Spectral Decomposition in HRS Kevin Gerlitz This PowerPoint presentation illustrates a method of implementing spectral decomposition within HRS by utilizing the Trace Maths utility.
What is Spectral Decomposition? 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. Buried Channel Seismic Signal Tuning A A A Spectral Decomposition Map 32 Hz A 32 Hz 64 Hz 64 Hz
Spectral Decomposition in Hampson-Russell 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
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.
Creating a Tuning Cube in Hampson-Russell 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 in and set its Usage to used
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_Mannville horizon and using a 63 ms window. The spectrum will be output starting from 300 ms. Click on the icon below to copy and paste the DFT Trace Maths script to your system. Dft_hamp.prs
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. (single trace showing amplitude spectrum) (from the File > Export Trace option)
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
Drawbacks of the Spectral Decomposition method 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.
Synthetic Wedge Modeling and Spectral Decomposition to Illustrate the Problems of Wavelet Effects Created a synthetic well with a 100 m thick channel
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
0 Hz = 80 ms period Strong low frequency component below channel Wavelet effect / Doublet
12.5 Hz = 80 ms period Separation 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
Interpretation Normal Polarity (positive frequencies) 37.5 Hz 26 ms 50 Hz 62.5 Hz 50 Hz 50 Hz 75 Hz 37.5 Hz 12.5 Hz 62.5 Hz 0 Hz
Reversed Polarity (negative frequencies) 62.5 Hz 25 Hz 25 Hz 62.5 Hz 75 Hz 50 Hz 37.5 Hz 75 Hz