Spectral Decomposition in HRSKevin Gerlitz

This PowerPoint presentation illustrates a method of implementing spectral decomposition within HRS by utilizing the Trace Maths utility.

The Spectral Decomposition process is best described in a paper by Partyka et al. “Interpretational applications of spectral decomposition in reservoir characterization”, The Leading Edge, March 1999, 353 –360.

Essentially, the amplitude and phase spectra are computed and plotted for a window over the zone of interest to create a tuning cube. Data slices of the common frequencies are extracted from the tuning cube and examined. Slices from the amplitude tuning cube are a useful tool for defining and mapping reservoir thickness. Slices from the phase spectrum volume are helpful in mapping geological discontinuities.

32 Hz

64 Hz

Spectral Decomposition Map

A’

Buried Channel

A A A’

32 Hz64 Hz

Seismic Signal Tuning

What is Spectral Decomposition?

The Problem:

Given a 3D seismic volume, use spectral decomposition to create a “tuning cube” and create data slices of the frequencies

A sand channel in the Blackfoot seismic dataset

Spectral Decomposition in Hampson-Russell

The Solution:

A tuning cube can be created using a Trace Maths script and slices extracted from this cube.

16 Hz Amplitude Map from a Tuning cube.

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.

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

You need the seismic dataset as an input variable for Trace Maths. I’ve renamed the input dataset to a Variable Name of inand set its Usage to used …

Creating a Tuning Cube in Hampson-Russell

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

Copy and paste the DFT_Hamp.prs Trace Maths script into the Trace Maths window. You will have to edit the start time (t1 = …), the window length (wLen = …) and the output time. In this case, I’m starting at the Lower_Mannvillehorizon 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.

You’ll 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 correspond to 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)

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…

0 Hz

16 Hz

32 Hz

48 Hz

64 Hz

80 Hz

96 Hz

By using a similar process with the DFT_Hphase.prs Trace Maths script, you can create maps of the phase angle for the appropriate frequencies.

16 Hz phase map

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 window may 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 the results. A synthetic wedge model and the results of spectral decomposition are described in the following slides.

Drawbacks of the Spectral Decomposition method

Created a synthetic well with a 100 m thick channel…

Synthetic Wedge Modeling and Spectral Decomposition to Illustrate the Problems of Wavelet Effects

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.

Created the tuning cube using a 80 ms window from the top horizon. This yields a spectral resolution of 12.5 Hz

Wavelet effect / DoubletStrong low frequency component below channel0 Hz = 80 ms period

12.5 Hz = 80 ms periodSeparation of top & base

25 Hz = 40 ms period

37.5 Hz = 26 ms period

50 Hz = 20 ms period

62.5 Hz = 16 ms period

75 Hz = 13 ms period

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

37.5 Hz

50 Hz

62.5 Hz 25 Hz25 Hz

62.5 Hz

75 Hz

75 Hz

Reversed Polarity (negative frequencies)