Mechanisms of large seismic events in platinum mines of the Bushveld Complex (South Africa)

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1 Sy Mhm f lg m v lum m f h Buhvld Cmlx (Suh Af) by D. Mlvhk*, G. v Awg, d R. Clk Sm v d ll flu bvd w lum m h Rubug, Suh Af, w vgd. W udd h u f xmly 300 lg m v dd Mm f h v w md fm mlud d l f - d S-wv. h vd mhm mlv m my. Aly f uy f h mm lu fmd h gf f h mlv m gl. Svl dumd f ll flu w dd dl. F h f h m mm w luld fm l mdl umg mvl f fld ll. h gm d mgud f h hl m mm gm wh h bvd (.. vd fm m d). h ul d h h ll flu fug h xmy f h f (wh f f h dm wvlgh f m wv) bl f gf f h lg v dd h m. Kywd m mm, ll flu, uml mdllg. Idu h Buhvld Cmlx f Suh Af h h mjy f h wld kw lum gu ml u. A umb f m d h Cmlx. Eh w h, l, d hllwly dg bd (h Mky d UG2 Rf) xd ug d mg mhd wh gl bly ll d uh ll. h w m Rubug h dud h xvly m u Mky Rf fmg bk f bu 4 5 km2 h. h f d glly bw 10 d 12 dg. Cu mg dh bu m. A mm xv m wk bd 22 d h m. M f h lld udgud ul lll h l bdy, dg h fgu f h h l. w uf dd h muhdd hd dm h wk fgu h f. All qud wh -xl gh wh 4.5 Hz ul fquy. Abu 2,000 v dd by h wk y vg, wh u m f v f mm mgud (m W ) 2.0 f bu 35 dy. h quly f m d hgh h m v g l gl - d S-wv ly f udgud, bu l f uf. h ly l fgu f h udgud ul f blm f l f h m u h f h u b d wh h f l bu gfly u h d ml h f. h lld f l my hv dm f vl hudd f m h d. I gl h bvd m vy lly ld h - h uly v md u wh h vu vl y. h lmd l wh glgl fu dyk, ful d hl. Dym flu f ll w dumd f m f h lg m v. I w, hwv, blhd whh h bvd dmg w flg h dl f h m u whh h dmg w ud by wv fm by m v. Svl flu f v h bk hv b dd, g fm h hy f m lg v d dg u v vl dy v, xm, v wk. h flu d ll u, wh h flu f ll h ldg f x flu, ug u f m v. h bk ll glly bl, hf h f ll u b vfd by d bv. * Iu f M Smlgy, Aul. Iu f M Smlgy, Suh Af. h Suh Af Iu f Mg d Mllugy, SA ISSN X/ vd Ju. 2010; vd vd J h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 112 JUNE

2 Mhm f lg m v lum m f h Buhvld Cmlx Mg-ld my h b xvly vd h mlgl d k mh lu. My ud vd f dff bw h mhm f m v bvd mg d h vm. I ul, h m f mlv m h vd mm d1 4, glly bud h f h flu wh vlum dfm f dj xv. Svl ud f m u mhm w d f lum m f h Buhvld Cmlx. O f h5 d ul f h ly f my w lum m h Rubug. h d w qud by -uf h. I w hw h gf f h v hv hd mlud f - wv lv h xd d fm ml h l mhm. h w h h v gd fm h uhg f ll h fwll. h bjv f h udy mv u uddg f h u mhm f h lg m v h m ud d dvlg mg d u g. W fu : Iv f h mm f v d f mdum d lg z m v Aly f vl ll flu g udgud bv, uml mdllg f h m u mhm, d m f h wh h mhm vd fm m d. Aly f m u mhm D M h 300 v dd by h wk 2009 w ld f dld ly f h u. h fllwg l hv b ud: Mm mgud bv 0.5 A l 10 ggd h u l wh h l f h wk (d h bud f h m ud d). h z dbu f h ld v hw Fgu 1. h lg, m W 2.5 v, ud Nvmb M h 40 v hd mgud g h 1.5. Sl xm f m d dd 2009 w d vfy h d f h. h f d w dd: Smll d mdum z ll (-m) m v h um h m h -wv mu b lzd lg h u- d w ud f vf f h. A v du w ld f h dd h vf,.. h h (zmuh, d d ll gl, m fl) whh yld h mll dff bw h lz f m h -wv d u- d w md. W h, m f ly, h dbd du d xlud h bly f h mulu flg f ll m f h m. h bbly f uh g dug ll, hwv, dd mll. h m f bvd f m gl wh xd llw u m h f h Ll bl A h f m f h -wv mu b ly wy fm h bl' u, vd m f hkg h d lmg h bly f h mulu flg f ll m D lg v h xm f - d S- wv mg fm d u l wv llw u hk h f d f dvdul lv ld f. Al f h du uld h df f f wh lbl d h. Mm v h m wvfm dd by h wh lbl h w ud f h m f m mm. h glly-bvd mly f m wvfm dd h m mk bl k dvg f lvly ml d quk mm v hqu ulzg mlud d l f gl f h - d S-wv. h mlud w luld h fquy dm, fm h lw-fquy lu f dlm. h mlud d ly d f dff wv d w wghd dg h h f h dg gl,.. h gl Vf f d f h m h udy f u mhm bd h xm f h f h m d. h mlud d h (l) f m wv dd dff d fm h u lyd mvly. h f ly qu kwldg f h d f h m, ud m h (.g. h flg f h m by bl fw g) my ul gf dv f h vd mhm. Numb f v Mgud Fgu 1 Fquy-mgud dbu f v ud h dld ly f u Ru m ( vy... dy) 420 JUNE 2012 VOLUME 112 h Jul f h Suh Af Iu f Mg d Mllugy

3 Mhm f lg m v lum m f h Buhvld Cmlx wh g d hd mll flu h ul f h lul. h mhml fu f mmz w fmuld h blu dff (L1 m) bw h mlud f bvd d yh gl, dg h l f u. h fu w mlzd uh wy h h mxmum vlu (1.0) dd qul mlud d l f h bvd d yh m wv f ll m, whl h mmum vlu (0.0) fld f f. A md vlu my b d ughly f bvd wv h bdly mdlld. A mf f 0.17 my, f xml, b dv f ml dgm bw bvd d yh d (qul mlud bu l) f 17 f m wv d f gm f h mg 83 f h wv. A mul f h wvfm w d f h md mhm. h muld wvfm w md wh h dd. Al f lw- fl blw h fquy bh yh d bvd wvfm vdd vldy f u xm. F bh h u v d wvfm mdllg, h mdum w umd b f d hmgu. Ily w k u by m f (fquy-dd) Q f. Fgu 2 dm h mhm f h lg v h d ug h dd bh-bll. h f h u-- h f ud h mhm v hw h OAL lw hmhl j. h (ISO) d dv (DEV) m l dlyd. h m qu lg h d f gv g, mlyg gf mlv -m dfm h u. Ah mkbl fu h ly vl f h x ( f 'wh' f h DEV bh-bll). h bvd wvfm md wh yh luld f h vd mhm h lw f Fgu 2. h gm bw bvd d yh gl bl h l d mlud f h dd l mul h - d S-wv mdlld ly f m f h, ulg mf f h l gl (d f - d S-wv, fl fm h h uf) dbly dud h yh wvfm hy fl wh h um f ml u d f hmgu mdum. h mm lu f mll z v hw Fgu 3. A h vu, h bd mhm h gf mlv m d x. h quly f mdllg f h bvd wvfm h b w (lw f f Fgu 3). h mlud d l f h -wv ly mdlld f m f h, whl h S-wv dud ly f ly m f h l (ld wh bu m f h u). h mf 0.18 h. OAL = 0.70 ISO DEV Suh W Dw Obvd Syh 007 (33 Lvl) 210 m 104 (35 Lvl) 510 m 003 (29 Lvl) 950 m 009 (31 Lvl) 1030 m 006 (Suf) 1290 m 010 (31 Lvl) 1680 m 105 (28 W) 2190 m 040 (32 lvl m) 3530 m 037 (26 Lvl) 4030 m 071 (dk) 4550 m 038 (Suf) 4820 m m [] m [] m [] Fgu 2 h bh-bll f h mhm f h lg (mw 2.5) m v dd Nvmb 2009 (). Syh wvfm f h mhm md wh dg bvd gl (bm). Obvd wvfm dlyd blu, whl yh d. S d, m, d hyl d hw h gh f h wvfm. Avl f - d S-wv kd ug -fld wvfm vulzd vl gy l h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 112 JUNE

4 Mhm f lg m v lum m f h Buhvld Cmlx OAL = 0.42 ISO DEV Obvd Syh Suh W Dw 009 (31 Lvl) 660 m 033 (29 Lvl) 1030 m 007 (33 Lvl) 1490 m 003 (29 Lvl) 1930 m 104 (35 Lvl) 2130 m 006 (Suf) 2300 m 040 (32 lvl m) 2250 m 037 (26 Lvl) 2480 m 010 (31 Lvl) 3200 m 105 (28 W) 3580 m m [] m [] m [] Fgu 3 Bh-bll f h mhm f mdum z (mw 0.7) m v dd Dmb 2009 (). Syh wvfm f h mhm md wh dg bvd gl (bm). h vulz d h m Fgu 2 Uy f h mm v A w hw h xml bv, h vd mhm mlv m. h m qu whh h f h m h lu gf, whh uld b f f h v du. h dd mm v du gv ly gl b lu. Dff f ( wk vg, u l, kg f - S-wv vl) llw h bly h h mhm uld du h bvd l d mlud f m wv wll. A ml hqu w ld ly h uy f mm v l h f h m. h 6-dml f bl mm (dg h x m f h mm ) w mld d hu gf ul (~ ml) f bl mhm w d. All h mhm (mm ) w d m f h bly du h mlud d l f h bvd m gl. A u y l ffd by Hud l.6 w fud b uful f h vulz d f h ul. Exml hw Fgu 4 d 5. h u y l dly mhm dg h vlum hg (lg h vl x) d dv fm dubl ul (DC) u (lg hzl x). N h h l vulz ly w dm f h 6-dml f mm. F, gl l f h l lud ll DC u vy f f h ful l d d f l v, lu dvy f l m mm. h dl f h u y l dbd h vvw7. Su y: bbly Exl 0.00 Dv 0.03 bbly Dy Fgu 4 Su y l d l f m h u (bl, l d h kg, vy ll) wh. Dm f h qul ( Exl, Dv, d Iml ) hw. Clug f h l fl bbl f u mhm f h v d Fgu 2. h m bbl mhm wh h Iml Iml JUNE 2012 VOLUME 112 h Jul f h Suh Af Iu f Mg d Mllugy

5 Mhm f lg m v lum m f h Buhvld Cmlx V B V A (b M, Mf = 0.18) V B (Mf = 0.22) V C (Mf = 0.20) Su y: bbly V C Exl 0.06 Dv 0.35 OAL = 0.14 ISO DEV OAL = 0.58 ISO DEV bbly Dy Iml 0.59 W dm h l f h hqu wh h v hw Fgu 2 d 3. h u y l f h f (lg) v (Fgu 4) h lu f hghly bbl mhm wh h Iml g. h bbly f mhm fm h Dv d Exl g qu lw. h d h mm lu hw h f Fgu 2 wll d m f f mlv m, h bd mlv m uld b dd gf. h fld h quf f bbl: 0.97 bbly gd h Iml u y, whl ly 0.03 gd h Dv, d h 'Exl' y (Fgu 4). h u y l f h d (mll) v (Fgu 5) h bd f bbl mhm dg lg 'Dv' d Iml g. h d h bd h vd ( B M ) mhm, vy f h lu (f V B d V C dlyd h fgu) l gm wh h dd m gl. I h h fd f h mlv m l h f h vu (lg) v h bbly f h Dv y f h m d bbly f h Iml (0.35 v Fgu 5). Fgu 5 Su y l f h v hw Fgu 3 dlyd h. h f h dff lu h l mkd by w: h vd mhm (V A), dv mhm (V B), d mlv mhm (V C). Bhbll f v B d C hw blw h g hmb h f h l h ul f l dg d h f h l l bbl f h mhm. h mk bl fm ufm mlg h f h x f h l d lul h bbl f dff u y dg h. h u y l w dvdd h qul- g (Fgu 4 d 5): h u g d xlv u (.g. bl), h mddl h dv u (.g. h flu), d h bm mlv u (.g. ll bu). h uml g (umm) v h g gv h bbly f h u. I ummy, h ly f h u mhm uy f h v vlvd h : Mug mlud d l f - d S-wv (h m f h dd mm v) g f ~ bl mhm g h mud mlud d l, d lg h wh h hgh bbl dvd fm h mf h u y l (ml h hw Fgu 4 d 5) Quf f h bbly f h Exl, Dv, d Iml by m f umm f h bbly d dg f h l. Rul h du f mm v d u y uy m w ld ll h ld v. I w fud h h vwhlmg mjy f v mlv m (ml h ml hw Fgu 2 d 3). h ly f u f h lu fm h h fu gf h dbu f bbl f h u y (Fgu 6) d h: Oly fw v hv gf xlv m. h v (wh x) l hv gf dv m, whh d h h xlv m my b fl h Dv y m mm 28 v (9 f h l umb) hv hgh bbly f bg h Dv y. I gl, h v ld fuh fm h f h h v h mjy f v f h Iml y. Numb f v Exl Dv Iml bbly Fgu 6 Hgm f h u y bbl f h lyd v. h f b (f h xmly ulkly mhm) l h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 112 JUNE

6 Mhm f lg m v lum m f h Buhvld Cmlx Aly f ul ll flu Obv I h w bfly db fu m v f whh udgud fm llwd ul ll b dfd h lkly u. O 27 Augu 2009 vzd (~ 5 5 m2) uh ll dymlly fld f h d lvl f f h m. h ll dwll w jd h gully d h f d f ~3 m (Fgu 7). h wk dd m v wh mm mgud 1.6. h v l u bh h h- d d h d ml h l f h udgud, whl h fld ll d h 95 l fd g (Fgu 7). Fv dy l ghbug ll f ml z l fld ml fh (Fgu 7). h m m W 1.8 m v hd b dd. A h vu, h l f h m u u wh h fld ll, bu d xlud h. h lg f h fu v, m W 2.5, ud h ghbug m Nvmb I h gf kbu dmg ud lg h dwll f hulg, d 18 m blw vzd uh ll lll h ul (Fgu 8). Svl m f h dwll w hd, d u 2 m f bk k w jd lg l f wk lll h d ju bv h ul (Fgu 9). O f, h uud f h ll l hwd gf dmg. A l 100 mm dym lu w bvd uhd k x h ll (Fgu 10). Bk k fgm fm h ll vd fm vy mll h uld b d u lk g (Fgu 11) f-zd d lg. I h h ll hd dubl ff h ul. I h f l, h f h ll d xmy h ul ud mlu h ul. Sdly, wh h ll fld h fld dym ld h ldy d ll dwll ud h bvd dym flu (Fgu 8). h l f h u f h Fgu 8 l f m lyu h f C 3 (). L uy f h mw 2.5 v Nvmb 2, 2009 (blw) lw h h. h fld ll wh h 95% fd g f h m u l Fgu 7 l f h f ll flu f C 1 d 2 (). h w hw h d f ll dwll j, d dk hdd m fl h dymlly jd. Iuf f h l fd g f h mw 1.6 v Augu (bm). h mw 1.8 v dd Smb h l fd g f ml h. Bh 95% d 68% fd g lud h fld ll, bu h m m vy f h ll, bum, d glgl fu l vd. h d h l f h m u d vd umbguu f h v wh h ll flu h udd Fgu 9 C-m dmg ubby lg h uh dwll f h ul 18 m blw h -f ll hw Fgu 8 (C 3) 424 JUNE 2012 VOLUME 112 h Jul f h Suh Af Iu f Mg d Mllugy

7 Mhm f lg m v lum m f h Buhvld Cmlx d ( f h xd f h k ud m f h lgh h bk wy - Fgu 14) h hggwll bv h gully w b lg h d f j,.. lll h lg h l f wk. h v f h gl bkwd wd h ll. Fu bvd h mg ll h E2 l ugg h ll w fld hughu. Fgu 10 Cuhd k x h ll h fld (C 3). l dym lu xdd 110 mm Fgu 11 Cmmud Mky Rf llug dym flu f h ll C 3 Fgu 12 l f h f ll flu f C 4 (). h w hw h mud d f ll dwll j. h hdd d h ll mvd dug uml mdllg ( Fgu 15D), d dk hdd m fl h dymlly jd. h lw hw h l uy f h d mw 1.9 m v Mh m v qu bl (Fgu 8). h 95 l fd g d 250 m h vl d, 170 m h h-h- d, d 80 m h -uh- d. h fld vzd ll wh h g. h fuh h f m W 1.9 v 27 Mh 2010, dd h m m C 1 d 2 dbd bv. A dym flu f uh ll ud wh h v. Sgf dmg ud h E2 l f d v dmg h gully x h ll h E1 l (Fgu 12). h dmg w h fm f bk k, wh fgm z vyg fm h m l h m l, wh m fgm bg bw 100 d 1000 mm dm. mb h bk f h E1 l h fld ll hw dym hg f u 130 mm (Fgu 13). h hg w h d ml h l. h ll dwll w jd lg l f wk whh llly fm h hggwll. h j mhlly d h (w xd) l f wk lvg l, fh lll h d f j. h kd Fgu 13 Buklg f mb lg wh h mld d f dym lu. Clu f u 130 mm w mud whl h l vg w ~20 mm dd by uml mdllg h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 112 JUNE

8 Mhm f lg m v lum m f h Buhvld Cmlx mdl, d h dff ( u(x) = u(1) (x) u (0) (x) d (x) = (1) (x) (0) (x)) w ud f h mu f h hl mm dg h x d h Adx. h hzl z f h u bx w h lg ugh vd mll mlud f u(x) d (x) v m d d ub-uf. I uh h flu f h bx d h mm uld b gld. lud fuh w lud Fgu 15 hwg, f h fuh udy, h lv l, d. Fgu 14 Ej f h ll dg (C 4) lg l f wk h hggwll. h kd d ulld h d f j, g h m d l (wh w) lg h l f wk h l f h u f h m W 1.9 m v u (Fgu 12), bu h dmg w bvd h gl f h f h v wh h fld ll bl. Mdllg f h u mhm h bvl dbd bv wh h hyh h ll flu dm m f h u f h dd m v. quvly vfy h, mdllg f m mm f h bvd ll flu w d ug budy-lm mdllg l. h w m h gmy d mgud f h mdlld mm wh h dg h f h bvd mm (.. vd fm h dd wvfm dbd vuly). El mdllg w fmd f h f h dd ug h -hu dvld d (Igd S S Mdl - ISSM). I h h mdl k u: Rgl (10 10 m2 ll z) md u f Mky Rf f h w m dd Vg ud by h m k mh. h ludd mlu K- wh h mj l bg ub-hzl. Dld (dw 1 1 m2 ll z) mg gmy h m f h lyd ll flu uudg (wh du f ~150 m). w v f h mdl w dd wh h ll (l ) d whu (fl ). h fld (mvd) ll w ld by bx wh d bm uf lyg lll h f 11 m bv d blw, vly. h h bx lyd h l f h u vlum (vlum V wh budy hw h Adx). h dbu f l dlm ((u(0) (x) d u(1) (x)) d ( (0) (x) d (1) (x)) v h d bm uf f h u vlum w luld f l d fl v f h Rul Cm f h mdllg ul wh bh udgud bv d m d ummzd bl I. h mu f lu mud udgud d l vg dvd fm h l mdl f h l d fl (wh d whu ll) hw h lum u mx. F ll h bvd lu muh hgh h h l vg. h xd ul h fm vlv l fug f k ud h xv, whh k u h l mdllg (.g. Fgu f h hdbk8). Cm f h yh mm (.. dvd fm h uml mdl) wh h bvd mm (.. vd fm wvfm f m v) h my. O h z f h u xd h m f m mm M mm mgud m W. Oh ld h gmy f h mhm. ully qufy h mlv u f h ll flu mhm w ud dd mu f vlum hg f h mm 7: Fgu 15 Fu l vw d xl h uml mdllg f C 4. Fgu 15A hw h mdl f h gl m l, d Fgu 15B-D uv zm-. Fgu 15C d D hw h u f mdl vg f h mvl f h ll (hdd Fgu 15D). A hugh h mdl hw Fgu 15E h dlm fl bv d blw h ll gly xggd h, h mxmum mdl dlm bg 10 mm 426 JUNE 2012 VOLUME 112 h Jul f h Suh Af Iu f Mg d Mllugy

9 Mhm f lg m v lum m f h Buhvld Cmlx bl I Cm f h bvd m u mhm d mdlld ll flu u mhm O f h l x f bh bvd d yh mhm my b md by m f h l wh hyhl xd mm (CLVD) M j. h l db h dv m f h dlzd ll flu whh h vg ly h d ml h f ( f Fgu 16),.. h d gld. Suh dlzd mhm wll hv h mj l x f gv g (mv) d hgl h f, whl h h w l x f h m v (dl) mgud d ld wh h f l ( f Fgu 16). h mly bw h dv f h bvd hl mhm M j d h hyhl xd mhm (DEV) M j w qufd ug h mlzd l ff: wh M j (DEV) h dv f h Mj. *Clu f h bv, d l vg f h mdllg wh M (ISO) h mlud f m f h f h mm, M (DEV) h mlud f h lg l m f h dv f h mm. Fgu 16 Mm d wh dlzd ll flu bul m: f mj d m l x f h mm lv h bdy (), dm f h mm () d bh-bll f h mhm (bm). h dlzd mhm d lg k mdl, whh v f h l k mdl dbd h mgh by Ak d Rhd 9. N h dm mlv m d dv m. h l qul h u Cmd L- V Dl (CLVD) mhm h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 112 JUNE

10 Mhm f lg m v lum m f h Buhvld Cmlx A fm bl I, h l m mm f h mdlld u m hgh h h md hugh mlgl g. h m h dym h (mlud) f h dd m wv my b xld by h mdlld ll flu ly. Ovm f h bvd M vlu gv m f h ug f h mdl. F, mdllg f l (d f ml) mvl f h ll huld d h hl M vlu, dug h dff bw h mdlld d md mm. N, hwv, h h d f h mdlld h mlglly md m mm ully vy gd. I u h ll flu mhm h m bu h dd lw-fquy m wv. h gml h f bvd d hl mm gm fllw: Sgf mlv m h lu. h vlum hg k lwy gv d f h m d h dv m kh dfm wh ub-vl x (wh h x f h bvd mhm f h Augu v). h f h hyhl mm M j (CLVD) (fld hgh vlu f h l ff S ). h g-h y f dfm f h Augu v my b xld by -uqu f h v ml h hw Fgu 5. Clu h v f lg umb f mm f v f dff z (fm m W 0.5 m W 2.5) dd w lum m h Rubug 2009 h hw h h mlv m dm h u mhm f h mjy f h v. A ly f h u f h mm v h fmd h gf f h ul. Fu f dym ll flu w vgd dl. I h h bvd dmg, gml m f h ll, d lu hv b dumd. A l mdl ug f h md-u f h m f h flu w dvd. ll flu w mdlld by mlly mvg h ll fm h mdl. h ulg l dlm d hg w vd hl mm. I h h mgud (l m mm) d gmy ( bw d dv m, h, d f h dv m) f h hl mm gl gm wh dg h f h bvd mm (.. vd fm h wvfm f m v ld wh h ll flu). h ul fm h dym flu f ll my b h gl u f lg d mdum z m v dd h m udd. Hwv, h bly f h u mdl xludd. F, h flu h xmy f h f (wh f f h lyd m wvlgh,.g. ~10 m f mll v d ~50 m f lg v) uld l b dbd by mm wh mlv m. Ll-l m bv g h vl d f m u huld b fuful dm bw h w mhm (ll flu d h flu h vy f h f). I g dff bw h u mhm h lum m d d-lvl gld m f h Wwd. M f h lg d mdum z m v dd h gld m hv dbl dv m h mm 10. h gmy f h m ( f dl l d l x) mk glly bl h v h wh h fu f k hd f md-u l (Ol h) wh l glgl uu. Akwldgm h wk h b d f ISS Il Ld lf-fudd h j Ru Mdllg f Sm Hzd. W hkful h k g f h m udd f gzg udgud v vg h ll flu. h du f h wh hm w g d fuful. W x gud Gy B d Hm Rb fm ISS Il Ld d h Iu f M Smlgy f h mdllg wk. Rf 1. MCGARR, A. Mm f Wwd m m. u d Ald Ghy, vl. 139,. 3/4, VAN ASWEGEN, G. d MEIJER, O. h mhm f m v ud ful m. dg f h Il Cf Euk 94, SILENY, J. d MILEV, A. Sm mm lu ll l: Smuld kbu d m-dud m v h Kg gld m, Suh Af. u d Ald Ghy, vl. 163, JULIA, J., NYBLADE, A.A., DURRHEIM, R.J., LINZER, L., GOK, R., DIRKS,., d WALER, W. Su mhm f m-ld my, Svuk M, Suh Af. Bull f h Smlgl Sy f Am, vl. 99, AREF, K., SOISWOODE, S.M., d JAGER, A.G. A m f my w m h Buhvld Igu Cmlx ug dff ll ym. dg f h Il Wkh Ald Rkbu Rh, Sg, Chl, My HUDSON, J.A., EARCE, R.G., d ROGERS, R.M. Su y l f v f h mm. Jul f Ghyl Rh., vl. 94(B1), JULIAN, B.R., MILLER, A.D., d FOULGER, G.R. N-dubl-ul hquk. 1. hy. Rvw f Ghy, vl. 36, JAGER, A.J. d RYDER, J.A. A hdbk k gg f bul hd k m. Sfy M Rh Advy Cmm, Jhbug, AKI, K. d RICHARDS,.G. Quv Smlgy: hy d Mhd. Uvy S Bk, Mll Vlly, Clf, REBULI, D. d MALOVICHKO, D. Sl-y v fu-y m v - g h dm f m Wlkm. SANIRE2010, Nhw Bh. Suh Af Nl Iu f Rk Egg, Vllg Club, W Lvl, 14 Ob 2010,. 428 JUNE 2012 VOLUME 112 h Jul f h Suh Af Iu f Mg d Mllugy

11 Mhm f lg m v lum m f h Buhvld Cmlx Il (bf h flu) Fgu A1 Sl f 'h u vlum' f ll flu Adx Sm mm f ll flu Sm d fm y dym d m vlum V my b mlly dbd ug h m hy f dlm d v h budy f h vlum. h w ul f l f V d : Bhvu f h mdum ud h umd b l h z f V mll h h wvlgh f m wv ud f mlgl ly. h lw-fquy f m d uld b dbd ug dff/d dlm u(x) d (x) h bw l d fl. h quvl umg -lk bhvu f dlm d m h,.. u(x, ) u(0) (x) + u(x) H() d (x,) (0) (x) + (x) H(), wh H() Hvd fu. I h f ll flu h l f 'h u vlum hw Fgu A1 my b ud. h mm luld fm h u(x) d (x) dbu h 1: wh (x) h wd ml h, ξ (0) h d h ( f V my b h), λ(x) d µ(x) h Lmé l mdul, δ j h Kk dl. Eum h d h Sl Sud Ed f h SAMM Jul, vl. 112,. 4, , ld Iflu f gdlum h muu d mhl f l d l l, by Z. Kh. h uh md lud h -uhʼ m. h -uh huld b ld fllw: Z. Kh Shl f Chml d Mllugl Egg, Uvy f h Wwd J.W. v d Mw Shl f Chml d Mllugl Egg d DS/NRF C f Exll Sg Ml, Uvy f h Wwd d A. K Advd Ml Dv, Mk. h Jul f h Suh Af Iu f Mg d Mllugy VOLUME 112 JUNE