Geology 554

Environmental and Exploration Geophysics II

Generating synthetic seismograms

The simple in-class exercise undertaken last time illustrates the relationship between wavelet properties, interval velocity and seismic resolution. Wavelet duration and shape are a function of frequency content and phase relationships. In this short exercise, you will compute the amplitude spectra of the data you are working with and also generate some seismic wavelets. Today, we explore use of computer tools that allow us to calculate spectra and estimate the resolving power of a given seismic data set. In particular you will be interested to estimate the resolving power of your project data. The following illustrations show you how to extract amplitude spectra from your data and also generate calibration curves to provide a quantitative – wavelet based – assessment of inherent resolution limits of your seismic data.

Calculating Amplitude Spectra

  1. Open your project in Kingdom Suite
  2. Bring up a line for reference

Figure 1: Seismic from a different part of the Stratton field showing roll-over in the Vicksburg.

  1. From the main menu bar select Tools > TracePAK> Survey Spectrum >
  2. Select your 3D survey from the survey list (should be only item in the list for those of you working with the Golden data set).

  1. Take the default Seismic Data Type of Amplitude (time).

  1. Click on subset and specify the Line and trace range. If you have an inline up select about 10 of those and you can take the default on the trace range.
  2. OK > Apply

Figure 2: Amplitude spectrum computed for the subset defined in step 6.

  1. There are different ways to define bandwidth. In general the term defines the range of frequencies between half-power points. In this exercise we’ll just use amplitude. Roughly identify the low and high frequencies where the amplitude of the spectrum drops to ½. In the above spectral plot this would be about 20 to 70 Hz.

9. With your Survey Spectrum window still open, select a deeper time window: e.g., 2.5 to 3.2 seconds (see below). Just select Subset again, specify the new time range; click OK to exit the subset window and then click Apply to generate the new spectrum.

10. Apply to generate the new spectrum.

11. How do the range of frequencies in this time window compare to that observed at earlier travel times. The examples shown here are from a different data set. So –what do you have?

Figure 3: Spectra for deeper portions of the data has a bandwidth that extends from approximately 10 to 50 Hz.


12. Cancel to exit

Footnote: the Spectrum for the shallow 0.5 to 1.5 second data may have smaller bandwidth

Next let’s compute a wavelet

  1. Go to Tools > TracePak > Wavelets
  1. Let’s generate a theoretical wavelet

3. Select the Butterworth wavelet (see next page).

  1. Since we’re interested to get a match to the shallower data let’s use the information gained from the spectrum in the 0.5 to 1.5 second range of the data. Specify the low and high pass cutoff frequencies based on the results you obtained above in the computation of the spectrum.

Note that I’ve specified slopes on the low and high side of 18 and 36 db/octave. I’ve also specified a sample interval of 0.0005 seconds or ½ millisecond and a wavelet length of 0.1 second.

5. Next

6. You can take the default name if you wish or give it a name like Butterworth:20-70.

Next let’s compute a synthetic seismogram (the convolutional model in action)

  1. Go to Project > SynPak
  2. Select well #15
  1. Click OK
  2. Take the default T-D chart under the T-D Chart Folder Tab
  1. Go to the Velocity Tab and select the RhoB log. This is a density log. In the GulfCoast areas the Gardner relation is often used to approximate velocity from density. The Gardner relationship is stated as where a ~ 0.23 when units of velocity of ft/s are used.
  1. Under the density tab select the RhoB log again
  2. Under the reference log tab select the gamma ray curve
  1. For wavelet, select the Butterworth wavelet generated above. Yours will probably be a 12-40 Hz. Butterworth.
  2. For trace to compare your synthetic to, select Extract Trace under the Trace tab

Make sure you specify the 3dMigration as the Seismic survey

Pick from traces within a certain radius (in this case 200 feet).

10. Click next to get the following display.

Figure 4: Extracted trace near well 15.


11. You don’t need to save the trace, just click Finish and select it from the list

After you’ve defined all parameters click Finish and you should get a display with lots of panels like that shown below (Figure 5).

Figure 5: Synthetic seismograms are located on either side of the traces selected from the 3D survey.

Make sure you save your synthetic >

Go to Synthetic > Save as > give it a name

Next let’s compute the calibration curve

  1. If you need to return to SynPak, go to Project > SynPAK
  2. From the well name list select the Stratton #15 well
  3. Click on the Select Existing radio button and
  4. Select the Synthetic (e.g. Well15) from the drop down list.
  5. The multipanel display generated earlier will appear showing various parameters (interval velocity, density, acoustic impedance (AI), etc. along with a plot of the wavelet, the synthetic seismic response and actual traces near the well.
  6. Go to Tools > Tuning Analysis and

  7. Select your Butterworth wavelet from the drop down window
  8. Examine the tuning analysis plot.
  9. What is the actual time that the normalized peak to trough amplitude rises to a peak (the point of maximum tuning)?

Reference tuning analysis plot


Exercise: Generate and save a wavelet with high and low pas frequencies derived from the 1.5
Exercise: Pulling it all together

1. Calculate the amplitude spectrum for your data set. Remember that your calculation window should be centered roughly on the Oligocene sand intervals.Make a screen capture of the amplitude spectrum you calculated. Paste it into a word file. Indicate the range of traces, lines and the time interval for which you calculated the spectrum. Note the peak frequency and bandwidth.

2. Describe the wavelet you generate and use to construct a synthetic. Measure off the peak frequency directly from the wavelet. Estimate this by measuring the interval time between the two side lobe troughs.

The time between side lobes is ______seconds

The dominant frequency is ______Hz.

3. GulfCoast sonic logs suggest that t’s for in the Oligocene sands in this area vary between 85 and 135 sec/foot. This corresponds to velocities of between approximately 11,800 and 7,400 feet/s. In a CO2 injection pilot northeast of Houston, CO2 injected into one of the C-sands produced a drop in velocity from 8500fps to 6000 fps. Based on your analysis of the tuning plots generated in this exercise calculate the minimum resolvable thicknesses for the layer before and after injection. Use the wavelet derived from your data set. Remember that the tuning times are two way times.

4. The minimum resolvable thickness of a given layer corresponds to the minimum resolvable one-way travel time through that layer multiplied by the interval velocity. The travel time varies with the interval velocity, so in this example the same layer has two different resolvable thicknesses. The velocity drop resulting from CO2 injection increases the minimum resolvable thickness.

5. Summarize your findings in a paragraph.

6. Turn in your brief discussion with illustrations next Monday – April 20.
The description below is from the help window accessed on the Kingdom tuning plot

Tuning Analysis Dialog


In an active SynPAK display, click on Tools>Tuning Analysis to activate the Tuning Analysis dialog. Tuning Analysis generates a plot of the selected wavelet and a tuning thickness chart for the selected wavelet. The purpose of the tuning thickness chart is to analyze the vertical resolution of the seismic data.

The Tuning Analysis dialog allows you to select a wavelet from the top window. The resulting tuning thickness chart shows three curves. The thin diagonal line represents perfect resolution, where the actual time thickness is always equal to the apparent time thickness. The wavelet shown at the top is convolved with reflection coefficients spaced at intervals corresponding to the actual time thickness to produce the apparent time thickness line (the bold, sinusoidal, black diagonal line that approaches the actual time thickess as thickness increases). Comparison of the thin and bold lines displays the resolution limitations imposed by the selected wavelet.

The apparent time thickness line is normalized to produce the normalized peak-trough amplitude line (third curve - a bold red curve that starts at the origin and ends with a normalized peak to trough amplitude of 1). In the graphic, the maximum of the normalized peak-trough amplitude is at about 0.0098 seconds (actual time thickness). The amplitude maximum that occurs at the tuning thickness is about 1.3, meaning that the tuned amplitude resulting from the reinforcement from the top and the base of the bed will be about 50% greater than a single from either the top or the base of the bed with no reinforcement or interference.

Dialog items include:

Select a Wavelet: allow you to select an existing wavelet. Click on the down arrow (q) and select a wavelet from the list.

Additional dialog items include:

Export allows you to export the values in the tuning chart to a file. A standard Windows Save As dialog is activated. Enter the file name and click on Save to complete the step and dismiss the Save As dialog.

Note:The file will contain the wavelet times and amplitude for every sample, and the tuning chart values of Actual Time Thickness (sec), Apparent Time Thickness (sec), and Normalized Peak-Trough Amplitudes.

Print allows you to print the tuning chart. A standard Windows Print dialog is activated. Set the print parameters and then click on OK to print the chart. Close dismisses the dialog.

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