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

Porosity relation with density and velocity Vb 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

Porosity relation with density and velocity Vb 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

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

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

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

Check-Shot Survey Layer 1 (V1, H1) Layer 2 (V2, H2) Layer 3 (V3, H3) S Z1 Z2 Z3 T Z

Vertical Seismic Profiling (VSP) Concept X0 T Z1 R1 Reflected Z2 R2 Direct Z3 Layer (V, H) R3 Z

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

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

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