Seismic attributes of time-vs. depth-migrated data using self-adaptive window

Tengfei Lin*, Bo Zhang, The University of Oklahoma; Zhifa Zhan, Zhonghong Wan, BGP., CNPC; Fangyu Li, Huailai

Zhou and Kurt Marfurt, the University of Oklahoma

Summary

Seismic attributes are routinely used to assist for seismic

interpretation and reservoir characterization. The more

commonly used geometric attributes include 1) reflector dip-

azimuth, 2) coherence, and 3) curvature. Most publications

seismic attributes were used in time-migrated data. While

interpreting seismic attributes such as coherence on depth

migrated data requires a slightly different perspective. First,

the samples are meters or feet rather than as milliseconds.

Second, Fourier Transform is necessary during the

estimation of seismic attributes. They are computed as

cycles/km (or alternatively as cycles/1000 ft) rather than as

cycles/s or Hertz, with the dominant wavenumber decreasing

with increasing velocities at depth. Third, we conventionally

use a constant user-defined window to calculate those

attribute, while the constant window size is not capable to

handle layers with different thickness at the same time, the

complexity of structure in seismic data makes it invalid,

especially for the depth migrated data.

In this paper we proposed a workflow to estimate the seismic

attributes using a self-adaptive window size by integrating

the result from seismic spectrum analysis. We test our

algorithm on both time and depth migrated data from an

oilfield of East China.

Introduction

Seismic attributes have been applied to seismic data since

their inception. Since the dominant wavelength increases

with increasing velocity which in turn increases with depth,

attributes such as coherence benefit by using a shorter

vertical analysis windows in the shallow section and longer

vertical analysis windows in the deeper section. Since most

coherence implementations are design to use a fixed vertical

analysis window, the interpreter simply runs the algorithm

using an appropriate window for each zone to be analyzed.

Both coherence and curvature are structurally driven

algorithms, with coherence computed along structural dip

and curvature computed from structural dip (e.g. Lin et al.,

2013).

Volumetric dip and azimuth volumes can be very valuable

interpretation tools (e.g. Chopra and Marfurt, 2007). They

are also the foundation for the structurally driven seismic

attributes. Chopra and Marfurt (2007) mentioned in their

book that Picou and Utzman (1962) introduced dip

estimation into 2D seismic interpretation. Finn and Backus

(1986) extended dip estimation to 3D as a piecewise

continuous function of spatial position and seismic

traveltime. Cerveny and Zahradnik (1975) introduced

Hilbert transform and application into geophysics to

calculate complex traces of seismic data. Luo et al. (1996)

described method to estimate vector dip based on a 3D

extension of this work. Marfurt et al., (1999) improved the

estimation of 3D vector dip by smoothing with mean or

median filters. In order to compensate for the blurring caused

by such smoothing, Luo et al., (2002), applied multiple

analysis window (Kuwahara et al., 1976) to generate an

edge-preserving smoothing algorithm. Later, Marfurt (2006)

modified this approach for volumetric dip calculations

where he used 3D rather than 2D overlapping windows.

One of the important application for volumetric dip is

structurally driven coherence. Bahorich and Farmer (1995)

published the first-generation 3-D seismic discontinuity -

coherence, by calculating localized waveform similarity in

both inline and crossline directions, to help distinguish faults

and stratigraphic features in seismic interpretation. Marfurt

et al., (1998) provided the second-generation, semblance-

based coherency algorithm, which improved the vertical

resolution. Gersztenkorn and Marfurt (1996, 1999) offered

the third-generation, coherence based on calculating the

eigenvalues and eigenvectors of the covariance matrix.

Volumetric dip and coherence

Geologically, we define a planar interface such as a

formation top or internal bedding surface by means of

apparent dips θx and θy, or more commonly, by the surface’s

true dip θ, and its strike, ψ (Figure 1).

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Figure 1. The definition of volumetric dip. (After Marfurt, 2006).

First, the algorithm estimates coherence using semblance,

the maximum coherence is calculated along the dip indicated

by the red dashed line. The peak value of this curve

estimates coherence, while the dip value of this peak

estimates instantaneous dip. To improve the accuracy of the

results, the multiple-analysis-window (Kuwahara et al.,

1976) and self-adaptive window are applied.

As for the coherence, we calculate the energy of the five

input traces within an analysis window first, and then we get

the average trace, and finally, we replace each trace by the

average trace and calculate the energy of the five average

traces. The semblance is the ratio of the energy of the

coherent (averaged or smoothed) traces to the energy of the

original (unsmoothed) traces.

High resolution seismic attributes estimation using self-

adaptive window

We define the window height as the half-height of the

analysis window, the window itself will always be centered

along dip.

Spectral analysis of the seismic data allows us to map the

dominant frequency (wavenumber) of the seismic source

wavelet as well as tuning frequency phenomena. If the

dominant source wavelet frequency (wavenumber) is 50 Hz

(10 circles/km), the dominant period is 0.020 s (0.100 km),

suggesting a half-window size of 0.010 s (0.050 km) for

attribute calculation. However, we know that the dominant

frequency (wavenumber) changes laterally and vertically

with thin bed tuning and attenuation effects, such that many

areas of the survey will be analyzed using a suboptimum

window.

Lin et al., (2013) added dip compensation to spectral

decomposition and noted that the apparent peak frequency

(wavenumber) and the real peak frequency (wavenumber)

are different by 1/cosθ in the presence of dip θ. Here, we are

going to use apparent peak frequency (wavenumber) to get

the window height.

𝐻𝑔𝑎𝑡𝑒 =1

2𝑓𝑝𝑒𝑎𝑘

the actual size may be a smaller or larger depending on the

data quality. For our data we use a size that will be 1.05 times

larger.

The following single trace example illustrates the workflow.

Figure 2. (a) The time migrated seismic trace; (b) frequency

spectrum (circles/s or Hz) of (a) seismic trace; (c) the original (blue

curve indicated by blue arrow) and smoothed (red curve indicated

by red arrow) peak frequency curves; (d) the original (blue curve

indicated by blue arrow) and smoothed (red curve pointed by red

arrow) self-adaptive window size (ms).

Figure 2 and Figure 3 show us the seismic trace, frequency

(wavenumber) spectrum and peak frequency (peak wavenumber)

curves as well as the corresponding self-adaptive window size of

time migrated data and depth migrated data, respectively. The

smoothing for peak frequency (wavenumber) is very necessary

because the existence of the abnormal values pointed by blue arrow.

The yellow arrows in Figure 2 and Figure 3 indicate the relevant

self-adaptive window size (ms for time migrated data; m for depth

migrated data). We can found that the self-adaptive size match the

seismic trace (time migrated data and depth migrated data) very

well.

Figure 3. (a) The depth migrated seismic trace; (b) wavenumber

spectrum (circles/km) of (a) seismic trace; (c) the original (blue

curve indicated by blue arrow) and smoothed (red curve indicated

by red arrow) peak wavenumber curves; (d) the original (blue curve

indicated by blue arrow) and smoothed (red curve indicated by red

arrow) self-adaptive window size (m).

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Application

The data is from an oilfield of east China. There are lots of

fault-controlled reservoirs, exhibiting strongly on the

seismic profile shown on both the time migrated and depth

migrated data in Figure 4. We found that the horizons are

much deeper in depth migrated data than the ones in time

migrated data. This is because the increase of velocity with

time (depth).

The sample increments are 0.002s and 0.01km for time and

depth migrated data, separately. We found the data focus on

the low frequency (wavelength).

Figure 4 shows us the seismic profile of (a) time migrated

data and (b) depth migrated data. The red arrows indicate the

faults, which are much clearer in depth migrated data and the

fault planes are more continuously. The orange arrows show

us the migration artifacts, the depth migrated data are

suffered more than the time migrated data. The green arrow

in depth migrated data indicates a lower frequency compared

to the time migrated data. For the blue arrow in depth

migrated, it gives us a clearly fault plane, which is blurred in

time migrated data. The frequency range is 0 – 40 Hz for

time migrated data, while the wavenumber range is about 0

– 20 circles/km for depth migrated data (Figure 5). We can

found that the wavenumber for depth migrated data is about

half of the frequency for time migrated data. The white

arrow in Figure 5 shows us the low peak frequency

(wavenumber) which should be a little higher. This is

because the existence of the migration artifacts. The black

‘y’ describes the main faults of the data.

Figure 4. Seismic profile of (a) time migrated data and (b) depth

migrated data.

The figure 6 indicates us the huge difference of

coherence profiles using two different algorithm. The red

arrow shows us the three main faults, they are clearer in

the profile with self-adaptive window, for both the time

and the depth migrated data, though the stair steps are

still existed. The orange arrows point to two faults, the

stair step phenomenon is obviously in time migrated

data, while the faults are continuous in depth migrated

data, and the noise are removed a lot for the coherence

profile using self-adaptive window. The black arrows in

Figure 8 (a) and (c) show us the vertical window

artifacts generated by user-define constant window,

while they disappear in Figure 8 (b) and (d) because the

usage of the self-adaptive window.

Figure 5. Vertical slices of peak frequency (wavenumber) of (a)

time migrated data and (b) depth migrated data.

Conclusions

The attributes calculation using user-define window is more

suitable to detect geology structures. The artifacts suffering

from constant window size can be removed by the proposed

algorithm Furthermore our technique has the ability to

improve both the lateral and vertical resolution of seismic

attributes, especially the vertical resolution both in time and

depth domain.

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Acknowledgements

We thank the sponsors of the OU Attribute-Assisted

Processing and Interpretation Consortium for their financial

support and BGP for permission to publish showing their

data. We also thank The National Science Foundation of

China (seismic multi-wave fields’ characteristics analysis of

the thin interbedded reservoirs, Grant No. 41204091)

EDITED REFFERENCE

Figure 6. The coherence profiles of time migrated data with (a) user-define constant window and (b) self-adaptive window; and the coherence

profiles of depth migrated data with (c) user-define constant window and (d) self-adaptive window.

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http://dx.doi.org/10.1190/segam2014-1579.1 EDITED REFERENCES Note: This reference list is a copy-edited version of the reference list submitted by the author. Reference lists for the 2014 SEG Technical Program Expanded Abstracts have been copy edited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES

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