American Oil and Gas Reporter - July 2020 - 58

SpecialReport: Geophysics & Computing
FIGURE 2
Angle of Incidence Overlaid on Migrated Angle Gather (Left)
and Offset Gather (Right)

hoff offset gathers must be transformed
to angle gathers. Computing an accurate
offset-to-angle transform is crucial to
predicting subsurface lithology and fluid
properties from seismic data.
The transformation from offsets to
angles mostly uses analytical expressions
that assume elastic properties vary only
with depth and are laterally homogeneous
(1-D assumption). With that assumption,
Kirchhoff offset-to-angle transform becomes
increasingly inaccurate as angles increase,
especially in the presence of anisotropy.
Figure 2 is a display of a migrated
seismic gather overlaid with the angle
of incidence, and compares offset gathers
and angle gathers. The amplitude distribution in the offset gather is quite different
from the angle gathers, and is much
noisier, especially at far offsets. Clearly,
the offset gathers are less reliable in
terms of amplitude preservation and may
provide unreliable inversion output. In
the offset gather, the reliable angle range
for impedance inversion is no higher
than 36 degrees. Beyond that, there is a
significant migration stretch as well as
prevalent noise.
Unfortunately, at angles less than 40
degrees, the Zoeppritz equation is relatively
insensitive to changes in density. This
often means that using such a range of
angles for density inversion will not yield
reliable results. In contrast, CRAM angle
gathers show reliable amplitudes at angles
up to 50 degrees, with more stability and
less noise.
58 THE AMERICAN OIL & GAS REPORTER

Well-To-Seismic Ties
Prior to performing impedance inversion, seismic data must be preconditioned.
The following steps were applied to the
data shown in this article: multiples suppression, increased signal-to-noise ratio
(median filtering), spectral balancing,
enhanced signal bandwidth with inverse
Q, higher-order gather flattening, and
wavelet unstretch.
A critical component of any seismic
inversion is wavelet extraction. Before
wavelet extraction, it is imperative to calibrate the seismic to the well markers
and remove any seismic-to-well mis-ties
that may exist. Furthermore, a good calibration is needed for building background

models for the impedance inversions.
A well tie tomographic approach was
used for the seismic-to-well calibration.
The approach uses the depth mis-ties to
globally update the seismic velocity model
and anisotropic parameters to minimize
mis-ties. This approach helps to minimize
the stretching and squeezing per well,
which often is required at the wavelet
extraction stage.
Because it is a tomographic approach,
it honors the correct ray path and accounts
for any lateral displacement, as opposed
to vertical stretching only, which is the
common approach. It also ensures that
the seismic data globally match all available wells in the project.
It is only after this step that the seismic
data is ready for wavelet extraction and
impedance inversion. Another advantage
of this tomographic approach is that
careful ties between the well logs and
the seismic minimize the need to change
the phase of the wavelet and improve the
chances of obtaining a zero-phase wavelet,
which in turn will yield markedly improved
inversion results.
Inversion Results
The inversion process uses the threeterm Fatti approximation to generate Pimpedance, S-impedance and density volume. Figures 3 and 4 show a comparison
of the inversion results using both migrated
offset gathers and CRAM gathers.
Figure 3 contains the background Pimpedance model (left), the inverted Pimpedance using offset gathers (middle),
and the inverted P-impedance using
CRAM gathers (right). The overall trends
in both inversion techniques are maintained, but the CRAM results show better

FIGURE 3
Resolution of Inversions from CRAM Gathers (Far Right)
versus Kirchhoff Gathers (Center)

American Oil and Gas Reporter - July 2020

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