earthdoc-20959

Shiraz 2009 - First International Petroleum Conference & Exhibition Shiraz, Iran, 4 - 6 May 2009

P25Application of Nonstretch NMO in SeismicReflection Data ProcessingB. Yousef* (University of Tehran), A. Javaherian (University of Tehran), H.Shini Kimassi (NISOC) & A. Moslemi (OEOC)

SUMMARYWe describe the implementation of nonstretch normal-moveout (NMO) correction which decreases thestretching effects of conventional NMO correction. Unlike conventional NMO, the method implies that thevelocity decreases with time for a finite time interval of a seismic pulse. In this method, stretching can beavoided by keeping the parallelism of NMO traveltimes as much as possible. This method has been testedon synthetic and real seismic reflection data. The advantages of nonstretch NMO include preservation ofhigher frequencies and reduction of spectral distortions at far offsets. In this method, a significant range oflarge offsets that normally would be muted in the case of conventional NMO can be kept and used, therebyleading to better stack. Nonstretch NMO could be advantageous for amplitude-variation-with-offsetpurposes.


Introduction The application of NMO has been recognized as an effective method of generating quasi-zero-offset traces in traditional common-midpoint processing. Artifacts of the NMO method relate to the NMO-stretch effects. Buchholtz (1972) and Dunkin and Levin (1973) showed conventional application of normal-moveout correction to a common-midpoint (CMP) reflection generates a stretch that increases with offset and decreases with zero-offset time. Shatilo and Aminzadeh (2000) introduced the technique implies constant normal moveout (CNMO) for a finite time interval of a seismic trace. Perroud and Tygel (2004) introduced the implementation, called nonstretch NMO, automatically, avoids the undesirable stretch effects that are present in conventional NMO. They applied their new method (Nonstretch NMO) to shallow seismic data including high resolution (HR) seismic data and ground-penetrating radar (GPR) measurements. In this paper, nonstretch NMO (Perroud and Tygel, 2004) are applied to seismic reflection data. Theory NMO correction is usually considered in a hyperbolic equation:

22 2

0 2( ) ,nmo

xt x tV

= + (1)

where x denotes the offset between the source and the receiver, refers to two-way zero offset travel time and , is NMO velocity which estimates the root-mean-square (RMS) velocity in a case of horizontal stratified earth. Equation (1) represents a hyperbola whose asymptote passes through the origin and has slope equal to V

0t

o

nmoV

1nm− . Ideally, the entire pulse

width must be shifted to the horizontal line 0t t= without any distortion. Traditional NMO correction moves the samples ( )t x τ+ in the vicinity of traveltime onto '

0t τ+ with equation:

2' 2 2

2( ) ( ( ) ) .onmo

xt t xV

τ τ+ = + − (2)

By comparing equations (1) and (2) the stretch ratio can be extracted. For avoiding stretching we try to parallel the hyperbolae traveltime (Figure 1). As depicted in figure 1, the traveltimes in conventional NMO converge to each other whereas in nonstretch NMO the traveltimes are almost parallel to each other. It can be if

' / ( ) /t h tτ τ =

'τ τ= , in this case, we obtain the following relation:

1/2

0

2( ) 1 ,( )nmoV V

t x tττ

−⎛ ⎞

= +⎜ +⎝ ⎠⎟ (3)

where τ is a time shift and ( )V τ is the adjusted velocity. It can be seen from equation (3) that, for the set of recorded events on a given trace, stronger effects on the stacking velocity are observed at shorter zero offset times. Also, we know that ( )V τ always decreases when the time shift increases. Therefore, even setting NMO velocity constant is not sufficient to avoid stretching, as it is done in the constant-velocity-stack (CVS) approach. In addition, the conventional increase of NMO velocity with time that results from interpolation the time-velocity distribution is going the wrong way and further increases the stretching effect of the NMO.


Figure 1 In conventional NMO (left) traveltime converges with x and in nonstretch NMO (right) separation between travel times remains the same with x. Implementation With equation (3) the original time-velocity point picked from conventional velocity analysis is replaced by adjusted velocity in the curve segment that was obtained by it. The quantity time shift (τ ) is obtained by inversing the bandwidth of the propagating signal. In this method, the time-velocity distribution is dependent on a trace in the τ range as for each sample in the τ range about the t the modified velocity calculated for all of traces. Because in the

0

τ range the velocity decreases with time, the interpolated NMO velocity between events will increase faster, and thus the NMO stretch effect will be increased between events (Figure 2, left). The problem arises when events cross each other and it can be solved by processing the reflection events one at a time. At first, the traveltime corresponding to each reflection obtained by the traditional velocity analysis. Then, for each event, we mute all samples above the corresponding hyperbola and below those for the next events and apply the nonstretch NMO. The process completes by summing all the events. Application to synthetic and real data We applied conventional NMO and nonstretch NMO correction to synthetic data in a model with four horizontal layers with a far offset of 2000 m. The results of both methods are shown in Figure 3. Stacking velocity selected for these events are 1700 m/s, 2265 m/s, 2595 m/s and 2986 m/s, respectively. A zero-phase Ricker wavelet of 30 Hz characteristic frequency was used as the source signal. Figure 2 shows the CMP gather after conventional NMO (middle), stretching increases with offset and decreases with t . The stretching severely decreases at far offset after nonstretch NMO method (left). In nonstretch NMO, the wavelet is sharper at far offset. As a result, the S/N ratio increases in CMP stack. Amplitude spectrum of all traces is depicted in Figure 4. In conventional NMO, the dominant frequency (30 HZ) of first event decreases but after nonstretch NMO it does not change.

0

We tested both methods on real data. Figure 5 shows a typical CMP selected from acquired data in southwest Iran. After velocity analysis we obtained the values of t and

then we applied nonstretch NMO (Figure 7) The first event corresponding to t s is depicted in Figure 6. The wavelets are compressed at far offset. To show these compressed wavelets, we have taken amplitude spectra for the first event at offset of 2000 m which is pointed in Figure 8. Conventional correction leads to significant reduction in the high frequencies.

0

=nmoV 0 0.8

Figure 2 The velocity distribution in the case of no interfering (left) and interfering (right).

Figure 3 Synthetic CMP for four-flat-layer with noise addition (left). Application of conventional NMO correction on synthetic data (middle). Application of nonstretch NMO correction on synthetic data (right).

Figure 4 Amplitude spectrum of all traces after conventional NMO (left) and nonstretch NMO (right). Conclusions Nonstretch NMO correction reduces the stretch effects of conventional NMO. This results higher spectral frequencies and smaller spectral distortion of shallow far offset reflected events. Following the nonstretch NMO correction, muting may be less compared with conventional NMO. Therefore, longer spreads of data may be used for CMP stack and AVO analysis, thus improving their resolution.


Shiraz 2009 - First International Petroleum Conference & Exhibition

Acknowledgments The authors thank A. Roshandel Kahoo for his useful comments on coding in MATLAB. Reference Buchholtz, H. [1972] A note on signal distortion due to dynamic (NMO) corrections. Geophysical Prospecting, 20, No. 2, 395–402. Dunkin, J. W., and Levin, F. K., 1973, Effect of normal moveout on a seismic pulse, Geophysics, 38, 635–642. Perroud, H. and Tygel, M. [2004] Nonstretch NMO. Geophysics, 69, 599- 607. Miller, R.D. [1992] Normal moveout stretch mute on shallow-reflection data. Geophysics, 57, 1502–1507. Shatilo, A., and Aminzadeh, F., 2000, Constant normal moveout (CNMO) correction: a technique and test results: Geophysical Prospecting, 48, 473-488.

Shiraz, Iran, 4 - 6 May 2009

Figure 5 A real CMP seismic gather.

Figure 6 Conventional NMO correction (top) and nonstretch NMO correction (bottom) data from Figure 5.

Figure 7 The nonstretch NMO of real Figure 8 Amplitude spectrum of last trace for CMP gather from figure 5. first event from figure 7.

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