Seismic method - Geophysics for the Mineral Exploration Geoscientist - page 360

between the regions above and below the interface. The
directions of the incident, re ected and transmitted
(refracted) rays are measured with respect to the normal
(perpendicular) to the interface (the vertical for the case of
a horizontal interface), and these angles are known as the
angles of incidence (

wavefront generated by the source loses energy. This is
another form of energy loss associated with wave propaga-
tion in addition to geometric spreading and absorption
(see Section 6.3.3 ) . The relative amount of energy, and
therefore amplitude, of the transmitted and re ected waves
depends on the angle of incidence and the change in
physical properties across the interface. Basically, the
greater the contrast in elastic properties, the greater is the
proportion of incident energy that is reflected. Conversely,
the smaller the acoustic impedance contrast, the more
energy that is propagated across the boundary.
For P-waves at normal incidence, the ratios of the
amplitudes of the reflected (A R ) and the transmitted
(A Trn ) waves, with respect to that of the incident waves
(A Inc ), are known as the reflection coefficient (RC) and
transmission coefficient (TC), respectively. They depend
only on the acoustic impedances each side of the interface
and are given approximately by:

θ Inc ), re ection (

θ R ) and transmission

( θ Trn ) (or refraction), respectively. They are de ned by

Snell

'

s Law:

sin θ sin θ sin θ

Inc Rfl Trn

¼ ¼ ð 6 : 8 Þ

V 1 V 1 V 2

From this, the relationships between the directions of the
incident, reflected and transmitted rays are given by:

sin θ Inc V 1

V 2

Trn ¼

ð 6 : 9 Þ

sin θ

and

sin θ Inc

A Inc ¼ ζ 2 ζ 1

A Rfl

θ Rfl ¼

1 ð 6 : 10 Þ

RC ¼ ð 6 : 11 Þ

sin

ζ 2 + ζ 1

For the re ected rays, the wave remains within the same
layer and travels at velocity V 1 ; and in accordance with
Snell

ζ 1
ζ 2 + ζ 1

A Trn
A Inc ¼

2

TC ¼ ð 6 : 12 Þ

'

is Law, the angle of incidence is equal to the angle of
reflection. The transmitted wave travels through the second
layer with a different velocity (V 2 ), and in a different direc-
tion, i.e. it is refracted. When V 2 is less than V 1 the trans-
mitted raypath is deflected (refracted) towards the normal
( Fig. 6.9b ), and when V 2 is greater than V 1 the transmitted
raypath is refracted away from the normal, i.e. refraction
brings the ray closer to being parallel with the interface
( Fig. 6.9c ) . We discuss implications of this further in Critical
refraction within Section 6.3.4.2 , When the incident ray is
perpendicular to the interface ( Fig. 6.9a ) , known as normal
incidence, the angle of incidence is 0° and the angles of
re ection and transmission are also 0°, i.e. the re ected ray
coincides with the incident ray, albeit with opposite direc-
tions, and the direction of the transmitted ray is unchanged.
Clearly re ection at an interface is a second mechanism
by which the down-going wavefront created by the seismic
source is turned around so it can be recorded by detectors
at the surface.

Note that

RC TC ¼ 1 ð 6 : 13 Þ

+

The reflection coefficient can only vary between 1 and +1.

An absolute value of 1 corresponds to all the energy being
re

-

ected by the interface. A negative RC occurs when the
incident wave is re ected by a layer of lower acoustic
impedance, and then there is an associated reversal of
polarity (a phase-sh t of 180°; see online Appendix 2 )
between the incident and re ected waves. These relation-
ships give reasonably accurate results for angles of inci-
dence up to about 15°, which is the usual case for seismic
re ection surveying.
Re ection coef cients in the geological environment
usually fall in the range ±0.2, which means nearly all the
incident energy passes through the interface into the
underlying layer. Under ,are ec-

tion can be recognised when the contrast in acoustic
impedance produces a reflection coefficient of roughly
0.05. It can be difficult to image the geology below a
strongly reflective horizon, owing to the lack of transmitted
energy. In the case of waterborne surveys, the water

' normal circumstances '

Energy partitioning
The energy of the incident wave is partitioned between the
transmitted wave that passes through and into the under-
lying layer, and the wave that is reflected and remains
within the upper layer. This means that the down-going

- air

and water water bottom interfaces are important physical

property contrasts. The re

-

ection coef cient at the former

is very close to - 1, the latter between 0.33 and 0.67