Converting the Vibroseis Zero Phase data into Minimum Phase
Cross-correlation is a measure of the similarity between two series f(t) and g(t) as a function of the displacement (lag) of one relative to the other.
Consider two real functions f(t) and g(t) that differ only by an unknown shift along the time (X) axis. By computing the cross-correlation, we can determine how much g(t) must be shifted to best align with f(t). The cross-correlation formula effectively slides g(t) along the axis and computes the integral of their product at each shift.
When the functions match, the value of (f * g) is maximized. This occurs because:
•When peaks align, their product contributes a large positive value.
•When troughs align, the product of two negative values is still positive, also contributing to a large correlation value.
The cross-correlation of f(t) and g(t) is equivalent to the convolution of f*(-t) with g(t) : (f * g) (t) = f* (-t) * g(t)
where f* denotes the complex conjugate of f.
Vibroseis Data Conversion:
Vibroseis source is a long train of sine waves of increasing or decreasing frequencies. Conventional impulsive source like dynamite produces a single discrete impulse for each event, whereas the Vibroseis source will show the event as a pulse train. In an uncorrelated seismic record, the pulse trains for each event overlap and cannot be separated by the human eye. However, after cross-correlation with the input sweep, each event should appear as a synthetic pulse which has the shape of the auto-correlation of the sweep.
Following are the advantages …
1.Since we know the form of the source signal, we can easily remove the back ground noise from the data using the source signal
2.We know the Vibroseis sweep frequency band, anything outside the frequency band limit of the sweep can be considered as a noise and that can be filtered out.
Figure 1. Schematic diagram of Vibroseis data Cross Correlation and Deconvolution (Image courtesy: SEG Wiki)
Why This Method is Used
•Vibroseis sweeps are long and non-impulsive. Correlation converts them into short wavelets
•Klauder wavelet is predictable and invertible. It enables stable deconvolution
•Produces clean seismic data with increased temporal resolution
•Works reliably on land and desert Vibroseis datasets
User recommendations:
In the Output data tab, users can save the Klauder Wavelet, Min Phase Decon Operator, Modeled Sweep Signal etc.
In the Output data tab, users can save the Klauder Wavelet, Min Phase Decon Operator, Modeled Sweep Signal etc.
Input DataItem
Input gather - connect/reference to Output gather that needs to be converted.
Input sweep - provide the vibroseis sweep signal as an input.
Execute deconvolution - this allows the user to perform deconvolution on the input data. By default, FALSE (Unchecked). Vibroseis data has broader side lobes, poor vertical (temporal) resolution. Deconvolution helps in removing the side lobes and increases the vertical resolution.
Vibroseis data - this section deals with the input vibroseis data. User should choose the parameters.
Cross Correlation Time - input field gather is cross-correlated by sliding the sweep across the input data. This removes the sweep from the input data and provides us normal seismic gather. Cross correlation time is used to determine how much time is required to match the sweep with the input data to remove the sweep from the recorded field data.
Sweep model - this section deals with the input field sweep. In order to match with the input data frequency band, we filter the input sweep with the following filter parameters. It gives a clean Klauder wavelet by performing the auto-correlation.
BandPass Fr1 - provide the lower frequency taper/slope
BandPass Fr2 - provide the low frequency to pass through
BandPass Fr3 - provide the high frequency to pass through
BandPass Fr4 - provide the high frequency taper/slope
Whitening factor - this stabilizes the output wavelet and increases the higher frequency.
Decon operator - this section deals with deconvolution. As we mentioned earlier, Deconvolution helps to get a cleaner sharp wavelet with better vertical resolution.
Decon Domain { Frequency, Time } - select the deconvolution domain. By default, Frequency.
In time domain, it creates the deconvolution operator by using the auto-correlation and prediction error filter. Whereas in the Frequency domain, it uses the amplitude and phase spectra of Klauder wavelet.
Noise - add percentage while noise to the deconvolution operator to stabilize the output.
Filter length - specify the length of the deconvolution operator. It controls the duration of the wavelet to be removed.
Auto-connection - By default, TRUE(Checked).It will automatically connects to the next module. To avoid auto-connect, the user should uncheck this option.
Bad data values option { Fix, Notify, Continue } - This is applicable whenever there is a bad value or NaN (Not a Number) in the data. By default, Notify. While testing, it is good to opt as Notify option. Once we understand the root cause of it, the user can either choose the option Fix or Continue. In this way, the job won't stop/fail during the production.
Notify - It will notify the issue if there are any bad values or NaN. This will halt the workflow execution.
Fix - It will fix the bad values and continue executing the workflow.
Continue - This option will continue the execution of the workflow however if there are any bad values or NaN, it won't fix it.
Skip - By default, FALSE(Unchecked). This option helps to bypass the module from the workflow.
Output DataItem
Output gather - generates output gather
Output Vibs Decon filter - generates deconvolution filter operator as an output
Min Phase Wavelet - generates minimum phase wavelet
Sweep - generates sweep as an output
Sweep Ato correaltion - generates auto-correlated sweep as an output.
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YouTube video lesson, click here to open [VIDEO IN PROCESS...]
Yilmaz. O., 1987, Seismic data processing: Society of Exploration Geophysicist
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