Velocities in limestone and sandstone

Problems in Exploration Seismology and their Solutions

Series	Geophysical References Series
Title	Problems in Exploration Seismology and their Solutions
Author	Lloyd P. Geldart and Robert E. Sheriff
Chapter	5
Pages	141 - 180
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	SEG Online Store

Problem 5.4

Assume that the velocity in calcite is 6.86 km/s and in quartz 5.85 km/s. What velocities should be expected for 10, 20, and 30% porosities in (a) limestone composed only of calcite; (b) sandstone composed only of quartz? Where do these values plot on lithology versus velocity curves (Figure 5.4a) and porosity versus velocity curves (Figure 5.4b)? Assume that the pore fluid is water with velocity 1.55 km/s.

Background

The velocity in a porous rock depends primarily on the matrix velocity, the porosity, and the nature of and velocity in the pore fluid. The empirical time-average equation [of the same form as equation (5.3b)] relates the specific transit time (reciprocal of the velocity) or slowness to the volume fraction of pore space $\phi$ and the remaining volume $\left(1-\phi \right)$:

${\begin{aligned}1/V=\phi /V_{f}+\left(1-\phi \right)/V_{m},\end{aligned}}$

(5.4a)

where $V$, $V_{f}$, and $V_{m}$ are the velocities in the saturated rock, the fluid, and the rock matrix, respectively.

Solution

Substituting $V_{f}=1.55\ {\rm {km/s}}$ in equation (5.4a) yields $V={\frac {1.55}{\phi +(1-\phi )(1.55/V_{m})}}$. For $\phi$ values of 10, 20, and 30%, we obtain the velocities in Table 5.4a.

Figure 5.4a.  P-wave velocities (various sources of data).

Figure 5.4b.  Velocity versus porosity (after Wyllie et al., 1958). The limestone values (plotted as crosses on both Figures 5.4a and 5.4b) are slightly high and the sandstone values (plotted as circles) are reasonable. The line in Figure 5.4b is the time-average equation.

Table 5.4a. Velocities calculated from porosities.

Rock	$V_{m}$	$\phi =10\%$	$\phi =20\%$	$\phi =30\%$
Limestone	6.86 km/s	5.11 km/s	4.07 km/s	3.38 km/s
Sandstone	5.85	4.58	3.76	3.19

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Table of Contents (book)

Also in this chapter

• Maximum porosity versus depth
• Relation between lithology and seismic velocities
• Porosities, velocities, and densities of rocks
• Velocities in limestone and sandstone
• Dependence of velocity-depth curves on geology
• Effect of burial history on velocity
• Determining lithology from well-velocity surveys
• Reflectivity versus water saturation
• Effect of overpressure
• Effects of weathered layer (LVL) and permafrost
• Horizontal component of head waves
• Stacking velocity versus rms and average velocities
• Quick-look velocity analysis and effects of errors
• Well-velocity survey
• Interval velocities
• Finding velocity
• Effect of timing errors on stacking velocity, depth, and dip
• Estimating lithology from stacking velocity
• Velocity versus depth from sonobuoy data
• Influence of direction on velocity analyses
• Effect of time picks, NMO stretch, and datum choice on stacking velocity

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