effect of seismic wavelet phase on post stack …effect of seismic wavelet phase on post stack...
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118 – Opal Hostel, Indian School of Mines, Dhanbad-826004;
10th Biennial International Conference & Exposition
P 410
Effect of Seismic Wavelet Phase on Post Stack Inversion
Chirag Jain*
Summary
E&P industry now a days greatly depends on inversion for interpretation of the data. Seismic data may be inspected and
interpreted on its own without inversion, but this does not provide the most detailed view of the subsurface and can be
misleading under certain conditions. Because of its efficiency and quality, most oil and gas companies now use seismic
inversion to increase the resolution and reliability of the data and to improve estimation of rock properties including porosity
and net pay. Inversion can be defined as deriving a model to describe the subsurface from field data that is consistent with the
data.
Keywords: Inversion, Wavelet Phase, Quality Controls and Wavelet.
Introduction
Seismic inversion is the process of converting seismic
reflection data into seismic impedance. Seismic acoustic
impedance is the product of density and velocity. Acoustic
impedance (AI) is a rock/layer property as it is related to
layers and not the interfaces. Since AI varies with
lithology, porosity, fluid content, depth, pressure and
temperature it can be used as a lithology indicator to map
flow units accurately, porosity indicator, hydrocarbon
indicator and a tool for quantitative analysis. Therefore
result of inversion greatly effects the interpretation and
finally decision making in the industry.
Theory and Method
Seismic inversion is based on the convolution model:
- Seismic trace is convolution of reflectivity R(t) with
wavelet W(t) plus noise
N(t): S(t) = R(t)*W(t) + N(t) (Where * is convolution)
- Assuming that the noise component is negligible:
S(t) = R(t)*W(t)
It is better to work in frequency domain than in time
domain and so when we convert the above equation in
frequency domain a problem arises: the lowest and the
highest frequencies will be missing. This happens because
of the band limited nature of the seismic data. The lower
frequencies are most critical to rock properties, because it
leads to determining fluid, porosity, and all other reservoir
properties needed to make a drilling decision. Therefore a
low frequency trend model is necessary in order to really
find out what is going on in earth.
Seismic inversion depends on a number of parameters (low
frequency model, wavelet phase, wavelength of wavelet,
frequency of wavelet, etc.). A good wavelet is the core of
inversion. This investigation takes account of variation in
phase of wavelet keeping all other parameters same. Gulf
of Mexico Data set (Public domain) is used for the
experiment.
Phase describes the relative timing relationships of the
various frequency components that make up the seismic
wavelet.
First of all data is loaded and the quality controls are
applied to test the quality of data. Well to seismic tie is
done using initial wavelet derived from the statistical
method. This is then followed by zero or minimum phase
wavelet estimation at the wells, where the reflectivity
series is known both from the well as well as from the
seismic. Synthetic Ricker wavelets of 15, 30, 45, 60, 75,
90, 120, 150 and 180 degree phase are then generated.
Each of above created synthetic Ricker wavelet is merged
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with the extracted wavelet to get 15, 30, 45, 60, 75, 90,
120, 150 and 180 degree amplitude-phase wavelet.
Figure 1 Phase rotation of a zero phase wavelet
Figure 2 All the extracted wavelets
Figure 3 Amplitude spectra of all the extracted wavelet
overlapped
Figure 4 Phase spectra of all the extracted wavelet
overlapped
Trend model is then created for each case. These wavelets
and trend models are then used for seismic inversion to
find out the reflectivity series away from the well. Every
step is followed by the quality controls to check the
accuracy. The results are as follows:
Figure 5 Inverted impedance zero degree phase wavelet
Figure 6 Inverted impedance 15 degree phase wavelet
Figure 7 Inverted impedance 30 degree phase wavelet
Figure 8 Inverted impedance 45 degree phase wavelet
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Figure 9 Inverted impedance 60 degree phase wavelet
Figure 10 Inverted impedance 75 degree phase wavelet
Figure 11 Inverted impedance 90 degree phase wavelet
Figure 12 Inverted impedance 120 degree phase wavelet
Figure 13 Inverted impedance 150 degree phase wavelet
Figure 14 Inverted impedance 180 degree phase wavelet
Observations
When zero degree phase wavelet is used for inversion,
results follows almost the same trend as the well data
follow. Thus indicating that inversion result is good. When
15 degree phase wavelet is used for inversion, it also
follows the geology of the area as described by well to an
extent which can be considered. However when we take
wavelet with phase 30 degree and greater the inversion
results disagree with the geology of the area, for instance
high impedance region becomes low impedance and
viceversa. For the case of 180 degree phase, the inversion
results show a relatively high impedance layer within
the low impedance layer with respect to the exact geology
of the area.
Conclusions
Zero phase or minimum phase wavelets are the most
desirable for interpretation. The degree of variation in
phase of the input wavelet greatly effects the inversion
results. The higher the phase shift, the higher is the error
in impedance results.
Acknowledgment
I'm very thankful to Dr. Ranjit Shaw, Principal Project
Geoscientist at Jason - A CGG Company and all the
members of JASON office at MIDC, Navi Mumbai for
providing me the assistance and guidance without which
this would not have been possible.
References
Al-Chalabi, M., 1997, Parameter nonuniqueness in
velocity versus depth functions; Geophysics, 62, 970-979.
Connolly, P., 1999, Elastic impedance; The Leading Edge,
18(4), 438-452.
Hosken, J.W.J., 1988, Ricker wavelets in their various
guises; First Break, 6(1), 24-33.
Simm, R. and White, R.E., 2002, Phase, polarity and the
interpreter’s wavelet; First Break, 20(5), 277-281.
Walden, A.T. and White, R.E., 1998, Seismic wavelet
estimation: a frequency domain solution to a geophysical
noisy input-output problem; IEEE Transactions on
Geoscience and Remote Sensing 36, 287-297. White, R.E.,
1997, The accuracy of well ties: practical procedures and
examples; Expanded Abstract RC1.5, 67th SEG Meeting,
Dallas.
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White, R.E., 1998, Stretch and squeeze – just keeping up
appearances? ; EAGE 60th Conference and Technical
Exhibition, Leipzig, Extended Abstract P138. White, R.E.
and Hu, T., 1998, How accurate can a well tie be? ; The
Leading Edge, 18(8), 1065-1071.