# Microseismic Source Location Method and Application Based on NM-PSO Algorithm

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Time Difference of Arrival (TDOA) Source Location Theory

- (1)
- The accuracy of the time difference information Δt between the initial arrival of the stress wave in the observation data;
- (2)
- The accuracy of the model parameters such as the velocity model information v and the performance of the related inversion strategy;
- (3)
- The influence of the sensor location on the completeness of observational information and the multiplicity of inversion results.

_{0}, y

_{0}, z

_{0}, t

_{0}) is the unknown parameter that needs to be solved, including the three-dimensional coordinates of the source S(x

_{0}, y

_{0}, z

_{0}) and the seismic time t

_{0}, T

_{i}(x

_{i}, y

_{i}, z

_{i}, t

_{i}) is the i-th sensor in the microseismic monitoring network, Its three-dimensional coordinates T

_{i}(x

_{i}, y

_{i}, z

_{i}) have been measured in advance, and the first arrival time t

_{i}of the microseismic wave can be obtained by the first arrival picking method.

_{i}(x

_{i}, y

_{i}, z

_{i}) is the propagation velocity of the microseismic wave from the source S to the i-th sensor, and D

_{i}is the distance from the source S to the i-th sensor.

_{0}, y

_{0}, z

_{0}, and t

_{0}represent the microseismic source parameters, which are unknown parameters to be determined; x

_{i}, y

_{i}, z

_{i}, and t

_{i}represent the three-dimensional coordinates of the i-th sensor involved in the calculation and the first arrival of the P-wave, respectively, belonging to known parameters; i = 1, 2, 3, …, n, where n is the number of effective sensors. When ${\gamma}_{i}$ = 0, the above equation transforms into:

## 3. Particle Swarm Optimization (PSO) Algorithm

_{1}, x

_{2}, ⋯, x

_{m}) consisting of m particles, where the position of the i-th particle is:

- (1)
- Initialize the particle swarm and set various parameters, including the randomly generated initial position and speed;
- (2)
- Select the appropriate fitness function according to the actual problem, and calculate the fitness value of each particle;
- (3)
- Compare the current fitness value of the particle with the optimal historical value. If it is better than the optimal historical value, replace its current position with the best position of the particle; If it is the optimal value of the group, its current position will replace the best position of the group;
- (4)
- Update the particles according to the formula;
- (5)
- If a good enough fitness value is not obtained or the maximum number of iterations is preset, go back to step (2).

## 4. NM Simplex Algorithms

## 5. Construction of NM-PSO Algorithm

## 6. Example Analysis and Verification

_{1}, B

_{1}, C

_{1}, and D

_{1}are set to form a cube array, and the seismic sources are randomly generated. 1, 2, and 3 are the three internal sources of the array, 4 is the source on the array boundary, 5 and 6 are the two external sources of the array, and the coordinates of the sensor and source are shown in Table 1, Table 2 and Table 3.

## 7. Engineering Verification

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Detector Number | X/m | Y/m | Z/m |
---|---|---|---|

A | 0 | 0 | 0 |

B | 0 | 1000 | 0 |

C | 1000 | 1000 | 0 |

D | 1000 | 0 | 0 |

A_{1} | 0 | 0 | 1000 |

B_{1} | 0 | 1000 | 1000 |

C_{1} | 1000 | 1000 | 1000 |

D_{1} | 1000 | 0 | 1000 |

Detector Number | X/m | Y/m | Z/m |
---|---|---|---|

A | 0 | 0 | 0 |

I | 100 | 0 | 4 |

J | 200 | 0 | 0 |

K | 400 | 0 | 0 |

L | 500 | 0 | 4 |

M | 600 | 0 | 0 |

N | 800 | 0 | 0 |

P | 900 | 0 | 4 |

D | 1000 | 0 | 0 |

Source Number | X/m | Y/m | Z/m |
---|---|---|---|

1 | 140 | 460 | 590 |

2 | 730 | 380 | 620 |

3 | 270 | 840 | 390 |

4 | 350 | 1000 | 740 |

5 | 540 | 270 | 1200 |

6 | 1110 | 640 | 330 |

Detector | Microseismic Source | |||||
---|---|---|---|---|---|---|

i | j | k | l | m | n | |

A | 152.92 | 207.30 | 192.62 | 260.14 | 268.77 | 264.61 |

B | 163.15 | 230.42 | 99.23 | 163.51 | 300.17 | 241.04 |

C | 235.63 | 182.73 | 169.57 | 198.32 | 294.94 | 100.57 |

D | 227.75 | 154.33 | 236.24 | 278.30 | 262.70 | 146.43 |

A_{1} | 126.73 | 180.07 | 212.74 | 219.82 | 128.66 | 268.52 |

B_{1} | 138.68 | 206.74 | 137.29 | 87.77 | 186.66 | 268.52 |

C_{1} | 218.57 | 155.12 | 193.41 | 138.81 | 177.82 | 152.29 |

D_{1} | 212.61 | 120.24 | 256.35 | 246.20 | 113.59 | 186.78 |

A | 153.20 | 205.80 | 192.68 | 260.47 | 268.18 | 265.80 |

I | 148.65 | 193.61 | 186.92 | 253.95 | 261.40 | 250.11 |

J | 149.98 | 179.55 | 184.13 | 250.17 | 255.42 | 232.87 |

K | 157.93 | 160.06 | 187.50 | 249.89 | 247.67 | 201.98 |

L | 164.77 | 150.75 | 190.18 | 247.75 | 244.62 | 188.36 |

M | 175.71 | 147.21 | 196.11 | 252.46 | 244.59 | 178.06 |

N | 199.48 | 145.21 | 213.84 | 264.52 | 250.59 | 155.78 |

P | 210.93 | 148.03 | 224.50 | 270.72 | 255.32 | 148.58 |

D | 228.89 | 154.07 | 233.52 | 278.25 | 262.28 | 146.66 |

Number | NM | NM-PSO | Original Coordinates | ||||||
---|---|---|---|---|---|---|---|---|---|

X | Y | Z | X | Y | Z | X | Y | Z | |

A | 146.05 | 249.06 | 755.22 | 139.03 | 244.63 | 747.43 | 134.6 | 238.3 | 740 |

B | 248.69 | 132.21 | 764.54 | 247.97 | 125.81 | 755.66 | 240.7 | 121 | 750 |

C | 144.49 | 122.68 | 776.78 | 139.16 | 118.79 | 768.54 | 133.9 | 114.9 | 760 |

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**MDPI and ACS Style**

Liao, Z.; Feng, T.; Yu, W.; Cui, D.; Wu, G. Microseismic Source Location Method and Application Based on NM-PSO Algorithm. *Appl. Sci.* **2022**, *12*, 8796.
https://doi.org/10.3390/app12178796

**AMA Style**

Liao Z, Feng T, Yu W, Cui D, Wu G. Microseismic Source Location Method and Application Based on NM-PSO Algorithm. *Applied Sciences*. 2022; 12(17):8796.
https://doi.org/10.3390/app12178796

**Chicago/Turabian Style**

Liao, Ze, Tao Feng, Weijian Yu, Dongge Cui, and Genshui Wu. 2022. "Microseismic Source Location Method and Application Based on NM-PSO Algorithm" *Applied Sciences* 12, no. 17: 8796.
https://doi.org/10.3390/app12178796