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Discrimination of Mine Seismic Events and Blasts Using the Fisher Classifier, Naive Bayesian Classifier and Logistic Regression

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Abstract

Seismic events and blasts generate seismic waveforms that have different characteristics. The challenge to confidently differentiate these two signatures is complex and requires the integration of physical and statistical techniques. In this paper, the different characteristics of blasts and seismic events were investigated by comparing probability density distributions of different parameters. Five typical parameters of blasts and events and the probability density functions of blast time, as well as probability density functions of origin time difference for neighbouring blasts were extracted as discriminant indicators. The Fisher classifier, naive Bayesian classifier and logistic regression were used to establish discriminators. Databases from three Australian and Canadian mines were established for training, calibrating and testing the discriminant models. The classification performances and discriminant precision of the three statistical techniques were discussed and compared. The proposed discriminators have explicit and simple functions which can be easily used by workers in mines or researchers. Back-test, applied results, cross-validated results and analysis of receiver operating characteristic curves in different mines have shown that the discriminator for one of the mines has a reasonably good discriminating performance.

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Abbreviations

ρ :

Rock density (kg/m3)

c :

Velocity of the wave in rock (m/s)

R :

The distance from the seismic source (m)

J c :

The integral of the square of the ground velocity

F c :

An empirical radiation pattern coefficient

Ω 0 :

The low-frequency plateau of the frequency spectrum of a seismic waveform

K c :

The Madariaga source model constant (S-wave)

α :

P-wave velocity

β :

S-wave velocity

u Mag :

Uniaxial magnitude

t Mag :

Triaxial magnitude

M 0 :

Seismic moment, \(M_{0} { = }{{ 4\pi \rho c^{3} R\varOmega_{0} } \mathord{\left/ {\vphantom {{ 4\pi \rho c^{3} R\varOmega_{0} } {F_{c} }}} \right. \kern-0pt} {F_{c} }}\)

M m :

Moment magnitude, \(M_{\text{m}} { = }\log \left( {M_{0} } \right){2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0pt} 3} - 6.0\)

f c :

Corner frequency, \(f_{\text{c}} { = }{{\sqrt {{{S_{\text{v2}} } \mathord{\left/ {\vphantom {{S_{\text{v2}} } {S_{\text{D2}} }}} \right. \kern-0pt} {S_{\text{D2}} }}} } \mathord{\left/ {\vphantom {{\sqrt {{{S_{\text{v2}} } \mathord{\left/ {\vphantom {{S_{\text{v2}} } {S_{\text{D2}} }}} \right. \kern-0pt} {S_{\text{D2}} }}} } {2\pi }}} \right. \kern-0pt} {2\pi }}\), S v2 and S D2 are integrals of the squared spectral displacement and velocity determined over P-wave and S-wave windows

E :

Total radiated energy, \(E = 4\pi \rho cR^{2} {{J_{\text{c}} } \mathord{\left/ {\vphantom {{J_{\text{c}} } {F_{\text{c}} }}} \right. \kern-0pt} {F_{\text{c}} }}\)

E s :

S-wave radiated energy

E P :

P-wave radiated energy

r 0 :

Source radius \(r_{ 0} { = }{{K_{\text{c}} \beta } \mathord{\left/ {\vphantom {{K_{\text{c}} \beta } {\left( { 2\pi f_{ 0} } \right)}}} \right. \kern-0pt} {\left( { 2\pi f_{ 0} } \right)}}\)

AR:

Asperity radius, \({\text{AR}} = 1.32\beta {{v_{\hbox{max} } } \mathord{\left/ {\vphantom {{v_{\hbox{max} } } {a_{\hbox{max} } }}} \right. \kern-0pt} {a_{\hbox{max} } }}\)

v max :

Maximum velocity record(m/s) from the root-mean-square trace

α max :

Maximum acceleration record (m/s2) from the root-mean-square trace

MD:

The maximum displacement, \({\text{MD}} = {{8.1Rv_{ \hbox{max} } } \mathord{\left/ {\vphantom {{8.1Rv_{ \hbox{max} } } \beta }} \right. \kern-0pt} \beta }\)

σ α :

Apparent stress (Pa), \(\sigma_{a} = {{\mu E} \mathord{\left/ {\vphantom {{\mu E} {M_{0} }}} \right. \kern-0pt} {M_{0} }}\)

μ :

Shear modulus of rigidity of the source material (N/m2)

SSD:

Static stress drop, \({\text{SSD}} = {{7M_{0} } \mathord{\left/ {\vphantom {{7M_{0} } {16r_{0}^{3} }}} \right. \kern-0pt} {16r_{0}^{3} }}\)

Δσ d :

DSD, dynamic stress drop, \(\Delta \sigma_{\text{d}} = 12.61\rho R\alpha\)

PV:

Peak velocity parameter, \({\text{PV}} = rv_{ \hbox{max} }\)

PA:

Peak acceleration parameter, \({\text{PA}} = \rho Ra_{ \hbox{max} }\)

Error:

Location error

N s :

Number of sensor used

N u :

Number of uniaxial sensor used

N t :

Number of triaxial sensor used

AS:

Apparent stress

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Acknowledgments

The ACG sincerely thanks the following organizations who provided funding for this research through the Mine Seismicity and Rockburst Risk Management project: Barrick Gold of Australia, BHP Billiton Nickel West, BHP Billiton Olympic Dam, Independence Gold (LighTNing Nickel), LKAB, Perilya Limited (Broken Hill Mine), Vale Inc., Agnico-Eagle Canada, Gold Fields, Hecla USA, Kirkland Lake Gold, MMG Golden Grove, Newcrest Mining, Xstrata Copper (Kidd Mine), Xstrata Nickel Rim, and The Minerals Research Institute of Western Australia. The first author thanks the partial support of projects (11447242, 41272304) of the National Natural Science Foundation of China.

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Authors and Affiliations

  1. School of Resources and Safety Engineering, Central South University, Changsha, 410083, China

    Longjun Dong & Xibing Li

  2. Australian Centre for Geomechanics, The University of Western Australia, Crawley, WA, 6009, Australia

    Longjun Dong, Johan Wesseloo & Yves Potvin

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  1. Longjun Dong
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  2. Johan Wesseloo
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Correspondence to Longjun Dong.

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Dong, L., Wesseloo, J., Potvin, Y. et al. Discrimination of Mine Seismic Events and Blasts Using the Fisher Classifier, Naive Bayesian Classifier and Logistic Regression. Rock Mech Rock Eng 49, 183–211 (2016). https://doi.org/10.1007/s00603-015-0733-y

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