My PhD Thesis, PDF 3MB - Stanford University

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$Drilling-induced tensile wall-fractures - Stanford University$

of the complicated geometrical spreading, we have difficulty to used the frequency shift method calculating attenuation logs for boreholes with invaded zones. Table 5.2 Estimation of Qp for open boreholes with invaded zones Given Qp 40 80 120 Estimated ? Q p (damaged zone, g=0) Estimated ? Q p (flushed zone, g=0) 15 17 19 25 36 58 5.3 APPARENT GEOMETRICAL SPREADING OF THE P WAVE IN COMPLICATED BOREHOLES The simulation tests in the previous section show that the frequency-dependent geometrical spreading is complicated in boreholes with invaded zones. It is difficult to determine the details of its frequency-dependent property. In this section I assume an apparent geometrical spreading factor expressed by 1 / z p . This assumption means that the effect of the frequency-dependent term exp(-gfz) will be included into 1 / z p selecting a proper power p. For a monopole source in a simple borehole, the geometrical spreading factor is 1/z for the P wave (Roever et al., 1974; Winbow, 1980). With the more efficient algorithm, I investigate the effect of complex invaded zones on the P wave geometrical spreading, i.e., to determine the power p for the complicated boreholes. Ignoring g and rearranging equation (5.4) yield - 125 - by
p 1 log [ z i 1 z i log [ ] R ( f ) i ] f ( z z ) oi i 1 i R ( f ) i 1 - 126 - . (5.9) I use equation (5.9) to estimate p from given model parameters and the synthetic micro- seismograms (Figures 5.3b, 5.5b and 5.7b) calculated in previous section. Three types of borehole models shown in Figures 5.3a (simple borehole), 5.5a (borehole with damaged zone), 5.7a (borehole with flushed zone) are used for this apparent geometrical spreading study. For each model, three P wave Q-values ( Q p =40, 80 and 120) are used to calculate three synthetic data sets. I use a Hanning window to extract the P wave (first arrival) and perform FFT to obtain the spectrum Ri(f). The peak spectrum amplitude Ri(fpeak) and the given model parameters are plugged into equation (5.9) to calculate the power p in the geometrical spreading factor 1 z p . With multiple data sets (corresponding to Q p =40, 80 and 120) and multiple source–receiver pairs, we calculate several values of p's by equation (5.9), and average these values to obtain the estimated power p in 1 / z p . The estimated results for three different borehole models are summarized in Table 5.3. Table 5.3 Estimation of p in the apparent geometrical spreading factor 1/z p borehole types Simple Damaged zone Flushed zone Estimated p 1 0.5 1.21
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SEISMOGRAM SYNTHESIS IN COMPLEX BOR
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I certify that I have read this dis
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developed in this thesis do not hav
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Finally, I would like to thank my w
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2.4.2 Cased borehole 2.4.3 Borehole
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6.4.3 Attenuation estimation from t
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3.4b Seismograms calculated using t
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List of Tables 2.1 Model parameters
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Seismogram synthesis can help us un
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calculate the wave fields (e.g., St
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modeling techniques to crosswell se
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oth synthetic data and field data.
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simultaneously determine both phase
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to measure formation properties fro
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x ( r , z ) are used. Since there
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normalized Hankel functions of n th
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(1 ) ?u r ( r ) (1 ) ? ( r )
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Figure 2.2 Pictorial explanation of
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Figure 2.3 Pictorial explanation of
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(1 ) (1 ) ( 1) (1 ) (1 ) ? ( r )
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imaginary angular frequency I also
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Figure 2.4 (a) Seismogram calculate
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Figure 2.5 (a) Seismograms calculat
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Table 2.3a Model parameters of a si
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profiling. Chen et al. (1994) gave
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Figure 2.7 (a) Configuration of the
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Figure 2.8a An invaded zone model u
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Two special examples for single bor
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measurement technique: seismic atte
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Let us start with the elastodynamic
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Substituting equation (3.2) into eq
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where { E pq with ( j) ( r ; l , n
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different dimensions. Moreover, R
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3.4 GENERALIZED REFLECTION AND TRAN
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3.6 DETERMINATION OF EIGEN FUNCTION
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Eigenvalues ( n ( j ) ) 2 and ( n
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peak frequency 1KHz. Figures 3.4b g
Page 75 and 76: Figure 3.4b A common source gather
Page 77 and 78: 3.5b). Figure 3.5a shows the synthe
Page 79 and 80: (a) Synthetic full waveform sonic l
Page 81 and 82: (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
Page 87 and 88: Under this model, the high frequenc
Page 89 and 90: the amplitude. In this study, I con
Page 91 and 92: and the variance to be 2 S 0 (
Page 93 and 94: o dl 18 ( f S f R ) / B 2 - 92 -
Page 95 and 96: Spectrum Shape Figure 4.3a A boxcar
Page 97 and 98: decreases from 370 Hz to 280 Hz ove
Page 99 and 100: Here, the index i represents the it
Page 101 and 102: comparison. We can see that the tom
Page 103 and 104: Figure 4.7 Synthetic test on 2-D at
Page 105 and 106: Figure 4.8 The data picked from the
Page 107 and 108: profile curves within the tomograms
Page 109 and 110: Figure 4.10 The attenuation and vel
Page 111 and 112: Chapter 5 Acoustic Attenuation Logg
Page 113 and 114: decreases with the increasing offse
Page 115 and 116: Assume that the intrinsic attenuati
Page 117 and 118: 2 i 0 ( f f ) i 2 R ( f ) df i
Page 119 and 120: Figure 5.3b Micro-seismograms calcu
Page 121 and 122: This simulation shows the central f
Page 123 and 124: Figure 5.5b Micro-seismograms recor
Page 125: Figure 5.8 Centroid frequency picks
Page 129 and 130: spreading. To understand how the in
Page 131 and 132: 5.9b, in fact, shows the velocity s
Page 133 and 134: The generalized reflection and tran
Page 135 and 136: eflection and transmission (R/T) co
Page 137 and 138: where, signs "+" and "-" refer to o
Page 139 and 140: Therefore, equation (6.5) is a disp
Page 141 and 142: [ ?v n ( ), ?v p , ?v s ] [ v n
Page 143 and 144: tested for three typical radially l
Page 145 and 146: Figure 6.2 A plot of the function d
Page 147 and 148: 6.4.3 Attenuation Estimation from t
Page 149 and 150: References Aki, K, and Richards, P.
Page 151 and 152: Parker, K., Lerner, R. & Waag, R.,
Page 153 and 154: A-2 ELASTODYNAMIC EQUATION IN TERMS
Page 155 and 156: ? (1 ) (1 ) ( 1) (1 ) ( r , k , )
Page 157 and 158: 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)
Page 165 and 166: 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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