American Oil and Gas Reporter - September 2015 - 91

SpecialReport: Reservoir Characterization
FIGURE 4A
Frequency Coverage in Conventional Inversion

Seismic velocity
Well, interpretation,...
Seismic reflectivity

Low-Frequency Trend
All inversions use a low-frequency
trend to replace the missing low frequencies in the seismic data. In addition, some
inversions use higher frequencies as a
starting model. The low-frequency trend
typically is derived by horizon-consistent
interpolation and extrapolation of the
well control. If the wells are distributed
poorly, seismic velocities are used to
control the lowest-frequency band.
The frequencies where the seismic
velocities are to be trusted depend on
their source. Typically, velocities from
normal move-out or migration are valid
up to 2-3 Hz. Velocities from tomography
and full-waveform inversion can go a
little higher. With conventional seismic
data, where the missing frequencies are
up to 6-15 Hz, there is a gap between
where the seismic velocities are valid
and where the seismic kicks in. The well
control must be interpolated to fill this
gap (Figure 4A).
With broadband seismic data, the gap
between the seismic velocity information
and the lowest seismic frequency is closed,
at least if the seismic data go down to 23 Hz (Figure 4B). For post-stack PP inversion, the low-frequency trend is defined
as P-impedance. For prestack data, three
trends are needed: P-impedance, S-impedance and density, or some other com-

Seismic velocity
Seismic reflectivity

bination of P-wave velocity, S-wave velocity and density.
So the P-velocity model coming from
processing needs to be transformed into
P-impedance, S-impedance and density
for the frequencies that are valid in the
velocity data. Typically, the transformation
is done with rock physics relationships
and/or using well control as calibration
points. For ultralow frequencies up to 3
Hz, the rock physics relationships are
generally not too complicated and regional
trends such as Castagna's mud rock line
or Gardner's rule can be used. It is always

advised to validate the relationships and
the trends used in the inversion by any
available well control.

Inversion Engine
Seismic inversion algorithms need an
input model. Depending on the algorithm,
the input model also may be used as a
starting model within the seismic frequency band, at least for the missing
seismic frequencies.
Even if the algorithm uses only a
specified maximum low frequency, some
algorithms are able to fill the gap using

FIGURE 5
Sparse Inversion of Layered Sandstone Impedance Model (Figure 1)
ssi_batch_2_19_100_2Hz_002Unc/inverted_impedance.mod
0
100
0.3
0.4
0.5
0.6
0.7

Time (s)

assuming smoothness of the phase spectrum in the seismic data. Every one of
these hypothetical wavelets is carried
through the inversion process. The inversions are carefully quality controlled and
ranked to come up with a "best" wavelet
for broadband inversion. Figure 3 shows
examples of conventional and broadband
wavelet estimates using well logs.

FIGURE 4B
Frequency Coverage in Broadband Inversion

0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5

SEPTEMBER 2015 91

American Oil and Gas Reporter - September 2015

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