46 9 ( ) Vol.46 No.9 15 9 Joural of Cetral South Uiversity (Sciece ad Techology) Sep. 15 DOI: 1.11817/j.iss.167-77.15.9.36 ( 183) 3 16 3 V e T e D e 3 TU46 A 167 77(15)9 349 8 Sesitivity aalysis of microseismic positioig accuracy based o distributio models of ifluecig factors GAO Yogtao, WU Qigliag, WU Shuchua, YANG Kai, DOU Lipig, YAO Pegfei (Key Laboratory of the Miistry of Educatio of Chia for High-Efficiet Miig ad Safety of Metal Mies, School of Civil & Eviromet Egieerig, Uiversity of Sciece ad Techology Beijig, Beijig 183, Chia) Abstract: Based o microseismic positioig equatio ad miimum error priciple, a iput ad output mathematical model for evaluatig sesitivity of microseismic positioig accuracy was costructed. Distace error betwee microseismic sources ad sesors, seismic wave velocity error ad trigger times error were selected as aalysis factors. Factor distributio factio was discussed by usig iformatio etropy, ad the correspodig expressio was obtaied by fuctioal variatio. Scheme of 16 groups was desiged by usig orthogoal method. Level value of each factor was give accordig to the factor distributio fuctio. Ad the global sesitivity aalysis was performed. The results show that three factors accord with uiform distributio i a give iterval; for both the iteral ad exteral field sources, seismic wave velocity error is the most ifluetial factor that affects the positioig results, ad the sigificat order from big to small of ifluece o positioig accuracy is V e T e ad D e. For iteral field source, all three factors have some sigificat ifluece o positioig accuracy; while for the exteral field source, oly the seismic wave velocity error has some sigificat ifluece o positioig accuracy, which may probably be affected by the iteractio betwee the factors or experimetal errors. The research coclusios may offer specific guidace for the accurate locatio aalysis of microseismic moitorig i the similar projects. Key words: microseismic; positioig accuracy; sesitivity; distributio model; errors 14 1 1114 1 (Foudatio item)(irt95)(frf-sd-1-a) (Project(IRT95) supported by the Program for Chagjiag Scholars ad Iovative Research Team i Uiversity; Project(FRF-SD-1-A) supported by the Fudametal Research Fuds for the Cetral Uiversities) E-mail: wuqigliagmy@163.com
343 ( ) 46 [1 3] ( ) ( ) Garso [4] [5] [6 1] [1] (PaD) [11] (LH-OAT) [1] 1 ( x, y, z ) ii ( = 1,, ) ( xi, yi, zi ) d i i i i i d = ( x x ) + ( y y ) + ( z z ), ( i = 1,,, ) (1) t t i ( ) v d v i + t = ti,( i = 1,,, ) () () 3 () ( di, v, ti) ( di, v, t i ) ξ ij (i=1,,, ; j=1,, 3) d + v t i = di ξi1 = v + ξi i = ti + ξi3 (3) i i i ) i1 ( x x ) + ( y y ) + ( z z ξ i i i3 (3) ( v ξ ) ( t t ξ ) =, ( i = 1,, ) (4) ξ ij ( i = 1,, ; j = 1,,3) ξ ij ( i = 1,,, ; j = 1,,3) ξ = (4) ( x, y, z, t ) ij 1 mi ϕ( x, y, z, t) = ξij (5) i= 1 ξij τij ( x, y, z, v, t, xi, yi, zi ) = (i=1,,, ; j=1,, 3) ϑ( X ) (5) 1 T 1 Ψ ( X) = ϑ( X) ϑ ( X) = τij ( x, y, z, t) (6) i= 1 Ψ ( X ) X (5) 1 T Ψ ( X ) = mi Ψ ( X) = mi ϑ( X) ϑ( X ) X R X R X = [ x y z t ] T D e V e T e 3 α 1, α,, α
9 3431 P1, P,, P H = P P P P P l P (7) 1l 1 l = H = P( α)l P( α ) = = 1 P( α ) P( α ) l α Δ Δ α = P( α) P( α) l P( α )l Δ α = = lim H = p ( α )l p ( α )d α lim l (9) p( ) lim P( α α = ) (8) (9) H + l H = p( α)l p( α)dα (1) [a, b] b p ( α )d α = 1 a δ H = J = p( α)l p( α) + λp( α) (11) ( ) [a, b] p( α) m m 1 α ( k = 1,, m) k αk k 1 p( α)d α= (14) a m 1 3 4 L16(4 5 ) 1 1 Table 1 Desig scheme based o orthogoal desig 1 D e1 V e1 T e1 9 D e3 V e1 T e3 D e1 V e T e 1 D e3 V e T e4 3 D e1 V e3 T e3 11 D e3 V e3 T e1 4 D e1 V e4 T e4 1 D e3 V e4 T e 5 D e V e1 T e 13 D e4 V e1 T e4 6 D e V e T e1 14 D e4 V e T e3 7 D e V e3 T e4 15 D e4 V e3 T e 8 D e V e4 T e3 16 D e4 V e4 T e1 4 J d ( J p ) = (1) p dα p = p( α) 1, a α b p( α) = b a (13), α < a α > b (13) 3 O 6 6 ( m) A( 5 5) B(5 5) C(1 5 5) D(5 1 5) E(5 5 1 ) F(5 5 ) H(3 64 746) I(673 7 1 ) v=5. m/ms 1::: 1 1 (BMS) 1 a [13] D e (m) V e (m/ms) T e (ms) 3
343 ( ) 46 1 Fig. 1 Distributio of sesors ad microseismic sources [, 6] [, 6% ] [, 3] 3 4 ( 16 ) 3 v 5 3 3 m /m( r ) 5.1 () 4 5 4 5 K jk j k K jk K jk R j j j R j 4 5 R j 1 R j V e T e D e V e T e D e ( 1 3 )( 4 ) () () 3 4 Table Value of three factors ad four levels of iteral ad exteral field sources usig orthogoal desig 3 H I 4 4 (1) () (3) (4) (1) () (3) (4) A 353.773 9 353.773 9 355.773 9 357.773 9 359.773 9 991.47 8 991.47 8 993.47 8 995.47 8 997.47 8 B 75.9 9 75.9 9 77.9 9 79.9 9 711.9 9 1 4.95 1 4.95 1 6.95 1 8.95 1 1.95 C 813.115 813.115 815.115 817.115 819.115 798.78 3 798.78 3 8.78 3 8.78 3 84.78 3 D 537.73 3 537.73 3 539.73 3 541.73 3 543.73 3 78.979 5 78.979 5 78.979 5 784.979 5 786.979 5 E 383.69 383.69 385.69 387.69 389.69 331.555 4 331.555 4 333.555 4 335.555 4 337.555 4 F 799.47 3 799.47 3 81.47 3 83.47 3 85.47 3 1 8.791 7 1 8.791 7 1 3.791 7 1 3.791 7 1 34.791 7 5. 5. 5.34 5.48 5.51 5. 5. 5.34 5.48 5.51 A 88.33 4 88.33 4 89.33 4 9.33 4 91.33 4 1.659 1.659 11.659 1.659 13.659 B 155.594 8 155.594 8 156.594 8 157.594 8 158.594 8 13.6 13.6 14.6 15.6 16.6 C 176.368 3 176.368 3 177.368 3 178.368 3 179.368 3 173.476 6 173.476 6 174.476 6 175.476 6 176.476 6 D 13.41 1 13.41 1 14.41 1 15.41 1 16.41 1 17.188 4 17.188 4 171.188 4 17.188 4 173.188 4 E 93.771 93.771 94.771 95.771 96.771 83.76 7 83.76 7 84.76 7 85.76 7 86.76 7 F 173.744 7 173.744 7 174.744 7 175.744 7 176.744 7 56.36 1 56.36 1 57.36 1 58.36 1 59.36 1
9 3433 3 Table 3 Positioig results of iteral ad exteral field sources m H I x =3. y =64. z =746. x =673. y =7. z =1. 1 D e1 V e1 T e1 3. 64. 746. 673. 7. 1. D e1 V e T e 13.633 7 61.75 763.535 6 675.654 4 73.158 8 1 6.51 1 3 D e1 V e3 T e3 194.87 61.583 5 781.368 7 678.341 7 76.345 7 1 5.796 3 4 D e1 V e4 T e4 175.94 1 63.93 3 799.58 1 681.11 6 79.619 8 1 78.91 8 5 D e V e1 T e 9.73 1 65.54 6 748.855 9 673.746 7.863 1 3.55 7 6 D e V e T e1.456 6 69.16 4 756.895 4 673.989 5 71.31 1 1 18.56 7 D e V e3 T e4 191.6 8 63.9 9 784.533 677.145 6 74.885 8 1 33.7 7 8 D e V e4 T e3 183.156 8 66.588 8 79.39 679.46 7 77.78 8 1 7.87 3 9 D e3 V e1 T e3 6.119 8 67.14 4 751.736 9 674.487 6 71.71 8 1 7.48 1 D e3 V e T e4 7.37 8 616.54 5 769.6 8 677.145 6 74.885 8 1 33.7 7 11 D e3 V e3 T e1 8.93 614.47 3 767.746 5 675.3 6 7.53 3 1 36.76 4 1 D e3 V e4 T e 19.33 7 6.893 785.385 677.8 8 75.784 1 6.84 8 13 D e4 V e1 T e4 3.141 68.683 9 754.641 675.5 1 7.575 7 1 1.567 14 D e4 V e T e3 14.88 5 61.45 1 76.898 7 675.496 5 7.976 1 5.741 9 15 D e4 V e3 T e 5.719 9 615.918 7 77.856 1 675.79 73.393 1 4.454 3 16 D e4 V e4 T e1 197.447 8 619.19 7 778.5 1 676.16 73.844 9 1 54.75 3 4 Table 4 Rage aalysis of test results for iteral field source D e V e T e 1 1 1 1 1 1 6.858 6 3 1 3 3 3 54.8 8 4 1 4 4 4 81.671 6 5 1 4 4.37 6 6 1 3 16.691 7 3 4 59.68 1 8 4 3 1 7.996 9 3 1 3 8.78 1 1 3 4 1 36.19 5 11 3 3 1 4 33.33 5 1 3 4 3 6.369 4 13 4 1 4 3 13.3 1 14 4 3 4 5.88 6 15 4 3 1 38.85 8 16 4 4 1 49.818 5
3434 ( ) 46 4 K j1 16.739 6.384 8 84.14 145.7 5 K j 151.15 9 15.6 7 19.684 4 144.57 3 K j3 138.665 5 184.686 159.869 7 144.51 3 K j4 17.19 6.855 7 19.16 3 145.48 3 K j 1 4.684 8 6.596 1.35 5 36.318 1 K j 37.781 5 6.45 7 3.41 1 36.131 8 { 1 L L } { K j1 L K jk L K jm} R = max K, K, K j j jk jm mi,, K j3 34.666 4 46.171 6 39.967 4 36.15 3 K j4 31.7548 65.713 9 47.54 6 36.31 1 R j 8.93 59.117 7 6.55 1.19 8 5 Table 5 Rage aalysis of test results for exteral field source D e V e T e 1 1 1 1 1 1 6.8 4 3 1 3 3 3 53.443 9 4 1 4 4 4 79.918 7 5 1 4 3.75 7 6 1 3 18.593 4 7 3 4 34.36 4 8 4 3 1 71.58 7 9 3 1 3 7.46 1 3 4 1 34.36 4 11 3 3 1 4 36.91 1 1 3 4 3 63.53 1 13 4 1 4 3 11.11 8 14 4 3 4 6.33 3 15 4 3 1 4.69 16 4 4 1 54.949 K j1 16.183.13 7 9.85 3 146.579 3 K j 18.186 1 15.753 5 134.471 4 13.48 K j3 141.866 8 165.343 6 158.464 1 146.39 K j4 13.776 6 69.71 7 159.633 3 146.558 7 K j1 4.45 8 5.553 4 3.1 6 36.644 8 K j 3.46 5 6.438 4 33.617 8 3.87 5 K j3 35.466 7 41.335 9 39.616 36.598 1 K j4 33.194 1 67.45 4 39.98 3 36.639 7 { 1 L L } { K j1 L K jk L K jm} R = max K, K, K j j jk jm mi,, R j 7.999 61.87 16.695 8 5.774 3
9 3435 m 1 i i= 1 r k= 1 5. ( ) Se = x K jk (19) 1 f j f e j 6 7 F 6 F D e = 1 87.36.1 (3,3) 9.457 ST = Sj+ Se (15) F 55 V e = 98.36 F.1 (3,3) 9.457 F T = e 8 157.43.1 (3,3) 9.457 M j Sj / f j F = = ~ F (, ) α f j fe (16) Me Se / fe 6 S T V e T e D e 7 1 ST = ( xi x) = xi ( x i ) (17) i= 1 i= 1 i= 1 S j j V e T e D e 99.43 F m m 1 1 F D e = 1.59.1 (3,3) 5.39 F V 81.738 e = j ( K jk ) jk ( i ) k 1 r K x (18) = k= 1 i= 1 F.1(3,3) = 9.457 F T e = 4.94 F. 1 (3,3) = 5.39 S e ( ) 6 Table 6 Variace aalysis of test results for iteral field source ( ) F F α 178.898 3 59.633 1 87.36 F.1 (3,3)=9.457 ** 7 771.6 3 59.41 55 98.36 F.5 (3,3)=9.8 ** 1 133.89 3 377.943 8157.43 F.1 (3,3)=5.39 ** e.139 3.46 9 84.18 1 7 Table 7 Variace aalysis of test results for exteral field source ( ) F F α 15.79 3 5.6 1.59 F.1 (3,3)=9.457 8 17.49 3 79.83 81.738 F.5 (3,3)=9.8 ** 47.65 3 135.688 4.94 F.1 (3,3)=5.39 e 99.43 3 33.143 8 783.83 1
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