Seismic wavelets and resolution - Seismic Amplitude - page 27

0º 180º 30º -150º 60º -120º 90º -90º

120º -60º 150 -30º 180º 0º -150º 30º

-120º 60º -90º 90º -60º 130º -30º 150º

Figure 3.7 Constant phase rotation of a zero phase wavelet - a useful description for wavelet shape. Blue numbers are referenced to positive
standard polarity and red numbers are referenced to negative standard polarity. Note it is usual to use the positive standard convention when
describing wavelet phase.

frequency than at a lower one. Attenuation also causes
seismic wave propagation to be dispersive (i.e. the
seismic velocity varies with frequency), and thus
changes to the phase spectrum depend on distance
travelled. For a Q value greater than about 10, velocity
should vary with frequency according to

Seabed
Response

Extracted wavelet
at 3000ms

-50

450

ln ð f 2 = f 1 Þ

TWT

ð C 2 C 1 Þ= C 1 ¼ , ð 3 : 2 Þ

0

500

π Q

where c 1 is the velocity at frequency f 1 and c 2 is the
velocity at frequency f 2 (O Brien and Lucas, 1971 ) . An

example of a modelled effect of Q on wavelet phase is
shown in Fig. 3.9 . Essentially low values of Q will give
greater phase rotation for a given sediment thickness
than higher values of Q.
Q can be measured on core samples in the labora-
tory (e.g. Winkler, 1986 ) , but it is not clear whether
the results obtained are representative of in-situ
values. At the seismic scale the easiest way to measure
Q is from a VSP (e.g. Stainsby and Worthington,
1985 ; see also Chapter 4 ). The method compares
direct (down-going) arrivals at two different depths
in a vertical well using vertical incidence geometry

'

50

Figure 3.8 Example of change in wavelet shape with depth.

Attenuation is parameterised by the quantity Q
defined as
Q ¼ 2 π= fraction of energy lost per cycle : ð 3 : 1 Þ

Equation (3.1) implies that the effect of attenuation is
to reduce amplitude at high frequencies more than at
low frequencies, because in any given subsurface path
there will be more cycles (i.e. wavelengths) at a higher

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