My PhD Thesis, PDF 3MB - Stanford University

More documents

Recommendations

Info

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

Substituting equation (3.17a): into equation (3.11a): we obtain C C ( j 1) ( j) C ( j) C ( j 1) C C ( j 1) ( j) ( j ) ( j ) T C ? ( j ) ( j ) T C ? ( j ) ( j ) R C ( j ) ( j 1) R C ( j ) ( j ) ( j ) ( j 1) R C T C ( j ) ( j ) ( j ) R C T ? ( j 1 ) ( j 1) R C ( j ) ( j ) ( j ) T C R ? ( j 1 ) ( j 1) R C - 165 - , . (B-3.1) Substituting the first equation in (2.17a) into the second equation in (B-3.1) and rearranging it as c c ( j 1) ( j ) ( j ) [ I R ? ( j 1) R ] 1 ( j ) ( j ) T c ( j ) ( j ) ( R T ? ( j 1) R ? ( j ) ( j ) T ) c Comparing equation (B-3.2) with equation (2.17a), we obtain T ? ? ( j ) ( j ) R ( j ) [ I R ? ( j 1 ) R ] 1 ( j ) T ( j ) ( j ) R T ? ( j 1 ) R ? ( j ) T . (B-3.2) . (3.18 again)
Appendix C Relationships between the Attenuation Coefficient and the Frequency Shift C-1 GAUSSIAN SHAPE SPECTRUM If the input amplitude spectrum S(f) is of Gaussian shape, i.e., S ( f ) exp [ ( f f o 2 2 S the centroid of S(f) is fo. The output amplitude spectrum is where R ( f ) S ( f ) H ( f ) exp [ ( f f o exp [ f R ( f o S 2 f 2 ray ) 2 ] , 2 2 f f f R R o dl ) 2 2 S , 2 S - 166 - ) 2 f dl 2 o ray f d ] A exp [ ( f f R ] 2 2 S ) 2 ] ,
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 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
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
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 and 126: Figure 5.8 Centroid frequency picks
Page 127 and 128: p 1 log [ z i 1 z i log [ ] R ( f
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: or rewrite it as ( j ) D 11 D 21 (
Page 169: a dl 12 ( f f ) / B o S R ray 2 C
show all

My PhD Thesis, PDF 3MB - Stanford University

Create successful ePaper yourself

Delete template?

Save as template?