Geoscience Reference
In-Depth Information
spikes and by replacing erroneous data, either by plausible constant values or perhaps
by values derived from another well. Over a particular interval, it may be possible to
calculate values for one log from other logs, e.g. density from gamma-ray and sonic; the
required relationships can be established from a nearby well where all the logs are of
good quality. Whatever replacement method is used, care is needed to avoid introducing
artificial sudden jumps in the sonic or density curves at top and bottom of the edited
interval, as they would generate spurious reflections in the synthetic seismogram. Logs
over hydrocarbon-bearing reservoirs should also be treated with great suspicion; if
there is significant invasion of drilling fluid into the formation, either or both of the
density and sonic logs may be recording values in a zone close to the borehole where
the hydrocarbons have been partly swept away by the drilling fluid, whose properties
are therefore not representative of the virgin formation. It is possible to estimate these
effects using methods described in
chapter 5
, but the results are often unreliable because
of uncertainty about the extent of the invasion and thus the magnitude of the effect on
log response. Finally, as noted above, the logs sample the subsurface only within a few
centimetres around the borehole, whereas surface seismic data respond to properties
that are averaged laterally over at least several tens of metres. Thus, for example, a local
calcareous concretion, which happened to be drilled through by a well, could show a
marked effect on logs but have no seismic expression because of its limited lateral
extent.
Even when the wireline log data are correct and representative of the formation, the
approach described above may not result in a correct synthetic calculation. Implicitly,
the method assumes that we can treat the propagation of the seismic wave through a
1-D earth model using ray theory. This is correct if the seismic wavelength is short
compared with the layer thickness. If the wavelength is greater than about ten times the
layer thickness (as will certainly be the case for surface seismic response modelled from
closely sampled wireline data), then it is more appropriate to approximate the subsurface
V
E
is calculated as follows. Suppose we have a stack of thin layers in each of which
there are log measurements of P velocity
V
p
, shear velocity
V
s
and density
ρ
. In each
layer we determine the shear and bulk modulus (
µ
and
K
) from the equations
µ
=
V
s
ρ
and
V
p
−
3
V
s
4
K
=
ρ
.
Over an interval (typically a quarter of the seismic wavelength), we then calculate the
arithmetic density average and the harmonic average of
µ
and
K
. These average values
are then used to calculate a mean value of
V
p
and
V
s
, using the same relations between
the elastic moduli and velocities as before. This effective medium calculation is known
