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Synthetic examples

sin cmp
sin,cmp
Figure 2.
Synthetic benchmark 3D cube with one curved surface event (a) and noisy data cube (b).
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tsin flt
tsin,flt
Figure 3.
(a) Travel time of the event in Fig. 2(a). (b) The imaginary part of $ f$ -$ x$ -$ y$ NRNA coefficients at a given shift $ {{a}_{x,y,{{i}_{0}}}}(f)$
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tpre2d tpre
tpre2d,tpre
Figure 4.
The results of $ f$ -$ x$ NRNA (a) and $ f$ -$ x$ -$ y$ NRNA (b).
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We demonstrate the effectiveness of the proposed $ f$ -$ x$ -$ y$ NRNA using two synthetic dataset. The first synthetic example involves only one curved surface. Fig. 2(a) shows the synthetic dataset. Three slices of Fig. 2(a) illustrate the Y=2.4 km, X=2.4 km and Time=1 s, respectively. The following figures in this paper have the same way for display. The traveltime of this surface is shifted sine function (Fig. 3(a)). We can find that the traveltime is not linear varying. Therefore, we cannot use stationary $ f$ -$ x$ -$ y$ prediction filtering to estimate the effective signal. Fig. 5(b) is the noisy data. This curved surface event is greatly contaminated by random noise. We respectively use $ f$ -$ x$ NRNA and f-x-y NRNA to attenuate the random noise and compare their results (Fig. 5(c)5(d)). The SNRs of $ f$ -$ x$ NRNA and $ f$ -$ x$ -$ y$ NRNA are 0.34 and 2.4, respectively. Although f-x NRNA has suppressed a lot of random noise, there are still some random noises in the result (Fig. 5(c)). Compared with $ f$ -$ x$ NRNA, $ f$ -$ x$ -$ y$ NRNA gives a better result. The curved surface event is very clear and consistent, which may be easier to automatic event tracking for interpretation. Fig. 3(b) shows the imaginary part of $ f$ -$ x$ -$ y$ NRNA coefficients at a given shift $ {{a}_{x,y,{{i}_{0}}}}(f)$ , which are smooth along with space axes. From the slice with 20.833 Hz (up slice in Fig. 3(b)), one can find that the coefficients reflect the information of traveltime or time shifts between circumjacent traces (Fig. 3(a)). From the frontal and lateral slices in Fig. 3(b), one can conclude that the coefficients are related to dips of events from the frontal and lateral slices in Fig. 2(a). The coefficient is zero if the event is horizontal (e.g. position B). The coefficients are respectively positive and negative if the events are upgoing (e.g. position A) and downgoing (e.g. position C). The estimated rusult of coefficients is consistent with theoretical analysis.

cmp0 cmp tpre2d tpre
cmp0,cmp,tpre2d,tpre
Figure 5.
(a) Synthetic 3D shot gather. (b) Noisy data. (c) The result of $ f$ -$ x$ RNA. (d) The result of $ f$ -$ x$ -$ y$ RNA.
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The second synthetic example is a synthetic shot gather with four hyperbolic events (Fig. 5(a)). Here, we consider anisotropy of the propagating velocity, so that there are intersecting events in Y slice but they are not intersecting in X slice (the second and third events). Comparing the results of $ f$ -$ x$ NRNA (Fig 5(c)) and $ f$ -$ x$ -$ y$ NRNA (Fig 5(d)), we can find that $ f$ -$ x$ -$ y$ RNA can remove more noise that $ f$ -$ x$ NRNA, especially for poor signals (for example, far offset of the events indicated by arrows in Fig. 5(a)5(d)). The SNRs of $ f$ -$ x$ NRNA and $ f$ -$ x$ -$ y$ NRNA are 0.95 and 2.61, respectively. Both of these synthetic examples demonstrate the proposed $ f$ -$ x$ -$ y$ NRNA can be effectively use to attenuation random noise for 3D seismic data cube.


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Next: Application on field poststack Up: Liu et al.: f-x-y Previous: f-x-y NRNA for random

2013-11-13