Seismic method - Geophysics for the Mineral Exploration Geoscientist - page 396

Section 6.6.9 ) and density ( Section 3.8.7.1 ) logs from the
drillhole. The calculated seismic response is known as a
synthetic seismogram. It is principally used to correlate
re ections with geological interfaces or sequences inter-
sected by the drillhole.
We showed in Section 6.3.4.2 that when seismic waves
encounter an interface across which there is a change in
acoustic impedance, both re ection and transmission of
the waves occur. The relative amplitudes of the reflected
and transmitted waves are defined in terms of the reflec-
tion coefficient (RC) and transmission coefficient (TC) (see
Energy partitioning in Section 6.3.4.2 ). Figure 6.44 shows
how a 1D synthetic seismic trace can be calculated. Firstly,
density and velocity data for the various stratigraphic units
are obtained from density and sonic logs. In the example
shown, velocity and density are constant in each layer so
changes in acoustic impedance only occur at their bound-
aries, so these are the only places where the re ection
coef cients are non-zero ( Fig. 6.44a ). The variations in
re ection coef cient with depth are then converted to
variations as a function of two-way re ection time, using
the velocity data ( Fig. 6.44b ). The plot of re ectivity coeffi- -
cients versus two-way time is known as the re ectivity
series. It is convolved (see Section 2.7.4.3 ), with a function
representing the wavelet created by the seismic source to
produce the synthetic seismic trace. Various idealised
source wavelets are routinely used for calculating synthetic
seismograms, in this case it is a type of zero-phase wavelet
(see Appendix 2 ) known as a Ricker wavelet. Figure 6.44b
demonstrates how seismic traces consist of repetitions
(reflections or echoes) of the source wavelet whose ampli-
tude is scaled by the reflection coefficient and whose rela-
tive arrival time depends on the position of the non-zero
re

Quarter
wavelength
(m)

60

NC/NF

50

SL

40 1/4

Dom

LM

30

6.0 km/s

5.0 km/s

CP 20

4.0 km/s

RP

3.0 km/s

10 2.0 km/s

TS

0

50 100 150 200

Frequency (Hz)

0.02 0.01 0.007 0.005

Period (s)

Figure 6.43 Length of a quarter wavelength for various combinations
of frequency and velocity. To provide context, also shown are the
lengths/heights of various well-known objects. CP - length of a

cricket pitch, LM - height of the Lincoln Memorial (Washington

DC), NC - height of Nelson ' s Column (London), NF - height of

-

Niagara Falls, RP height of the posts at the Twickenham rugby

ground (London), SL

-

height of the Statue of Liberty (New York),

TS - height of a two-storey house.

vertical resolution is a few tens of metres in most cases for
typical survey parameters.

6.7.2 Quantitative interpretation

A variety of computer software for 2D and 3D forward and
inverse modelling of seismic responses is available, mostly
from the petroleum sector. Varying degrees of subsurface
complexity can be accommodated, from constant-velocity
planar layers through to velocity and density distributions
of almost any degree of complexity described by values
specified on a network of nodes.
The seismic waves may be approximated as rays and,
usually, particular raypaths can be specified. Raypaths are
fast to compute but a major shortcoming, especially in
geologically complex terrains, is that diffraction cannot
be easily accounted for in the models. Wave-based algo-
rithms can compute more physically realistic models, but
they are much more computationally intensive.

ection coef cients in the re ectivity series. When re ec-

tion coef cients are negative the polarity of the source-

wavelet within the trace is reversed.

In reality, there will be many closely spaced non-zero
re ection coef cients within the re ectivity series. This
means it will be hard to identify the individual occurrences
of the source wavelet due to the interference of numerous
echoes. This situation is mimicked in Fig. 6.44c by increas-
ing the length of the source wavelet relative to the re ect-
ivity function. The resulting trace becomes increasingly
complicated, and is often dif cult to relate to speci c
acoustic impedance contrasts. This is a signi cant observa-
tion since it demonstrates that a

' echo '

6.7.2.1 Synthetic seismograms
A particularly common and simple form of 1D forward
modelling compares seismic observations in the vicinity of
a drillhole with the response calculated from sonic (see

' '

in a seismic
dataset, such as shown in Fig. 6.40 , is not from a single
level or bed. Instead, it is a composite response of many

re ection