Page 56 - Petrophysics

30 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

More than 100,000 detectable earthquakes occur each year around
the globe, and most of these originate at specific focal points (a point of
maximum intensity within the crust) [ 1-31. Two types of waves emanate
from the focal point of the earthquake: compression and shear waves.
Compression waves travel through all materials by moving particles
forward and backward. Shear waves, however, can propagate only
through solids by moving the particles back and forth perpendicular to
the direction of travel. A worldwide network of seismographs records
the paths and velocities of these waves, making it possible to locate the
focal point of any earthquake and to infer the composition of the interior
of the earth.
Compression waves (P waves) travel at a velocity approximately two
times the velocity of the shear waves (S waves). The velocities are
functions of the elastic properties and density of the materials through
which they travel:
P I
..=[ (K +4G/3) 'I2

and

where: Vc = velocity of the compression wave, m/s.
V, = velocity of the shear wave, m/s.
K = bulk modulus, Pa.
G = shear modulus, Pa.
p = density of material, kg/m3.

EXAMPLE

Calculate the velocities of the compression and shear waves
through limestone: K = 7.0336 x lo1' Pa, G = 3.1026 x lo1' Pa, p =
2,7 10.6 kg/m3.

SOLUTION

I
vc= { [7.0336 + (4/3)(3.1026)] x lo1' 'I2 = 6,419.5 m/s
2,710.6

[ 3.1026 x
vc = = 3,383.2 m/s
2, 710.6