Geology Reference
In-Depth Information
9.2 Deterministic inversion
There are a number of different approaches to
deterministic seismic inversion and no attempt will
be made here to outline them all. In addition, there is
no clear consensus that any particular inversion algo-
rithm is better than the others and it can be argued
that careful evaluation of each step along the way is
probably more important than choice of algorithm.
The main focus will be to outline the general prin-
ciples and investigate issues of quality control.
reflectivity is estimated through a deconvolution of
the seismic trace for the seismic wavelet. Owing to the
fact that the output is a broadband reflectivity
sequence, this type of approach is described as a
'
inversion (of which there are a number
of different types). To achieve an absolute impedance
inversion requires the merging of the reflectivity solu-
tion with a low-frequency impedance component.
One approach is to input a value for the uppermost
impedance layer and apply the recursive formula. In
practice, owing to trace-to-trace variability, this
requires a model based on well data or a generalised
geological to constrain the solution.
The observation that the seismic trace can be
constructed from a few large reflection coefficients
gave rise to an approach called sparse spike inversion.
The Maximum Likelihood method of Hampson and
Russell (
1985
) and the L1 Norm method of Olden-
burg et al. (
1983
) are examples.
Figure 9.3
illustrates
the principle behind sparse spike inversion, showing
the relationship between the well log impedance,
reflection coefficient series, the seismic trace and the
approximation of the impedance from the sparse
spike solution. Sparse spike inversion using
constraints to reduce non-uniqueness and find the
inverted solution remains a commonly used method.
A strength of sparse spike inversion is that it
attempts to produce the simplest model consistent
with the seismic data. Thus it pays close attention to
broadband
'
9.2.1 Recursive inversion
Early attempts to obtain absolute impedance from
seismic involved scaling the seismic section to reflect-
ivity, adding a low-frequency component (derived
from an interpolation of well data or stacking veloci-
ties scaled to impedance values) and applying the
recursive formula (i.e. the inverse of the reflection
coefficient formula) (e.g. Russell,
1988
):
1+r
i
1
AI
i+1
¼
AI
i
:
ð
9
:
1
Þ
r
i
This approach is flawed because the wavelet is not
addressed, but it serves as a useful introduction.
9.2.2 Sparse spike inversion
It is better to think of deterministic inversion as the
convolutional model in reverse. Thus in
Fig. 9.2
the
Seismic
Trace
Wavelet
Rc
AI
Recursive formula
or iterative
modelling scheme
(with constraints)
Deconvolved
with
=
Blocky
impedance
result
199
Figure 9.2
The concept of seismic trace inversion to impedance.
