American Oil and Gas Reporter - September 2015 - 90

SpecialReport: Reservoir Characterization
and constraints. They can positively or
negatively affect the inversion results.
For instance, a popular constraint to use

is the Gardner constraint. This constraint
forces the density from inversion to follow
the more stable P-impedance. This is ac-

FIGURE 2
Acoustic Impedance Inversion Slices of Conventional (Left)
And Broadband (Right) Data

Source: Menne D. Schakel and Peter R. Mesdag, Fully Data-Driven Quantitative Reservoir
Characterization by Broadband Seismic. presented at the 2014 Society of Exploration Geophysicists Annual International Meeting, held Oct. 26-31 in Denver (SEG Expanded Abstracts, 2502-2506).

FIGURE 3
Conventional (Green) and Broadband (Black) Wavelets
Wavelet

600,000

Wavelet

400,000
200,000
0
-200,000

-250

-200

-150

-100

-50

0
Time (ms)

1e+07

5e+06

30
40
50
Time-frequency (Hz)

100

90 THE AMERICAN OIL & GAS REPORTER

150

200

250

Phase Spectrum

Phs spc (deg)

Wavelet (Amp spc)

Amplitude Spectrum

20
0
-20
-40

30
40
50
Time-frequency (Hz)

ceptable if the rock actually obeys the
Gardner rule, but the constraint can render
the density useless as an independent parameter for reservoir characterization.

Estimating Wavelets
Conventional seismic data typically
have a low-frequency cutoff somewhere
between 6 and 15 Hz, depending on the
acquisition, the penetration of the seismic
wave into the subsurface, and the processing applied to the data. To capture
these frequencies accurately in a wavelet,
the wavelet length needs to be between
60 milliseconds (15 Hz) and 150 milliseconds (6 Hz). The most accurate way
to estimate a wavelet is by using well log
information.
For prestack seismic data, P-sonic, Ssonic and density well log curves are
needed. As a rule of thumb, the timeequivalent extent of the curves needs to
exceed two to three times the wavelet
length to achieve wavelet stability. Goodquality well curves of sufficient length
are not always available, but with good
rock physics modeling, it is generally
possible to generate the necessary well
log information.
On the other hand, for broadband seismic data, depending on the way the data
were acquired and processed, the seismic
low-frequency cutoff is somewhere between 2.5 and 4.5 Hz. This calls for
wavelets that are in excess of 400 milliseconds. Well curves that extend over a
time interval of more than a full second
are extremely rare. It is clear that well
logs that are too short cannot entirely
predict the necessary low-frequency behavior of the seismic wavelets.
To circumvent this limitation, a twostep method has been developed to estimate broadband wavelets. In the first
step, the "best" wavelet is estimated in a
conventional manner (referred to as a
conventional wavelet). In this process,
the wavelet length is made as long as the
data will bear (i.e., the wavelet length is
increased to the point where stability of
the estimation process becomes an issue).
In the second step, the seismic amplitude spectrum is extracted using long
time windows. The resulting smooth amplitude spectrum is colored by the well
log amplitude spectrum and merged with
the conventional wavelet phase spectrum.
On the low-frequency side of the spectrum,
where the conventional wavelet phase is
not defined, several hypotheses are tried

American Oil and Gas Reporter - September 2015

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