My PhD Thesis, PDF 3MB - Stanford University

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4.3 Validation test coefficient and spectral centroid 4.4 Seismic attenuation tomography 4.4.1 Practical considerations 4.4.2 Numerical tests 4.4.3 Field data: one dimensional geological structure 4.4.4 Field data: two dimensional geological structure 4.5 Conclusions Chapter 5 Acoustic Attenuation Logging in Complicated Boreholes 109 5.1 Frequency shift phenomenon in real sonic logs 5.2 Attenuation logging using the centroid frequency shift method 5.3 Apparent geometrical spreading of the P wave in complicated boreholes 5.4 An example of field data 5.5 Conclusions Chapter 6 Normal Modes in Radially Layered Media and Application to Attenuation Estimation 131 6.1 Introduction 6.2 Normal modes in radially layered media 6.3 Q-values of normal modes 6.4 Numerical examples 6.4.1 Normal modes 6.4.2 Attenuation of the Pseudo-Rayleigh wave - 9 -
6.4.3 Attenuation estimation from the Pseudo-Rayleigh wave 6.5 Conclusions References 146 Appendix A 149 A-1 S wave potential in radially symmetric media A-2 Elatodynamic equation in terms of potentials A-3 General solution in a fluid-filled borehole ( j ) A-4 Explicit expressions of elements {e } nm A-5 Derivation of the modified R/T matrices A-6 Derivation of the generalized R/T matrices Appendix B 158 B-1 Explicit expressions of coefficient matrices B-2 Derivation of the modified R/T matrices B-3 Derivation of the generalized R/T matrices Appendix C Relationships between attenuation and frequency shift 163 C-1 Gaussian shape spectrum C-2 Rectangular shape spectrum C-3 Triangular shape spectrum - 10 -
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: 2.4.2 Cased borehole 2.4.3 Borehole
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 and 24: oth synthetic data and field data.
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
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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
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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
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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 -
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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
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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 )
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( j ) ( j ) ( j ) ( j) ( j ) ( j) E
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- 160 -
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( j) E 31 ( j) E 32 ( j) E 33 ( j)
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or rewrite it as ( j ) D 11 D 21 (
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Appendix C Relationships between th
Page 169:
a dl 12 ( f f ) / B o S R ray 2 C
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My PhD Thesis, PDF 3MB - Stanford University

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