of 13
7/30/2019 Chapter3 2012 Figures
1/13
Packing of uniform spheres
Cubic packing
least compact (f = 47%)
Orthorhombic packing
most compact (f = 26%)
Diagonal
cross-sectionFront view
Diagonal
cross-section
Front view
7/30/2019 Chapter3 2012 Figures
2/13
Porosity relation with density
and velocity
Vb
Vp
Fluid
Vm=Vb-Vp
MatrixRock
rb(f) = rff + (1-f) rm1 / ab(f) = f/af + (1-f) / ama: P-wave velocityr: Density
f: Porosity
b: whole rock (bulk)
f: pore fluid
m: solid matrix
7/30/2019 Chapter3 2012 Figures
3/13
Porosity Relation to Density and P-wave Velocity
0
1000
2000
3000
4000
5000
6000
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Porosity
Den
sity(kg/m3),P-waveVelocity(m/s)
P-wave velocity
Density
7/30/2019 Chapter3 2012 Figures
4/13
Estimation of VNMO
After
NMO
True
T-X
High
VNMO
Low VNMO
DTNMO(X) X2 / (2T0 VNMO2)
T
X
T0
Before
NMO
Best
VNMO
7/30/2019 Chapter3 2012 Figures
5/13
Comparing velocities
VRMS (tangent to true T2-X2
curve at X2 = 0)T2
X2
True T2
-X
2
curve
Vs (best-fit line to true T2-X2
curve )
T
X
VRMS (tangent to true T2-X2
curve at X2 = 0)
True T-Xcurve
Vs (best-fit hyperbola to true T-X)
7/30/2019 Chapter3 2012 Figures
6/13
Determination of layers interval velocity, thickness,
and depth from true T-X data
(1)There are three ways to find the interval velocity VN in the Nth layer given the true T-Xcurves of the top and bottom interfaces (N-1 and N):
A.Using VS:1. Fit two separate hyperbolas to the small-offset traces of the N-1 and N th true T-X
curves.
2. This gives us the stacking velocities VSN-1 and VSN.3. Apply Dixs formula to calculate VN from VSN-1and VSNand T0N and T0N-1.
B.Using VNMO:1. Perform NMO correction to the small-offset traces of the N-1 and Nth true T-X
curves until these curves are completely horizontal.
2. This gives us the NMO velocities VNMON-1 and VNMON.3. Apply Dixs formula to calculate VN from VNMON-1 and VNMON and T0N and T0N-1.
C.Using VRMS:1. Fit high-order polynomials to the small-offset traces of the N-1 and Nth true T-X
curves (e.g., fitting a 3-term polynomial: 42
2
10XCXCCT ++= ).
2. Compute the RMS velocities VRMSN-1 and VRMSN C1 of the N-1 and Nth best-fitcurves.
3. Apply Dixs formula to calculate VN from VRMSN-1 and VRMSN and T0N and T0N-1.(2)Determine the thickness of the i-th layer as: 2/
0 iiiTVH D= , where i=1,2,,N.
(3)Determine the depth to the bottom of the N-th layer as: =
=
N
i
iNHZ
1
.
7/30/2019 Chapter3 2012 Figures
7/13
y = 9.425E-08x + 7.080E-01
R2
= 9.947E-01
y = -3.434E-16x2
+ 1.107E-07x + 6.662E-01
R2
= 9.994E-01
0
1
2
3
4
5
6
7
0.0E+00 1.0E+07 2.0E+07 3.0E+07 4.0E+07 5.0E+07 6.0E+07 7.0E+07
X22
T2
2
./3005
10107.1
1
./3257
10425.9
1
72
82
smV
smV
RMS
S
=
=
=
=
-
-
Correct model parameters are:
Layer
(i)
Vi
(m/s) Hi (m) True RMS Velocity (m/s) Zi (m)
1 2000 600 2000 600
2 4000 400 2646 1000
7/30/2019 Chapter3 2012 Figures
8/13
X T(X) X/Z X2
T2
0 0.800 0.0 0 0.640
49 0 .800 0.0 2390 0.640
98 0 .801 0.0 9581 0.641
147 0.802 0.1 21635 0.643
197 0.803 0.1 38661 0.646
247 0.805 0.1 60813 0.649
297 0.808 0.1 88298 0.653
348 0 .811 0.2 121380 0.657
400 0 .814 0.2 160391 0.663
454 0 .818 0.2 205741 0.669
508 0 .823 0.3 257933 0.677
564 0 .828 0.3 317585 0.685
621 0 .833 0.3 385455 0.694
680 0 .840 0.3 462474 0.705
741 0 .847 0.4 549803 0.717
806 0 .855 0.4 648894 0.731
873 0 .864 0.4 761588 0.746
944 0 .874 0.5 890256 0.764
1019 0.88 5 0.5 1038 004 0.784
1100 0.89 8 0.5 1208 984 0.807
1187 0.91 3 0.6 1408 895 0.833
1283 0.92 9 0.6 1645 788 0.864
1390 0.94 9 0.7 1931 476 0.901
1511 0.97 2 0.8 2284 090 0.945
1653 1.00 1 0.8 2733 121 1.001
1825 1.03 6 0.9 3330 301 1.074
2044 1.08 3 1.0 4176 294 1.174
2345 1.15 1 1.2 5499 020 1.324
2821 1.26 1 1.4 7959 060 1.590
3836 1 .50 4 1.9 1 471646 0 2.261
4019 1 .54 8 2.0 1 615415 2 2.396
4235 1 .60 0 2.1 1 793122 0 2.562
4493 1 .66 4 2.2 2 018920 3 2.768
4813 1 .74 2 2.4 2 316234 0 3.035
5222 1 .84 3 2.6 2 726906 6 3.395
5774 1 .97 9 2.9 3 333927 9 3.915
6580 2 .17 8 3.3 4 329125 3 4.744
7926 2 .51 2 4.0 6 281636 8 6.310
y = 9.425E-08x + 7.080E-01
R = 9.947E-01
y = -3.434E-16x2 + 1.107E-07x + 6.662E-01
R = 9.994E-01
0
1
2
3
4
5
6
7
0.0E+00 1.0E+07 2.0E+07 3.0E+07 4.0E+07 5.0E+07 6.0E+07 7.0E+07
T2
2
X22
7/30/2019 Chapter3 2012 Figures
9/13
7/30/2019 Chapter3 2012 Figures
10/13
CVS
7/30/2019 Chapter3 2012 Figures
11/13
Check-Shot Survey
Layer 1
(V1, H1)
Layer 2
(V2, H2)
Layer 3
(V3, H3)
S
R1
R2
R3
Z1Z2Z3
Z
T
7/30/2019 Chapter3 2012 Figures
12/13
Vertical Seismic Profiling (VSP)
Concept
Layer
(V, H)
R1
R2
R3
Z1
Z2
Z3
Z
TSX0
Reflected
Direct
7/30/2019 Chapter3 2012 Figures
13/13
Sonic Well Logging
Tool
Tool (sonde) used for
conventional sonic well logging
(after Sheriff and Geldart, 1995)
