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Abstract

To eliminate the location error of MS/AE (microseismic/acoustic emission) monitoring systems caused by the measurement deviations of the wave velocity, a MS/AE source location method using P-wave and S-wave arrivals for unknown velocity system (PSAFUVS) was developed. Arrival times of P-wave and S-wave were used to calculate and fit the MS/AE source location. The proposed method was validated by numerical experimentations. Results show that the proposed method without the need for a premeasured wave velocity has a reasonable and reliable precision. Effects of arrival errors on location accuracy were investigated, and it shows location errors enlarged rapidity with the increase of arrival errors. It is demonstrated the proposed method can not only locate the MS/AE source for unknown velocity system but also determine the real time PS waves velocities for each event in rockmass.

1. Introduction

Geophysical methods, statistical analysis, microseismic monitoring, and in-seam seismic techniques, have shown an increased significance in rock physical mechanics and mining engineering in recent decades [1–21]. In particular, the developments of seismic monitoring provide a scientific basis for controlling the rockburst and seismic hazards.

The seismic location, one of the most important parameters for a seismic monitoring, is very important for rockburst control and warning in a mine through the seismological method of the prediction of the areal rockbursts, which could improve the safety performance of deep geotechnical engineering. Researchers have developed many acoustic emission or seismic source location techniques [1, 2, 7, 22–32]. The problem of locating a signal source using time difference of arrival (TDOA) measurements also has numerous applications in aerospace, surveillance, structural health, navigation, industrial process, speaker location, machine condition, and the monitoring of nuclear explosions [1, 33–45]. And some of which are mature technologies and are widely used in the location of acoustic emission or seismic source.

However, for the existing technologies based on AE or seismic source, a given wave velocity or practical pre-measured wave velocity of the propagation medium is required. It is well known that the wave velocity is influenced by the materials, size, and surface conditions of transmission media and other factors. When the input wave velocity is different from the real wave velocity of the measured object, an error would occur in the system [46]. The average wave velocity is different from that of various regions, and the actual location of the occurrence of rockburst is not necessarily in the predetermined wave velocity area. The measured wave velocity is affected significantly by the distance between sensors; the measured P-wave velocity of the general container is between 2800 and 3100 m·s⁻¹ when the distance is large while that is about 5000 to 6000 m·s⁻¹ when the distance is small [41]. The large location errors can be induced by inaccurate average wave velocity. Both of these conditions result in some errors between the pre-measured wave velocity as an input in the positioning system and the actual wave velocity of the area where the rockburst occurs; hence, it would result in a large positional error [41]. To quantitatively study the location errors induced by deviation of sonic speed, the line and plane location tests were carried out in [47], and some interesting conclusions were summarized: the results show that for line positioning, the maximum error of absolute distance is about 0.8 cm. With the speed difference of 200 m/s, the average value of absolute difference from the position error is about 0.4 cm; for the plane positioning, in the case of the sensor array of 30 cm, the absolute positioning distance is up to 8.7 cm. It shows the sonic speed seriously impacts on the plane positioning accuracy; the plane positioning error is larger than the line positioning error, which means that when the line position can satisfy the need in practical engineering, it is better to use the line position instead of the plane location, and the plane positioning error with the diagonal speed is the minimum one. Dong et al. analyzed above the drawbacks systematically in [48]. Velocities of P-wave and S-wave are obtained by blast experiments in existed methodologies. Two clear disadvantages were discussed. Firstly, active times are different because the premeasured velocity is obtained before the real-time seismic event. The fact is that the velocity in rockmass is changing all the time, and the velocity in different time would be not the same. Secondly, propagation traces are different (i.e., the traces of the wave propagation for blast experiments are always different from the wave propagation for real-time events), which would induce a big error because of the different average velocities in different propagation traces. The above drawbacks are further discussed in Figure 1, and the traces between blast source A and sensors were expressed as $A_{1}$ , $A_{2}$ , $A_{3}$ , and $A_{4}$ , and the average velocity of the four traces is supposed as $V_{A}$ ; the traces between seismic source B and sensors were expressed as $B_{1}$ , $B_{2}$ , $B_{3}$ , and $B_{4}$ , and the average velocity of the four traces is supposed as $V_{B}$ . Considering the active time, $V_{A}$ is not equal to $V_{B}$ at different time; while considering the active space, propagation traces are different, and $V_{A}$ is also not equal to $V_{B}$ .

Figure 1

Location schematic diagram for different trace and different time.

In present work, we proposed a an innovative MS/AE source location method without the need for premeasured P-wave and S-wave velocities, which can calculate MS/AE source locations in unknown velocity networks.

2. Methodology

The microseismic n sensors are placed in a location area, and they are not in the same plane. Three-dimensional coordinates of the microseismic sensors are known, which are ( $x_{1}$ , $y_{1}$ , $z_{1}$ ), ( $x_{2}$ , $y_{2}$ , $z_{2}$ ), …, and ( $x_{i}$ , $y_{i}$ , $z_{i}$ ). When the microseismic event occurs, the sensor i receives the MS/AE source signals and arrival times of PS waves are recorded as $t_{α i}$ and $t_{β i}$ , respectively. The distance between MS/AE source and received station (sensor) i is $R_{i}$ . The average velocities of PS waves (P-wave and S-wave) are expressed as α and β, respectively.

The distance from MS/AE source to sensor i can be expressed as

\begin{matrix} R_{i} = α t_{α i} = β t_{β i} . \end{matrix}

(1)

The time difference of arrival times between PS waves is given by

\begin{matrix} t_{β i} - t_{α i} = \frac{R_{i}}{β} - \frac{R_{i}}{α} = R_{i} (\frac{1}{β} - \frac{1}{α}) . \end{matrix}

(2a)

Supposing an equivalent parameter consider

\begin{matrix} (2 b) & \tilde{v} = {(\frac{1}{β} - \frac{1}{α})}^{- 1} = \frac{α β}{α - β} . \end{matrix}

(2b)

Equation (2a) and can be rewritten as

\begin{matrix} (2 c) & t_{β i} - t_{α i} = \frac{R_{i}}{β} - \frac{R_{i}}{α} = \frac{R_{i}}{\tilde{v}} . \end{matrix}

(2c)

Then, the distances between MS/AE source and received stations i, as well as the distance between MS/AE source and received stations j, are obtained as follows:

\begin{matrix} R_{i} = \tilde{v} (t_{β i} - t_{α i}), \end{matrix}

(3a)

\begin{matrix} R_{j} = \tilde{v} (t_{β j} - t_{α j}) \end{matrix}

(3b)

According to the distance formula of two point in the space, for sensors i and j, (4) and (5) are given as follows

\begin{matrix} {(x_{0} - x_{i})}^{2} + {(y_{0} - y_{i})}^{2} + {(z_{0} - z_{i})}^{2} = R_{i}^{2}, \end{matrix}

(4)

\begin{matrix} {(x_{0} - x_{j})}^{2} + {(y_{0} - y_{j})}^{2} + {(z_{0} - z_{j})}^{2} = R_{j}^{2} . \end{matrix}

(5)

The left side and the right side of (4) added the left side and the right side of (5), it can be expressed as

\begin{array}{l} {(x_{0} - x_{i})}^{2} + {(y_{0} - y_{i})}^{2} + {(z_{0} - z_{i})}^{2} \\ + {(x_{0} - x_{j})}^{2} + {(y_{0} - y_{j})}^{2} + {(z_{0} - z_{j})}^{2} = R_{i}^{2} + R_{j}^{2} . \end{array}

(6)

Submitting (3a) and (3b) into (6), it can be rewritten as

\begin{array}{l} [{(x_{0} - x_{i})}^{2} + {(y_{0} - y_{i})}^{2} + {(z_{0} - z_{i})}^{2} \\ + {(x_{0} - x_{j})}^{2} + {(y_{0} - y_{j})}^{2} + {(z_{0} - z_{j})}^{2}] \times {({\tilde{v}}^{2})}^{- 1} \\ = {(t_{β i} - t_{α i})}^{2} + {(t_{β j} - t_{α j})}^{2} . \end{array}

(7)

Equation (7) can be expressed as

\begin{array}{l} Δ t_{i j} = {(t_{β i} - t_{α i})}^{2} + {(t_{β j} - t_{α j})}^{2} \\ = f (x_{i}, y_{i}, z_{i}, x_{j}, y_{j}, z_{j}, x_{0}, y_{0}, z_{0}, \tilde{v}) . \end{array}

(8)

In (8), sensor coordinates

(x_{i}, y_{i}, z_{i})

(x_{j}, y_{j}, z_{j})

, and dependent variable

t_{α i}

t_{β i}

t_{α j}

t_{β j}

are known parameters, and

x_{0}

y_{0}

z_{0}

and

\tilde{v}

are unknown parameters. There are four unknown parameters; therefore, it needs more than four sensors to get the solutions by solving the nonlinear equations. This method was called PSAFUVS (MS/AE source location method using P-wave and S-wave arrivals for unknown velocity system).

Equation (8) is a nonlinear fitting problem with a single dependent variable. According to all the observed data $(x_{i}, y_{i}, z_{i}; x_{j}, y_{j}, z_{j})$ , (8) can determine a regression value

\begin{matrix} Δ {\hat{t}}_{i j} = f (x_{i}, y_{i}, z_{i}, x_{j}, y_{j}, z_{j}, x_{0}, y_{0}, z_{0}, \tilde{v}) . \end{matrix}

(9)

The difference between

Δ {\hat{t}}_{i j}

and

Δ t_{i j}

can describe the degree of deviation between the regression value and observed values.

Due to $(x_{i}, y_{i}, z_{i}; x_{j}, y_{j}, z_{j})$ , if the degree of deviation between $Δ t_{i j}$ and $Δ {\hat{t}}_{i j}$ is smaller, it shows that the fitted line and experimental points could fit better. The sum of squared deviations of all observations and fitted values is

\begin{matrix} Q (x_{0}, y_{0}, z_{0}, \tilde{v}) = \sum_{i, j = 1}^{n} {[Δ {\hat{t}}_{i j} - Δ t_{i j}]}^{2} . \end{matrix}

(10)

Equation (10) describes the deviations between all observed and experimental values. Therefore, the MS/AE source parameters

(x_{0}, y_{0}, z_{0}, \tilde{v})

can have values such that the

Q (x_{0}, y_{0}, z_{0}, \tilde{v})

will reach a minimum as follows:

\begin{matrix} Q (x_{0}, y_{0}, z_{0}, \tilde{v}) = \sum_{i, j = 1}^{n} {[Δ {\hat{t}}_{i j} - Δ t_{i j}]}^{2} = \min . \end{matrix}

(11a)

$P_{i j} (x_{0}, y_{0}, z_{0}, \tilde{v})$ is a parameter to express the fitting error for each set of observations and fitted values as follows:

\begin{matrix} (11 b) & P_{i j} (x_{0}, y_{0}, z_{0}, \tilde{v}) = {(Δ {\hat{t}}_{i j} - Δ t_{i j})}^{2} = mi n_{i j} . \end{matrix}

(11b)

Equations (11a) and $(11 b)$ are the nonnegative function of $x_{0}, y_{0}, z_{0}, \tilde{v}$ , so it always has the minimum. The coordinates of the MS/AE source location and the equivalent velocity ( $x_{0}, y_{0}, z_{0}, \tilde{v}$ ) can be obtained by solving (11a) and $(11 b)$ . According to $α = \sqrt{3} β$ , $(2 b)$ can be rewritten as

\begin{matrix} \tilde{v} = \frac{\sqrt{3} β^{2}}{\sqrt{3} β - β} = \frac{\sqrt{3} β}{\sqrt{3} - 1}, \end{matrix}

(12)

α and β can be obtained by resolving (12).

For a simple MS/AE source location problem, only $x_{0}$ , $y_{0}$ , $z_{0}$ should be solved. Equation (11a) is a nonlinear fitting problem with a single dependent variable. The commonly used nonlinear fitting methods include Levenberg-Marquardt (LM), Simplex Method (SM), Quasi-Newton Method (QN), Max Inherit Optimization (MIO), Self-Organizing Migrating Algorithms (SOMA), and Global Optimization (GO) [27, 31, 48]. Dong et al. discussed the location error of the different method [48], and analyzed results show that it is easy to trap a local optimum value using MIO, QN, and LM simply. It is suggested that the selection of MIO, QN, and LM simply should be careful. The joint use of GO as well as MIO, QN, and LM can significantly improve positioning accuracy. The SOMA, SM coupled with GO, MIO coupled with GO, and LM coupled with GO, which are more stable with the high positioning accuracy, should be recommended preferred methods to locate MS/AE source coordinates. Therefore, in present work, The SOMA coupled with GO was used to fit the MS/AE source locations using (11a) and $(11 b)$ .

3. Validation with Numerical Experimentations and Discussion

In numerical experimentations, the location network includes 6 sensors $S_{1}$ , $S_{2}$ , $S_{3}$ , $S_{4}$ , $S_{5}$ , and $S_{6}$ . Their coordinates are (600, 100, 500), (300, −500, 200), (400, 300, −250), (−300, −200, 400), (200, 600, −300), and (−350, −450, −550), respectively. The average P-wave velocity and S-wave velocity in the medium are 5500 and 3175 m/s, respectively. The original times of MS/AE sources are supposed as 0 s. According to the relationship between distance formula, the coordinates of MS/AE sources A, B, C, D, and E as well as their arrivals are obtained and listed in Table 1. The sensor and the spatial distribution of MS/AE source locations are shown in Figure 2 (all coordinates are in the length unit: meter). The MS/AE source locations were calculated by the PSAFUVS using arrivals in Table 1 and coordinates of sensors. The arrivals is accurate result with a accuracy 0.000001 s. The location results calculated by accurate arrivals were expressed as E0 (the error is approximately equal to 0) and listed in Table 2. Compared results between authentic values and fitting results of dependent variables were listed in Table 3. It shows that the calculated coordinates (C) of A, B, C, D, and E using PSAFUVS are consistent with authentic results (T), and the fitting values are approximately equal to authentic values. To further verify the proposed method, the α and β were recalculated using (12), and the calculated results were compared with the authentic α and β. $\tilde{v}$ is 7510.767. α and β are 5497.88 and 3174.30 m/s which are approximately equal to authentic values 5500 and 3175 m/s, respectively. Results prove that the proposed PSAFUVS is reasonable and reliable with a high precision for the unknown velocity system.

Table 1

Arrival times of MS/AE sources.

Sensors	A		B		C		D		E
	(100, 200, 300)		(200, −250, −180)		(−350, 550, 120)		(400, 300, 380)		(−280, 380, 450)
	P	S	P	S	P	S	P	S	P	S
$S_{1}$	0.099586	0.172511	0.156923	0.271835	0.20323	0.352052	0.055863	0.09677	0.16815	0.291283
$S_{2}$	0.133609	0.231448	0.084677	0.146685	0.225	0.389763	0.150195	0.260181	0.196944	0.341162
$S_{3}$	0.115351	0.19982	0.107165	0.18564	0.158703	0.274919	0.114545	0.198425	0.178033	0.308404
$S_{4}$	0.104447	0.180931	0.139527	0.2417	0.14584	0.252637	0.156448	0.271013	0.105908	0.183463
$S_{5}$	0.132366	0.229295	0.156078	0.270371	0.126151	0.218529	0.139941	0.242417	0.166768	0.288889
$S_{6}$	0.211058	0.365612	0.125889	0.218075	0.218855	0.379119	0.25648	0.444295	0.236629	0.409909

Table 2

Location results and error of MS/AE source coordinates under different reading errors of arrivals.

Sources	E0			E1			E2			E3
Sources	x	y	z	x	y	z	x	y	z	x	y	z
Locations
A	99.84	200.11	300.01	99.62	197.74	298.60	104.59	196.01	282.83	23.38	169.48	298.38
B	200.13	−250.03	−179.98	199.68	−250.14	−178.76	191.63	−244.53	−161.62	6.42	−76.88	26.21
C	−349.90	549.74	120.03	−351.57	552.78	119.51	−392.80	604.08	127.11	−752.04	1051.38	254.27
D	399.69	299.74	379.51	398.40	301.27	379.58	374.79	265.48	327.16	930.39	449.65	549.21
E	−280.25	380.36	450.18	−279.72	379.75	447.11	−310.42	433.43	495.68	−186.53	156.04	340.15
Errors
A	−0.16	0.11	0.01	−0.38	−2.26	−1.4	4.59	−3.99	−17.17	−76.62	−30.52	−1.62
B	0.13	−0.03	0.02	−0.32	−0.14	1.24	−8.37	5.47	18.38	−193.58	173.12	206.21
C	0.10	−0.26	0.03	−1.57	2.78	−0.49	−42.8	54.08	7.11	−402.04	501.38	134.27
D	−0.31	−0.26	−0.49	−1.6	1.27	−0.42	−25.21	−34.52	−52.84	530.39	149.65	169.21
E	−0.25	0.36	0.18	0.28	−0.25	−2.89	−30.42	53.43	45.68	93.47	−223.96	−109.85

Table 3

Comparisons between authentic values and fitting results for the E0 condition.

Sensor $i (j = 1)$	A		B		C		D		E
Sensor $i (j = 1)$	T	C	T	C	T	C	T	C	T	C
1	0.010636	0.010636	0.02641	0.02641	0.044296	0.044296	0.003347	0.003347	0.030323	0.030323
2	0.014891	0.014891	0.01705	0.01705	0.049295	0.049295	0.01377	0.01377	0.035961	0.035961
3	0.012453	0.012453	0.019363	0.019363	0.035654	0.035654	0.008709	0.008709	0.032158	0.032158
4	0.011168	0.011168	0.023644	0.023644	0.033554	0.033553	0.014799	0.014798	0.021177	0.021176
5	0.014713	0.014713	0.026268	0.026268	0.030682	0.030682	0.012175	0.012175	0.030075	0.030075
6	0.029205	0.029205	0.021703	0.021703	0.047833	0.047833	0.036948	0.036948	0.045188	0.045188

Note: 1, 2, 3, 4, 5, and 6 indicating the values calculated using (8), and i is equal to 1, 2, 3, 4, 5 and 6, while j is equal 1.

Figure 2

Spatial location of sensors and MS/AE sources (unit: meter).

As we all know, it is always difficult to read the accurate arrivals because of limitations of technologies, personal error, or machine error. In present work, the errors are considered as three levels within E1 [0.000001, 0.00001], E2 [0.00001, 0.0001], and E3 [0.0001, 0.001], which are randomly generated by random function of Microsoft Excel. The calculated location results of the three levels were also listed in Table 2. Compared results between authentic values (T) and fitting results of MS/AE sources A, B, C, D, and E for error levels E0, E1, E2 and E3 are shown in Figure 3. From Table 2 and Figure 3, we can conclude that the location errors enlarged rapidity with the increase of arrival errors. The error E1 results in errors within 3 m, and the minimum and maximum are −0.28 and −2.98 m, respectively. The error E2 results in errors within 55 m, and the minimum and maximum are −3.99 and 54.08 m, respectively. The error E3 could induce errors more than 500 m, and the minimum and maximum are −1.62 and 530.39 m, respectively. Figure 3 also shows that the differences between fitted values and authentic values increased with the enlarging of arrival errors. The induced location errors were further investigated by absolute distance errors between real MS/AE sources and fitted MS/AE sources in Figure 4. It also clearly shows the absolute distance errors enlarging exponentially with the increase of arrival errors, and the location errors for A, B, C, D, and E are increased from 0.19, 0.13, 0.28, 0.64, and 0.47 m to 82.49, 331.61, 656.54, 576.49, and 266.39 m, respectively.

Figure 3

Comparisons between authentic values and fitting results: (a) source A, (b) source B, (c) source C, (d) source D, and (e) source E.

Figure 4

Comparisons of absolute distance error for different arrival errors.

4. Conclusions

A new MS/AE source location method PSAFUVS was developed to address the difficult problem of the location errors for microseismic monitoring system induced by wave velocity measurement deviation. The proposed method was validated by numerical experimentations. Results show that the proposed method without the need for a premeasured wave velocity has a reasonable and reliable precision. It is demonstrated that the proposed method can not only locate the MS/AE source for unknown velocity network but also determine the PS wave real-time velocities for each event. Effects of arrival errors on location accuracy were investigated using PSAFUVS, and it shows location errors enlarged rapidity with the increase of arrival errors. The absolute distance errors between real MS/AE sources and fitted MS/AE sources were further discussed, and results show the absolute distance errors enlarging exponentially with the increase of arrival errors.

Footnotes

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this article.

Acknowledgments

The authors gratefully acknowledge the financial support of National Natural Science Foundation of China (50934006,41272304), National Basic Research (973) Program of China (2010CB732004), China Scholarship Council (CSC), Doctoral Candidate Innovation Research Support Program by Science & Technology Review (kjdb201001-7), Scholarship Award for Excellent Doctoral Student from Ministry of Education of China (105501010), and Support Program for Cultivating Excellent Ph.D. Thesis of Central South University.

References

Chen

J. C.

Hudson

R. E.

Yao

Maximum-likelihood source localization and unknown sensor location estimation for wideband signals in the near-field

IEEE Transactions on Signal Processing 2002 50 8 1843 1854

2-s2.0-0036685484

10.1109/TSP.2002.800420

Hardy

H. R.

Jr. Wang

Wang

Development of a simple mechanical impact system as a non-explosive seismic source

Geotechnical and Geological Engineering 2011 29 1 137 142

2-s2.0-78650511001

10.1007/s10706-010-9374-9

Senatorski

Apparent stress scaling for tectonic and induced seismicity: model and observations

Physics of the Earth and Planetary Interiors 2008 167 1-2 98 109

2-s2.0-42649089762

10.1016/j.pepi.2008.02.006

Šílený

Milev

Source mechanism of mining induced seismic events—resolution of double couple and non double couple models

Tectonophysics 2008 456 1-2 3 15

2-s2.0-47049094757

10.1016/j.tecto.2006.09.021

Tang

Yang

Optimal design of microseismic monitoring networking and error analysis of seismic source location for rock slope

Advanced Materials Research 2011 163 2991 2999

2-s2.0-78651388604

10.4028/www.scientific.net/AMR.163-167.2991

Hudyma

Potvin

Y. H.

An engineering approach to seismic risk management in hardrock mines

Rock Mechanics and Rock Engineering 2010 43 6 891 906

2-s2.0-78149465128

10.1007/s00603-009-0070-0

Dong

Peng

Prediction of rockburst classification using Random Forest

Transactions of Nonferrous Metals Society of China 2013 23 472 477

Dong

Zhou

Nonlinear model-based support vector machine for predicting rock mechanical behaviors

Advanced Science Letters 2012 5 806 810

X. B.

Dong

L. J.

Zhao

G. Y.

Huang

Liu

A. H.

Zeng

L. F.

Dong

Chen

G. H.

Stability analysis and comprehensive treatment methods of landslides under complex mining environment—a case study of Dahu landslide from Linbao Henan in China

Safety Science 2012 50 4 695 704

2-s2.0-84856423655

10.1016/j.ssci.2011.08.049

10.

Dong

L. J.

X. B.

Q. Y.

Comparisons of random forest and support vector machine for predicting blasting vibration characteristic parameters

Procedia Engineering 2011 26 1772 1781

11.

Dong

L.-J.

X.-B.

Interval non-probabilistic reliability method for surrounding jointed rock mass stability of underground caverns

Chinese Journal of Geotechnical Engineering 2011 33 7 1007 1013

2-s2.0-80051572950

12.

Dong

L.-J.

X.-B.

Interval parameters and credibility of representative values of tensile and compression strength tests on rock

Chinese Journal of Geotechnical Engineering 2010 32 12 1969 1974

2-s2.0-78651421872

13.

Dong

Zhao

Gong

Fisher discriminant analysis model and its application to predicting destructive effect of masonry structure under blasting vibration of open-pit mine

Chinese Journal of Rock Mechanics and Engineering 2009 28 4 750 756

2-s2.0-65449134018

14.

Dong

L.-J.

X.-B.

Bai

Y.-F.

Fisher discriminant analysis model for classifying top coal cavability of the steep seam

Journal of the China Coal Society 2009 34 1 58 63

2-s2.0-61349101840

15.

Dong

L.-J.

X.-B.

Gong

F.-Q.

Unascertained average clustering method for classification of grade of shrink and expansion for expansive soils and its application

Journal of Central South University 2008 39 5 1075 1080

2-s2.0-56549097104

16.

Dong

L.-J.

Peng

G.-J.

Y.-H.

Bai

Y.-F.

Liu

Y.-F.

Unascertained measurement classifying model of goaf collapse prediction

Journal of Coal Science and Engineering 2008 14 2 221 224

2-s2.0-50649099944

10.1007/s12404-008-0046-9

17.

Dong

Bai

Liu

Unascertained average grade model for surrounding rock classification on hydraulic tunnels

Proceedings of the 2008 International Symposium on Safety Science and Technology: Progress in Safety Science and Technology, Volume VII, Parts A and B

2008

18.

Dong

Liu

Bai

A Fisher discriminant analysis model for classification of rocks surrounding in tunnel

Proceeding of the Information Technology and Environmental System Sciences (ITESS '08)

2008

19.

Dong

Wang

Comprehensive evaluation seismic stability of slopes based on unascermined measurcmem

The Chinese Journal of Geological Hazard and Control 2007 18 74 78

20.

Dong

Zhu

Comparisons of Logistic regression and Fisher discriminant classifier to seismic event identification

Disaster Advances 2013 6 8

21.

Dong

Comprehensive models for evaluating rockmass stabilitybased on statisticalcomparisons of multiple classifiers

Mathematical Problems in Engineering 2013 2013 9

395096

10.1155/2013/395096

22.

Kennett

B. L. N.

Marson-Pidgeon

Sambridge

M. S.

Seismic source characterization using a Neighbourhood Algorithm

Geophysical Research Letters 2000 27 20 3401 3404

2-s2.0-0034353046

10.1029/2000GL011559

23.

Tian

Chen

X. F.

Review of seismic location study

Progress in Geophysics 2002 17 1 147 155

24.

Nivesrangsan

Steel

J. A.

Reuben

R. L.

Source location of acoustic emission in diesel engines

Mechanical Systems and Signal Processing 2007 21 2 1103 1114

2-s2.0-33750507479

10.1016/j.ymssp.2005.12.010

25.

Waldhauser

Ellsworth

W. L.

A double-difference Earthquake location algorithm: method and application to the Northern Hayward Fault, California

Bulletin of the Seismological Society of America 2000 90 6 1353 1368

2-s2.0-0034451815

10.1785/0120000006

26.

Knapmeyer

Location of seismic events using inaccurate data from very sparse networks

Geophysical Journal International 2008 175 3 975 991

2-s2.0-57049144988

10.1111/j.1365-246X.2008.03862.x

27.

Dong

Tang

Gong

Mathematical functions and parameters for microseismic source location without pre-measuring speed

Chinese Journal of Rock Mechanics and Engineering 2011 30 10 2057 2067

2-s2.0-80355136187

28.

Dong

L. J.

X. B.

Three-dimensional analytical solution of acoustic emission or microseismic source location under cube monitoring network

Transactions of Nonferrous Metals Society of China 2012 22 3087 3094

29.

Geiger

Herdbestimmung bei Erdbeben aus den Ankunftszeiten. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 331–349. 1912 transliterated in English by FWL Peebles & AH Corey: probability method for the determination of earthquake epicenters from the arrival time only

Bulletin of St. Louis University 1910 8 60 71

30.

Dong

Gong

An analytical location method for acoustic emission and microseismic sources

China Patent, 2012

31.

Dong

A location method for acoustic emission and microseismic sources

China Patent, 2012

32.

Dong

Closed-form solutions of acoustic emission source location for minimal element monitoring arrays of rectangular pyramid and circular column

Disaster Advances 2013 6 13 11

33.

Anderson

K. R.

Robust earthquake location using M-estimates

Physics of the Earth and Planetary Interiors 1982 30 2-3 119 130

2-s2.0-0020411435

34.

Anderson

K. R.

Epicentral location using arrival time order

Bulletin of the Seismological Society of America 1981 71 541 545

35.

Antolik

Ekström

Dziewonski

A. M.

Global event location with full and sparse data sets using three-dimensional models of mantle P-wave velocity

Monitoring the Comprehensive Nuclear-Test-Ban Treaty: Sourse Location 2001

Berlin, Germany

Springer

291 317

36.

Belchamber

Collins

Acoustic emission source location using simplex optimization

Journal of Acoustic Emission 1990 9 4 271 276

37.

Brandstein

M. S.

Adcock

J. E.

Silverman

H. F.

A closed-form location estimator for use with room environment microphone arrays

IEEE Transactions on Speech and Audio Processing 1997 5 1 45 50

2-s2.0-0030784571

10.1109/89.554268

38.

Flanagan

M. P.

Myers

S. C.

Koper

K. D.

Regional travel-time uncertainty and seismic location improvement using a three-dimensional a priori velocity model

Bulletin of the Seismological Society of America 2007 97 3 804 825

2-s2.0-34347253050

10.1785/0120060079

39.

Source location error analysis and optimization methods

Journal of Rock Mechanics and Geotechnical Engineering 2012 4 1 10

40.

Kennett

B. L. N.

Non-linear methods for event location in a global context

Physics of the Earth and Planetary Interiors 2006 158 1 46 54

2-s2.0-33748163006

10.1016/j.pepi.2006.03.006

41.

X. B.

Dong

L. J.

Comparison of two methods in acoustic emission source location using four sensors without measuring sonic speed

Sensor Letters 2011 9 5 2025 2029

2-s2.0-84855795162

10.1166/sl.2011.1540

42.

Mellen

Pachter

Raquet

Closed-form solution for determining emitter location using time difference of arrival measurements

IEEE Transactions on Aerospace and Electronic Systems 2003 39 3 1056 1058

2-s2.0-0344704085

10.1109/TAES.2003.1238756

43.

Nicholson

Application of 3D empirical travel times to routine event location

Physics of the Earth and Planetary Interiors 2006 158 1 67 74

2-s2.0-33748167832

10.1016/j.pepi.2006.03.008

44.

Nicholson

Sambridge

Gudmundsson

Hypocenter location by pattern recognition

Journal of Geophysical Research B 2002 107 6 ESE 5-1 ESE 5-19

2-s2.0-0037054704

45.

Dong

Hypocenter relocation for Wenchuan Ms 8. 0 and Lushan Ms 7. 0 earthquakes using TT and TD methods

Disaster Advances 2013 6 13 10

46.

Pavlis

G. L.

Booker

J. R.

The mixed discrete-continuous inverse problem: application to the simultaneous determination of earthquake hypocenters and velocity structure

Journal of Geophysical Research 1980 85 4801 4810

2-s2.0-0019138526

47.

Q.-Y.

Dong

L.-J.

X.-B.

Yin

Z.-Q.

Liu

X.-L.

Effects of sonic speed on location accuracy of acoustic emission source in rocks

Transactions of Nonferrous Metals Society of China 2011 21 12 2719 2726

2-s2.0-84855785903

10.1016/S1003-6326(11)61115-1

48.

Dong

Tang

Main influencing factors of microseismic source location accuracy

Science and Technology Review 2013 31 26 32

A Microseismic/Acoustic Emission Source Location Method Using Arrival Times of PS Waves for Unknown Velocity System

Abstract

1. Introduction

2. Methodology

3. Validation with Numerical Experimentations and Discussion

4. Conclusions

Footnotes

Conflict of Interests

Acknowledgments

References