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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.