1. Packing of uniform spheres
Orthorhombic packing
most compact (f = 26%)
Cubic packing
least compact (f = 47%)
Diagonal
cross-section
Diagonal
cross-section
Front view
Front view

2. Porosity relation with density and velocityVb Vp
Fluid
Vb - Vp
Matrix
Rock
rb(f) = rf f + (1-f) rm
b: whole rock (bulk)
f: pore fluid
m: solid matrix
a: P-wave velocity
r: Density
f: Porosity
1 / ab(f) = f/af + (1-f) / am

3. Porosity relation with density and velocityVb Vp
Fluid
Vb - Vp
Matrix
Rock
rb(f) = rf f + (1-f) rm
b: whole rock (bulk)
f: pore fluid
m: solid matrix
a: P-wave velocity
r: Density
f: Porosity
1 / ab(f) = f/af + (1-f) / am

4. Types of velocities Earth’s surface ith layer Nth layer
DT0i = vertical traveltime across ith layer
Vi = interval velocity of ith layer
T0i-1 = total vertical time to top of ith layer
Ti = total vertical time to bottom of ith layer

5. Comparing velocities X T2 T X2 True T2-X2 curve
VRMS (tangent to true T2-X2
curve at X2 = 0) T2
Vs (best-fit hyperbola to true T-X )
True T-X curve
VRMS (tangent to true T2-X2
curve at X2 = 0) T
Vs (best-fit hyperbola to true T-X ) X2

6. Estimation of VNMO X Low VNMO T0 After NMO Best VNMO High VNMO Before
True T-X T
DTNMO(X) ≈ X2 / (2T0 VNMO2)

7. Check-Shot Survey Layer 1 (V1, H1) Layer 2 (V2, H2) Layer 3 (V3, H3) SZ1 Z2 Z3 T Z

8. Vertical Seismic Profiling (VSP) ConceptX0 T Z1 R1
Reflected Z2 R2
Direct Z3
Layer
(V, H) R3 Z

9. Vertical Seismic Profiling (VSP) Example
VSP data showing a strong reflector “A” at a depth of about 9850 ft (after Hardage, 1997).

10. Sonic Well Logging Tool
Tool (sonde) used for conventional sonic well logging (after Sheriff and Geldart, 199g)

11. Sonic Well Logging Data Example
Example of a sonic well- log (after Hardage, 1997)