Vibroseis Similarity Test - A Python Solution
Wakeel Ur Rehman
Exploration Geophysicist | Python Programmer | Data Scientist | Rock Physics Enthusiast
Vibroseis Similarity tests for controlled-source land seismic surveys are routinely performed to assess the output performance of vibrator mechanics. These tests are crucial to make sure the output source energy (Ground Force) of vibrator matches the desired input (Pilot Sweep). ?Mathematically speaking, the objectives of these tests are to check/QC the similarity of Pilot sweep (Reference sweep generated in DPG) with the vibroseis Ground force sweep (calculated in DSD through collective response of accelerometers on Reaction mass and Base Plate).
Correlation (in terms of Auto-correlation / Cross-correlation) and Fourier Transform are two fundamental mathematical operations for assessing the similarity of ideal input and vibroseis output sweeps in different plots/domains. Auto-correlograms of reference and Ground Force (GF) sweeps (i.e. correlation of Reference sweep with itself and correlation of Ground Force with itself) is usually plotted to see the similarity between both signals. Correlation wavelet, which is another way of looking at similarity of Reference and Ground Force sweeps, is obtained through absolute value of cross-correlation of Reference and Ground Force Sweeps. The frequency-time plot can be used to see the frequency variation with time. The amplitude spectra of Reference/Ground Force sweep can be analyzed for distribution of amplitudes for each frequency component, through Fast Fourier Transform (FFT) of each Reference and GF sweep signals. Phase lag, measure of phase lag between Reference & GF signals, is obtained Transfer Function of power spectra obtained through function of cross spectral densities of (1) GF with reference and (2) reference with reference. Spectrogram plot is useful to see the spectrum of all fundamental + harmonic frequencies of the vibrator output. Distortion graph shows the level of incoherency between Reference and Ground Force signals and Fundamental Force (amplitude) shows the magnitude of fundamental force generated in each step. Both are calculated as:
Where,
Real Peak is Cross-Correlation peak (Ground force * Reference)
Imag Peak is Cross-Correlation peak (Ground force * Imaginary Reference)
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Autocorrelation peak is ground force RMS value (Ground force * Ground force)
I have implemented the formulae to generate all QC plots of Vibroseis similarity test in Python. The python code reads the SEGD file of routine similarity test. The code separates the channels data as:
The First three signals (Uncorrelated) on the subplot A are True reference (), reference (R) and Ground Force (GF) signals. Auto-correlograms of Reference and Force channels could be analyzed as a first QC step (First figure in Subplot B). Their match shows the similarity of vibrator output with the ideal input sweep (Reference). Another QC step is to analyze the amplitude of cross-correlation of True reference and Ground Force (GF) signals, where signal loss (in dB) could be analyzed (2nd figure in Subplot B). Similarly, Time Vs Frequency analysis (for Frequency variation rate df/dt), Frequency vs amplitude analysis could be performed over Reference sweep signal to analyze the reference signal (3rd and 4th figure in Subplot B). Phase lag (5th figure in Subplot B) is an import QC step to analyze the similarity / discrepancy of vibrator output (F) sweep signal with its input signal. The measure of distortion in Force signal and the reference sweep (6th figure in Subplot B) is another useful plot to check the integrity of the hardware of vibroseis. Other QCs are measure of Fundamental and peak forces (in lbs or %) computed from force sweep signal (Bottom three figures in Subplot B).
Distortion caused by the harmonics of fundamental signal can be visualized through spectrogram (figure in Subplot C) which is Short Time Fourier Transform (STFT) of Force signal sweep. On spectrogram we can analyze the extent of harmonics generated by fundamental signal.
Senior Geophysicist at Independent Consulting
1 年congrats, good testing
Geophysics, dedicated to exploration 2D & 3D Seismic
1 年I love this. Good job, excellent. loaded up more
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1 年Excellent work. An associate of mine has been using python to simplify some attribute logging and plotting routines that became just too diverse and complicated (and huge!) for some macro-heavy Excel workbooks.
General Manager at Seismic Pros Consultants
1 年Good work getting this all worked out and putting it together in a usable format. The only thing which I feel that you have oversimplified is distortion. Distortion in vibroseis comes from four possible sources. The first is distortion in the pilot sweep which can exist in a very small degree due to having a digital system generate an analog output. The current state of vibroseis electronics is such that we can pretty much ignore this in operation. Next, the hydraulic system. This includes the accuracy of the valve which follows the pilot sweep, the condition of the hydraulic hoses and of the seals on the mass. At lower frequencies the maximum flow rate of the hydraulic oil and the available mass travel come into play as well. The final intrinsic source of vibroseis distortion is the mechanical system that supports the vibroseis on the baseplate. This includes the construction of the baseplate itself which determines its stiffness along with the airbags and suspension arms. Lastly we have ground conditions which determine how cleanly the baseplate rests on the ground as well as any movement of the baseplate caused by slippage across the ground or gravel which can be embedded further in the ground or broken during the sweep.
Seismic QC Rep (Field) Currently looking for work
1 年Nice Job. If you want a few extras though, have a look here: https://seismatters.com/SMSim3.html