Page 134 - Introduction to Petroleum Engineering

SEISMIC WAVES 121

Wavelength
Direction of
Amplitude wave motion

Compression Rarefaction

FIGuRE 7.3 Longitudinal P‐wave.

Waves are characterized by amplitude, wavelength, and frequency (Figure 7.3).
The wavelength is the length of the wave from one point on the wave to an equivalent
point on the wave. Wave frequency is the number of waves passing a particular point
during a specified interval of time. Typical seismic frequencies range from 5 to
100 Hz (Bjørlykke, 2010, page 380). Vibrational energy from the source propagates
as a packet of waves known as a wavelet. The wavelet has a dominant wavelength λ
d
and a dominant frequency f . The amplitude of the wavelet varies from zero to total
d
amplitude and back to zero over the length of the wavelet.

Example 7.1 Seismic Wave Travel Time
A seismic wave propagates through the crust of the earth at a speed of 5 km/s.
The seismic wave propagates vertically downward to a depth of 2000 m and is
reflected back to the surface. How long does it take for the seismic wave to
make the round trip?

Answer
The travel time downward is 2000 m/(5000 m/s) or 0.4 s. The time to make the
round trip is called two‐way travel (TWT) time and is two times 0.4 s so that
TWT = 0.8 s.

Seismic velocities depend on the physical properties of rock. The relevant rock
properties are shear modulus, bulk modulus of rock grains, and mass density of the
medium. Shear modulus is the ratio of shear stress to shear strain. Bulk modulus
refers to the bulk deformation of a rock subjected to confining pressure.
The P‐wave was originally called the primary wave because the P‐wave arrived
before the S‐wave. The S‐wave was called the secondary wave because it arrived