependent geometrical spreading and attenuation estimation for P waves. I find that the geometrical spreading 1/z is not true for boreholes with invaded zones. It is difficult to estimate S wave attenuation from the direct S wave in acoustic logs. The S wave is immediately followed by tube waves. We may not extract the complete S wave train from a acoustic log. An alternative way, called partition coefficient method (Cheng, et al., 1982), can be used to estimate S wave attenuation from tube waves, or normal modes. The dispersion relation, which gives the phase velocities of normal modes, is very important for studying normal modes in acoustic logging. It has been studied by many authors, e.g., Biot (1952), Cheng and Toks ??o z (1981). Chen (1993) used the generalized R/T method to compute the normal modes in horizontal layers. In Chapter 6, the generalized R/T coefficients method is further developed to determine the dispersion relation of normal modes in radially multi-layered media. This approach can - 23 -
simultaneously determine both phase velocities and corresponding eigen functions for normal modes in a borehole with an arbitrary number of radial layers. Based on this new dispersion relation, a general formula which describes the attenuation property of each mode in absorptive media is derived. We may use this formula to estimate the S wave attenuation from tube waves. - 24 -
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 and 22: modeling techniques to crosswell se
Page 23: oth synthetic data and field data.
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
Page 75 and 76:
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
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3.9 CONCLUSIONS A semi-analytical a
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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
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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
Page 145 and 146:
Figure 6.2 A plot of the function d
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6.4.3 Attenuation Estimation from t
Page 149 and 150:
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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