Page 135 - Introduction to Petroleum Engineering

122 RESERVOIR GEOPHYSICS
after the primary wave. The velocity of P‐wave propagation V in an elastic, homo-
P
geneous, and isotropic medium is
( K +(43 G ) )
/
V = B (7.1)
P
ρ
where K is bulk modulus, G is shear modulus, and ρ is the mass density of the
B
medium. The corresponding velocity of S‐wave propagation V is
S
G
V = < v P (7.2)
S
ρ

Example 7.2 P‐Wave and S‐Wave Velocities
Dolomite has bulk modulus K = 95 GPa, shear modulus G = 46 GPa, and density
3
ρ = 2800 kg/m . Calculate compressional wave velocity in m/s and shear wave
velocity in m/s.
Answer
9
A consistent set of units is obtained by first converting GPa to Pa (1 GPa = 10 Pa
2
9
and 1 Pa = 1 N/m = 1 kg/m·s ): K = 85 GPa = 85 × 10 Pa and G = 55 GPa = 55 × 10 Pa.
2
9
Compressional wave velocity is
)
K +(43 G ) 85 ×10 9 + / (43 55 ×10 9
/
V = = = 7519 m/s
P
ρ 2800
Shear wave velocity is
G 55 ×10 9
V = = = 4008 m/s
S
ρ 2800

7.1.1 Earthquake Magnitude
An earthquake occurs when the crust slips along a subsurface fault. Seismic wave
vibrations caused by the slippage are detected by a seismograph that records the
amplitudes of ground movement beneath the instrument. Charles F. Richter devel-
oped a scale (Richter, 1935) to measure the magnitude of earthquakes in southern
California using a Wood–Anderson torsion seismometer (Wood and Anderson,
1925). A copper mass suspended by a thin wire would rotate when the seismometer
moved. The seismogram was made when a beam of light was reflected onto photo-
sensitive paper from a mirror on the copper mass.
The Richter scale expresses the local magnitude M of a vibration on a Wood–
Anderson seismograph as L