ANALYSIS OF SOURCE LOCATION ALGORITHMS Part I: Overview and non-iterative methods

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1 ANALYSIS OF SOURCE LOCATION ALGORITHMS Par I: Overvew and non-erave mehods MAOCHEN GE Pennsylvana Sae Unversy, Unversy Park PA 1680 Absrac Ths arcle and he accompanyng one dscuss he source locaon heores and mehods ha are used or earhquake, mcrosesmc and acousc emsson sudes. The presen paper provdes an overvew o he prncples o source locaon mehods as well as a dealed analyss o several prncpal approaches, ncludng raxal sensor mehod, zonal locaon echnque and nonerave algorhms. The accompanyng paper s devoed enrely o he erave mehods because o her parcular mporance. A horough and n-deph analyss s provded or he dervave and Smplex mehods n order o develop a undamenal undersandng o he mechancs o hese mehods. 1. Inroducon An accurae acousc emsson (AE) source locaon depends on many acors and a suable source locaon mehod s one o hem. To have a proper knowledge on source locaon mehods s no jus essenal or operaonal reasons, such as daa gaherng, processng and nerpreaon. I s probably more sgncan or monorng plannng. When he even locaon s a prmary concern, a key ssue or success s how o acheve he requred locaon accuracy. In order o answer hs queson, he role o he locaon mehod has o be deermned. One has o be able o selec he mos suable algorhm(s) or he gven condon and o be able o evaluae s capably o resolvng he ancpaed problems. The goal o hs and he accompanyng papers s o help readers o esablsh a perspecve vew on source locaon mehods. In addon o he dealed analyss o he algorhms hemselves, he emphass s he locaon prncples and mechancs. The presen paper dscusses how a source locaon mehod may be vewed and a smple classcaon s presened o characerze he herarchy o locaon approaches and mehods. A dealed analyss s hen gven o several prncpal approaches, ncludng raxal sensor mehod, zonal locaon echnque and non-erave algorhms. The accompanyng paper s devoed enrely o he erave mehods because o her parcular mporance. The ocus o he dscusson s he dervave and Smplex mehods. In order o develop a undamenal undersandng or hese mehods, an n-deph analyss s carred ou or a number o problems ha are o boh heorecal and praccal mporance. These problems are: concep o nonlnear locaon, mechancs o erave mehods, sably o locaon sysems, and opmzaon mehod and error analyss.. An Overvew o Source Locaon Mehods A source locaon mehod n hs arcle reers o a mahemacal procedure ha deduces he daa rom physcal observaons o he normaon o he even orgn expressed as hypocener parameers. J. Acousc Emsson, 1 (003) Acousc Emsson Group

2 Traxal sensor approach A source locaon mehod can be vewed n many deren ways. In erms o physcal normaon ha s ulzed, here are wo dsncve approaches: he raxal senor approach and he arrval me approach. The raxal sensor approach makes use o wo ypes o physcal daa: amplude and arrval me. Wh hs approach an even locaon s dened by s relave dsance and azmuh o he sensor, whch are deermned by P- and S-wave arrval me derence and he amplude normaon n hree orhogonal drecons. I s called he raxal sensor approach snce 3-componen ransducers have o be used. Arrval me approach The arrval me approach ulzes only arrval me normaon. Whle hs normaon s no resrced o specc wave ypes, P- and S-waves are he ones mosly used. The major advanage o he arrval me approach over he raxal sensor approach s he relably o he physcal daa ha s ulzed. Arrval me normaon s consdered much more sable han amplude normaon as ravel mes are less sensve o he change o he medum properes. I s because o hs reason he approach has been used n mos locaon cases. Pon and zonal locaon Arrval me mehods prmarly reer o he algorhms ha are desgned or he pn-pon locaon accuracy. Because o he exensve use o hs ype o algorhms, he ocus o hs arcle s he represenaves o hese algorhms. Zonal locaon, whch also uses only arrval mes, may be consdered a specal case o he arrval me approach. Zonal locaon reers o hose mehods ha are used o deny wheher an even s rom a predened zone based on prmarly he rs-h sensor locaon. The locaon prncple o he arrval me approach s relavely smple. Wh hs approach a number o sngle-elemen ransducers are needed. These ransducers are nsalled a suable posons where acousc emsson/mcrosesmc (AE/MS) acvy can be eecvely deeced. The arrval me uncon s hen esablshed or each ransducer n erms o observed arrval me, velocy model, and sensor coordnaes. The ollowng s he smples orm o hs uncon: ( x x) + ( y y) + ( z z) = v( ) (1) where, he unknowns, x, y, and z are he coordnaes o he source; s he orgn me o he even, x, y and z are he coordnaes o he h ransducer, s he arrval me a he h ransducer, v s sress wave propagaon velocy, and =1,,..., N,..., M. Here, N denoes he number o unknowns and M denoes he number o equaons. In order o solve or he unknowns, s clear ha he condon M N mus be sased. When M = N, we can deermne he unknown precsely; when M > N, he problem becomes over deermned and a regresson mehod has o be used or he opmum soluon. Eq. (1) represens arrval me uncons ha assume a consan velocy model. Non-erave algorhms A se o nonlnear equaons as dened by Eq. (1) can be solved eher eravely or noneravely. Non-erave mehods reer o hose algorhms ha solve he source locaon problem dened by Eq. (1) whou nvokng any numercal approach. 15

3 The non-erave mehods are, n general, smple and easy o apply. Users do no have o worry abou many compuaonal problems ha hey would oherwse have o ace, such as choosng he guess soluon, seng he convergency creron, and, especally, handlng he problem o dvergence. These mehods are also quck because o he non-erave naure. The major shorcomng o hese mehods s her nlexbly n dealng wh velocy models. Evenually, hey have o assume he same velocy or all saons. Wh he consderaon o he complexy o arrval ypes, hs assumpon severely lms he meanngul applcaons o hese mehods. The Inglada's mehod and he USBM mehod are represenave n hs caegory and wll be dscussed n hs paper. Ierave algorhms The erave approach, on he oher hand, s much more lexble n handlng arrval me uncons. As hs capably s essenal n dealng wh a wde range o praccal problems, he erave approach s o prmary mporance n source locaon. The erave approach covers a large array o algorhms, rom emprcally based sequenal searchng mehods o hghly sophscaed dervave mehods. Geger s mehod and he Smplex mehod are consdered mos mporan ones wh hs approach. These mehods wll be dscussed n he accompanyng paper whch s enrely devoed on he subjec o erave mehods. A classcaon o he source locaon mehods based on he above dscusson s presened n Fg. 1 and our dscusson wll closely ollow he logc shown by he low char. I has o be emphaszed ha hs classcaon s developed manly or he convenence o he dscusson and should no be nerpreed as a serous eor o classy he source locaon mehods. The dealed dscusson on he locaon algorhms wll be spl no wo papers. The presen paper covers he raxal sensor mehod, zonal locaon echnque and wo non-erave algorhms: Inglada mehod and USBM mehod. The second paper deals exclusvely wh he subjec o erave algorhms. Source Locaon Traxal Approach Arrval Tme Approach Pon Locaon Zonal Locaon Non-erave Mehod Ierave Mehod USBM Inglada Geger Thurber Smplex Fg. 1. Classcaon o AE/MS source locaon mehods. 16

4 3. Traxal Sensor Approach The raxal sensor approach s based on he dea ha he spaal poson o a pon s known, hen he spaal poson o any oher pon can be expressed n erms o s relave dsance and azmuh o he known pon. The unque advanage o hs approach s ha he source locaon can be carred ou rom a sngle locaon. The approach s hereore crcal or hose deep level applcaons where long drll holes are requred or he sensor nsallaon. The approach has been ulzed or varous deep level applcaons, such as rockburs sudy (Brnk and Mounor, 1984), sably o peroleum reserve se (Albrgh and Pearson, 1979), and geohermal engneerng (Albrgh and Pearson, 1979; Bara and Bachelor, 1989; Nsuma e al., 1989). 3.1 Locaon prncple The geomery o he raxal sensor approach s llusraed n Fg.. Here he locaon o a raxal sensor, TR, s known. Source S s o be deermned n erms o s relave dsance, d, and s azmuh (α, β, γ). Fg.. The geomery assocaed wh raxal sensor approach (Aer Hardy, 1986). Based on he P- and S-wave arrval mes, he relave dsance can be expressed as v pvs d = ( s p ) () v v p s where d s he dsance rom he source o he sensor, v p and v s are he veloces o P- and S- waves, and p and s are he arrval mes o P- and S-waves. The relave azmuh (α, β, γ ) can be deermned by he amplude o he receved sgnals. Assumng ha A x, A y and A z are he ampludes o hree muually orhogonal componens o he sgnal. The drecon cosnes o hs sgnal relave o he sensor are and l = A / x A m = A A y / p = A / z A (3) A = A + A + A (4) x y z 17

5 where l, m and p are he drecon cosnes o he sgnal relave o he sensor. The relave azmuh s smply α = cos 1 ( l) β = cos 1 ( m) (5) γ = cos 1 ( p) Usng sgnal ampludes o deermne he relave azmuh s based on he ac ha, or a compressonal wave, he rs parcle moon s n he drecon o propagaon (Hardy, 003). 3. Leas squares soluon or azmuh When here are n ses o observaons, such as l = A / A, x y m = A / A, = 1,,, n p = Az / A, he bes soluon dened by he leas squares mehod s: ( n l = 1 n ( m = 1 n p = 1 ( l A x / A ) ( m A y / A ) ) = 0 ) = 0 ( ( p A z / A ) ) = 0. where l, m, and p are he bes or l s, m s and p s. Solvng he above equaons, we have l = m = p = ( A x n ( A / A ) y n ( A / A ) z n / A ) (6) 3.3 Dscusson Traxal sensor approach s ound exremely useul or hose deep level applcaons where borehole drllng s requred or he sensor nsallaon. Snce borehole drllng s a very expensve operaon, has o be mnmzed. Wh he raxal sensor approach, he requred locaon accuracy may be acheved wh a sngle or ew sensors whch eecvely reduces he reques or borehole drllngs. In addon o s cos bene or deep level applcaons, here are wo echncal advanages assocaed wh he raxal sensor approach. Frs, mproves he sably o he source locaon soluons or hose ousde array evens as he approach uses boh P- and S- wave arrvals. Second, allows one o analyze he saus o he ground moon a he sensor locaon, whch s crcal or sudyng even magnude and source mechansm. 18

6 The major echncal problem assocaed wh he raxal sensor approach s he sably o he azmuhal angles as ampludes are much more sensve o maeral properes and srucures han ravel mes. A echnque ha could mprove he problem s called hodogram (Doebeln, 1975). Wh hs echnque, amplude daa rom wo componens are cross-ploed and an ellpcal gure s obaned. The major axs o he ellpse s consdered he drecon o wave propagaon n he plane. Fgure 4 shows he hodogram o parcle moons deeced by wo horzonal sensors. Fg. 3. Hodogram o parcle moons deeced by wo horzonal sensors (aer Hardy, 003). 4. Zonal Source Locaon Zonal locaon s a source locaon echnque ha denes a predened zone as he even locaon based on, prmarly, he locaon o he rs rggered sensor. I s he smples orm o use arrval mes or source locaon. I he nework s relavely dense wh a good coverage, he echnque oers a quck and relable dea on he general area where he even ook place. The concep o zonal locaon and s applcaon o large srucures orgnaed rom AE sudes n maeral scence (Arrngon, 1984; Fowler, 1984; Tede and Eller, 198; and Huon and Sorpk, 1976). The dea o he zonal locaon s demonsraed n Fgure 4. Here he monorng regon s dvded no a number o prmary zones, and each zone s assocaed wh a parcular saon whch s he rs one o be rggered when he source s locaed whn he area. Based on he locaons o he laer rggered saons, he prmary zone s urher dvded no smaller ones, such as he second-h sub-zone and he hrd-h sub-zone as llusraed n he gure. The sub-zones provde he beer dea on he relave azmuh poson o he source n he prmary zone, bu oers no mprovemen n he radal drecon. The problem may be overcome by wo smple echnques. The rs one s o compare he observed arrval me derence beween he rs and he laer rggered saons wh he assocaed heorecal lm. The heorecal lm s he dsance beween wo sensors dvded by he velocy. The rao o he 19

7 Fg. 4 The geomery assocaed wh he zonal locaon mehod (aer Hardy, 003). observed arrval me derence o he heorecal lm s an ndcaon o he even locaon. The larger he rao, he closer he source o he rs rggered saon. I he rao reaches o one, he source s a or behnd he rs rggered saon. I s zero, he source s on he cenral lne beween he wo saons, or on he board o he prmary zone. The second echnque s o use he P- and S-wave arrval me derence o esmae he dsance rom he rs saon, whch can be done by usng Eq. (). In comparson wh he mehods desgned or he pn-pon locaon purpose, he zonal locaon approach has wo dsncve advanages. Frs does no need o deermne he precse ray race, whch s oen very dcul when he srucure under he sudy s complcaed. I s largely because o hs reason ha he zonal locaon becomes one o he prmary mehods used n he non-desrucve esng ndusry. The oher advanage o he mehod s ha poss no reques on he mnmum number o saons o be rggered. Lack o he sucen saons or precse source locaon s a requenly observed problem. When hs s he case, he zonal locaon becomes he only alernave. An mporan assumpon made wh he zonal locaon approach s ha all saons are rggered by he same wave ype, presumably by P-waves. Ths, however, may no necessarly be he case. In ac, AE sysems are oen rggered by S-waves nsead o P-waves. Ths s because ampludes o P-waves are oen much lower han ha o S-waves, and hs phenomenon s shown n Fgure 5 by an AE sgnal recorded by a raxal sensor. In addon o he S-wave rggerng, expermenal condons may also play an mporan role. For nsance, was observed by he auhor n he es o a waer-lled ank car ha he sensor a he oppose sde o he calbraed source was rggered nsead o hose closer ones on he same sde. Ths s because he waer-borne P-wave ha rggered he sensor a he oppose sde was less aenuaed whle he meal-borne waves ha had supposedly rggered he nearby sensors were largely absorbed by he waer. 0

8 Fg. 5. AE sgnals deeced usng a raxal monorng ransducer (aer Hardy, 003). I s undersood rom he above dscusson ha he zonal locaon echnque, as any oher source locaon mehods, s subjec o errors and he causes or he error are no uncommon. Thereore, he soluon by he zonal locaon should no be auomacally assumed correc and should be examned s possble. 5. Inglada's Mehod We now begn our dscusson on non-erave mehods. Non-erave mehods are an mporan caegory n he amly o locaon algorhms. They are smple and easy o use, and, n ac, he basc ones used by AE praconers. Inglada s mehod and USBM mehod are consdered he represenaves n hs caegory and we dscuss Inglada s mehod rs. 5.1 Algorhm Inglada's mehod (Inglada, 198) s a non-erave, analycal soluon o he source locaon problem dened by Eq. (1). The mehod s bes sued or smple source locaon problems where he number o sensors used s mnmum and a consan velocy model can be assumed. Inglada mehod sars wh squarng Eq. (1): ( x x) + ( y y) + ( z z) = v ( ) (7) or = 1,, 3, and 4 and hen lnearzes he sysem by subracng he rs equaon rom hree remanng ones, whch yelds: 1

9 where and a x + b y + c z = e (8) a b c e + = x = y = z x 1 y 1 z 1 = 0.5( R R = v ( ) 1 1 R = x + y + z 1 = x1 + y1 z1 R + v ( 1 )) or =, 3, and 4. Three lnear equaons dened n (8) can be solved or x, y and z n erms o by usng Cramer's rule. The soluon s as ollows: M 1 N1 x = + D M N y = + D (9) M 3 + N 3 z = D where D s he deermnan gven by a b c D = a3 b3 c3. a 4 b4 c4 M j and N j, or j = 1, 3, are also he deermnans. They are smlar o D, bu wh he jh column o D replaced by (e, e 3, e 4 ) and (, 3, 4 ), respecvely. Subsue hree equaons dened n (9) back o one o he equaons dened n (7). Snce x, y and z n (9) are all expressed n erms o, hs back subsuon yelds a second order equaon o wh he orm A + B + C = 0 (10) where A, B and C are consans. Eq. (10) s a quadrac uncon o and here are wo soluons, say, 01 and 0. Subsung 01 and 0 no Eq. (9), he correspondng soluons are (x 01, y 01, z 01, 01 ) and (x 0, y 0, z 0, 0 ), respecvely. 5. Idenyng non easble soluon Usually, one o hese soluons wll no be physcally easble and can be easly dened. For nsance, he soluon can be mmedaely elmnaed s calculaed orgn me s laer han

10 he observed arrval me(s). Oherwse, a urher check s necessary n order o deermne he rue source locaon. Ths s usually done by subsung he soluons back no he nonlnear sysem dened n Eq. (1). There s, however, he possbly ha boh he soluons sasy hose nonlnear equaons, whch are called mulple soluons. When he problem o mulple soluons s encounered, he arrval me daa rom an addonal sensor s requred o deny he rue source. 5.3 Mulple soluons The problem o mulple soluons s no caused by he Inglada s mehod. Raher, s due o he non-lnear naure o he locaon ormulas. I can be shown ha he problem wll occur only when he mnmum number o sensors s ulzed or locaon compuaon (Ge, 1988). Fgure 6 llusraes he mulple soluons assocaed wh a -dmensonal array. Fg. 6. Dsrbuon o mulple soluons (Aer Rndor, 1981) 5.4 Applcaon condons Inglada's mehod s smple and easy o use. In ac, s probably he smples algorhm or solvng a se o equaons dened by Eq. (1). Users however need o be aware o s operaonal condons. Frs, s undersood rom he dervng process ha he algorhm assumes he same velocy or all saons. Ths assumpon may resrc he meanngul use o he mehod n many cases and should be valdaed beore s applcaon. 3

11 Second, he algorhm uses only a mnmum number o sensors ha s mahemacally requred or he pn-pon locaon, ha s, he number o equaons s equal o he number o unknowns. Because o hs requremen, no opmzaon mehod can be appled o he algorhm. From an error conrol pon o vew, one should use as many sensors as possble. There are wo mporan reasons. Frs, he locaon accuracy s undamenally deermned by he sensor array geomery (Ge, 1988). Usng more sensors n general wll lead o he beer array geomery. Second, he daa se s sascally more relable when more sensors are used. Chrsy (198) demonsraed ha he algorhm ncorporaed wh he leas squares mehod would yeld he beer source locaon accuracy han Inglada mehod. For hese reasons, one should consder o use he algorhms wh he opmzaon capably he locaon daa s avalable rom sensors ha are more han he mnmum. 6. The USBM Mehod The USBM mehod s a non-erave algorhm or he source locaon problem dened by Eq. (1). I was developed n he early 1970s by he researchers a he Uned Saes Bureau o Mnes (USBM). The developmen o hs mehod was par o he Bureau o Mnes' eor o make he acousc emsson/mcrosesmc (AE/MS) echnque an eecve engneerng ool or deermnng he sably o rock srucures. The mehod was rs publshed n 1970 and was urher moded n 197 (Leghon and Blake, 1970; Leghon and Duvall, 197). Snce hen has become he major mne-orened AE/MS source locaon mehod used n Norh Amerca. 6.1 Algorhm Le D represen he dsance rom he source o he h ransducer, D = ( x x) + ( y y) + ( z z) (11) and rewre Eq. (1) as D = v( ). (1) Subrac he rs equaon rom he res whch are all dened by Eq. (1), D D = v( 1) (13) 1 where, =, 3,..., m. Squarng and smplyng he above equaon, hs yelds e ( a x + b y + c z) d + = D1 d d (14) where a b c d = x 1 x = y 1 y = z 1 ) z = v( 1 e = x + y + z ( x + y + z ) The non-lnear sysem dened by (14) can be lnearzed by subracng he nd equaon rom he res o hem. Ths process yelds, 1x, y +,3z = h + g v + (15) 4

12 where,1, a = ( b = ( c = (,3 = g h e = a ) b ) c ) e = 3, 4,, m. Eq. (15) denes a lnear sysem. where In marx noaon, he lnear sysem dened by Eq. (15) can be wren as 3,1 3, 3,3 A =, m,1 m, m,3 Ax = b (16) x x = y, z h b = h 3 m + g 3v. + g v m 6. The leas squares soluon I s mporan o noe ha he USBM mehod requres he arrval mes rom a leas (n + 1) saons, where n s he number o unknowns. For nsance, here are ve saons, A s a 3 by 3 marx and unknowns, x, y and z, can be solved exacly. I here are arrval mes rom more han ve saons, he source locaon has o be dened sascally. Wh he USBM mehod, he error s convenonally dened as he sum o squares o resduals and he correspondng leas squares soluon s (Srang, 1980): A T Ax = A T b (17) or x = (A T A) -1 A T b The orgn o me s no gven n x; bu can be obaned by subsung x back no (1). 6.3 Velocy as an unknown The velocy can be esmaed by he USBM mehod and hs can be done by consderng v as an unknown varable n Eq. (15) and movng g v rom he rgh hand sde o he equaon o he le, such as: =, 1x +, y +, 3z gw h (18) where w = v. 5

13 Whle s an addonal reedom o rea he velocy as an unknown, an exra cauon should be exercsed o use hs eaure. The man reason s he errors and unceranes assocaed wh he arrval me normaon. I he velocy s reaed as an unknown, we have he less chance o solae he arrval me errors o he places where hey occur. Insead, hey may be accommodaed by a alse velocy value, creang an even worse suaon. 6.4 Dscusson The USBM mehod s a arly sragh orward algorhm or solvng a se o non-lnear equaons dened by (1). Wh hs mehod he orgn me s elmnaed by subracng he rs equaon rom he res. The resulng equaons are hen lnearzed and orm a lnear sysem. There are wo basc condons o use he USBM algorhm. Frs he mehod assumes he same velocy or all saons, and second requres a leas one more equaon han he number o unknowns, ha s, he condon m n + 1 mus be sased, where m and n denoe he number o equaons and unknowns, respecvely. For nsance, we need he arrval me normaon rom a leas 5 saons n order o solve a problem o 4 unknowns, such as x, y, z, and. The major advanage o he USBM mehod over he Inglada s mehod s ha all avalable arrval me normaon can be used smulaneously or he source locaon calculaon. Ths allows he sasc analyss o be carred ou, an mporan approach o mprove he locaon accuracy. There s anoher smlar algorhm whch s called he ISA Mne's mehod, and readers may reer o Godson and McKavanagh (1980) or deals. 7. Conclusons In erms o he physcal daa ulzed or source locaon, we have wo dsncve approaches: he raxal sensor approach and he arrval me approach. The mporance o he raxal sensor approach may be vewed rom wo perspecves. Frs, he source locaon can be carred ou rom a sngle sensor locaon, whch becomes a parcular mporan advanage when sensor nsallaon s expensve. Second, provdes he daa ha allows one o characerze he saus o sress wave a he pon, whch s crcal or he urher sudy o he source mechansm and source parameers. The lmed use o he raxal sensor approach s prmarly due o he wo praccal reasons. Frs, he amplude daa s more suscepble o maeral srucures and properes, and hereore, he mehod s less sable han he one ha uses only arrval mes. Second, hree sngle-elemen sensors wh spread locaons n general gve he much beer daa or source locaon han a raxal sensor. Thereore, he arrval me approach s normally he choce rom a cos-bene pon o vew unless here are some oher specal consderaons. Zonal locaon echnque s consdered a specal case o he arrval me approach snce all oher mehods n hs caegory are or pn-pon locaon purpose. Zonal locaon echnque s smple and easy o use. Users, however, sll should pay aenon o arrval ypes. The echnque s based on he assumpon ha all sensors are rggered by he same ype o wave. As was dscussed n he paper, hs mgh no be he case. 6

14 There are wo major branches whn he arrval me approach: non-erave and erave. The Δ algorhms ha are convenonally called and used by AE praconers are nonerave. Inglada and USBM mehods are he represenaves n hs caegory. Non-erave mehods are smple and easy o use n ha hey requre lle neracon rom users. The major derence beween hese wo mehods s ha Inglada mehod s lmed o he mnmum number o sensors whle USBM mehod does no subjec o hs lmaon. A common problem wh hese wo mehods s he assumpon o a sngle velocy, whch severely resrcs her vald applcaons. The soluon o he problem o he sngle velocy assumpon s o use he erave mehods, whch are dscussed n he accompanyng paper: Analyss o source locaon algorhms Par II: erave mehods. Acknowledgmens I am graeul o Dr. Kanj Ono or hs encouragemen o wre my research experence n he area. I hank Dr. R. Hardy or hs horough revew and he anonymous revewer or hs commens and suggesons o mprove he manuscrp. Reerences Albrgh, J. N. and C. F. Pearson (1979). Mcrosesmc monorng a Byran Mound sraegc peroleum reserve, Inernal Repor, Los Alamos Scenc Laboraory, Los Alamos, March Albrgh, J. N. and C. F. Pearson (198). Acousc emsson as a ool or hydraulc racure locaon: experence a he Fenon Hll ho dry rock se, Socey Peroleum Engneerng Journal, Augus 198, Arrngon, M., (1984). In-su acousc emsson monorng o a seleced node n an oshore plaorm, Proc. 7h Inernaonal Acousc Emsson Symposum, Senda, Japan, Ocober 1984, Bara, R. K. and A. S. Bachelor (1989). Induced sesmcy durng he hydraulc smulaon o a poenal ho dry rock geohermal reservor, Proc. 4h Conerence on Acousc Emsson/Mcrosesmc acvy n geologc srucures and maerals, The Pennsylvana Sae Unversy, Ocober 1985, Trans Tech Publcaons, Claushal-Zellereld, Germany Doebeln, E. O., (1975). Measuremen sysems, McGraw-Hll Book Company, New York, Chrsy, J. J., (198). A comparave sudy o he Mner and leas squares locaon echnque as used or he sesmc locaon o rapped coal mners, M.S. Thess, The Pennsylvana Sae Unversy, College o Earh and Mneral Scences, Unversy Park, Pensylvana, Augus 198. Fowler, T. J., (1984). Acousc emsson esng o chemcal process ndusry vessels, Proc. 7h Inernaonal Acousc Emsson Symposum, Senda, Japan, Ocober 1984, Ge, M., (1988). Opmzaon o ransducer array geomery or acousc emsson/ mcrosesmc source locaon, Ph.D. Thess, The Pennsylvana Sae Unversy, College o Earh and Mneral Scences, Unversy Park, Pensylvana, Augus

15 Godson, R. A., M. C. Grdges and B. M. Mckavanagh (1980). A 3-channel rock nomse source locaon sysem, Proc. nd Conerence on Acousc Emsson/Mcrosesmc acvy n geologc srucures and maerals, The Pennsylvana Sae Unversy, November 1978, Trans Tech Publcaons, Claushal-Zellereld, Germany Hardy, H. R. (1986). Source locaon velocy models or AE/MS eld sudes n geologc maerals, Proc. 8h Inernaonal Acousc Emsson Symposum, Tokyo, Japan, Ocober 1986, Japanese Socey or Non-Desrucve Tesng, Tokyo, Hardy, H. R. (003). Acousc emsson/mcrosesmc acvy, A.A. Balkema, Lsse, Neherlands. Huon, P. H. and J. R. Skorpk (1976). A smpled approach o connous AE monorng usng dgal memory sorage, Proc. 3rd Inernaonal Acousc Emsson Symposum, Tokyo, Japan, Sepember 1976, Inglada, V., (198). De berechnung der herdkoordnaed enes nahbebens aus den enrszeen der n enngen benachbaren saonen augezechneen P-oder P-wellen, Gerlands Berage zur Geophysk 19, Leghon, F. and W. Blake (1970). Rock nose source locaon echnques, USBM RI 743. Leghon, F. and W. I. Duvall (197). A leas squares mehod or mprovng rock nose source locaon echnques, USBM RI 766. Nsuma, H., K. Nakasuka, N. Chubach, H. Yokoyama, and M. Takanohash (1989). Downhole AE measuremen o a geohermal reservor and s applcaon o reservor conrol, Proc. 4h Conerence on Acousc Emsson/Mcrosesmc acvy n geologc srucures and maerals, The Pennsylvana Sae Unversy, Ocober 1985, Trans Tech Publcaons, Claushal-Zellereld, Germany Rndor, H. J., (1981). Acousc emsson source locaon, Bruel & Kjaer, Techncal Revew, No.. Srang, G. (1980). Lnear algerbra and s applcaons, Academc Press Inc., New York, New York. Tede, D. A. and E. E. Eller (198). Sources o error n AE locaon calculaons, Proc. 6h Inernaonal Acousc Emsson Symposum, Susono, Japan, Ocober/November 198,