2273 spectral decomp

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Spectral Decomposition in HRSKevin Gerlitz

This PowerPoint presentation illustrates a method of implementing

spectral decomposition within HRS by utilizing the Trace Maths utility.


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The Problem:

Given a 3D seismic volume,

use spectral decomposition to

create a tuning cube and

create data slices of thefrequencies

A sand channel in the

Blackfoot seismic dataset

Spectral Decomposition in Hampson-Russell


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The Solution:

A tuning cube can be created using aTrace Maths script and slices

extracted from this cube.

16 Hz Amplitude Map from aTuning cube.


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For comparison, a conventional

amplitude envelope extraction of the

mean value in a window 30 ms below

the Lower Mannville horizon from

slide 1.

The channel is oriented north-south

in the center of the window.


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Ensuring that the 3D seismic volume is displayed, click on Process -> Utility -> Trace Maths

You need the seismic

dataset as an input

variable for TraceMaths. Ive renamed

the input dataset to a

Variable Name of in

and set its Usage to

used

Creating a Tuning Cube in Hampson-Russell


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Call the output volume something meaningful. I am going to calculate the spectra over a 63 ms window in

this example.


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Copy and paste the

DFT_Hamp.prs Trace Maths

script into the Trace Mathswindow. You will have to edit

the start time (t1 = ), the

window length (wLen = ) and

the output time. In this case, Im

starting at the Lower_Mannville

horizon and using a 63 ms

window. The spectrum will be

output starting from 300 ms.

Dft_hamp.prs

Click on the icon below to copy and

paste the DFT Trace Maths script to

your system.


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Youll also need to know something about the DFT and the script

The Trace Maths script will plot the amplitude spectrum starting from 0 Hz up to the positive

Nyquist frequency. The frequency resolution is given by the inverse of the time window.

In my case, my dataset has a 2 ms sampling rate which corresponds to a Nyquist of 250 Hz (=

1/(2*0.002) ). For a 63 ms window, this corresponds to a frequency resolution of ( 1/0.063 = )

16 Hz. My first sample point will correspond to 0 Hz and my 16th data point will correspondto 250 Hz. The amplitude spectrum is placed starting at the output time of 300 ms, which

corresponds to the start of the dataset.

(from the File > Export Trace option)(single trace showing amplitude spectrum)


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After Trace Maths has created the Tuning cube, create slices of the various frequencies.

In my example, the slice at 300 ms is 0 Hz, 302 ms is 16 Hz, 304 ms is 32 Hz, etc


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0 Hz


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16 Hz


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32 Hz


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48 Hz


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64 Hz


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80 Hz


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By using a similarprocess with the

DFT_Hphase.prs Trace

Maths script, you can

create maps of the phase

angle for the appropriate

frequencies.

16 Hz phase map


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Trace Maths scripts are slower to run than compiled code. The time to process 800 traces with a 63

ms window on my 1 GHz PC was 6 minutes.

There is a trade-off between the length of the data window and the spectral resolution. Using a longer

window will provide better resolution in the frequency domain. On the other hand, a long windowmay be contaminated by the response from the underlying and overlying events of the zone of

interest. Having a high sampling rate may improve the situation but simply resampling the data will

not add any new information.

Viewing the frequency slices and interpreting the results as zone thickness can be misleading due to

wavelet effects. Like most geophysical imaging tools, care must be taken in the interpretation of theresults. A synthetic wedge model and the results of spectral decomposition are described in the

following slides.

Drawbacks of the Spectral Decomposition method


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Created a wedge model synthetic using a 5/10 50/70 Hz bandpass

wavelet (dominant period of 33 ms). The channel thickness was changed

from 1 m to 100 m with a 1 m increment => each Inline corresponds to

the thickness of the channel.


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Created the tuning cube using a 80 ms window from the top horizon.

This yields a spectral resolution of 12.5 Hz


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Wavelet effect / DoubletStrong low frequency

component below channel0 Hz = 80 ms period


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12.5 Hz = 80 ms periodSeparation of top & base


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25 Hz = 40 ms period


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37.5 Hz = 26 ms period


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50 Hz = 20 ms period


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62.5 Hz = 16 ms period


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12.5 Hz

37.5 Hz

0 Hz

Normal Polarity (positive frequencies)37.5 Hz 26 ms

50 Hz

50 Hz

50 Hz 62.5 Hz

62.5 Hz

75 Hz

Interpretation


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37.5 Hz

50 Hz

62.5 Hz 25 Hz25 Hz

62.5 Hz

75 Hz

75 Hz

Reversed Polarity (negative frequencies)

2273 spectral decomp

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