Petrophysics MSc Course Notes Sonic (Acoustic) Log
Dr. Paul Glover Page 187
16.10.3 Synthetic Seismograms
A synthetic seismogram is a seismic trace that has been constructed from various parameters
obtainable from log information. It represents the seismic trace that should be observed with the
seismic method at the well location. It is useful to compare such a synthetic seismogram with the
seismic trace actually measured at the well to improve the picking of seismic horizons, and to improve
the accuracy and resolution of formations of interest.
It should be remembered that the observed seismic trace is primarily a record of the ability of
interfaces between formations to reflect elastic waves. This ability is called the reflection coefficient
R. The reflection coefficient depends upon the properties of the rock either side of the interface, and in
particular on its acoustic impedance. The acoustic impedance is the product of the seismic velocity and
the density of the rock.
Thus, if we can derive the density and seismic velocity of a set of formations from logs, we can derive
a synthetic seismogram. The procedure is as follows.
• Obtain a density log, ρ(z), for the interval of interest. This is best obtained from a FDC log, but
approximations can be made from the sonic log by using the sonic log to derive porosity, and then
if the densities of the rock matrix and formation fluids are known, the density of the rock can be
calculated.
• Convert the density log in depth to that against two-way time using the TTI information from the
sonic log.
• Obtain the elastic wave velocity log, V(z), from the sonic log using Eq. (16.1).
• Convert the elastic wave velocity log in depth to that against two-way time using the TTI
information from the sonic log.
• Multiply these two values for each depth to give the acoustic impedance log, AI =ρ(TWT)V(TWT).
• Calculate the reflection coefficient for each interface from the acoustic impedance log using;
1122
1122
12
12
VV
VV
AIAI
AIAI
R
ρρ
−
=
+
= (16.9)
where the subscript 2 refers to the formation below an interface, and the subscript 1 to the
formation above it.
Note that the reflection coefficient will only exist at interfaces, and is zero in between.
• Apply a multiplying factor to the reflection coefficient log to account for the fact that the seismic
response will be attenuated with depth. This factor reduces with increasing two-way travel time
(i.e., as depth increases).
• Convolve (multiply) the modified reflection coefficient with a chosen zero phase wavelet that
represents the seismic data with which you wish to compare the synthetic seismogram.