Intelligent Detection of Small Faults Using a Support Vector Machine
Abstract
:1. Introduction
2. Basic Principles of VMD and a SVM
2.1. Basic Principles of VMD
- For each mode, calculate the related analytical signal through the Hilbert transform;
- For each mode, adjust the respective estimated center frequency by adding an exponential term and transform the frequency spectrum of the mode to the baseband;
- Estimate the bandwidth by performing Gaussian smoothing on the demodulated signal.
- Mix the analytical signal in each component with a pre-estimated center frequency and modulate the spectrum of each mode into the response base frequency band:
- 2.
- Calculate the square norm of the demodulation signal gradient above and estimate the bandwidth of the modal signal. Introduce the constraint conditions to construct the optimal variational model to minimize the sum of the aggregate bandwidth of each component:
- 3.
- Introduce the quadratic penalty factor and Lagrange multiplication operator to change the constrained variational problem into the unconstrained problem (the transformation from constrained to unconstrained is equivalent here and the proof is no longer expanded). The quadratic penalty factor α can ensure the accuracy of signal reconstruction in the case of Gaussian noise and the Lagrange multiplier can ensure the rigor of model constraints. The “saddle point” of the augmented Lagrange expression is obtained by using the alternating direction multiplier algorithm and the determination accuracy ε is given to be greater than 0 until the iteration stop condition is satisfied:
- 4.
- At the end of the iteration, k-IMF components are obtained.
2.2. Basic Principles of a SVM
2.3. Small Fault Prediction Process Based on VMD and a SVM
- Based on the characteristics of small faults in coal seams, construct the fault model containing a coal seam and carry out the forward simulation;
- Add random noise to the forward seismic records and, then, use VMD for denoising. Analyze the denoising effect of VMD and the response characteristics of different seismic attributes to the fault, and select the related seismic attributes with good response effect to the fault for fault identification.
- Take the exposed fault data of the coal seam and its seismic attributes as the learning samples, use the SVM for learning and training, and apply the small fault prediction to the actual seismic data of the coal field.
3. Fault Forward Modeling
3.1. Modeling
3.2. Analysis of the Faults’ Seismic Response Characteristics
3.3. Analysis of the VMD Denoising Effect
4. Intelligent Identification of Small Faults in Actual Seismic Data
4.1. Geological Survey of the Working Area
4.2. Introduction of Learning Samples for Small Fault Identification
4.3. Intelligent Recognition of Small Faults
- 1.
- Instantaneous amplitude. Amplitude attributes are the most widely used and the most effective attributes to reflect the property characteristics of underground areas. The instantaneous amplitude attribute is a reflection of the intensity of seismic wave reflection. Its main characteristics are the difference of wave impedance in the formation and the presence of faults in the local minimum position, so it is well applied in fault identification. Figure 10 represents a diagram of the instantaneous amplitude attribute of the study area. It shows evident anomalies, with the cool color bands in the property map generally corresponding to fault areas.
- 2.
- Waveform difference. The waveform difference attribute is one of the best seismic attributes for fault characterization, because the seismic wave will scatter when passing through the geological anomalous body, resulting in obvious differences. Therefore, it can obtain clearer imaging results than other traditional attributes. There are faults in the local maximum of the waveform difference and the maximum value increases significantly with the increase of the fault drop. In Figure 11, the warm color band area with maximum value is clearly distributed, showing warm-color band patches like a network and the effect is relatively ideal.
- 3.
- Instantaneous frequency. Instantaneous frequency is the seismic attribute obtained by sampling the midpoint, one by one, according to the frequency of the trace set, revealing the fault at the local extremum. In Figure 12, the boundary, marked by an abrupt change in tone, is the theoretical fault development position, which can better identify the small fault and improve its multi-solution problem.
- 4.
- Instantaneous frequency bandwidth. The bandwidth attribute is the width between high and low cut frequency in seismic data. It mainly reflects the characteristics of seismic waveform in seismic data and can be used to analyze the heterogeneity of the formation, in its local extreme value location and where there are faults. Therefore, the application of this attribute is useful to identify of small faults in the study area. In Figure 13, the boundary, marked by an abrupt change in tone, is the theoretical location of the fault development, which is roughly consistent with the interpretation of results map.
- 5.
- Attenuation coefficient. The attenuation coefficient is an important parameter to describe geological body anomaly. In the subsurface of non-uniform geological bodies with different attenuation coefficients, the seismic reflection wave has different response characteristics under the condition of energy attenuation. There is a fault at the local minimum of the attenuation coefficient. When the fault drop is small, there is response, but its characteristics are not clear. In Figure 14, the minima of the attenuation coefficient correspond essentially to the fault location in the interpretation map, but the characterization of small structures is not obvious.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
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The Layer Number | Lithology | Vp (m/s) | Ρ (g/cm3) | H (m) |
---|---|---|---|---|
1 | Loess | 1800 | 2.00 | 200 |
2 | Mudstone | 2800 | 2.30 | 200 |
3 | Coal seam | 1600 | 1.45 | 3.5 |
4 | Mudstone | 2800 | 2.30 | 400 |
Instantaneous Amplitude | Instantaneous Bandwidth (Hz) | Instantaneous Frequency (Hz) | Attenuation Coefficient | Waveform Difference |
---|---|---|---|---|
4865.85 | 3.83517 | 61.8614 | −1.16212 | 0.993938 |
4691.47 | 8.36608 | 47.3904 | −1.75026 | 0.999402 |
3367.27 | 15.4594 | 37.2179 | −1.48514 | 0.999242 |
4816.77 | 31.1756 | 14.9254 | −0.32169 | 0.807862 |
4335.54 | 7.60931 | 3.26045 | −0.11131 | 0.9649 |
4732.01 | 13.6524 | 29.0931 | −0.30216 | 0.998345 |
4640.61 | 26.8337 | 6.92003 | 0.230915 | 0.993288 |
4727.22 | 18.4564 | 9.90255 | −0.06904 | 0.995208 |
3249.05 | 7.72003 | 24.5849 | −0.65415 | 0.990835 |
3885.62 | 7.17641 | 52.268 | −0.62079 | 0.97217 |
3256.59 | 9.88172 | 27.0562 | −0.66764 | 0.98829 |
2505.36 | 30.301 | 30.3608 | −0.15021 | 0.998515 |
3309.52 | 55.3597 | 34.3742 | −0.30375 | 0.998786 |
4502.35 | 47.2056 | 63.902 | −1.2301 | 0.999504 |
4972.27 | 36.4524 | 62.9385 | −1.16251 | 0.998994 |
4696.00 | 28.0408 | 94.7015 | −1.58393 | 0.999197 |
719.34 | 13.9524 | 229.188 | −0.87734 | 0.991868 |
2775.05 | 13.1616 | 9.08372 | 0.199544 | 0.995766 |
3941.9 | 9.01527 | 18.1962 | −6.79774 | 0.997587 |
2253.69 | 5.14017 | 18.2883 | 1.66724 | 0.9997 |
Instantaneous Amplitude | Instantaneous Bandwidth (Hz) | Instantaneous Frequency (Hz) | Attenuation Coefficient | Waveform Difference |
---|---|---|---|---|
13503.2 | 26.6158 | 50.3789 | −6.56801 | 0.615492 |
12227.2 | 13.5381 | 53.4608 | −3.1951 | 0.743877 |
10612.7 | 12.5301 | 55.7597 | −1.80342 | 0.923876 |
6799.5 | 23.1988 | 49.4058 | −0.79238 | 0.359729 |
5396.46 | 14.6464 | 56.2389 | 3.6954 | 0.861492 |
6569.41 | 48.1424 | 60.8557 | −2.22876 | 0.7840 |
6365.06 | 14.984 | 63.1589 | −1.17686 | 0.580568 |
5345.1 | 71.7198 | 45.9598 | 1.24509 | 0.521775 |
6510.88 | 18.7914 | 44.837 | 2.90394 | 0.947705 |
7363.17 | 42.0982 | 38.2898 | 2.66776 | 0.498144 |
6768.65 | 20.2626 | 29.7787 | 1.50676 | 0.910921 |
6459 | 101.062 | 21.9129 | 0.361587 | 0.660132 |
5253.02 | 56.5836 | 23.3189 | 0.210612 | 0.22914 |
7881.42 | 25.9743 | 55.2104 | 0.584787 | 0.968271 |
8481.98 | 27.0701 | 51.8925 | 0.711785 | 0.979323 |
9205.73 | 29.8944 | 47.3958 | 0.845123 | 0.982747 |
16388.2 | 130.616 | 52.1675 | 1.86948 | 0.984059 |
16737 | 22.7612 | 50.4621 | 1.91701 | 0.633132 |
16507.2 | 1.3384 | 50.0274 | 2.77459 | 0.923009 |
15678.8 | 5.48461 | 50.3258 | 4.89534 | 0.991588 |
Instantaneous Amplitude | Instantaneous Bandwidth (Hz) | Instantaneous Frequency (Hz) | Attenuation Coefficient | Waveform Difference | |
---|---|---|---|---|---|
Fault | 3812.174 | 19.43976 | 43.77568 | −0.85761 | 0.98417 |
Non-fault | 9502.684 | 35.36561 | 47.54187 | 0.521237 | 0.754949 |
Instantaneous Amplitude | Instantaneous Bandwidth (Hz) | Instantaneous Frequency (Hz) | Attenuation Coefficient | Waveform Difference | |
---|---|---|---|---|---|
Fault | 4138.72 | 13.8024 | 29.72695 | −0.63747 | 0.996677 |
Non-fault | 7622.295 | 24.58655 | 50.35235 | 0.778454 | 0.822746 |
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Zeng, A.; Yan, L.; Huang, Y.; Ren, E.; Liu, T.; Zhang, H. Intelligent Detection of Small Faults Using a Support Vector Machine. Energies 2021, 14, 6242. https://doi.org/10.3390/en14196242
Zeng A, Yan L, Huang Y, Ren E, Liu T, Zhang H. Intelligent Detection of Small Faults Using a Support Vector Machine. Energies. 2021; 14(19):6242. https://doi.org/10.3390/en14196242
Chicago/Turabian StyleZeng, Aiping, Lei Yan, Yaping Huang, Enming Ren, Tao Liu, and Hui Zhang. 2021. "Intelligent Detection of Small Faults Using a Support Vector Machine" Energies 14, no. 19: 6242. https://doi.org/10.3390/en14196242