ELECTROSEISMIC AND SEISMOELECTRIC MEASUREMENTS OF ROCK SAMPLES IN A WATER TANK

Transcription

1 ELECTROSEISMIC AND SEISMOELECTRIC MEASUREMENTS OF ROCK SAMPLES IN A WATER TANK Zhny Zhu, Dn R. Bun, nd M. Nf Tköz Eh Ru Lby Dpmn f Eh, Amph, nd Pny Sn Mhu Inu f Thngy Cmbdg, MA 0139 ABSTRACT An mgn wv m wv n ndu m wv du h kn nvn bd n h dub y n fudud pu mdum. In h pp, w bv h u fd gnd und h d xd by n pu n w nk. Th m m wv mud n h w nk ym nfm h h dd m gn ndud n pu mp du h kn nvn. Th m nd m fquny-pn n B ndn nd Wy gn mp mud fquny ng f 15 khz 150 khz. Th xpmn mumn hw h h ff f h u, bkgund n, nd m m nvn pd vy y. W u h m nd m nmzd upng ffn n h k mp nd mp hm wh h h un. Th vn nd f h nmzd upng ffn n gmn wh h h pdn. Th mumn mhd n h pp ud b ud nvg h m nd m pp f pum xpn ppn. INTRODUCTION Th n dub y n h nf bwn d nd fud n fud-ud pu k (Mgn. (1989); Pd (1994); Pd nd Hn (1996)). Whn h fud n y, h mvb f hg. Whn m wv ppg n fudud pu k, h m wv gn v mvmn bwn h fud nd k mx. Cnquny, h mvng hg ndu n fd. Th fd w b n mgn wv whn h m wv ppg n nf whh n nnuu n u,, mhn pp (Mkhv. (000); Zhu nd Tköz (003, 005)). Th p d m nvn. On h h hnd, f h n fd n h w n h fud-ud pu k, h mvng hg n h fud u fud mvmn. Th v mvmn bwn d nd fud gn m wv. Th p d n m nvn. Th m nd 1

2 m nvn d h fud nduvy, k py, pmby, p z,. Sm nd m mumn md n Eh uf n bh my pvd nfmn bu h ubuf pp (Mkhv. (1997); Zhu nd Tköz (005)). Em by xpmn (Zhu. (1994, 1999); Rpp nd Mgn (00)) wh d yd nd bh md hwd h m wv ndud wh d bud n fud-ud fmn n bh. Dkmn. (005) dmnd h m upng ffn wh mp mumn n h by. Fd- m mumn (Thmpn (005); Thmpn. (005)) dd pb umun f nu g g. Th u dmnd dmnn f g nd dph f hn 1000 m. Rpp nd Mgn (00) udd h h fquny dpndny f m nvn n pu mdum nd dvd h fquny-dpndn m vg upng ffn: ( P(,) *+) & J # & # 1( ) ) J1( ) ) = $! $ ' 1! (1) ( V (,) % J () ) " % ) J () ) " wh % "# $ =! wh ΔP(ω) nd ΔV(ω) h m pu nd vg ngu fquny ω, ε h d nn, ξ h z pn, h p du, J h B funn, ρ nd η h fud dny nd vy, pvy. Th hy hw h h fquny-dpndn bhv f h m nvn funn f h p z. Th m nvn fm ngy m ngy d m mpn pp f h pu mdum, nudng p z, pmby, nd fud pp. Sud f m nvn mgh pvd nw mhd xp fmn pp wh nw pm dffn fm dn m uvy n w ggng. In h pp, w f bv h u fd gnd und d xd by hghvg pu. W hn mu h u fd wh nd whu k mp n w nk nfm h h m gn gnd n h pu mp. W mu h m pn n ndn nd gn h fqun f 15 khz-150 khz nd u h vg upng ffn. In h m mumn ym, w mu h m nvn n h k mp. Th mud m nd m nmzd upng ffn mpd wh h h un. ACOUSTIC FIELDS AROUND THE ELECTRODES T ndu n fd n fud-ud pu mdum, h d mu b n n wh h fud. Whn hgh-vg pu nnd h d, u wv gnd und h d du h hm ff ndud by h un nd hmdn f w mu. Th phy mhnm nvvd m ghnng nd

3 d hund dung m. Bu h ff ndud by h un fw n w, h u wv n d h hp nd m f h d. W bvd h u wv gnd by h ng d n m w nk n u by. Th xpmn up hwn n 3-D dgm (Fgu 1) nd n pn vw (Fgu 1b). Th ng d md fm b w wh 1. m nd dm nd 1.5 m ud dm. Th mvmn png f h hydphn (B & K8103).0 m/. Th u 500 V qu pu 6 µ n wdh. Fgu hw h u wvfm dd h hydphn mv ng h dffn dn wh p h d (n A, B, nd C n Fgu 1b). Fm h v m nd h wvfm vn n Fgu, w nfm h h w dffn f u wv gnd by h pv nd ngv d, pvy. I hud b nd h whn dng h wvfm, w u m dy vd h nfun xd by h u pu. Th mpud f h nfun bu 00 m hgh hn h u gn f n. N h h f v fm h pv d (Fgu ) ng hn fm h ngv d (Fgu b). Bu h w nk m, nnd gund wh n n hugh h p m h hd qupmn. Thf, h fd und h pv d hud b ng hn h und h ngv d. I mpn n h un ndu n u wv n fud, whh, n gn, n m nvn bwn nd u ng. I vy mpn phnmnn b w f n m mumn, n h ff my ng hn h gn f n h d fud mvmn n h p p. In yd md, w bv h m gn gnd und h d nd h nf du h m nvn. Fgu 3 hw yd md wh pxygud nd nd Lu bk. Fv f w d bud n h nd dffn dph. Eh d h w d h m dph wh.0 m png. Th f f d h nf bwn h nd nd Lu bk. Th d xd wh qu pu f 500 V n mpud, nd P wv ndu d h m wv h bm uf f h Lu bk. Th d nd md mmd n w nk. Fgu 3b hw fv u wvfm dd by h ndu whn h pu nnd h d dffn dph. Fm h v m n Fgu 3b, w h h w knd f u wv, ndd by w w. Th f wv v h m m (n h m f m 0.05 m). Th nd wv h hgh mpud, nd v vyng m. Th f wv wh h m v m n u wv gnd h nf bwn nd nd Lu du h m nvn. Bu h fd ppg muh f vy hn n u wv, h ppgn m fm h d h nf n b gnd. A f h m wv nvd h nf, ppg hugh h Lu bk P wv vy, nd hn dd by h ndu. Thf, f h wv v h m m f m, whh h v m n h Lu bk. Th nd v n Fgu 3b h dffn v m dpndng n h dph f h d. Th h nf h d, h h u wv v. Fm h v m w knw h h u wv gnd und h d, ppg hugh h w-ud gud nd nd h Lu bk, nd hn v h Lu bk' bm uf. Th xpmn u nfm h h w u 3

4 wv du m nvn. On ndud und h d nd hn ppg m wv n h md. Th h n nvd h nf bwn h nd nd h Lu bk. Bu h ffny f m nvn n nf w, h mpud f h nvd m wv wk. I vy mpn p h w m wv n ny uf m mumn. Th ppgn f h m wv gnd und h d h m h dn m uvy. ELECTROSEISMIC SIGNALS GENERATED IN POROUS ROCKS W nx nvg m gn n pu k mp n h w nk. Th mumn mu b md n g nugh nn p h m wv ndud n h k mp fm h wv gnd und h d nd ny fn fm h nn w. W ppy ng n bu wh hgh vg (150V-180V) h u. Th n fquny f h u v fm 15 khz 150 khz n d nvg h fquny-dpndn f h m nvn n k. Th hgh vg u w nfun h wk m gn dd wh hydphn. If nnuu n wv w ppd h u, hwv, h nfun wud b ng w x n h m gn f n. Fgu 4 hw h w-nk mumn ym n u by. Th d md f v mh 5.5 m by 5.5 m wh 50 m png nd d n h mdd f h nk. Th pv nd ngv u d nn h upu f pw mpf pvd h u gn. A hydphn (B & K 8103) d bhnd h ngv u d vd h nfun f h pv u d n h hydphn. Rk mp.5 m hk pd n h pv u d. Tw p pn mumn d (V+ nd V-) pd n h w d f h mp d h vg h mp. Th p-w nduvy und ms/m. Th dn (n hwn n Fgu 4) fm h hydphn h d f h w nk bu 9 m. Fgu 5 hw h u fd n h mumn ym dffn n fqun whu ny k mp. F, w d h ng u nfun, wh n fquny v wh h u fquny nd wh mpud muh g hn h h gn. Fm h v m, w n dmn h h h u v gn fm h pv ngv u d w h fn fm h bk d w (hwn n Fgu 4). W p h dffn mp h pn hwn n Fgu 4 nd d h u fd gnd by n pu wh 100 khz n fquny nd 150 V n mpud. Fgu 6 hw h u wvfm wh Lu, Aumnum, B ndn, mn, nd Cnn ndn mp, w wh n mp. Th pm f h m d n Tb 1. Th d wh n mp pn hwn, nd h u wv gnd by h pv nd ngv d n b n ( 1). Fm h h, w n h h wv gnd und h pv d v hn n 1 bu h P-wv 4

5 v f h mp hgh hn h w vy. Th mpud dpnd n h nmn ffn bwn h mp nd w. Aund 0.16 m (Fgu 6), w bv h m gn n 4, 5, nd 6, ndud n h pu k mp du h m nvn n h pu k. N gn und 0.16 m dd n 3 nd 4 bu Lu nd umnum nn-pu nd mpmb m. Tb 1: Th pm f k mp Smp nm Dny (g/m^3) P-vy (m/) S-vy (m/) Py (%) B ndn Cnn ndn Lmn Wy gn In d nfm h h u wv dd 0.16 m h m gn ndud n h k mp by m nvn, w p h B ndn mp bwn h u d nd mv h mp wd h pv d (Fgu 7). Fgu 7b hw h u wvfm whn h mp mv nmny. W n u h v m f h m gn fm h gmy f h mumn ym. Th mpud nd v m f h m gn vy ny wh h mp n. Th h png bwn h mp nd h pv u d, h hgh h mpud. Th ppn vy ud fm h p n h wvfm v h w vy f 1480 m/. Th d n nd nk fn d n hng dung h mp mvmn. Th xpmn nfm h m gn n b ndud n u mumn ym nd pd fm h u wv und h d nd h nfun f h u. W my ppy u xpmn ym mu h m nvn wh h dffn k mp nd u h m vg upng ffn. Th fquny dpndn f h vg upng ffn mgh b ppd udy h p z f h k mp. ELECTROSEISMIC VOLTAGE COUPLING COEFFICIENTS W ndu h m mumn n h w nk ym (Fgu 4) wh B ndn nd Wy gn mp. Fgu 8 hw h m wvfm dd wh ndn (Fgu 8) nd gn (Fgu 8b) und h m nmzd. In h d, h nfun f h u nudd hw h u fqun nd h hgh mpud mpd wh h m gn. In Fgu 8, h u wv dd bwn 0.3 m 0.4 m ndud n B ndn du h m nvn. In Fgu 8b, h nvn pdu wk gn hgh fqun du h py nd pmby f Wy gn bng muh w hn ndn. Fgu 9 d h u gn h mp f B ndn (Fgu 9) nd Wy gn (Fgu 9b). Th mpud f h fd h mp dffn, bu h v ph dn. Th mn h h f h k mp 5

6 quvn pu n. Th ph hf f h wv dffn fqun du h ph h f h pw mpf, whh pvd h hgh vg u. Whn w mu h m gn n Fgu 8, h gn p hugh 60-dbpmpf. W n dmn h fquny pn f h pmpf wh ndd funn gn nd dg p. Thn w my h mpud dd n Fgu 8. Th mpud (ΔP(ω)) f h m gn nd h vg dffn (ΔV(ω)) h mp n b dmnd fm Fgu 8 nd 9, hn w u h m vg upng ffn (ΔP(ω)/ ΔV(ω)) h dffn fqun. Fgu 10 hw h nmzd m vg upng ffn n B ndn (Fgu 10) nd Wy gn (Fgu 10b) fqun f 15 khz 150 khz. In h fgu w hw h h u ud by Eq. 1, umng h p du f ndn nd gn 80 µm (Fgu 10) nd 0 µm (Fgu 10b), pvy. In h h un, 3 ρ 1000 kg m, ξ 80 mv, nd η f w vy 8.9" 10!4 P. Cmpng h xpmn u wh h h un, w h h vn nd f h m vg upng ffn dn. W w h pk n h xpmn upng ffn (ΔP(ω)/ΔV(ω)) dffn fqun (Fgu 10). Th p z n k n ng vu. Th w h pk n h upng ffn ky du h dffn dbun f p z n h pu k. SEISMOELECTRIC SIGNALS GENERATED IN POROUS ROCKS Bd n h pnp f h m nd m nvn, w knw h w ff vb. An un n ndu m wv n pu k mp. A m wv n ndu fd n h m k mp. T bv h vb phnmnn, w ndu h m mumn wh h m up n h w nk nd wh h m k mp. Fgu 11 hw h up f h m mumn. A pw hydphn (Md LC-34, C Ind., In.) ud f h u u nd xd wh h m ng n bu pu h w ppd h u n h m mumn. Th h hydphn (B & K 8103) n h k mp d h u fd und h mp. Tw pn mumn d d h vg (V1 nd V) h mp, whh ndud by h un du h m nvn n h mp. N fd n b ndud n w nk f h n pu mdum. Hwv n u xpmn, vn whn h n pu mdum n h w nk, h mumn d d n nd h nn f h hgh-vg u wh h n qupmn n h by. Fgu 1 hw h ung gn whn h u hydphn xd by h ng n bu h dffn n fqun wh k mp pn. Th h bkgund n n u m mumn ym. W d gn gnd wh h dffn mp, whn h u hydphn xd wh n pu wh 100 khz n fquny. Fgu 13 hw h u fd n h mp ( 1), h fd whu ny mp ( ), nd h fd wh h mp f Lu p ( 3), umnum p ( 4), mn ( 5), nd B 6

7 ndn ( 6). Th u wv ( 1) dd by h mumn hydphn (B & K 8103). Th gn dd wh h mumn d (V1). Cmpng h gn n -6 wh h u wv ( 1), w nn ny m gn n h Lu nd umnum mp ( 3-4), bu w gn n 5-6, wh v m h m h u wv n 1. Th mumn hw h m nvn n pu k mp. Nx w ndu m xpmn nfm h h gn ndd gnd by h u wv n h k mp. Whn h B ndn nd h d mv n h w nk (Fgu 14), w d h gn wh n (V1) f h pn mumn d (Fgu 14b). Th mpud f h gn n Fgu 14b mn nn wh h ppn vy qu h w vy f 1480 m/. Bd n h v m nd h dn bwn h u hydphn nd h k mp, w nfm h h gn gnd by h u wv ppgng h k fwd by h m nvn n h k mp. W mu h m gn n h B ndn nd Wy gn n h ym hwn n Fgu 11. Fgu 15 hw h u fd n h B ndn (Fgu 15) nd Wy gn (Fgu 15b) gnd by h u hydphn h dffn fqun. Fgu 16 hw h gn dd wh h mumn d V1 (bu) nd V (bk) h B ndn (Fgu 16) nd Wy gn (Fgu 16b). W d h ng nfun f h u bf 0. m n Fgu 16. Th ph f h nfun h mp dn, nd h mpud ghy dffn. Th m gn f V1 (bu) nd V (bk) dd und h v m f h u u wv (und 0.3 m n Fgu 16 nd und 0.6 m n Fgu 16b). Th m gn dd mp n fquny hv h m mpud nd h pp ph. Th phnmnn hw h h gn ndud nd h k mp du m nvn. Th pu k quvn n u wh h m pn nd pp pzn h k, nd gnd by h u fd vyng fqun. Bu h py f h gn mp (0.8%) muh hn B ndn (19.9%), h mpud f h m gn n h gn wk hn n B ndn. Bd n h u mpud (ΔP(ω)) n Fgu 15 nd h mpud f h m gn (ΔV(ω)) n Fgu 16 h dffn fqun, w n u h nmzd m upng ffn (ΔV(ω)/ ΔP(ω)). Fgu 17 hw h m upng ffn n B ndn (Fgu 17) nd Wy gn (Fgu 17b) n h fqun fm 15 khz 150 khz, gh wh h h u ud wh Equn 1. Th xpmn u wh B ndn n Fgu 17 hw h m vn h h upng ffn. Th m dffn bwn h xpmn nd h u n Fgu 17b du h m mpud f m gn. 7

8 CONCLUSIONS Bu n u gn gnd by h un und d, vy mpn p h u wv fm ny m gn d pu mdum mumn. W h bkgund n n h mumn ym, nd pu h dffn mp vy f dn fm h u nfm h h dd gn bd n h m nd m nvn. Th m nd m gn n b ffvy pd fm hug u nfun nd h bkgund n. W nvg h m nd m nvn n dffn k mp wh u w nk mumn ym n h fquny ng fm 15 khz 150 khz. In h m xpmn, h fd gnd by ng n pu ndu m wv n w-ud pu k mp. In h m xpmn, h m wv gnd by hydphn xd wh h m ng n pu ndu n gn n h mp. W mu h fquny pn f h m nd m nvn nd mpd hm wh hy pdd upng ffn. Th mumn u hw h pb nhp bwn h p z nd h fqunydpndn upng ffn. Th xpmn nd mumn ym pvd mhd fuh nvg h pp f m nd m nvn n k mp, uh h nhp bwn h nvn nd fud nduvy, mpu, PH vu,. ACKNOWLEDGEMENTS W wud k hnk Pf. D. Mgn nd D. P. Rpp f h vub uggn nd ufu mmn. Th wk w uppd by h Eh Ru Lby Bh nd Au Lggng Cnum nd Fundng Mmb Cnum. REFERENCES Dkmn, H., E. Hbzhm, nd A. Kuhnk, 005, Dmnn f kn upng ffn: 75h Annu Innn Mng, SEG, Expndd Ab, Mkhv, O. V., M. W. Hn, nd M. N. Tköz, 1997, Em nvgn f h hw ubuf: Fd mumn nd num mdng: Gphy, Mkhv, O. V., J. Qun, nd M. N. Tköz, 000, Ung bh m mumn d nd hz fud (pmb) zn: Gphy, 65, Mgn, F. D., E. R. Wm, nd T. R. Mddn, 1989, Smng pn pp f Wy gn wh ppn: Jun f Gphy Rh, 94, Pd, S., 1994, gvnng qun f h upd mgn nd u f pu md: Phy. Rv. B, 50, Pd, S. R., nd M. W. Hn, 1996, Em wv pp: J. Au. S. Am., 100,

9 Rpp, P. M., nd F. D. Mgn, 00, Fquny-dpndn m: J. f Cd nd Inf Sn, 54, Thmpn, A. H., 005, Emgn--m nvn: ufu dvpmn ugg vb ppn n xpn nd pdun: 75h Annu Innn Mng, SEG, Expndd Ab, EM.5, Thmpn, A. H., S. Hnb, J. Bun, T. Muy, R. Rhk, J. Wd, P. MCmmn, J. Sumn, G. Hk, M. Bxby, W. R, B. Wh, M. Zhu, nd P. Pzk, 005, Fd f m hydbn dn: 75h Annu Innn Mng, SEG, Expndd Ab, EM.8, Zhu, Z., C. H. Chng, nd M. N. Tköz, 1994, Ekn nvn n fud-ud pu k mp: 64h Annu Innn Mng, SEG, Expndd Ab, SL1.1, Zhu, Z., M. W. Hn, nd M. N. Tköz, 1999, Expmn ud f kn nvn n fud-ud bh md: Gphy, 64, Zhu, Z. nd M. N. Tköz, 003, Ch m mumn n bh md: Gphy, 68, Zhu, Z. nd M. N. Tköz, 005, Sm nd mmgn mumn n fud bh md: Gphy, 70, F45-F51. 9

10 Fgu 1: Shm dgm f m mumn n w nk (Fgu 1). Th ng d md fm b w. An pu qu pu wh 50 V n mpud nd 6 µ n wdh ppd h d pd by 10 m. A hydphn f Typ B & K 8103 mv ng h n A, B, nd C (Fgu 1b) d h u wv. 10

11 Fgu : Sm wvfm dd n h w nk (Fgu 1) whn h hydphn mv ng Ln A (), Ln B (b), nd Ln C (). Tw u wv wh dffng mpud ndud und h pv nd ngv d, pvy. () 11

12 (b) Fgu 3: A yd md wh pxy-gud nd nd Lu bk ud wh p w f 0.7 ms/m n nduvy (Fgu 3). Fv p f h d bud n h nd. An qu pu wh 500 V n mpud nd 6 µ n wdh ppd h d nd n u P wv ndu d h m wv n h bm uf f h Lu bk. Em wvfm (Fgu 3b) dd wh h ndu whn h d dffn dph xd. Tw w nd w m wv. Th f, gnd h nf, v h m m (0.038 m 0.05 m). Th nd, gnd h d, v dffn m. 1

13 Fgu 4: Shm dgm f m mumn n w nk. A ng n bu f 150V-180V n vg nd 15 khz-150 khz n fquny x h u d. Th mumn d d h pn h mp, nd hydphn f Typ B & K 8103 mu h u fd n h w nk. n g m E Sgn whu ny mp n w nk Ngv d (<0.05m) Su nfun Pv d (0.35m) Rfn fm w 150kHz 140kHz 10kHz 100kHz 90kHz 70kHz 50kHz 30kHz 0kHz 18kHz 15kHz 1kHz 10kHz 7kHz 5kHz Tm (m),=0,nmzd=00 13

14 Fgu 5: Au fd h dffn fqun dd by h hydphn n h w nk whu ny mp. Th w nd h pn f n: h u nfun, u wv gnd by h pv ngv d, nd h fn fm h w nk w. n g m E Cnn SS Lmn B SS Aumnum Lu Au wv 1 mpy Ngv Pv 0 d d Sd f. Bk f Tm (m), =0u,nnzd 80 Fgu 6: Au wvfm whn h mp Lu ( ), umnum ( 3), B ndn ( 4), mn ( 5), nd Cnn ndn ( 6) mp (p). Th u ng n pu wh n fquny f 100 khz. T 1 h u wv whu ny mp. () 14

15 (b) 3 ( n g m E Em wvfm B ndn 1480m/ S=4 m S=7 m S=10 m S=13 m S=16 m S=19 m Ngv Pv 0 d d Sd f. Bk f Tm (m), =0u, f=100khz,nnzd 00 Fgu 7: hm dgm (Fgu 7) f m mumn ym whn B ndn mp mv bwn h u d. Th pn f h mp 19 m fm h pv d nd mv n nmn f 3 m. Th hydphn d h u fd (Fgu 7b). Th w nd h n n h w nk nd h png n hw h m gn. Th ppn vy bd n h n p qu h w vy. 15

16 n g () 1 ELm wvfm n B ndn B ndn 150kHz 10kHz m E kHz 80kHz 65kHz 50kHz 40kHz 30kHz 5kHz 0kHz 18kHz 15kHz Tm (m), nmzd 100 n g m E (b) ELm wvfm n Wy gn Wy gn 150kHz 10kHz 100kHz 80kHz 65kHz 50kHz 40kHz 30kHz 5kHz 0kHz 18kHz 15kHz Tm (m), nmzd 100 Fgu 8: Em wvfm dd wh h B ndn (Fgu 8) nd Wy gn (Fgu 8b) mp n h w nk fquny ng fm 15 khz 150 khz. Th wvfm wh hug mpud bf 0.3 m h u nfun. 16

17 Fgu 9: E gn dd wh mumn d f V+ (bk) nd V- (bu) n B ndn (Fgu 9) nd Wy gn (Fgu 9b). Th ph f h vg V+ nd V- dn. 17

18 p u C 3.5 Nmzd Vg Cupng Cff. n B ndn g V d z m N Thy, =80um V mud Fquny (khz) p u C g V d z m N Nmzd Vg Cupng Cff. n Wy gn Thy, =0um V mud Fquny (khz) Fgu 10: Nmzd m vg upng ffn (ΔP(ω)/ΔV(ω)) mud n B ndn (Fgu 10) nd Wy gn (Fgu 10b). Th h vg upng ffn ud wh h p du f 80 µm (Fgu 10) nd 0 µm (Fgu 10b). 18

19 Fgu 11: Shm dgm f h m mumn n w nk. A ng n bu wh 150V-180V n vg nd 15 khz-150 khz n fquny x h u hydphn (Md LD-34). Th mumn d d h pn h mp. A mumn hydphn f Typ B & K 8103 pd n h mp mu h u u wv vng h mp. 19

20 E gn whu ny mp n g S E kHz 10kHz 100kHz 80kHz 65kHz 50kHz 40kHz 30kHz 5kHz 0kHz 18kHz 15kHz Tm (m), nmzd 00 Fgu 1: Bkgund n whu ny mp, dd by h mumn d V1 n Fgu 11. Th fquny ng fm 15 khz 150 khz. 0

21 d n Sm gn n mp B ndn Lmn Aumnum u A 3 1 Au wv Lu bk Whu mp Tm (m), =0u, f=100khz,nnzd 100 Fgu 13: Au wvfm ( 1) n h mp nd h wvfm whu ny mp ( ), whn h mp Lu ( 3), umnum ( 4), mn ( 5), nd B ndn ( 6). () (b) 1

22 3 ( n g m S (b) Sm gn 1480 m/ Tm (m), =0u, f=100khz,nnzd 400 Fgu 14: Shm dgm (Fgu 14) f m mumn ym whn B ndn mp wh h mumn d mv n h u fd. Th mumn d V1 d h gn (Fgu 14b). Th png n nd h m gn, wh ppn vy bd n h n p qu h w vy f 1480 m/. v w u () B ndn Su u wvfm 150kHz 10kHz 100kHz 80kHz 65kHz 50kHz u S kHz 30kHz 5kHz 0kHz 18kHz 15kHz Tm (m)

23 v w u (b) Wy gn Su u wvfm 150kHz 10kHz 100kHz 80kHz 65kHz 50kHz u S kHz 30kHz 5kHz 0kHz Sd f. 18kHz 15kHz Tm (m) Fgu 15: Au wvfm n h k mp f B ndn (Fgu 15) nd Wy gn (Fgu 15b) gnd by h u hydphn h fquny ng fm 15 khz 150 khz. 3

24 Fgu 16: E gn dd wh h mumn d V1 (bu) nd V (bk) h B ndn (Fgu 16) nd Wy gn (Fgu 16b) h fqun fm 15 khz 150 khz. Th u nfun bf 0. m hv h m ph, bu h m gn f V1 (bu) nd V (bk) hv pp ph (und 0.3 m n Fgu 16). g n p u C E - S d z m N Thy, =80um S-E CC mud Fquny (khz) 4

25 g n p u C E - S d z m N Thy, =15um S-E CC mud Fquny (khz) Fgu 17: Sm upng ffn (ΔV(ω)/ ΔP(ω)) n B ndn (Fgu 17) nd Wy gn (Fgu 17b) h fqun fm 15 khz 150 khz, nd h h upng ffn ud wh h p du f 80 µm (Fgu 17) nd 15 µm (Fgu 17b). 5