# Analysis of Pseudo-Random Sequence Correlation Identification Parameters and Anti-Noise Performance

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## Abstract

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## 1. Introduction

^{n}− 1. In 1980, Duncan and Edwards of the University of Toronto in Canada applied m-sequences to electrical prospecting. By selecting an appropriate frequency bandwidth and transmitting-receiving distance, the detection of subsurface objects in the shallow (500 m) and deep (40 km) layers was completed [16]. In 1979, Cunningham applied pseudo-random sequence to the vibroseis control technology of seismic exploration, using its autocorrelation properties to effectively weaken the side lobes of seismic response and improve vertical resolution [17]. In 1982, He Jishan proposed ${a}_{k}^{p}$ pseudo-random electrical method based on the dual-frequency induced polarization method [18,19]. In about 2000, Ziolkowski, Hobbs, and Wright et al. of the University of Edinburgh established a multi-channel transient electromagnetic method (MTEM) based on correlation detection. It uses the extracted impulse response peak time or the late response of the multi-transmission step response to estimate the resistivity distribution of the earth and has achieved good results. Zhang W. et al. conducted a single-line MTEM survey in Baertaolegai-Fuxingmen silver-lead-zinc polymetallic ore investigation zone [20]. Xue G.Q. et al. summarized the research progress of MTEM and gave the field examples the MTEM method in the environment of land and sea [21,22]. Xie X. et al. confirm that time-lapse LOWTEM (long offset & window transient electromagnetic) will have bright prospects in remaining oil monitoring [23]. The results of Zhao G.Z. et al. show wavelet analysis is capable of detecting possible correlation between EM (electromagnetic) anomalies and seismic events [24]. He Jishan, Tang Jingtian, and Luo Weibin et al. have done a lot of research on theoretical analysis of pseudo-random sequence signals of controllable source electromagnetic methods and data interpretation of multi-channel electromagnetic pulses [25]. The success of the development of a pseudo-random electrical apparatus has greatly improved the research of the method.

## 2. Earth Impulse Response Correlation Identification

#### 2.1. Pseudo-Random Sequence Electromagnetic Detection Working Equipment

#### 2.2. Comparison of Identification Methods

## 3. Correlation Identification Parameters Analysis

## 4. Anti-Noise Performance Analysis of Correlation Identification

^{−7}–10

^{−9}. Figure 10a shows the superposition of the excitation field of m-sequence and the sine-wave noise. We take the period of m-sequence $N=255$, the symbol width $\Delta t=1/6000\text{\hspace{0.17em}}(\mathrm{s})$. The amplitude of sine-wave noise is 10

^{−7}, 10

^{−8}and 10

^{−9}, respectively. The identification errors obtained by the correlation identification method are shown in Figure 10b. It can be seen that when the sine wave noise amplitude is equal to or lower than that of the pseudo-random response, such as when the noise is ${10}^{-8}\mathrm{cos}(2\mathsf{\pi}\times 50t)$ or ${10}^{-9}\mathrm{cos}(2\mathsf{\pi}\times 50t)$, the m-sequence has a strong suppression ability. The identification error ranges are −6.99–3.898% and −0.343–0.7427%. When the noise amplitude is amplified 10 times, that is, ${10}^{-7}\mathrm{cos}(2\mathsf{\pi}\times 50t)$, the maximum value of the identification error reaches −73.12–35.45%. It is shown that when the noise signal amplitude is larger than the excitation field amplitude of the pseudo-random sequence, the m-sequence gradually weakens its noise immunity.

^{−7}into the excitation field of the pseudo-random sequence. When the DC noise amplitude is taken as 10

^{−7}, 10

^{−8}and 10

^{−9}, respectively, the correlation errors are shown in Figure 12b. The calculation results show that when the DC noise amplitude is higher than that of pseudo-random response by one order (noise amplitude is taken as 10

^{−7}), the maximum identification error in the entire impulse response period is −5.296%. When the DC noise amplitude is equivalent to the pseudo-random response amplitude (noise amplitude is 10

^{−8}), the maximum identification error is −0.1766%. When the DC noise amplitude is less than that of pseudo-random response by one order (noise amplitude is taken as 10

^{−9}), the maximum identification error is only 0.3353%. Therefore, when the DC noise amplitude is equal to or lower than the pseudo-random excitation field amplitude, the presence of DC interference hardly affects the identification result.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

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**Figure 3.**Identification results of linear convolution and linear correlation. (

**a**) The field excited by pseudo-random sequences; (

**b**) cross correlation of emission signals and response signals; (

**c**) the earth impulse response extraction result; (

**d**) the identification error.

**Figure 5.**Calculation result of discrete cycle correlation method. (

**a**) The field excited by pseudo-random sequences; (

**b**) cross correlation of emission signals and response signals.

**Figure 6.**Identification results of cyclic convolution and cyclic correlation. (

**a**) The earth impulse response extraction result; (

**b**) identification error.

**Figure 8.**Power spectral density (PSD) of periodic m-sequences with different periods and symbol widths. (

**a**) PSD of m-sequences with N

_{1}= 15 and ∆t

_{1}; (

**b**) PSD of m-sequences with N

_{2}= 31 and ∆t

_{1}; (

**c**) PSD of m-sequences with N

_{1}= 15 and ∆t

_{1/2}; (

**d**) PSD of m-sequences with N

_{2}= 31 and ∆t

_{1/2}.

**Figure 9.**The earth impulse response extracted with sine-wave noise. (

**a**) Sinusoidal noise signal; (

**b**) cross-correlation of m-sequence and noise signal; (

**c**) earth impulse response extraction result; (

**d**) identification error.

**Figure 10.**Suppression of sinusoidal noise by m-sequence. (

**a**) Superposition of excitation field and noise signal ${10}^{-7}\mathrm{cos}(2\mathsf{\pi}\times 50t)$; (

**b**) identification error of different amplitude noise; (

**c**) superposition of excitation field and noise signal ${10}^{-8}\mathrm{cos}(2\mathsf{\pi}\times 50t+5\mathsf{\pi}/12)$; (

**d**) identification error of different phase noise; (

**e**) superposition of excitation field and noise signal ${10}^{-8}\mathrm{cos}(2\mathsf{\pi}\times 150t)$; (

**f**) identification error of different frequency noise.

**Figure 11.**Suppression of Schumann frequency noise by m-sequence. (

**a**) Superposition of excitation field and Schumann frequency noise signal; (

**b**) identification error of different Schuhmann frequency noise.

**Figure 12.**Suppression of direct-current (DC) interference by m-sequence. (

**a**) Superposition of excitation field and DC interference; (

**b**) identification error of different DC interference.

n | $\mathit{N}$ | ${\mathit{R}}_{\mathit{a}\mathit{m}}$ | ${\mathit{R}}_{\mathit{c}\mathit{m}}$ |
---|---|---|---|

3 | 7 | 1.42 × 10^{−1} | 0.71 |

4 | 15 | 6.66 × 10^{−2} | 0.60 |

5 | 31 | 3.22 × 10^{−2} | 0.35 |

6 | 63 | 1.58 × 10^{−2} | 0.36 |

7 | 127 | 7.78 × 10^{−3} | 0.32 |

8 | 255 | 3.92 × 10^{−3} | 0.37 |

9 | 511 | 1.95 × 10^{−3} | 0.22 |

10 | 1023 | 9.77 × 10^{−4} | 0.37 |

11 | 2047 | 4.88 × 10^{−4} | 0.14 |

$\mathsf{\Delta}\mathit{t}(\mathit{s})$ | ${\mathit{t}}_{\mathit{p}\mathit{e}\mathit{a}\mathit{k}}(\mathit{s})$ | $\mathit{\rho}(\mathsf{\Omega}\cdot \mathbf{m})$ | Error |
---|---|---|---|

1/1000 | 1.000 × 10^{−3} | 125.6637 | 16.22% |

1/2000 | 5.000 × 10^{−}^{4} | 251.3274 | 67.55% |

1/3000 | 6.667 × 10^{−}^{4} | 188.4956 | 25.66% |

1/4000 | 7.500 × 10^{−}^{4} | 167.5516 | 11.70% |

1/5000 | 8.000 × 10^{−}^{4} | 157.0796 | 4.720% |

1/6000 | 8.333 × 10^{−}^{4} | 150.7964 | 0.531% |

1/7000 | 7.143 × 10^{−}^{4} | 175.9292 | 17.29% |

1/9000 | 7.778 × 10^{−}^{4} | 161.5676 | 7.712% |

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**MDPI and ACS Style**

Song, X.; Wang, X.; Dong, Z.; Zhao, X.; Feng, X.
Analysis of Pseudo-Random Sequence Correlation Identification Parameters and Anti-Noise Performance. *Energies* **2018**, *11*, 2586.
https://doi.org/10.3390/en11102586

**AMA Style**

Song X, Wang X, Dong Z, Zhao X, Feng X.
Analysis of Pseudo-Random Sequence Correlation Identification Parameters and Anti-Noise Performance. *Energies*. 2018; 11(10):2586.
https://doi.org/10.3390/en11102586

**Chicago/Turabian Style**

Song, Xijin, Xuelong Wang, Zhao Dong, Xiaojiao Zhao, and Xudong Feng.
2018. "Analysis of Pseudo-Random Sequence Correlation Identification Parameters and Anti-Noise Performance" *Energies* 11, no. 10: 2586.
https://doi.org/10.3390/en11102586