Deconvolution Bryce Hutchinson Sumit Verma Objectives: -Understand the difference between exponential and surface consistent gain -Identify power line noise is the frequency spectrum and remove it -Grasp what deconvolution is doing to the data

Exponential Gain 1. Choose the band pass volume we created last week as the input. 2. Set the Exponential Gain Constant to 2 Exponential gain multiplies each trace by an exponential function of the form e (nt) where we define what the exponential gain constant (n). So, according to the formula the gain factor will increase with increasing time (which you can think of as increasing depth).

Bandpass

Bandpass with Exp gain See the effect of Exponential gain! exponential gain : exp(nt) or e nt, we kept n=2 and t= time. What is this noise ? /// Have you seen it in exam!

Noise in the frequency spectrum There is a consistent noise at 60Hz in the frequency spectrum. Zoom in to see it better, also take note of how the noise looks in both the trace and frequency spectrum 1. Click the seismic analysis icon 2. Choose Frequency Analysis Window from the dropdown menu. Then the green plus to view it. Zoomed in Power line noise

Surface consistent (SC) gain I’ve copied the input windows for each of flow icons in this slide. I have put the flow icon in the top right of each window to show you which input it represents. 4. For SCApply, you will not have a choice of inputs yet. Be sure the bin size is set to 220. You must run the SCApply before these options will appear! 1. Choose the bandpass data as the input 2. We want to create a tight window around the power line noise in the notch filter 3. Change the offset bins size in the Options tab and select the Entire Trace in the Window tab Power line noise removal

Surface Consistent Scale Why : Surface-consistent scaling is used on land seismic data in order to compensate for the effects of the highly variable near-surface layers and variable source and receiver signatures and coupling. M. Turhan Taner and Fulton Koehler (1981). ”Surface consistent corrections.” Surface consistent corrections, 46(1), How in this software : In the SCScale the average amplitude (Mean or RMS) of each input trace is computed. Each trace scalar is assumed to be of the form: Trace Multiplier = Shot multiplier x Receiver Multiplier x Offset dependent Multiplier x CMP multiplier. By utilizing logarithms, this equation becomes a sum of factors rather than a product. The sum can then be solved by the usual Gauss-Seidel iterative process.

Surface Consistent Gain 1. Run the flow again, and now you will have inputs for SCApply 2. Your output should appear something like this. Don’t worry about subtle differences between this image and yours, we ran our flow in a different order. Compare the bandpassed data and SC gained data, what differences do you see?

Before sc gain What is this noise ? /// Have you seen it in exam!

After sc gain what step removed it ??? Do you see a better amplitude balance?

We have done several experiments to change You can change: Iterations and offset bin size. And Time window

We experiment here ! Surface Consistent Scaling Deconvolution Surface Consistent Deconvolution Surface Consistent Scaling Surface Consistent Deconvolution Experiment # 1 Experiment # 2 Experiment # 3 We will complete this part here ! We will upload this in lab 7b!

Defining a timegate Define the top and bottom of the timegate. Double click to end your pick. You can define the window on the raw data.

Deconvolution 2. Set the Decon Type to Zero-Phase (since our source was vibroseis) 3 1. This is the deconvolution flow. Use the SC gain data as the input. This is seismic was acquired with Vibroseis! 4 5 Surface Consistent Scaling Deconvolution Experiment # 1

Decon assumptions The earth is composed of horizontal layers of constant impedance 2.The source generates a compressional wave at normal incidence – there are no shear waves 3. The source wavelet does not change as it travels – it is stationary 4.The noise component n(t) is zero 5. The source waveform is known 6. The reflectivity is random (autocorrelation and spectra are similar) 7.The seismic waveform is minimum phase and thus has a minimum phase inverse minimum phase inverse Dr. Marfurt’s class slide Vibroseis has zero phase source wavelet !

Decon assumptions 16 The earth is composed of horizontal layers of constant impedance The earth is composed of horizontal layers of constant impedance decon works if the multiple generators are flat decon works if the multiple generators are flat The source generates a compressional wave at normal incidence – there are no shear waves works ok at near offsets works ok at near offsets The source wavelet does not change as it travels – it is stationary The source wavelet does not change as it travels – it is stationary use time-variant decon in running windows use time-variant decon in running windows The noise component n(t) is zero design operator on noise-free parts of the data; design decon operators on stacked traces and then apply to prestack data design operator on noise-free parts of the data; design decon operators on stacked traces and then apply to prestack data Dr. Marfurt’s class slide

Decon assumptions 17 The source waveform is known The source waveform is known If source wavelet is minimum phase, you can obtain a near perfect result The reflectivity is random (autocorrelation and spectra are similar) The reflectivity is random (autocorrelation and spectra are similar) If the source wavelet is not known, you are in serious trouble! The seismic waveform is minimum phase and thus has a minimum phase inverse The result of spiking decon is degraded if the source wavelet is not minimum phases (Yilmaz, 2001; p 190) Dr. Marfurt’s class slide In VISTA they have Zero Phase decon, in which they calculate zero phase decon operator.

Deconvolution Spiking Decon: -Wiener Levinson algorithm -Auto-correlation of a segment of the trace which normally varies with offset (think normal equations) is computed Further – Zero Phase: -Forward Fourier Transform is calculated giving the amplitude and phase spectrum -Phase spectrum is then set to zero and an inverse transform is performed -Resulting in a zero phase equivalent of the spiking (minimum phase) operator. -The zero phase operator is then convolved with the data resulting in an image showing the reflectors much tighter The autocorrelation function looks like: Assume the Earth’s input x t is a series of spikes approximated by a random Gaussian distribution:

Output 2. Set Compare your output deconvolution to the SC gained data and to the band pass data. What changes do you see? Input for SC gain

After SC gain Output

After Zero phase decon Output

Please check the amplitude spectrum. After Deconvolution After Surface consistent gain Before Surface consistent gain Notch filter to remove the powerline noise Deconvolution shows better balance in frequency spectrum.

Deconvolution generates some artifacts on the higher frequencies Output After Zero phase decon

So we apply band pass filter to remove the noises After Zero phase decon and bandpass filter

Experiment : 2 Surface Consistent Deconvolution

Experiment 2 Result!

After Zero phase decon and bandpass filter Experiment 1 Result!

Which one do I like better ! Processor’s dilemma !

Acknowledgement ! Dr. Kurt Marfurt Thang Ha Marcus Cahoj for giving inspiration for this lab.