Geoscience Reference
In-Depth Information
Both surface wave types are dispersive. Dispersion occurs when different frequency compo-
nents of the surface wave travel at different velocities, which causes the surface wave to become
more spread out in length the farther the wave propagates. Dispersion is a result of different surface
wave frequency components having different penetration depths coupled with vertical changes in
soil and rock elastic moduli and density, which are the properties governing seismic wave velocity.
Consequently, surface wave dispersion can provide insight as to the vertical seismic velocity struc-
ture in the shallow subsurface. (Note: The dispersion of body waves is considered to be negligible.)
8.3.3 a
s P e c t s
of f
s
e i s M i c
w
a v e
P
R of P a g a t i of n
The seismic energy source is usually assumed for analysis purposes to occur at a point location,
especially in situations where artificial energy is applied for seismic investigation of the subsurface.
Again, this point source is positioned at or near the ground surface for most seismic geophysical
surveys. Seismic surface waves generated at the source propagate away from the source as a contin-
ually expanding circular wavefront along Earth's surface. Seismic body waves propagate away from
the source into the subsurface as a continually expanding hemispherical wavefront (Figure 8.7).
Geometrical spreading of the seismic surface or body wavefront results in a decrease with time
of the seismic wave amplitude, and hence energy intensity, at any point along the wavefront as it
continues to expand. Basically, as the seismic waves propagate outwards, the total seismic energy
generated at the source is being distributed over a greater and greater diameter circle for surface
waves and over a larger and larger hemisphere for body waves. Seismic wave amplitude and energy
are also reduced due to frictional dissipation of elastic energy into heat. The amount of seismic wave
frictional dissipation is dependent on the nature of the soil or rock material through which the wave
passes. The combined effect of geometrical spreading and frictional dissipation is called attenua-
tion,
A
, and for body waves can be expressed with the following relationship:
−
α
r
Ae
r
A
=
0
(8.3)
where
A
0
is the initial body wave amplitude, α is the frictional dissipation adsorption coefficient,
and
r
is the radial distance of the wavefront from the source location (Sharma, 1997). Attenuation is
frequency dependent, with the higher-frequency components of a seismic wave having been found to
attenuate more rapidly with distance traveled than the lower-frequency seismic wave components.
Transformations of seismic body waves incident on a subsurface interface between two soil
and rock layers are depicted in Figure 8.8. Solid and dashed arrowhead lines represent seismic
wave travel paths, and the Figure 8.8 schematics are based on the assumption that Layer 2 P-wave
S
t
1
t
2
fIGURe 8.7
In a uniform soil and rock medium, seismic body waves propagate away from the source (
S
) as
a continually expanding hemispherical wavefront. Arrows represent the direction of travel at points along the
wavefront. The size of the arrows represents attenuation effects causing the wavefront amplitude and energy
intensity (energy per unit wavefront area) to be less at time
t
2
than at earlier time
t
1
.
