bulletin of the seismological society of america. vol. 58, no. 6~ … · 2017-02-27 · bulletin of...
TRANSCRIPT
Bulletin of the Seismological Society of America. Vol. 58, No. 6~ pp. 1899-1932. December, 1968
LARGE SCALE PROCESSING OF SEISMIC DATA IN SEARCH OF
REGIONAL AND GLOBAL STRESS PATTERNS
BY A. BnN-MENAHEM, H. JAROSCH Am) M. ROSnN~AN
ABSTRACT
A composite computer program has been devised for a fast reduction of multi- station seismic data in the period range 5 0 - 5 0 0 sec for mantle surface waves and 2 0 - 1 0 0 sec for body waves.
The analysis aims at the reconstruction of the seismic source from the spectrum of its far radiation field and the correlation of its parameters with its depth, size and regional environment.
The capability of the computational procedure has been demonstrated in two studies of WWNSS records: one includes a spectral analysis of surface waves from a shallow shock in the Kurile Islands; the other includes a spectral analysis of P waves from 9 shocks in the depth range 550 -700 km at Fiji, Mariana, Java, Japan, Peru and Brazil.
Other applications of the proposed data processing routine are foreseen; a tsunami warning system and focal depth determination from spectral modal ratios.
It is believed that a persistent search for stress patterns, based on the processing of a sufficiently large sample of seismic events, is essential to any future program of earthquake prediction.
INTRODUCTION
A major problem in seismology is the development of dependable numerical pro- cedures for the extraction of source information from the various seismic signals.
Chief among them is the spectral equalization method. (SatS, 1955; Tukey, 1959; Aki, 1960; Brune, 1961; Ben-Menahem and ToksSz, 1963; Kasahara, 1963; Toks6z, Ben-Menahem and Harkrider, 1964). According to this method one isolates on the seismogram certain wave forms which correspond to seismic rays or modes. These wave forms are separated from the records, transformed into digital form and then subjected to a Fourier analysis. The spectrums are then compensated for whatever "happened" to them on their routes from the source to the stations. Effects such as dispersion, attenuation and instrumental distortion are taken into account. Finally, one compares the amplitude and phase residuals with theoretical source models in order to determine the physical parameters of the source. (Ben-Menahem, 1961; Haskell, 1963; Ben-Menahem and Harkrider, 1964; Brune, 1964; Ben-5.[enahem, Smith and Teng, 1965; and Aki, 1966).
This equalization procedure is applicable to the entire spectrM range from body waves of 20 second period to periods of the order of one hour. (Alsop and Brahe, 1965; Teng and Ben-Menahem, 1965).
Recent studies in this particular field have furnished us with an incomplete picture of the seismic source. Most of these previous studies were based on data from a single seismic event. Since the establishment of a world-wide network of standard stations by the USCGS, studies have been made of single events around a network of stations. However, in order to obtain a fuller understanding of the nature of the seismic source, it would be extremely helpful to study many earthquakes from many regions, achier-
1899
1900 BULLETIN OF TI-IE SEISMOLOGICAL SOCIETY OF AMERICA
ing through the resulting distribution of events a much firmer basis for the drawing of more general conclusions regarding the mechanism of earthquake sources.
We shall now turn to a detailed description of the computational procedure,
ANALYSIS OF SURFACE WAVES
With the aid of modern ultra long-period seismographs it now becomes possible to record mantle Rayleigh and Love waves from shocks with a Richter magnitude that is as low as 5½ (Figure 1). Had the WWNSS been equipped with seismographs of this kind, the present suitable data for source studies would have increased by a factor of at least ten. With the recordings of the WWNSS, however, we must restrict ourselves to magnitudes higher than 7. For lower magnitudes it is difficult to obtain a good azimuthal coverage for most source locations.
PASADENA, Z
DISPLACEMENT SEISMOGRAPH
Tg =85 sec Ts =60 sec T=50
05 5 0 0 0 RI 06 O0 O0
06 50 O0 07 O0 O0 R2
08 50 O0 ,~D 5 09 O0 O0
At =-17.4 sec
SOUTH SANDWICH ISLAND REGION FEB 9, 1966
56.7S 25.7W to=O4 40 28.4 M : 5 { - - 6 ½ , H:27km.
FIG. 1. Displacement seismograms of mantle ~ayleigh waves from an earthquake in the inter- mediate magnitude range. (By courtesy of Mr. l~alph Gilman and Dr. Stewart W. Smith, Cali- fornia Institute of Technology, Pasadena, California.)
Let us therefore assume the availability of a readable set of long-period seismograms with a fair azimuthal coverage. Assume also that the origin time, the source coordinates and the source depth are known, and that the relevant Rayleigh and Love signals have been separated from the records and digitized. To speed up the identification and separation of the various signals from the records, we found it quite useful to prepare a routine which prints for each station "arrivals" and "departures" of Love and Ray- leigh waves, corresponding to a few chosen group velocity windows.
Figure 2 summarizes the chain of operations relevant to the first stage of the data analysis. Let a time-interval on the seismogram be represented by the function If(t) ./(to, tl)} where I = i for to < t < ti, and I = 0 for tl < t and t < to. Its Fourier transform (the trace spectrum) was defined by us as
ft tl F ( ~ ) = f ( t ) e - i~ ' dr. 0
(i)
REGIONAL AND GLOBAL STRESS PATTERNS 1901
Using the modified trapezoid rule to evaluate the integral the program then prints amplitudes, phases, normalized amplitudes and log (amplitudes) for any specified set of frequencies. The program was designed with multi-station input data in mind, namely, with the object of minimizing the visual and manual labor of the research staff by letting the computer do most of the routine work, including simple decisions.
The output of the first stage is obtained simultaneously in two forms: (1) as corn-
SURFACE WAVE ANALYSIS PROGRAM PT.I-FOURIER OR POWER SPECTRUM ANALYSIS
AT FRG
N
N R
PRINT T
N
r
~ANS ER
CO~PUF~WlNL<
b J Q
FIG. 2.
Q P I
q
N
N
Y
Flow diagram for a routine Fourier analysis of multi-station seismic data. Y = YES, N = NO. Connections (1) and (2) lead to Figures 3 and 14.
purer sheets on which the trimmed, detrended, filtered and tapered (if so required) Signals are plotted nnd their Fourier spectrums tabulated and plotted, and (2) as tape or card output carrying the same information.
This output serves as the input to the second stage, which is summarized in Figure 3. The reader should keep this scheme in mind while we explain its details in the sub- sequent figures.
The theoretical background of the equalization method is as follows:
1902 ] ~ U L L E T I N O F T H E S E I S M O L O G I C A L S O C I E T Y O F A M E R I C A
The source is assumed to be specified as a product of three factors: (1) the spatial factor, which depends upon the equivalent force system; (2) the temporal factor, which is the Fourier transform of the source time function; (3) the finiteness factor, which arises from the hypothesis that the rupture along
the fault moved horizontally with a uniform speed over a finite distance. The spatial factor, like the other two factors, is complex; it is determined by the
orientation of the source, its depth, and the structure of the layered medium through which the signal propagates. As the signal spreads out on its way to the recording station, its spectrum is modified by:
SURFACE WAVE ANALYSIS PROGRAM PART I I - SOURCE MECHANISM
<
OF SN. ~ , SN. i VELOCITY I [pRINT
OBSERVED COMPUTE PHASE COMPUTE SEARCH FOR BEST RAYLEIGH AN D VELOCIT(ES FROM FIT OF FAULT LENGTH LOVE RADIATION PHASE SPECTRA INITIAL PHASE AND RUPTURE pATTERN
AMPLITUDE OBSERVED AND FIT OF DIP AND CALCULATED
SPECTRUM DIRECTIVITY SUP ANGLES
COEFFICIENTS FROM CALCULATED I AMPLiTUOE SPECTRA [RAOIATION RATTERNj
C OFLF:C!C, 2 'NM E
FIG. 3. Flow diagram for quasi-automatic derivation of source parameters from multi-station surface wave data.
(i) attenuation due to the inelasticity of the upper mantle; (2) dispersion, geometrical spread, and polar phase shift over a spherical Earth; and (3) the filtering and directional effects of the recording instrument. The compensation for these distorting agents is known as the amplitude and phase equalization of the signal's spectrum.
In the case of earthquakes which exhibit multiple arrivals of both even and odd orders, the "directivity method" can be used to determine the fault length and the rupture speed (if any) from records of a single station. A ratio of spectra of even and odd arrivals is fitted to theoretical curves for various combinations of fault length and rupture speed. This ratio, known as the directivity, can perhaps be better visualized if one imagines the radiation field of a moving antenna of finite length. The spectral
R E G I O N A L AND G L O B A L S T R E S S P A T T E R N S 1903
ratio of the forward to the backward fields is diagnostic of the radiator's length and speed.
Once the source parameters have been determined from the direetivity, an immediate comparison is made with the extent of the aftershoek zone. Previous results indicate that there is some relationship between the "direetivity fault length" and the after- shock extent.
The phase equalization method can be used only if the phase velocities over the
P~IGIN a - I LATITUDE= L1~0~0~ t ONCI TUD[ - I~5.1CO
STATION L&T|TUDL Lf]N~ITUnE bZIWUTH yNV.AZINUTH D[STIDEG) OISTIKM| CIRCLE
A-I 1%650 145.1cO 0 C u 0 ~OOo9.15 GUA~ 1 3 . 5 ~ 8 1 ~ 4 . q12 1 ~ 1 . 7 6 1 . 7 0 5 . q ~ ~,65,~L, ~ C O o g . 2 1 MAT" 36°542 138. Z19 341.71 15fl°44 17.q3 Iqq4°47 40015°17 SHKb 34.530 132.678 325.98 140.~9 18.51 2C5~.85 ~OOLS.ZJ &NPl 25.183 121.517 2~5,61 9%5& 72.49 25C2*2t 4bOOS.34 DAV~ 7.08~ 125,575 239,38 54.B3 22.67 2523.47 40053*~0 MAN" ] ~ ° 6 6 7 121.0P3 2 ~ 1 . 6 8 74*55 23.46 2610.79 ~b067*79 ~aG~ 16°411 12O.~0 ?~b.20 75.5b 23.5~ ;O18.35 4bUOe*Sb SEO~ 37.567 12~ .qb7 322.35 133.55 23,88 2656,59 ~0U31*75 RAB$ - 4 . 1 9 3 152.171 152.88 343.84 24*&4 2743*22 4001~.2b PNG~ -9 .40g 147.154 175.80 355.qq ?fl. QC 3216.53 40609.47 HKC~ 22.30~ I14.172 280.81 59.57 28,98 3225.14 40067.15 HN5* -0 ,432 15q.947 151,80 333.16 32.34 36C0,30 4bU27,3~ OAR - 1 2 ° 3 ~ 3 13U,8~3 2~4*qg 24°0& 3 ~ . 7 q 3Rb7,97 ~UUI�*73 NMA$ 1 2 . 2 1 0 i09,212 263.43 7 3 * ~ 35.?~ 3g?I,2~ 4 0 & b 8 . 2 0 CTA$ -ZO*OBH 14b*254 17B.29 358.29 3g,46 43qz,og aOU~9.~l CHG" 18,790 98 .g77 276.92 PI.C,B 43,46 483&.66 4U0b~*~5 ADA 51.863 -176.655 ~3.63 237.34 ,3 .~8 ~ 7 9 . ~ 9 4bU~7.55 SNG* 7 ,173 lO0 .&20 2~C.20 6g .~7 #4, R~ 4 q g 2 * ~ 40007*31 LEM" - 6 . 8 3 3 107*~17 238.23 53°8Z 45 ,2q 5041.~7 4U052.29 BIND -b,�OO IC7.650 238.13 53.75 4~.31 5043.25 40052.ZO NOU - 2 Z * 3 1 0 16b*~51 152*35 331.B0 ~6.5g 5185*33 4 0 u ~ * 9 6 SHL m 25 .567 g l , ~ 3 2~7,23 85*54 4g .23 5477.b3 ~O~bJ*B7 HOW ~2.~17 M~.3~g 2E3°b8 ~I .8b 5~°53 5577*g& 4006b.75 KIP ~ 21*623 -158,C15 77,53 278. q0 53*06 5906.01 4006b.31 RIV~ - 3 3 ° 5 2 9 151*15~ 173,72 352. Be 5~*44 ~ 4 7 . 7 7 4~009.8b &FI * -13.909 - 1 7 1 . 7 7 7 124*81 307.14 53.q5 b004*53 ~0049.39 ~DE~ - 3 4 , q67 13~.7;~9 1P6.4~ 7 .40 54.~C 6076*82 40U~g.�u MUN* - 3 1 , g 7 5 116.227 2(8 .P7 32,35 5B°28 64Bb°~3 40083°03 P ~ 7~*1~3 --156mg~0 ~8*3~ 245°63 6 | * ~ q bB3Z.43 4bO~5.Ub NDI$ 28. b83 77 .p17 2o2,66 81 .q5 61.q~ 6885,64 4C0b0.18 TAU* -~Z, gIO I~7*320 178.1~ 357*63 62,23 6924.66 40u¢9.21 COt~ b4.900 -147.7°3 26.23 2~7.60 67.74 &972°59 4UOZU*84 ~AHO 31.550 74*333 2~6*2~ 8Z. 1~ &3.g7 7116.3b 40USl*~b KOD 1b*733 7 7 . ~ 7 272*&1 73.10 65.67 7308.65 4U068.94 WFL* - 4 1 . 7 8 7 174.767 156.01 32g,4z 66*54 7404.0~ 4UOIg*Uu ~000 1 ~ , 5 3 3 7 ~ , 8 5 0 2~2.32 7 6 . 1 7 66*57 7440.~7 4u066.34 R~R~ - 2 1 . 2 1 7 -150.773 124.54 303.14 67 .4~ 7511.2b 4005u.18 O U ~ 30°IA8 6~ .q5~ 2qb ,g~ 78*25 70.4& 78~7*'7g 4Cb57*57 PPT - 1 7 * 5 3 3 -1~q*5~3 I15*59 796.9~ 73.99 8235.89 ~b05?*81 ~5H* 36.311 5 q , 5 8 ~ 3 6 3 ° 5 9 76.49 7 5 * 1 6 5358.24 4OUSU.bB CMC* b 7 , 8 3 3 - I15*0~3 22.7( 2~6.50 75.67 ~407.35 ~OUI~.O5 ~OR~ 44.55b -123°313 47°~0 Z55,23 77,61 562~*91 46O41*14 L~N • 46 .750 - l ~ l . 8 1 0 ~4*5~ 285.79 7 5 * ~ ~676.O6 ~ 0 0 ~ . ~ 1 N~R~ 51 ,~00 - 1 ~ . ~ 3 357.31 17.50 7q.57 8727*39 4UOug. Z8 RKS~ 37*877 - 1 2 ~ * ~ 5 53.3~ 287.15 5&,26 ~ 4 . e 4 40U4 / ,b~ KE~O 69*757 27*~15 3~ I .R~ 57*39 M~.~( ~g87.44 ~0Ol4*92 RIG* 70.a17 2 1 . ~ 3 3~3.43 52*89 81.94 9 1 C 2 . 1 ~ 40UI4.Ui CCG • 77 .167 - b l . l ~ 3 5.72 3~5*13 87*1 ~ 912~*47 ~OOuq.?5 SH|$ 29. b44 52.526 2~8.74 71.72 52.69 9197.39 40u55.iO T A ~ 35 .675 46*3P7 3¢~,00 69.3~ P4,55 9401.21 4OO45.2b P~S 3~.148 - I 1 8 . I~7 75.53 ~8g.~6 8~*57 q406.34 ~OO50.Ib 80Z* 45*600 - l l l . b ~ 3 ~3°3G Zq2*q3 ~5,0 o 9458°89 40067°2~ G$C~ 35 ,302 - l i b . @ C 5 54.35 290.~1 85.23 9477.Za 4004~.b5 PLNO 3~*353 -11E*8~2 56.1g 2qO*t~ 85*E6 g54~*84 4U05b.45 DUGm 40o195 - 1 1 2 . 6 1 3 ~ * b 3 Z92*S2 86*38 g6c3.74 4 0 ~ 4 ~ . 8 ]
Fro. 4. A computer output o~ a distance-azimuth subroutine for a network of WWNSS.
great circle path from the source to the station are known. If the path is mostly continental or purely oceanic, appropriate phase velocities must be employed. The essence of this method is basically a careful "bookkeeping" of the phase history of the signal. The thumb rule is, that all phase advances due to propagation, sphericity, source to station geometry and instrumental distortion, must be subtracted, and all phase retardations (such as the initial phase due to time dependence and finiteness) must be added to the phases of the Fourier analysis. The algebraic signs of the Fourier phases depend upon whether the Fourier transform has been performed with
ioJt e-i~,t e o r
190~t : B U L L E T I N O F T H E S E I S M O L O G I C A L S O C I E T Y O F A M E R I C A
Once the phases have been stripped of everythh~g which "happened to the signal on its way to the station", interpretation in terms of source elements begins. Theo- retically, for the horizontal component of displacement due to a point source, the sum of the spatial phases of two opposite-going signals must (for a shear fault) be exactly equal to ~/2. If the source is of the propagating rupture type, the sum will be equal to ~/2 - ,f, where f is the frequency and r is the time of rupture.
Next, the remaining phases are explained in terms of the orientation angles of a displacement vector at the source. This is done with the aid of an inversion program which calculates theoretical phase spectrums for various orientations and depths in a multilayered flat earth model.
Figure 4 shows a typical output sheet which gives the necessary geometrical dis- tances and angles from the source to the recording station network.
Figure 5 shows a sample of the amplitude equalization procedure. The second and
CflROESTED &MP[ITUDF SPECTOUM I ~ I I | PERIOD AMPINI, I ) ATT AIN$ CnRRAMP 1 5,0OOOF -3 2,0030F 2 5,646BE 3 2.901BE - I 4o?D26F ? 6.6225F I 2 5,2000F -3 1,92~IE ? 5.g~OPF 3 2.6~P3E - I ~.O431E ~ 4,~Sg~F 1 3 5,~OOOE -~ I.851~E 2 5.qgl2F 3 ?o3807F - I 5.104oE Z 4,°132F l
%@000[ -5 1,7q57F ? 5m6R74L 3 2,2657E - I ~°5~7~F ~ 4°4@~2E I 5 5.~OOCF -~ 1 , 7 ~ I E ~ 5~37~PF ~ 2,C522F -1 6oO~g~ ~ 4o2~73F 1 6 5.O000r -~ 1.6067E ? ~,3742F 3 l , q ~ 3 1 E - I 6.613BE ~ ~.155~F 1 7 5, SDDOF -3 1.612qF 2 <,751FE 3 l . eS@BF - I 7,15e3F 2 4.~lqTF [
b,~OOOF -3 1,5675F ~ 6.26gCF 3 I,~B36E - 1 7 ° 7 0 7 ~ 2 ~ , ~ O F I q b, bOOOF -3 Io5"152t ? 6.615~F ~ 1.6023F - I 8,?BIDF 2 6.97736 1
| 0 5 , 8 0 0 0 F -3 1,47G~E ) 5.6283~ 3 I,~@~2F - ] B.@703~ ? 5 ° 4 0 0 8 E I 11 7,0030f -3 1,4286E ~ ~.381~F ~ I.IOC7F - 1 q.474~F 2 5 . 6 ~ 7 4 F 1 12 ?.2000F -a 1.3~89E P b.O~6IE 3 l°lqOTF - I l .COqS~ 3 5°0~95E 1 13 7 , ~ 0 3 0 E - 3 1 , ~ 5 1 4 E ~ 5 , 7 3 ~ 5 F ~ 1 . l q C T F - 1 l ° n 7 2 3 E 3 4o4@~OE l I* ?,SOOOF -3 1,3158E ? 5,2484F 3 I.I~32F -I 1.1366E 3 4.~b80~ I I~ 7,803~ r - 3 1 , 2 8 7 1 E ? 4°505~F ~ 9 . 7 6 ~ 3 E - 2 I.2O?~F ~ 3 , 8 3 0 6 F I I~ @.OO30E -.3 1.250~E ? 3.616~F 3 I.C264F - I I°26~5E 3 ~o7734E 1 17 8.20DOE -3 1.21O5F P 2.5~07F 3 I,C138~ - I 1.335o~ 3 ~,IOI4E 1 18 B.4OOOE -3 1.1905E ~ 2.5042F ~ I.O013F - 1 1.40~1~ 3 1.77@1E 1 lq 8,6030E -3 1.1628F 2 Z.6346F a °,B@OgF -2 1,47~IE ~ 1.8C53E I 23 8.8900E -~ 1 . 1 ~ 5 4 E ? ~.9384~ 3 9.76~3F -2 I.~42~E ~ l.q~64F 1 ?1 9. OODOE - 3 l . l l l l f ? 3 . 1 1 2 3 ~ 3 0 . ~ 1 2 4 F -2 1 , ~ 1 3 1 ~ 3 ? .G~ &3F l 22 9, SDDOE -3 I.O87DE 2 3,10o4 c 3 o ° o ~ -? I . ~ 'xt; ~ ?.0375E 1 23 9,4DOOF -3 1,5638E ? 3,ObBR~ ~ P,73eq ~ - ) 1.7~5~F ~ 1,9~72F I 2~ %6000F -3 1,04lTE ? 3oOEO~F ~ ~.47' 5F -? l .~27:E ~ l,qSbOF l 25 9 . 8 0 0 0 ~ - ~ | ° O ? 3 A E ;' 3 . 0 6 8 ¢ F 3 7 , R I l l c - 2 1 ,COROt ~ 2 . 0 6 3 4 r 1 25 I.DO30F - ] I,OOODE :" 3.1503F 3 7 ,2 '~P7r -? I . °712 c 3 2.1O~OF I
FIG. 5. A computer output for amplitude equalization of surface wave signals from a network of WWNSS. The particLflar result shown here is for a Rayleigh wave R8 recorded at Aquila, Italy from the Kurile Islands aftershock of October 20, 1963.
third columns from the left list the frequencies and the periods, respectively. The fourth column lists the Fourier amplitude spectrum over the given frequency range. Next is the physical attenuation factor e -~c~)A where -~(~) is the frequency dependent attenuation factor, and A is the central angle in radians from station to epicenter.
The column AINS lists the amplitude response of a critically damped and zero- coupled WWNSS seismograph system:
AINS (~) = MJ/(~02 + J)(~g2 + J ) where M is a constant pertinent to the magnification at the recording station. Ex- plicitly M ~--- M#0 where M0 takes one of the values: 6000, 3000, 1500, 750, 375. For a general reference see tIagiwara (1958).
Finally
C0R RAMP -- (AMP) (INV.AZC~I%) ~ A. (ATT) (AINS)
Letting INV.AZ be the inverse azimuth at the station, measured clockwise from
REGIONAL AND GLOBAL STRESS PATTERNS 1905
north, then
INV.AZCOR = 1 for U, (vertical displacement) at all angles.
1 sin (INV.AZ)
1 cos (INV.AZ)
for N S Love waves and E W Rayleigh waves
for E W Love Waves and N S Rayleigh waves
The corrected amplitudes are given in units of ram-see.
I - 7 , O0 !
32 33 34 35 36 37 38 39 4.o ','1 . 2 *,3
45 4.6 ~7
4q '50 51 "SZ
53 5*. 55 56 57 58 ~9 60 6 ! 62 63
~5
67 68 69 70 71.
7~ 7 ,
?b ?? 78 79
81
FI 3 1 0 Z * * O l C - 7 q 6 5 . 0 ) F I l l T i l l C ( I ) A ( ] ) F ~ I J R I I I P H | N ~ I I ) F I N I I I I i P H J ~ F l l )
3 . 1 0 0 0 0 E - 3 3 . 2 2 5 8 1 E 2 5 .~2800E 0 2 . 6 7 0 1 9 E - 2 l . G 1 5 5 7 ~ C ~ , 2 4 7 q 6 F - I 0 - I . 6 1 ? b ? F 3 . 2 0 0 0 0 E - 3 3 .125uOE 2 5o36&00 [ 0 l o 9 9 7 g l E - 2 1 . 0 ~ 8 8 7 E 0 6 . ZO954F - t 0 - 1 o 6 ~ 0 8 4 E d 3 . 3 0 0 0 0 E - 3 3 . 0 3 0 3 0 E 2 5.31ZOOE C ' - 1 o 1 3 0 7 2 F - 2 1o~70~9E G ~ o I T I 2 ~ E -I ~ - l . 6 q q O 3 F O' 3 . 4 0 0 0 0 E - 3 2 . 9 # 1 1 8 E 2 5o25#COE 0 - ~ . 5 6 3 0 0 F - 3 1 . 1 ~ 9 4 2 F 0 5 . 1 3 3 2 2 E -1 o - 1 o 7 2 7 3 0 E O' 3o50000E - 3 2 . 8 5 7 | ~ E 2 5 .1790GF O 8 . 0 7 0 9 7 E - 2 I o 1 5 4 3 0 F C ~ . o q ~ 3 ~ F -1 0 - l * b 7 5 1 ~ E 3 . 6 0 0 0 0 E - 3 2 .?TT78E 2 5 . 1 2 1 0 0 E G 1.354gGE - 1 1 .2C462E 0 ~ .C57~2E - I 0 - I . 6 7 & S q E 0 3 . 7 0 0 0 0 E - 3 2 . 7 0 2 7 0 E 2 5 . ~ 6 7 0 0 [ C 1 . 8 3 6 q 4 F - 1 1 . 2 ~ 0 0 5 £ 0 5 ; 0 2 0 0 9 E -1 0 - 1 . 6 ? ~ 3 7 F C 3 , 8 0 0 0 0 ~ - 3 2 , 6 3 1 5 8 £ 2 5. C0400F 0 2 . 9 2 3 9 2 E - t 1 . ~ 2 0 ~ 9 F 0 5 . 9 ~ 2 7 5 ~ - I U - l . b 2 ~ S T C, 3 . q 0 0 0 0 E - 3 2 . $ 6 4 1 0 E 2 ~ .&570CE O 3 . ~ 5 1 3 ~ E - 1 l o 3 8 6 0 0 F 0 5 . g ~ S h l F - I u - 1 . 6 3 5 4 ~ F 4.000DOE - 3 2 . 5 0 0 0 0 E 2 4,919GCE 0 3 . 6 7 8 9 2 F - 1 | . * 5 6 b ~ F 0 5 ,qOSb6F - i o - 1 . 6 7 q ~ 1 [ C 4 . 1 0 0 0 0 E - 3 2 . 4 3 9 0 2 E 2 ~ .867CU~ 0 ~ . 7 8 3 6 7 E - 1 1 . 5 3 1 9 9 F 9 5 . 8 7 1 9 C F - l ~ - l . b ~ C 8 2 F t 4 . 2 3 0 0 0 E - 3 2o3BO95F 2 ~ . 8 1 ~ C ~ [ 0 5 . 9 1 5 ~ 3 F - 1 1 .61C63E 0 5 . 8 3 5 3 4 E - t 0 - 1 , 6 ~ 2 5 8 [ O 4 . 3 0 0 0 0 E - 3 2 , 3 2 5 5 8 E 2 ~,78UOOF C 6o5911gE - I l o ~ 9 0 1 C ~ 0 5 . 7 q s q q F - 1 0 - 1 . 6 1 0 8 ~ F 4.~O0uOE - 3 2 . 2 7 2 7 3 E Z ~ . 7 4 3 0 0 L C 7 . 3 4 ~ 3 4 E - 1 1 . 7 6 8 0 ~ 0 5 . 7 6 2 8 ~ £ - I 0 - 1 . 6 0 9 8 8 ~ 0 4 . 5 0 0 0 0 E - 3 Z .ZZ222E 2 ~ . 7 1 3 0 0 ~ C 7 . 7 9 3 ~ 7 E - I 1 . 8 ~ 3 1 5 ~ 0 5 . 7 2 6 8 8 E -1 0 - 1 . 6 3 6 ~ 4 F 0 4.60000E -3 "2,17391E 2 4.~8000E 0 8.54675E - I l .qlSSgE C T ,bg l I3F - I ~ -1.62~97F 0 4 . 7 0 0 0 0 E - ) 2 . 1 2 7 6 b E 2 4. b4~OCE C' q . ~ 5 5 ~ [ - 1 1 . q ~ 5 9 1 ~ 0 5 . 6 5 5 5 9 £ -1 ~ - 1 . 6 1 5 8 8 ~ 0 ~ . 8 0 0 0 0 E - 3 ZsO833~E 2 ~.~1300[ 6 1,0496~ O 2.65518E O 5.62L26~ - I ~ -1.567~7E C ~eQ~OUOE --~ 2.0408~ ~ ~.~9500E 0 [.C~476~ C 2,1~&2~[ 0 5.58514F --I U --l.6~?q?F 0 5oO0000E -~ 2,000OOE 2 ~.56500[ 0 1,1478~£ 0 ?,Ig385E 0 5o5~'e2S£ -I 0 -Io6C103F e 5.10000£ -B 1.96078£ 2 4.5&500[ $ l,lgOql~ 0 2.26404F (I ~.5155Bf -I 0 -I,~)558F 0 5,20000E -3 I.q2)O8E 2 4.52#00~ C 1.24177E 0 ~.3383C[ 0 5.&81(~ -1 d -1.66463F 0 5*~O000E - 3 Io88679~ ? ~.SG350E G 1.29648[ C 2.WI*ZBF C 5.&&678~ -~ [J -I,~&243F 0 5e~00006 - 3 1,85185~ 2 4 . ~ 8 3 0 0 E U 1.Bs~gRE 0 2 . ~ g 2 0 g ~ 0 ~ . & 1 ~ 7 2 £ - I U - l . ~ 7 4 ~ , F c. 5,53000E -3 1,81818£ 2 ~.wsgso[ C l.~550gF O 2.57012[ S 5,~78S8~ -I 0 -io6~2W2F 0 5,60000£ -3 1.78571£ 2 4. W3bGOE 0 I,56065~ O 2,8~61&F [' 5,3W525~ - I C -|.67C03F C 5.10000£ -3 Io75439E 2 ~,&195C[ C ]o6|2B5[ G 2,7|858~ 0 5.311R4F -] 0 -I,6B7*IF C 5.80GOOE -3 1.7241~E 2 ~.*03GOE 0 1.67041E 0 2.78668F 0 5.27865£ - ! O - ] .6 ,41~F C 5.90000E -3 I,69492E 2 *o39200~ 0 1.68264F 0 2o85C41F 0 5,2~567£ -I 0 -|o69234E e 6,GOOOOE -3 Iebbb6?E 2 4,38160[ V. Io698~3£ O 2.91008F U ~,Z1290[ - ] 0 -|.73244F e 6,|O000E -3 I,b3934~ 2 4.3bOGt~F 0 ].81~64E 0 2 . g b 6 9 7 F 0 5,|80~6~ -[ 0 -I.665&TF ,) 6.ZOOOOE -3 1.6129QE 2 W. 33900F 0 i.94721~ 0 3.0188bF 0 ~ . 1 4 8 0 3 E - I O -Io5864~L 0 6 . 3 0 0 0 0 E - 3 1 . 5 8 7 3 0 E 2 &.32906F 0 1.96977[ 0 3.06e94£ 0 5 . 1 1 ~ l E -I 0 -1.61076~ C b.&~OOOE -3 |,56250E 2 *,31900E 0 logqb12E O 3oI1678F C 5,98401E -I ~ -|o62~06F e b.~OOOOE - 3 1 .5~8~6E 2 ~o30500F 0 2 . 0 6 9 7 8 E O 3 . 1 5 2 8 5 F 0 5 . 0 5 2 3 3 F - I 0 - 1 . 5 9 8 3 1 E 0 6,bOOOOE - 3 I.~1515E 2 4.29106F 0 2.14~IIF 0 3 . 2 0 7 5 3 E O 5 . 0 2 0 8 6 ~ - I 0 -I,56051E C 6 . 7 0 0 0 0 E - 3 1 . 4 9 2 5 ~ E 2 ~ .28100E 0 2 . 1 8 8 7 6 [ 0 3 . 2 5 1 1 8 F 0 ~ . 9 8 9 6 1 E - ! 0 - 1 . 5 6 1 3 8 F 0 6 . 8 0 0 0 0 E - 3 1 . * 7 0 ~ 9 E 2 ~,2710(,~ 0 2.23233E 0 %29*19~ O * . q $ ~ S b E -I U - 1 . 5 5 7 7 2 E 6 .?O0f f0E - 3 1 . ~ 4 9 2 8 E 2 ~ .2b20OF 0 2. 26806F 0 3 . 3 3 7 0 2 E O ; . 9 2 7 7 4 E - I u - 1 . $ 6 1 7 3 E O 7 . 0 0 0 0 0 E - 3 1 . 4 2 8 5 7 E 2 4.25BOOF 0 2 . 3 0 7 ~ 1 F 0 3 . 3 8 G I T P ' O ~ . 8 9 7 1 2 E -1 0 - 1 . $ 6 2 5 7 E 0 7 . 1 0 0 0 0 E - 3 1 , 6 0 8 4 5 E 2 *.2~BOOE 0 2 . 3 r , 1 2 3 F O 3 . 4 7 4 1 7 E 0 ~ . 8 6 6 7 2 E - I O - 1 , 6 0 9 6 1 F O 7.200UOE - 3 | o 3 8 8 8 9 £ 2 4. Z430LE O 2 . 2 9 7 0 2 E 0 3 . 4 6 9 4 5 ~ C ~ .B~653E -1 0 - | . 6 ~ 6 0 8 ~ O 7o30000E - 3 1.3698bE 2 4.23756[ O 2.3G~qTE 0 3,51624E 0 ~.80654[ -I 0 -I.6q~92E O To~OOOE -3 1,35135£ 2 W, 2320CF C 2.3C702F 0 ~,56~51E 0 ;,77677[ -I 0 -I.735|8F O 7.50000E -3 |,33~33F 2 W, 23075F 0 2,259~4E O 3o61401E ~ 4o7WT21E - 1 0 - l e R 2 8 8 9 F 0 7.53000~ - 3 1,31579~ 2 ~.2295UE 0 2,21311E 0 3.66429E 0 ~.717856 -1 0 -1.92797~ 0 7.?O000E - 3 1 . 2 9 8 7 0 F 2 * . 2 2 8 2 5 £ 0 2 . [ 6 6 8 2 £ O 3 . 7 1 ~ 7 8 E 3 ~ . 6 8 8 7 C ~ - | 0 - Z . C I b 8 3 F 0 7 . 8 0 0 0 0 E -~ 1 , ~ 8 2 0 5 F ? 4. Z27COF 0 2 , 1 2 0 9 8 £ 0 3 . 7 5 4 7 7 F 9 * . 6 5 9 7 ~ E -1 U -Z .10@76~ C 7 . 9 3 0 0 0 E -3 I . Z ~ 5 8 2 [ 2 ~ . 2 2 5 5 C ' 0 2 . 0 T q O I F 0 ~ .~1339C C. ~ . 6 % ~ 1 c -1 C - 2 . 1 9 7 ~ F O 8.00OOOE -~ |oZSOGOE 2 4.?2"~q(,~ G 2 o C 3 7 5 8 £ 9 ~ o 8 5 9 6 6 F ~ ~o~ l ~47~ -1 L, - 2 o 2 ~ ? : ~ F 0
FIG. 6. A c o m p u t e r o u t p u t for phase equa l iza t ion of sur face wave s ignals f rom a n e t w o r k of WWNSS. T h e pa r t i cu la r resu l t s h o w n here is for a Ray le igh wave R2 recorded a t S t u t t g a r t , G e r m a n y , f r o m the Kur i l e I s l ands a f t e r shock of October 20, 1963.
An example of a phase equalization is given in Figure 6. The wave R2 had traveled a distance of 31024.0 kin. along the major arc from the Kurile Is. to Stuttgart. The time difference between the origin-time and the onset of the filtered time series was 7965.0 sec. The appropriate phase velocities (in kin/see) for that path are listed in colunm four. The spatial initial phase of the far-field vertical component of R2 is generally given by
PHASE(I) = A ( I ) - FRP(I ) -- Pt I INS(I) -1- I F IN(I ) [ + ]STEP[ -- POLAR
• Sut.z ~tun s ut. xtAxszp st ossqd l~tq tut lSt~sd~ "(o0) q~:~ou aq~ o~ so~tz~s pus 'oosds-jlqsl t otusooo po:~o£sU~inm s ut (O(I) ~t°t~s°°Ist.P ~tI'O/XI6osidst p s ~o ~stt~ s~. oo~nos o~: L "(y '~) uot~s~uot.~o'ooxnos pus (~') qc~dop 6oanos '(£) potJod
73(]01~ 31N'¢300' 3001~1 Hg137XV~I 7VJ.N31~IV(]NrI-I
oO :~/~'~
i + ol)
"~ o o~ ",,,~£o~
• tu~ ££=q "w~l O01=q o9~=~ , , '~ o99 ==~ f~-~-~
7=lflO~ OINV300 3(]01~1 Hgr~71Y~ 7YlN31~VONrL4
oO =~ All \\\ °06 ,~(~
o0
oO oO
o0 "~s 001:1 oO
~q uoAt~ s~ mo~s£s ~Si~2A2A oq~ ~o~ ~ouvapv ossqd is~omn~sm, oq~
(I96I 'moq~uolY -uo~t) oo~nos mmmos oq~ ~o ~uo~xo imuoz~Ao q o+ onp uo[#~p~t~o~ ossqd = ~%I~I
(~.~Is os~r:[d :miod) { = EVqOcI
(sc~:un OlO:t.o m. 'do~s ~tnn op:s.tAvo H oq~ ~o ossqd is~oods otij~) {-- = dX~LS
£~!,t~iod is~uomnotqsu! + (s~tun Olmti.o u!) oou~Ap~ os~qd is~uomn~sut, oqj~ = ~KIHcI
(s~t.un o[aat.a m.) osvqd s.ts£isus-am.ano~I aqj~ = clH$
oo~ -- m. £~I.00IOA os~qd = D
oos/so[o~;o m. £ouonbo~I = f
L = N ~96L ~ f+N = V
oidmqsxo ~uosoJd ~no e I
VDIHX~V 30 XJi~tlDO~ 'IYDIDO~IO~I0t~ XH~L 30 I%IJ~XTIflE 906I,
"qL '~L 'L 'soan~.t~I ut. ~oqs ea~ so~m lt~!oI£~ E ao1 suae~3~d uot.~t.p~a i~a[.d~2~ emo~
osao~ut oq~ uo ~llt.puodop 'oaoz ao -~ aoq~t.a s ! ~T soA~m oao~ I ao~I "tao~Xs ~ut.,~X-ssoacI eq~. uo popaoaoa SOA~m q~ToiXsE ao~ oaaz seC~SaXlS s T UOT#aOaaoa £#I.asiod [~uemnac~s -m. oq~ L "aldmsxo c~uosoad ano m. oIqTSTI~OU oq oc~ puno~ ss~ ossqd ssouo~.mj oq~ L
73C]OIN (]731H$ 30C)IN Hg1371V~ 83HglH J.S[
',,,~o,~ ~ .o =~/// --.,'% =06 ='(~
o0
o0 o0 "w~££=4 ~,~-~,. "LUll 001 :q
o0 "aas 001=1 o0
qL "m~I
-1300!,N 7V.LN3NI/NO~ 3(]01~ Hgl3"]/kVN ~I3HgIH 15 I
'w~ ££:4 ~ oO :~ /// \X\ °06=X~
't-u~l 0:4 __ "w',l £g:4 __
o0 o0
'w~t~:4 ~ tmlO01=4
~d o0 'oes O01=J. o0
73Q0~ 7VIN3NU.NOO'.3(]OIN HOI37XV~ 7VIN31NVQNN3
'uJ>l ££=4 /~~ .o :~/// \SS
(cjI)
""'H 0 --4 "~ ogZ't,g=~ ogZ'~'g=R
009 :X ~ X*- T ~--~.,_
°W"I ££:4 oO oC~=~ .o6
• w~1001:4 oO og9 :~
~L "DI~I
7300M 7VlN3NIIN03 '3QOl~ HOI37,Vff~I N3HOIH ~l ,rot ££=4 ~
oO :~/~---~\\
~ (o£1
oO "tu:1 0 =4 "~££=4
o0 °0 "mH ££:4 "w~1001 =4
¢ ~n 'oes gg =L
.o ,O
2~061 ~XHffJ.dS¥cI SSXHaSS 'IVffO~ID (~NV ~VNOIDXH
,p,.: a(,)f 0~ = i(~)o~1 = p)o¢2
(°'a~ m.s ,~ u!~ + °'a~ soo ~ m.s + o0a,( soo)l (co)of/l = (¢o)0q
oaanos oq,~ ~v ~uomoavidst.p ivac~aads oR# (00)0/2 o9 pozt.i~ui -aou uoaq s~q (~n 'on "n) = /2 uo!c~s~s ~u!aaosqo oqc~ ~s ao~aaa ~uemoa~ids!p oq&
"o09~ ~ ~ ~ o0 '006 ~ ~ ~> o0 ooanos oltc~ #~ SOlSU~ dt.p pu~ des eq# oa~ {? puv ~ SOlSUV oq,L "@96I) aoP~.a~iaVH puv moqvuo1~-uo a ui sv om~s oq# st. uot.~o~
(9) "0g soa (~g m.s ,~ m.s {) -- 0g u,.s (~ m.s ~ soa) = ad
0 soa (~ soa ,~ soa) + 0 u!s (~g soa ,~ re.s) = ab
"~ -- Ig
(~) ff Lo-Jj L(~-7~j - (~,)~
+
(T~) L,..o~; - t ~o (~)',..o 4- t ~s. /,°.~/
, -v,-- a L s'~' J (,',)~z~
(e) 0 soa (~g soa ~ u!s) + 0 m.s (~ soa ~ soa) - = ~5
(~)
~-v~- a L S'p J (°')°;2
mao~ S~OlUO~.Suom~.p oq~ m. uoc~t.aa~ £ic~uo!uoAuoa oq u~a po#~inolva oar s'uotallvd p~,aa& pla~f-avf oq# qat.qx~ tuoz~ suotssoadxo at.s~q otI~ L "@961 'aoP!a -:~avH !g96I '[ImiS~H) mst.[vmao~ aop,.a~iavH-iio~[sv H oq~ uo posvq st. OUlOqas uot~vina -Ira [~avomnu oR& "sppom qgava ~t~ snouvA ao~ (L96I) aopv~aVH pma @96I) aopg -:,[otv H puv tuaqvuol/V-no~[ £q poc~vlnaiva puv po~v[nmaoj £[c~t.at.idx9 uooq svq oamana~s s,qc~av a aqa pus not.~vauovo oaanos 'opom '£auonboaj 'rq~dop no oauapuodop apti&
YDIH~I~V ~O X~L~IDO9 qVDIDO~IO~SIX9 XH~L ~IO NI~LX"I'IfI~ ~06I
(a~/jo uo~.~nuo~s oA.~ssoaxo oq~ ao 3 uoDaoaaoa qs Su!pniam.) ~H puv *~/~o o!~qsa i~ac~aods oq~ s~oqs g oan~.d t "oanc~dna jo poods oq~ pu~ qc)~uo[ s,~in~ 0~4~ aoj o~m~.c~so ~i~ q~t.~ dn omoo snq~ puv sazano iso~.#oaooqc~ jo ~os ~ o# £#~.ADooa~.p pOAaOSqO Oq# JO #tJ ~soq aoJ qoaqsos £qsm om '~oaqs ~Ioo~[sao~jqs oq#jo ~tlo~xo ot O 3o st.s~q ot Duo o:~.a~s s,qin~ l oq~ .ioj oniqsA IqSDtUI. US ~utsson O "#soq~-ssouo#t.ug out.qmoa qs UlaO~aod o# Injosn o~o~ozotD s~ c~i "suot.suom~.p s,ooanos oq# ~o oDsou~s!p s~. pIog uot~s.~ps~ oq~ jo £2~otatu£ss OtkL
(t) • - o -- (o .'o 'o6)o
(0 -- 06 !£eI '06)°~ --= (0 !0 '~t~)°~1
(0 + 06 .'06 '06)~/2- ---- (0 ~0 'O)"f2
(0 -- 06 .'~t~-- '06)'~ ~ (0 !0 'S~)~
pu~ o~ 'sao#otu~a~cI uo~.~uot..to oq~ pu'~
• ooanos uo!~ools!p a~oqs ~s go £a~otuoo D "o L "oI,~
, ~ yso~ S
H3AH3SBO
oi~uv q~nult.z~ oq~ uo suao~d oq~ jo oouopuodop ol D o~o!pm, o~ (o0 'o'~ 'o~)D uoDs~ou oq~ ~m.sD_ "scarp uso%sd-uotj~t.pqsa jo tlOIS.IOAl.t[ 011# O#UI. ssouonbmn-uou oonpos~ut. £~m qotlI~ c~s!xo sllot.~sIo~ ut~s#;too #~q~ (9) o# (3) suot~qsnbo moa/oouo #~ sAxo[Io J ~I
• ssouo%mg s,oo~nos oq# aoj pu~ c~jl.qs os~qd alslod oq~ aoj 'c~uotuns~s -m. ~m.paooos ol D jo uot#ao~st.p opn#t.idmqs pu~ ossqd oH# aoj po#ooa~oo uooq £psoai~ oAqs~[ (~) pros (17) '(8) suot.~nbo m ~Ut.anodd~ S~uouoclmoo ~uomoo~iclst p oq# ~qc~ potunssqs s~ ~I "(L96I) q~u!~ pus tuoq~uol~-uo~t £q poc~o!pm " uooq ssq (£) o~ (g) suo D -~nbo ut ~ut;['soddqs ~p ~uOmOlO ~soxs oq~ jo oIoa oq~ L "q~s~t oq# 30 sm.p~a oq~ s ! ~ oaoq~ '~n_(V IllS. V-~) SI ~qC~ 'oaoqds qs aoAo uot.#qs~qsdoad oA~s~ .mJ mao~ ~utpuodsosaoo oq~ Xq poo~sldoa uooq s~st I ' ~_(.t-~8) £IOUI~U 'oo~ds-jps q oq~ .~oAo p~soads ot.~OUlOO~ oq~ ao 3 oiqt.suodsos m~o~ oq~L "~o.*/°/2 = (co)°/2 '(~)H = 0)f oouopuoclop omt~ do~s-~.un ~ a%I
• (o L oan~.~d) "ooanos oq~ ~s os~q ao~ooA ~s s ! (°'a ' °~a ,ooa) .uo~jsOOlS~.p oq~ ~qs dtun~ ~uomoo~ids.~ p jo ~unoui~ oqc~ ~moq 0/2
606I s~s{~wt ssff~t~ qwou9 a~v uvxomx~t
-puodop I'~tDnm!zs s~. aol pa~ssuodmoa ao~i#an ~ s.~ uoDs#s qa~o #~ mna#oods opn3~.Idm~ po#aaa.IOa o~4% JI "sapn~t.idurg im.#.tut, oq# ptlv Sos'eqd i'at.3t.ut, o~[3 ulo.t~ uot.#aunj aun.# s,oaanos oq~ jo uoDan.~suoaoa oq# q~noaq~ paqaso.t st. sTsgt~u'~ oq# jo o~#s I~U~ aq/L
• oAt.snlouoo su'aom ou £q st as~o ,veino.~#a~d s.N # aol oouopi.Ao ott# '(q0I o:m~t.~) 006 = X 'o0~ = ~? Lt°.[#nI°s °1t# p,t~o# ~sq_~'~omos st. ss~,q oq~ q~noq#iV "s~sp oNa~ aAoq isuoDt.pp~ ~msn £q oiq'~AlOSaS st sos~a ~sotu m. qot.t[_,v,, ssouonblun-uou '~ poaput, s~. 31. #~q# smoqs os~a s[q~ .lO 5 (tQ uoDsnba ~o uoDaadsm " u V "aos 99I = £ aoj pota.v~qo uo~.#nlos oq~ uloaj s,iojjtp oos 00g = £ aoj v~sp ~ndut. ot D tuoa~ pout.s~qo uoDnios oq% ~st[# o#o K "ossa v ~ons ,Ioj s#inso.I o1t~ ~t.qtqxo ~0I pun 0I '6 saan~t.~I "sttot.#~Aotosqo oil# It~t.~A po,rgdmoo pu~ po%~o[d st. ao[oqo
IS~ aq<L "(o~ + ~'0(oI)(o~ - "~'~) P~'~ (o~ + "~e)(oI)(o~ - "~'~) ss uo~is~ s~. plat aou~ s ~.~,( pu~ ~<.<~ prano~ ~m.a~ H .o081(oQ)0:~( !o06(oe)0: ~ soi~u~ ~o p~.s~ v
7•VV ~iXIM/A etI~ %s pepzoo~ ~/pu~ t~ s~A~m, q3iei£g~ poztl~ube ~o oT~z i~a~oods oq~ s2aoqs
0I III~X00q~I, "llOt~olln. ; _~tAI~oo$t.. .p ot{~ to uot~tnot~o, etlt%noa'~, ao~ ~nd~uo ao~nduloo ¥ "8 "DI~I
1 .... t .... l .... I .... l .... i .... i .... l .... I""I .... I .... I .... l .... I .... I .... l .... l''"i .... i .... i''"
Zv~ll"
~itLl °
[lutz •
66(C4"
• g'L"M '{9610Z 100'$11 ~t'll~IrlX'. ilIi/llt
i''°'i .... I .... I .... I ..°" , .... , .... I .... I .... I .... I .... I .... 1 .... i .... i .... I .... l .... J .... 1 .... l'''°l 0~0" ~10 ' 910" rIO ' ~tO" 010" 800" 900 " ~'00" ~00 0
t iz#,u" 1
~,4L it "o
,,~ I tl "~Z
ii. tl'~.t.
~LZ~O'6L <,~. #t.tl" La ~o J(c" COI
[-x~vs (~.ov) xs~(~ov) 7 ~o,~,,~
: tuns aq~ ~utz.tmt.tlt.m £q uaa~#vd ,,~soq,, '~ #t. o# s#g pu'a (£auanbaa~ uosoqo s ~s) s~pn#t.idtus pozTisnbo poanssom jo #os sm. so,is # qat.t[~v,, out.#no.i qaasas "a posi.Aop oA~l t oA~ '[oo9 r iNasn "a o~m. smsa~oad uao~sd t~oDs!pva aqa uam o# aopao u I
• uI2 I e L paooxo ~ou pt.p m.~t.,io s,:,iaoqsao~s oq~ ~'~ o.in~dna oq~ jo ~ua~xo oq~ ~'~q% ~t moa~ opnla~ma X~3m o3A "uoDs~s [tVV oq~ ~'~
var~t~gv ato xCLalOO~ rlVDIDOrlO/AIgI~[9 ~tH~L ~IO NI&X"IrlflE 016I
"o96 = Y 'ogg = 9 :papIo[£ qo.t~os oqJL • oos 9'99I J ° P°T~od ~ ~°t s~.~o~d po~osqo ~ns~oa po3~inai~ 0 "6 "oI~I
! .... ]°*''I .... ] .... J .... v++''+ .... i .... l .... I .... l .... l'"'l****I" ''" ........ I**~ ..... f*''*? .... !
t :^~,'v',¢ • t
• , T m~ "*~Z "T
t
i ? :~no~l'7
i r ;nn~o( *?
, r : "+e'++'t "~' + :+O*tr~l+ " ~'
I :oa-t%.?
T ~n~c .f
03A~13S80 . , , , ~,~o-~
I s anenn~-~ , l -'.nnoo~, *
l .... l''*'l .... I .... l .... i .... I .... l .... I .... l .... I .... ] .... ] .... l .... I****]*'''1 .... £ .... f .... t .... f t(r.r*l rr~*e~ fvC "+;~ ~L +".Z ~CC'J+ GGg*+~ ~;JC'U+ ;dU *k)~- Out'J( OoJ *PT r
~uhOaJ~ v°~l iF S~A~ H~I31~+O ~k~ h~]llYd ~'rlJVlO~t" ~l:,~Htt~en
"J .... 1 .... ~ .... l .... I*°''J .... [ .... I'''+J .... l*'''l .... 1 .... ] .... I .... ;***.! .... T
,~o .11 ¢;¢ .)111 r
0 :}~;~c T'7 6 :°° "t'l*~ * T
L) "~pFTI ?*? ~ :on ~t*~Z "T
u ~tco(''l f, * m,~n,),~ .?
u ~z?ll~*T o :One')F*7 o :)('O ne?* ] R ~1 ~rt:" * ;'
~/lOf*T ~ :,-)n ,y)~ • 7
.... +°¢'" + ' o96='( ' ogg:£
I161 SX~I:t~V~I ¢JSX~Iff~ ~IV~IO~ID q~V qVNOIOXE
gI6[
• ~oo~[s zoddn oq~ to ~qm~ ot(~ m u~oqs st (oL6 = ~( '098 = g) ~I nso~ I~Ug oq~ q~t~ qo.z~o~ oq~ to o~ ~¢~1 oq& "I~nbo
-+t.p~.~ pol.~iuoi~o pu~ poA.~osqo lo +g ~.soq ~o I qo.reos lo sliuso.~ ~[+l~ Indluo :tolndmoo V "OT "0I~
• "*'l'***I .... I .... l''''l .... i .... | .... I*'''I .... l'''']''''l .... l''**l''*'$ .... l''''l .... l''''t .... t +
^ ~no'~l*sz
1 9oo~+'1
• . T ;~o'~;'*?
1 ~qnt "f T "~'t~ * t "
• $ T ~n ~n¢ -f
• T :n~ r'~e, -¢
Q3^~13880 ~ ~,.,,-,r~,, ..
? ?o,~nnO .~
(((4(tl £CQ'(~ r~-ob {CJIUL LCLIJ9 ~o~*O~ OGC'O~ CJO*O[ O~LeJ~ ,)Lju* ~? S~NO~tt dO2 IV S]AyM H'~|]l~Vd ©L~ hUAllYd ~rll~feY~ £fcA~41~;gO
G'~u cc~.ez 6¢C'0+ Ou+'O+ ~Jc*J~ GdO'OE c~c*ol .3o+'~t
+/+¢l+'? C1 +1
u l(f;" t *Z a n'r
to~z~*'7 q nT qooa)nor c nT
u t~ ZQrr,*? r OT
0 =Z?¢?~*( T ~T
o Igi*l)*l P fi
o t(6llr*? q
t) :if opoo *;~ T 6
o yneqF~'l ¢ U y~ZOII'| ¢ o -'.16e~.l + "" * •
o ~£~qZ'T ~ t
o l'nZ¢l('? 1, t o 3/e~. )'q * )' Z o tt~¢r Q'I .! o o :,'+~ *,6 o+; *'~ # o u +v,,m*1 , o
o ]111~'? 1 o u :I~I,+1 / t-I rlr ¢ o 11o1~+'t + m
o ~srT~e*l ~z o ~¢f~r-£ "1 ¢ g ; j l*j ~re*7 q g
°***
$$ $
$
II
$
• 1141
Q]IV~AO7V3
o/.6 =X ' o99:2
=.nnnno .~ ~:ln ,',,lr) • Q _~nn,lon -1
_~nnoo~.T
:,'wJ'~6 * T
"m:I 9g = z/'o~t~ = g '006 = ~ uot.c~nios att3 3aoddns (~/'/) sa&~ q~toiX~ K to sasmtd ivtc~t.ut. 'snq& 'sonla ivuo~.#tpp~ ~m.plo.~ n! Intosn osI~ oa~ sos~t[cI i~r.3~.t~, pu~ suo.~c~o~ IV~.~!uI
• uo~.3aosaoa ssauo3.m~ Wa3aads I~UO~.Suoea~.p-ouo sopnIam, vii PnV II soan~,.~I u! (a) uo!3aog "uo~.3aun~ avJt.~ aq3 o3u! a~o/I ao~a~ oR# aanp -os3m. II.m 'a[qts~ot Xli~a~.sX~tcI st. r~aViea '3uo3xo IVUOr.Suova~-o~a3 v 'os~o:'IVI "o~/I °~I![ soa~qoq ao3a~l st.q# ~o o~aoa~ i~lI3nmt.z~ oq~ L "(i96i 'tuotI'aUOlaI-uo~t) [X/X u!s] ao~a~t oR3 soanpoa~m. 3uo~xo I~UOt.Suom!p-ouo ~¢ "sot.auonboaj aoq~.q o113 jo £~a~p oAt.3~[oa oq~ soou~quo s£~a~i~ 'ii~lns sa~o~ao~ I 'ssouo~.l-arg oq3 3~tc ~ pouo!c~u~m oq plnotis 31
• spot.zod suoia~A Jo I sli~to~,~d ox'~ q~lOl£~ H "~0I ",I~I g'/. ~, M
N:)OH$~I3J...4V $'11 3"ll~lnN
°0
x
. xx ~ ii
~o
,,0 .O N
1
1 "(0I '6 sosn~t.eI) suzoc~c~d uoic~.tp~z
li~toi,<~Ii oq3 jo uot.ssoAm, oq3 q~nostt3 aot[z~o p~m.~3qo suor.c~nlos ou~id 3in~j o~a 3 oqc~ ~o t oznpooozd s~.q3 pa3~adoz oAm I o~a ooanos oq# 3~ uot.3~3uot.zo Im.3~cIs oq~ jo ssouonbtun-uou oq3 jo osn~ooff "uot3oun~ do~s 3t.un ~ 3o mnir3oods poz.tlmuzou oq# q3.l~ c~t poa~dtuoo pu~ oos/om 9 = of 3~ o~soA~ st, lt~ jo on[~A oq3 Xq suot.3~3s II ~ 3o si~npt.soz o~2oA~ olt3 poz!l~maou oA~q 0m oao H "~II P~ II so~n~!~I m. ~aoqs s*. oldm~xo uV "ooanos oqc~ 3~ ~o!3 -ounj OlXlt.3 oq3 jo mns3oods oq3 o# i~uo~.3aodoad oq 3snm Stlt~lXlOZ a0AO#~ItA~ UOqqt '0OUO
~[6[ g~H~a~w gg~Hxs ~lVKO~m U~V ~IVKOIO.~H
sos~qd 30 aoqmnu £uv 3o SllOtyac~s poc~aaios aotF~o amos puv 8gKAkM daoaa c~s sam 9 inAt.aan poc~aodxo oq~ soqmdmoa m~a~oad oxI& "sos0dand uot.c0aagI.qmap~, ao~ pappn st. q~uoAo oqc~ jo uot.~d~.aasop a~.aamn~x-vqdin amo~ .m.~.ao 3 ° am,.c~ arc ~ pun qctdop Üqc~ 'ao~uoa~.do oq~ jo uotjt.sod po~mt.:~so oqq~ II~ta~ clt. £Iddns oc~ oAnq o~ m~a~oad aa~ndmoa aria ash o& • oiqnAaosqoun oa~ sasvqd amos so~una ,t~dop puv soa~vc~sI.p ut.~c~aoa c~ v 'pau.~ncNo oq pinoa samt.~ i~Ataa~ poc~aodxa oqc~ ~vq~ as ui.~.ao 3o OVal 3 pa~vmt.c~so o~[c~ oc~ p0pp~ oq o:~ p~r 4 qom!~ osoq& "soSqSttd snot.a~a oqc~ 3o som~.# IOaVaq~ ottc~ m.n#qo 'sc~anqa ao soiqvc~ om~.#-ioaqsac~ ~msn 'uoqc~ pun 'uo!c~s ~ o~ oau~c~s.tp aq~ o~ndmoa 'c~uoao oqc~ 3o ut.~!ao 3o am B aq~ pu~ qcMap aqc~ 'aocmaa~.do aq~ jo oc~vm*.~so Sut.~s~.xa oqc~ o:,IVC~ oc~ s~. oanpoaoad 2a~m.pao aq&
• slopout ooanos o~c~ aot sllaa~c~cI tmt.cps~.pqsa OA~eA OAO' I "q0I "OI~I
3.06
NOOHSH3I,.4V 8"11 371HnN S3AVM 3A07 O3AH3S~O
/"
3
N. ," ,._.,,. oO~=X ./
O3.LV"If)O~ ~ /
o0 N
• spaoaoa oqc~ uo sosvtid oqc~ ~o uo!c~vagF~uop,, p!dqsa jo suvom ao 3 osoa~s poau aq~ ~2,~AkM jo ~[ao~#ou ~90~51 aq~ moaj pom.~aqo spaoaoa to aaqmnu #~aa~ ~ ~m.ssoaoad ai.N3 A
SXAV3 A X(IO~ gO ~I~XqCVK v
"008 = ~ 'o06 = ~ uot~nlos oAt.~nuao~i~ ol D ~aoddns soA~m d 3 ° suo.~om i~t3t.ut, pu~l[ aoq)o oq~ 1I O 'q~nmt.z~ oltc~ 3o <luopuodoput. 't~/~ st. oaanos oqc~ ao 3 anita ina!c~oaooq~ po~atpoad oq& "(~I aanN~.d)
YDIHailAI¥ ~IO X~LXIDOS ~IYDIDO'IOIA!SIXS XFI,1; ~IO Nlff~XqKI£1ff :PI6[
• som~.:~ isA.uas oq~ ~o psoc~sm. (,) s:,ISFa:~ss Sm.~m.ad ,qq 1no po~m.od oas sossqd oIqsaaosqou;l "lnd~no jo sc~ooqs aoqlanj go pac~m.ad oa~ sam D i~uoDt.pp~ oqc~ '~saao~u! jo oas sam3qd uo:~ usqc~ oaom ossa m. puv 'om.[ aad somg~ I~A!aa~ ~oc~ oc~ dn c~m.ad iiDt msa~oad oqqL nodders qa~o a%I "opn[am. o:~ asooqa oat
• ssouo#t.ug isum.suomt.p-ouo ao t c~unoaa~ o~ off/uoF~aun I p3ac~aods oq:~ Xq Pm.IdDI nm (V) mnac~oods opnc~t.idm~ oq& (t~) "896I '0g aoq°~ao t ° ~Iaoqs oq~ lo ooanos oq~ :~s poc~3u -*fl~.ao ~sq~ soa~a oaslans OFmSm jo xmF03z~.ivnbo opna!idms moa I pau!~c~qo s~ ~I "u°!~aunt om~.c~ -ooanos poz!i~maou oqc~ to (0m)0/2/(m)0f2 mnac~aads opnc~.idm~ poAaosqo oq,T, (y) "~II-II "sDIX
II "D~X OI • AON 3 FI031:I~
08" Bl" 91" t~l" ~l" Ol" BO" 90" t70" I I I I I I I I I I I I I I I I 0
~ ~,0
08"0
081
09I
008
~L I [ I I I I I I I I I I 0
- Og'O
- \. 38"1
- (8) ' "I "" \\\ 391
- 30"8
I I I I I I I I I-- l- I • F- I J I 0
~, - ot~'o II°~ d3.L9 --~ .....
- 08 "0
- "-.... -08"1 \
N "~\ 09'1 c~ og~:£ ' o06-:~ ,,, o
::o 00'8 c)
-4 m
-- I I ' I I I I I I~-----.L~ I --I I I I I I 0 cJ
.............. ~5 .... d~gg .............. ~ - ovo
o08:~ ',,0 " ",.,., -08"I
(V) .... ~ "' 09"1
' >I30HS~I3i.:IV Sql 3ql~lN~ 'S3AW'a Hgl3qAV~:I \ -00"8
I I I I ] t I I I J I I ', I I Or"8 O@ 99 001 0~8
• oos 'C]OIH3d
~[6I Si~t&~¥cI S~I~,ES qvgoqo ~xXV ~IVKOIO~ttI
'uo~.#~Iod~#u ! .[o~ ~uq 's~Iq~& ~/-f gq# uo .<li~gue~sg pas~q ii ~ oa~ pa~n ~a[q~ ~,L "(g~6I) ~oIq~iL I~a!~oIoms!o~ UolInff-~Xoajjof otIC~ u.~ E pu~ ~/
jo ~om 9 oq~ aoj po~n ouo oqc~ o~ i~a~.~uop~, st. qaVpa poqc~om v '~/gI" = g oa ,,oav, jan~,, moa~ 'qc~dop ~o ~onI~i ~I ao~ ooa~op ouo go si~ao~m, c~v soiq~c ~ om[.c~-lOA'ga ~ ~no~:[~l oq~ osi~ pu~ 'uot.~sonb ut. suot.c~v~s oq~ ii ~ ~o so#vmp, aooa oqc~ spioq ~ps#t. mva~oad oq~ L
OI "A3N3~031~ -~
0~" 81" 91" ~1' ~1" or 80" 90" IK)" I i I i i i I i I I I I I I I I
f
,,gt, =~ =06=X \ \
I I I I I I I I I I I I I I I I
=08 ~ °06 Y
(~) ,,
I I I I i i I F f F I I ~ l l ~--
d31s ~~
3
3t,"O
I I I
(v)
I I I
:)8 '0
39'1
:o
.-t m
3 a
..-4
3~'1
39"1
30";~
0
3VO
08"0 3~'1
39"1 ;D
, ~ DO'i~
-i Ill
I I I [ I I I I I i I I
oOe=9' oO6 =~\ 39" I
• >I3OHSU3.L_-IV S'11 3"ll~n>l ' S3AVM 3AO"I \~00;~
I I I I I I I J I I 1_ I ~Ot~~ 99 001 Og~
"oas' GOl~13d
¥OIHXIA!V ~IO X$,~'IOO~ qVOIOOqOIAISI~IS ~IH~ ~IO iqlL~IqqflE 9161
d~ 'dOff '~aR 'E..SIg 'ERE 'gg 'E ~ 'E
ddd 'S'd 'S'oJ 'dd 'dXd 'dad 'd d 'd
: sasntld 9I ~m..UOlIOJ oq~ uina$oad ano u! papnlam " al~ ixou I[!& "soul D inA!aas pac~aadxo oq~ ~m.M.~ 'm.$!ao lo am D po~nuiF~so oqc~ o~
poppn aao.~a pom.n~qo snqc~ soui~.c~ iaanac~ oR& "s~lnsoa osnqd s~.qc~ ~o uo!t~ao[aa ~ 'uo~.clnm.q -uioa ~/-V olqnaaasqoun un aoj sna~ oI~us~aaa oq~ jo saauaoa anal aq~ jo auo uaAa JI
• uoDNodaa~m " anou![ jo sassoaoad aoat D £q paui.n~qo uaq~ sn~ ouiF~ [~n~an oq& "oi~u~aaa aqc{ op!sm, oaoql~ouios ~m.oq aau~s~.p pun q~dop poa~.sop oq~ tDD~ 'ausid 7-V art m. OlSUV~aaa n jo saouaoo oq~ uiaoj pou!v~qo snq~ s~m.od anal oq& "dn pa~[oo[
-soAv~ qs~.oigs}i pus oaoq qaoq jo suaocnsd um.~!psa pus sossqd isD~.u~ s~.A pom.sc~qo s s oaanos o~Ic~ c~v mo~s4;s-oaaot oR& "~I "o~g
S o0#1 oO(:JI o091 oOZI o081 o061 oOOg oOIg oOg;~
oOII- - ~ / (~/ o~#=~ / \~ ° '°oo. I \ 4"
O
\ + ,,098 o0011 ,~lx _ / ¢
.06 - , ", ~" + 74 -5 - oOZZ "ln8
\ "* " + ION 008 ,~a] ~ I ~ ~08g
I */4,~ o0Z
-" i 06g o09 * ~g ,,~ 00£
.~ "/" 9££"
4" ~ * *~; °?° • 0£ ~ oO I £
' ' o01> o0£ oOZ oOI oO o0(3£ o0#£ o0££ oOZ£
N
oaa.st soiq~c~ (~/ 'V) ott~ ui. (~0"1~9) pu~ (80"I~9) '(~0"~9) '(g0"~9) so~.a~ua oq~ 'o8L'89 oouv~s!p oqcl pu~ 'saolomoIt.:, [ 06I svA~ qgdop at D oidui~xo aoj H "uo)[~c~ oao.*~t aauvls.tp poa~.sop aq~ o~ soV~uo ~soanau o~.,a~ oq~ uioq~ jo qana aoj pun '~[~dop jo san[hA ~saanau ol~ at D aoj pa~insuoa oaol~ solqn ~ aq~ osnltd qasa ao~ "sapn~.~N a[a~uoaoa~ ~msn 'spoq~oui panpun~s £q s! aa~uoa~.do pun uo[~nls noai~oq oaunas.~p oq~ jo uoDn~ndmoa at{&
• osoas uiot[a ao1 poou oq~ oaoqa~ suo~.~oaaaoa aomui auios q~.a '(996I) ~.noqsui~.qs pun (£96I) sDna& '(f96I) ~.uot[sui!q~ puv sXoa~o£ Xq poc~nduioa soui!~ uioa~ ua~n~ uaoq OSln oanq sani~A
/,[6[ NNkI~&VcI SSg~I&S "IVgOqO (II~V rIVNOIO~[~l
.tsaUt.l s s~ oiausm s,q~sH oqa $ut.zopt.suoo pus 'Xzoaqa £s~ jo £a~.pI.lSA aqa *ut.mnssy • sa~Isnbqa~sa o~st.pomaaam, pun doop jo £pnas
aq~ ~ot iooa auaiTooxa us moq$ sadism st.q~L "o~usz apmt.u~sm apt.m ~ zoj pus saausast.p {saauoat.da asom ~s smm~omstas no aauammoad at.aqa ut. pus suot.suomt.p ooanos aOliSms qat.~ aasxnsuommoo oq oa £at.It.qs ~.oq~ ut. ot.I soAs,~t £poq ~o saDt.lsDuaaod ~uaas[ oq~L
• sa~sA~ £poq jo svu~ F poaslOSt, oa a[qs0t.Idds osIs st. 's~sp OAS~ oo~J~ns jo uo~3on p -oa oq~ qat.,~ uoDaouuoa ut. aat.ia~a poqt.aasop 'uo!aszt.lsnba opnat.[dms jo poq~am aq&
"sat.hal poat.sap oq~ auaoq Ia£ ~ou ssq--splag ssaa~s isqoi ~ pns saoaomsasd aaanos jo aouopuad -op qadop 'suaa~asd ssoaas ISUOt.~oa jo smaoa ut. 'aldmss isa~.ast~s~s o~as I £[oAt.asloa s[.q$
$$
|~ .It 4 * 9[ b~ II $ ~ I ¢
~t u~ II * t * IZ tg II i £~ l1
• * * 11 fl II * * * OI 6 II
t~ ~* li fl f? I g £~ II LE 1 I
• * * Ot ~l IT * * * 91 Ol II ~ vt [1 * • * * * * * * *
l 8t l[ * * G[ 9~ I ~ 1 09 ll it * * * £~ b~ II * * *
tl ~l it ?I IT ll ~ ~1 I[ ££ tl II
-o,,, : .... : *** • * * IT II * * t~ [111
It t~ li * i * U~ O~ |l * * * ul iC it ~f ~l 11 OS O~ II k tl 11 9~ be It 19 r? I1 ¢£ ti II Ot 0~ |1
• * * l !l IT * * * th ~ II
uu ul it * * * tl b~ II ~S £~ II t,l bt Ii * * * * t , , , * vt l~ l I * * * * * * * * *
e~ ~ it ~1 lZ 11 S bd II O ld II
l oL iI * * * bk LC II ol £i II el t~ "lI bf ~I II tk ~¢ II I~ ~l II t u~ it 0 ~l II i~ ~I II 9 9I 11 it l* li * * * e~ hc ll b~ I¢ 11 ,l Ut kl * m * 1 e~ 11 O~ L~ lI u~ it It * I * et Bt 11 ~I ~e il ~i ul it * * * 0 ~ II UL £~ II
b~ SOS $$* $
"Rs = ~, pn~ d d = dd, '9SKA4_M_ II s ocl ooanos
uoA~S s mo~l somp, IOaS~< ons~-gpoq lo uo~.~<sino[~o aoj ou!~,no~ ~oclndmoo lo ~nd3n 0 "gI "DI,ff
¶~ 5$* $ dd d~d dd* d 19t01 l~I(] *,0. I IV 15
11 * * II * * 11 * * II 61 0I II * * II II II
I1 * * 11 I£ II II * * II tS 01 II * * II $9 II 11 91 II • 6S 8
I* * * II * * II * * II * * I1 * * ll * * IT 9S 6 IT t ll II * * • II 6 II SS 01 (I * * II 6£ 0l II ~ II II * * II * * • 19 B II ~ * II * II * *
I * *
II * * II * * ll 9 L1
I oS 6 I * * I t I[
I * * I 0I II
I1 01 0I II * * 11 * * II * * II * *
d Dd
* * * * * * * ql'q~l ~v~ II 9z II II ~l 6 ll ~o'fq *^I-
ll 6 fl II ¢q 0I I1 q?*10 *,Vs IT * * * ~£ g IT ~Z'~? *uw*
I1 I£ tl II ~1 Y1 II ~o'OI *~n~ ..... ~ ~ ~.~ .r.,, lI ~ Zl II Z? I l 0~'19 rid
II 19 EI II fl II 11 Z~'fl ld~
II * * * II 9 II 09"~ *gWd
* * * * * * * 0l'F~l *COd * qG ~I II 0£ ~1 I* 6l'~9 SVd * 1~ 91 II * * * hl'lOl .4X9 * * * * * * * Zq'60l *09fl
II 0£ 0l II if O II E?'O~ flON II ~ 9| II I ~1 I1 16"fll *~D N * * * * * * * ~O*6fl *VNN II * * * 1 l IT 61"gt *VaN
* * * * * * * 69"LA1 *IYN IT i ?I ll 9~ 6 ll E~'tq *NNW
, * * , , * * 9~'|fI ~P~
* 9 9I II O~ fl I1 96"66 *~i II * * * ~? 5 I1 0~'fZ *NVW , , * , * * * of'ill *IVW
* ~ ~l IT ~Z [I lI 6f'18 *Of13 * * * * * * * 90'111 *Sdl * * * * * * * if'g~l *Odl
II ~I 91 II 8g 11 II ff'flZ *NO1 I1 IZ 0I I1 gZ 9 IT 60"9b *~33 * Z 9I IT ~£ £1 II 0Z'66 ~V3 II ~9 ZI 11 9£ 01 11 gI'99 *NIl * C~ tI ll ~I ~I IT Z£'Z~ *ql~ * 9~ SI IT 01 £I II 9~'f6 *N9~ I1 6~ ~l [I 9~ 01 l ! 69"g9 00~ II ki II Tl ~Z 6 11 gl'f9 *dl~ * g£ ~l [I fl ZI 11 gZ'I8 *^a~ * It ~I 11 IZ £1 II fl8"~6 E3P * 9 OI II 79 £I IT f~*00l *I3P * l~ ~l II IZ £I II 61"96 *151
dd* d IOqOllSlfl N~IIVI$
0 61 ~9 11 LG It 9~ I* ~¢5 9I 6£ £1
9~ Ig L ~I 6~ 61 £~ ~I £E 0i~ £~ 91 99 £I
lift ~.Z b£ 0~ £ 91 It# Ill Ol 61 i~Z 91 9£ 01 91 fil
9~ gl
9¢t 91 9£ 1~ 0 ~1
£ 0~ I~a 6I 09 tl I U~ 9I ~Z 6~ ~Z 0l bl Si 0I 9~ LI £I £I £9 GI OI tl 9~ El
6~ LI £ ~I
ttt~ lI
da
jo UOF~S~oadaoaut ' oqa 'osn oa o[dmts pus ~us~oio aas saNostuaqa spoq~om osati~ oit.qsA • sainsoa Sm.~soaaam. amos pa.~apuaa 'svnpt.at.put " aaq~o £usm pus £a!saaM.ufi stno~ I "~S an dnoa~ ~aa!oa d oAs~-S~ oq~ '£ao~sAaasqo uo!m.mo(I s~s~aO oq~ o~ anp st. qaNa~ 'aaoJ~a st.q& "aI~US uoDszt.aslod oq~ jo poq~am aq~ pun uot.~om ~sag jo poq~am oq~ Aq oasp oa passooo~d uaoq OASq 'II6I SS ~I0Sq ~S~ Ss ~ut.asm.$t..to amos 's:@oqs 000I usqqL a.mi/~
• ms~o~d stq~ 1o ~nd~no aqa jo oldmss pa~ut.~d s s~oqs ~I oJn~t.d "somt.a ~/-f aq~ 1o asq~ qat.~ am.I m. st. qot.qAx £asJnoos us 'pnooos ano m.q~tA~ st ssaooJd uo~3siodJa~m ' Jno .to £asJnoas oq< L
VOIkKRI/~V dO X~LIKIDOS ~IVDIDO~IOIAI~IIK9 IKH,L dO NI<L~'YILIIK ~6[
(6)
F~9~177 = (~)Vl -- [~.< L~- J (.,)..,~
(£) (~)a,.a{(~.~ ~oa) adaq 4- (v.z soa) ,ad*q 4- (v.~ ~oa) oad0q}.
'maoj sso[uo:s -uam:p Sm.a~OliO J oqc~ m. c~svaoa oa~ pIOU avj o~tc ~ c~v s~ln~ avat[s moaj ~oAvat AS' pu~ HS' 'd jo s~uamaav[d~.p i~acpad~ iva:~aaoaq~-£va atlC ~ 'm.oaoql papunodxa £aooqc~ oq~ .~m.gi- 1
• gi~u~F oav~ £poq po~v[oe: ~o s!eJi~u~ om.c~noa ao; m~a~:p ~o1¢ I "fI "mcI
q> NOIlONN4 3~lJ-
31Nd~03 ONV ~NtO3dS 03193WW09 3SITV~MON
t NNB21~d NOII~IO~N 031~7n97~9
ON~ O3Aa3SSO I 107d ONV 1Nl~d
t S370N~ dlTS ONV dig NO N~31t~d
NOIIVIOVN 30 113 1938 ~OJ H9~3S
3SNOdS3B 7~iSNN9 'IN~N~ISNI'39N3983AIO
ONV NOlld~OSSV :NO3 NOIiO~ 90
~N~iD3dS 193NN09
] / (3SNOdS38--~
~ 2N3NNalSNt 31ndAOD) / A~iSNI 3NIINO~SNS
(ADN3AO3N3 ~\ 40 NOI13NA3 SV ISA~I9 \
30 3SNOdS3N $311qd~03) / $38iSI7~9 3NIINO~ISASj
t (SNO.LOV9 30N39N3AI(] £ NOI/~/IqN3 J.lV 31~dt~09)
AIGIIV 3Ni/noaans /
aantona±s ININd
p'd'~'o
~SINVHD3F~ 30NROg-ll'ld V~VNOONd SISAq~NV 3A~M-AOO8
"(g96I) ~uo& puv qc~Fu S 'moqv.uofv-ua~[ £q passnas~.p uooq £pvaa[v oavt[ qF~ap s~i "I,I oan$:~I m. pom.[cmo ~t. aanpoaoad uoDvz:ivnbo apm:idm~ aq& "c~uomna~sm. Sm.paoaaa a,t~ o~ anp ~m.aac~IU (~) !£~:auo~oaa~oq iv~snaa oc~ anp Sm.ao~i ~ (g) !q~av[~ iva:aa~id~ v m. aauo~aaA:p pu~ uo.~v -nuo~v (I) :oar ~ao~a~ o~aq& "[~u$~.s aq~ jo maojaAv,~ aq~ ~u!d~qs m. c~a~d ~Ioo~ qa!qa~ ~aoc~avj oqc~ ii v aoj 'ouo £q ouo 'c~aaaaoa puv oaanos oq3 o~ uo~.c~v~s oqc~ moa~ :,iavq £va oqc~ oavac~ Xvm o.~ 's: ~vq/L "[vu~:s oq~ jo £ao~s~.~[ oqcl no puadop qa:Wa sao~a~ jo aaqmnu v jo ~anpoad v, sv piag a~j oqc~ c~ sosind S' puv d jo smna~aod~ oq~ uodn ~iooi £vtu oa~ 'mo~g.gg
616[ ~*vHaa;±va s~a~a;s "Ivao'io q~v ~lV~VOIDa~I
-stos oq~ jo oousApqs assqd ao~.ano¢I = (co) S~IHd "ISU$. ~s Vu!~. a° oqa jo os~qd ao~.ano<I aqa s.t (co) IHd osw "[(co) GV][(co) ~OV][(co) &SNIV]/(m) V = (co)°V umnI°° axou oqa u I -(e96[) "p9 ~a uosaopu vut uoat~ vq.sp- 0 jo st.ssq oqa uo po~.ndmoa uooq s'aq (~/'V)~ uotc~oun~ oq& "ppom q~as a isa!aoqds sm. oauo~aoat.p isa!aaomoa~ pus uo,ysnuoc~as isa~.s_gqd vIc~oq oa anp opm~.[dms oas.~- d oqc~ jo ao~osj ~o.~anm.m W isaoa oEa st. (co)(iV • otgoad iv~snaa uosotp oqc~ ao~ (~96I 'l v ~a moqsua}v-ua~t ) aoc~asj opncli.idms osuodsoa isasnao go~ss H oq~ soA~.~ (m)~OV umnioa oq& "~m.idnoa oaoz pun Sm.dmsp isa~.a,.aa an 'aas 00I ~o po!aod aaaomousAisS qs pxls aas 0g jo po~.aod mninpuod s qa~.~ qdvaSomst.os -*a!aoioa Smpag-ssoa d s aoj (0co ,q po~.idTainm ) osuodsoa opnc~.idms isauomnaasm. oqa smoqs umnioa ~xou oR& "ISUS~.s ismfl~.ao oqc~ jo opna~.idms ao~.an%I oqa soa~.$ (m)V umnioa oq& "ao£s I *at.aopa-Axo[ s qc~.a~ aDnsm aoddn us ao~ iopom $aoquoan O s ~q paas[ -hints ~oeq ssq uo~.~sas eqa as oan~anaas Isasnaa oq~ L "so S sasr oq~ u~. ~iaoqs daop s UlOa~ O1NcI ~s popaoaoa SOASA~ d ao~ out.~noa ~mssoaoad al D ~o oldmSs s s~aoqs gI oanS.tcI
• uoTasc~s $m.paoaoa oqa cls ~uI.aoeis I Isasnaa oqc~ oc~ onp noDaoas~.p oq~ ao~ pun c~uomnaasu.t ~m.paoooa oqc~ jo saaajjo oqc~ aoj poaooaaoa uooq oasq qa~.q~a snot.asaaosqo IVa~aods ao~ Iopom oast.adoadds us ss aaaos usa sot~sa auomoos[dst.p SSalUOt.Suamt.p osoq&
• um.c~aunj om~.c~ s,oaanos ~o mnac~aodg--(co)0/~ ~[nsj jo soas--~p
• oaanos ~o qc~dop--~/ • saAse~x-Xpoq jo saaqmn~ aas&--'a l ' ea/
"(9) pun (g) suo~.}snbo m. pougo(i--v d ' sb ' a d ' sb aaanos oq~ c~s SOlSUS d~.p pun d.qs oAtaaadsoE-- ~ 'X
saaaamsasd uot.q~sdIsstG--' 0 ' e 0 sm.p~sa oSsaoas s,q~asa--~
Ist.mosg[od oapuoSa~I--dd • uo~.a~c~s pun oaanos uoa~oq oi~us isaauoO-- v
"SOASA~ Xpoq JO oauoSaomo pus oauopput. ~o soiSus oa~.c~aods%I--v.z ' 0, • s[suSt.s oas~a-gpoq paaslost " ~o sossqd isaaaods--'¢ ' e~,
• q~clop s,oaanos ~s ot.c~sa uosS!Oci--'~
(£,~) ~5§- = ~a ~d{- = sq
~d~ - oq_ = ia ~d- = tp
ab = 0) % = 0p ~g m.s ,< m.s {- = 0q
(it) (8) 08 d -
O.IOq:',A
(or)
[-~v-~7-] (co)of/
-- [v ~] L-EF j _ (~)'%~
VDIHatIA!V ~O X~[IDO~ "IVDIDO"IOIN~IXS $[H,.L ,frO Nlff~XrI"Iflg 0~6][-
V aoJ pa~vnisAo oa~ (co)0 V sopn:~t.[dm~ pozt.i~nbo oq~ 'c~,iaAa atmszos uoAt~ Xuv ao d
"(g~6[ 'smas~t.EI) saIq~] '~.z- v oq~ moaj uo.t:~[odao:~ut a~,ou![ ~ £q pout.~qo UOlF~ st "++z 'uo~.c~c~s ~ aoj V uoAt.O
"sda g000" = fv jo s[saao~ut, as (ulo~oq) sda 610" = f oc~ (do~) sda 9000" = 0/tnoaj spuac~xo a~usa Xauanboa~I "smna~ -aads oas~a £poq ~o uo*.c~sz~ivnba assqd pu~ apn~.idm~ aoj ou~noa ao~ndmoa jo ~nd~n O "9I "oI~t
[ ~O+[~°& - q JdbE%+B - I- ~L91%'%
0 J%LbL°o - q lEOne*L- [- ~[99°~
Jv~uv%- 0 3ZgOl'Z- i- +b+lO'+ O ++t~%*b- C J+YB~'9- l- +++6+'9
a ~¢%~V*9- 0 3C0E£'~- L- b�gL~*~
,a ~,J%L'~- 0 3961Z'9- l- d9~60"9
U =¢LbL*%- 0 3%~LL*£- 1- ~Lb~*9 v J~i~b*~- 0 3~£~'E- I- dlBZg'9
O ~bb~b%- 0 3Z6OI*E- I- 310~b'9 U ao~L~'k- 0 3ILeU'Z- I- ~Ik9"9
O ~O~OL°C - 0 ~b0~Z'Z- I- fl~L~U°9
aL&Ol'~- 0 3LgLL°I - I- ~9~6"9
L~IoIHo IM|QIHd IRIBJIhO
0 3b++='[ I- J+++['~ + +£L£~'1 +- ++O++'l C ++k++°l 6 $++o+°+ O +++b+'L I- +++bO'Z Z 3+�ZZ't +- 36333"! ~ all@+'t ~ +O+�i'+
u =~b)i'[ l- dig(~'~ c ~olig'l ~- ~ZoSZ'I L 3LO6~'I £ ~bL~6"i
[- ~i~i'~ I- ~LUgO°I + aI~+9"l +- 3Lb6Z'I C J9U+8"l t ~9+9"+
I- ~6U~'9 ~- :L�dO'L Z dL�~O't %- d0G1E'I C 3B~'l £ A9%II'Z
[- aEUB~'[ l- ~bGO'I- ~ 36L~'~ ~- 3~9%£'1 C ~ILL°I g 3b~B0"l ~- ag~9%'9 I- ~ZOIE'[- ~ ~�ZE0°E %- ~RI~E'I C 3ZlRL'I ~ ~OL3L'6 ~- aCLB¢'£- 1- ~ILgS?[- Z ~b~9~°E +- 3L9~£'1 C ~aCtL°I Z ~lb~°k
[- ~IL�~'@- I- ~LSI�'~- E ~807°~ ~- ~IBgt'l U d89S9"1 ¢ =b[+l°£ t- +t+u+'+- l- 3+Zu+'Z- Z +BBZl'; +- +s[+i'I c 3+I++'I + +lyo+'Z l- 3I~BB*9- I- 301~1"£- ~ ~�Yi'~ ~- 3606£'I C aLL~9"I ~ d6toG'l
I- $?Ilz'b- [- 3~b9"~- ~ ~bEBL°L %- $80bt'I C 3%S09"I I 3ikL[°9 0 Jl�b0"I- l- ]EELb'L- ~ =10BE'b %- ~t~Ci'I b 369~'I 1 ~b~t~'[
O 0 0 ~- ~L~'l C O (MlShllk= {HIIHe I~IOV l~IOV tMIBDV (RISNIV
:k~gO+l
~L090*I
:g~L0°l ~gbLO'[
~bkg0"t ~oCO't
~O¥[b'L ~99[k'L
~gIO*Y
~LLgb'~
~Ool0"l
++LZg'~
1- iObLI°l I- ~ZZOL'~
NO|lOW lV3II~3A
0UO0"~( E9~'£9 00~+~ C06~'~ C0~8+L 0000+~| 8~9~+0L 00kk+~ 0009+~ C000+8 00~0°~I £0~'09 00UO°E 006~'~ C00L'9 OO~O°~ El~9°~g O0~L'~ OOg~*g CO~O'g
~N|INU30e3~NJ£fl~-HAI ~JA¥1 Al]3Ol~^ ~O1 ~8~k~lf~ ~J~|~¥d
H I~ OH~
9NI~J~Vl 33#~bf~ Nb ~N3flI3NI $3AYR AOCE
CLu~'~+~ 1+ bI d Z-¢1 9m+
• (~o) (IIH~t + (co) ~IOIHd - (co) SNIHd - (o~) IHd = (co) OIHd
:aAsq am utun[oo ~ss I olt~ m. £[[snt.d "oslnd oq~ jo isAtaas ~sJ U aq~ pus m.S!~o jo om[~ oq~ ~aoo~oq (spuooes) om~.~ m. eouoJoj~.p oq~ s~. 01 pus 'lsu~.~s po~slOS [ oq~ o~m~.+suoo ~a~.q~ sopom oq~ ii s o~ *xommoo oq o~ pomnsss 'oos/m~ Im. IsuSt.s a~ D jo £~I00[0A es~qd aq~ st. 9 'uI~ Im. oous~s~.p [sa~uoo[do oq~ ~m.aq 7 ,(0~ _ 9/V)eo = (~) (Ilnd • os~qd osuodsaa i~snao s,iio~ISSH = (o~)IIOIHA "s~.un oioa~.o m tuo~sXs qd~om
(996I) ouna{I prln aoptt~qO pun (996I) moq~uo1~-noa pun ~ua& '(~96I) navqvsnN "~t#oq ao 'oaanos oqc~ ~o ssou
-aa~.utj oitq~ ao oaanos oqc~ c~n uoDann J am D oqc~ aoqc~t.o o~ onp oq q~sntu 'suao~c~vd rdoDn~.pva oqq~ ao~ ~oq~ ~ut.c~aoaaoa ~alf~ 'Xauonbo4t no sopn~t.idmqs oqc~ ~o oanapuodop gun 'snq& • sda I0"0 jo sa!auonbaa~ oq~ ua~op cmopuodopm.-£anonboa~ oan so, inn ~ Olt.S~I<~ pun avoqs ~uoaj slna~.aav q~aoat.p aq~ jo snaoq~qsd raoDqs~.pna oq~ 'Xaooq~ £qsa aopao-c~sag o~ Sm.paoaa v
• (I96I) aogol/v p~in c~anqutoc~g ~¢q uoa~$ SV~ oamanac~s Imsnaa uoploD-gwa~nG oq& "aos eg usq~ ao~voa~ spo~.aod ely
"(006) ~s~o pav2~oc~ (o0) q~sou moaj ~Dnmtzv jo notga~n~ s~ pa~:~oid oar sapn~t.Idm V ":,Iaoqs doop ~ u~oa~ sa~v~
'm~ OGD=q ' 'b'9=~ V3S 'qA'qP £961' 91 "330
"aas O~=.L
-,,06
)/ Q3A~3SBO
saanc~anac~s oA~:~ otic~ uoa~qLoq poaDou s~. oauoaojj~.p qmvag~.u$t.s o N "uoD~zt.iqsnbo ~o ssoaoad orqc~ uo uot.c~s~s ~u.~paoaoa oq3 ~v oamanac~s [~s~snaa oq~ 7o ~ao~jo oqcL so~qsa~.pm. LI oan$t.¢[
• qtin%~ odX}-aqsotis dt.is-d.t p ~o Iopotu ~ poaao~ -oad ao~ndtuoa oqc~ 'oao H "9I °an~.¢I m. po~uosoad oaqs :,iaoqs doop m.n~aoa qs ao~ s~insolt • soavm oanjans ao~ g[snoDoad po~nat.pul, sau.~ I ouins oq~ ~uoi~ iopom oaanos inat.:~oaooqq~ v ocL c~j c~saq -~ aoj poc~anpraoa uoq~ s~. qaavas V "oaanos oqq~ punoav suot3ms jo ~iaoa~qtou
YDII:IX?VV ~IO X~LXIDO~ ~IVDIDO'IONNIXN alia; AO NI~LX~I~I~Iff ~61
'(f)ofl o~vq~, oaojoaoq~ po~aodxo st. ~I -o~u~a apn%u~tu o~Tpoma~u.~ ot{~ u T ~:,IaOqS doop jo ~uo!suatm.p oaanog o~t~ c~noqv no~.~vu~aoju T aiqvaoTa~oa 'oaojoaotI~ '.ga,i~a ~ou ii.~,u aos 001~ > Z > O[ o~uva po!aod otI:~ a~. so~v~a £poq po,.aod Suo~ I "saa~OmOlp I jo ~uoc~ ,*ao~ ~ jo aopao oql jo ~som ~v s.~ (L > _1/~) s~IOOt[~ doop jo ooano~ oq~ jo ozt.g otIc~ c~Ic ~ ua~otI~ oa~q
"(o0) rDa°u ruoj~ osTm~iaolo poan~oru ~ooa~op u T q~nmt.zv o~oTput " si~3aouxnbi -oan~ona~ ps~naa ~o slopouI o~, pu~ ~povod ano~ ao2~ ~o~ Zd ~o 8uao~qq~d uoT~Tp~3a poAao~qo "LI "m~t
73QOM 7VISflHO N3Q~IOO-AVMOfI(J:I~ 73(30R EI3AV7 AJ.IOO73A MO-I 9EI38N3J.N9: Y
"ur4 t~£G=q ' 8"(~.M V3$ VONVE b961 ' 91 "J.~)O
; "o~1
-o06
V 8
e-i-
©
©
o ~
II
k
P.
0
i ~ I ~
--- I
T
/,/o_,,
/,/ c ~
.~.-.
0 °,~
~ m -r 0
ffl
SOURCE'S TIME - FUNCTION
o,o o o 0 o ~,
II/ o~
~i~ >° =° ~, ~ >,
I I I __t SOURCE'S TIME- FUNCTION
ro o* .l~ -- .t0 oJ .~, b b b o b o b b I I I 1 T I I
- --F--X-. I[ 12~ ~///* =
~Y
#
¢.- :~<
- ~/. 2,, ~ _
~ z ~
f/ - m
i--4 I -~
I I, .--~ L I I ._.
"o
0 ~ 0
o~-
?:,
0
asaq~ '~uaaa atmstas s moaj saAsA~ ~D pus ~/ ' ~D ' ~/3 ° £~!P.qswAs oq~ ~m.mnss V • Ass 'tm~a H is aa~uaa aa~ndmoa
atmstos s Ol £a~amaIal £q ~og Ol pamnsss aq IIt.ax suot.lSlS osoql moaj s~s(I "osuodsoa pot.aod-~uo[ aa~in us q~.t~ qdaa$omst.os luomaaslds~.p W.xsva s qlt.at paddtnbo oq plnoqs UO!lSlS qas~ "paqst.iqslsa oq pinoo Isso O ag,.as d aql uo suoIlslS 0I amos 3o :,Iao,~lau V :mac~sSs Sm.uas~a Sm/aolioj oql ~uDsa~$ns aas OAk "pac~so~ pua dn los aq pinoqs aanpoaoad isuot.c~saodo us uaql 'lao!oad pa~!saaat.p st.q~ m sdnoa~ qaasosaa aaqlo 3o s~u!pug aqc~ qcq~ oaaSs qa~.q~a paaoAoas.~p aas suaa~sd aA~.Isioaaoa amos H "luoc~uoa £~aoua s,~.msunsl oqc~ ol scmomolo aaanos oqc~ acrsios ol opsm oq c~snm laojja u v "SSN~AkAk otD 3 ° soaNaas aq~ moa~ uosoqa spaoaaa uo possq oq Sam Spins £asm.mt.Iazd aq& "JlOS:g. mols£s ~utuas~ ilsaaao oql 3o c~asd ss osIs aOlS I pus '!msunscr poc~staosss us 3o £1t.suoo~ut. oqc~ oc~ saola -msasd oaanos at.rust.as 3o uot.crs[aaaoa oIq!ssod s jo £pn~s £asu!ml.[aad s ao 3 [oo~ in3osn s ss aAaos £sm 'zaldsqa snotAoacI s ut. paqvoso p 'out.lnoa ~mssoooad SOASm-OOsJans oq&
• snao 3 aqc~ c~s £qdsa~odol out.aamqns oq# qlpa saa~amsasd oaanos otmstos oq:~ 3o UOl.~Sut.qmoa OlqSaOAS 3 amos £q pouaoao$ st. ilouomouoqd oqqt c~sqc l q~aodxo Ol olqsuossoa s~. c~,. 'pooc~saapun ilo~a c~ou s.t s!msunsc~ 3o mst.usqaam uot.~saauoS aql qSnoql -[V "aut.aSc~ oq~ 3o soaoqs oqc~ no stmsuns I ~llt.Tg�~ssAo p poanpoad ~ioq a�N%I-mnaa p aqcr m. poaanaao qa.N.~ s~aoqs ao[sm aq~ 3o ~so~ "~. oaoqs mmpom p~.ntt oqc~ pus aOOlJ usaao poqanwIp aqc~ uaa~ac~oq ~ut.idnoa S~aaua oqc~ m. a[oa c~uslaodmt, us £Nd Sam cmaaa aqc~ 3o uot~sanp IISaoAo aq~ pus 'uoDaun 3 om~ 3 s,aaanos OR1 'ao~aoa luomaas[ds~.p aq~ 3o uOt.lSCma!ao oqc~ 'oaanos oqcr jo ozI.s aql Isqc~ st.soqcrodgq us ol eraoddns spuoI so'4snbqlasO ,to~sm amos £q st.mvuns~ 3o uoDsaauo~ lua[.a~o oq& "uta~fi~ ~uzuotm~ .~u~vuns~ V (I)
S~OlmVOlqaa V al~O~
(996I) ~'~sssaIH pu~ ~AvX~poH (g) (996I) ounz~t PU~ dos[v (g)
(~96I) auna~ pu~ .mpu~qO (I)
-oR Is!;IuI 0~ (g) aWd
~o1£~ 06 so~*~A £po~I (9~) O soa~3k £P°~t 06 SOA~A~ ~poff L6
soA~A~ £po~ 06 so~ M £po~ ~II so~pA £po~ 0L sOA~A& £poff L6
(I) uo~ .tag O ooaaI /~A-~t 06 soAs3A XpoK 86 so~_s M Xpoff 9H SOA~M Xpo~t ~L
siss[~u v sooaZa~ )o NIoI~ d~[S
gL
(06) 9~ 09 6~
06 g~
i u I 90I I S~
ltsn~I npm. H
qsn3-InpuIH ~o s ~pus a so s ~pu~a
I!ZSz~-nao~ gr~
~o q~no s ~o s ~pu~
I!ZVa~ ~soAt
-n,to~i ~uDuo~a g
{9-9 LOg~g61
{9 ~9I }9 ~$2
{9 9
~9 9
9 L-~9 {9
saoaSa(~ opn;Iu~w~ dK[ u°D~a°~I 'S 'O "D
119
0~'9 009
g~2
0g9 gI9 999
m- 4 qlda(I
~[ 6"0/,
F0L 6'Lg[
2[ g'6gI
.4a 9"6LI O~gl 0"80I
M TIL
N 9"9g
i% 9'9g SV9 S ~'~ S I'6
S I'g~ S 0"~
SO'6 ,
~'69 S ~'~ M V~9 S ~'~
1"6~I S g'Ig i i
saaJ~a(I saaa~o( I apm opm,
LV60-H:
~-~0-~ 61-gV~O 6g-gff-I~ gO-6~-IO
II-9I-9~ ~-~-~l~
0~-9VI8
90-9g-~'I gg-Lg-lg
~0-I0-I1~
(£~¢9) ul~izo
3o ova!&
~96I 'g~ "u~£ g-at
396I '9 X[n£ PcI
~96I 'g £In£ g-I~ g96I 'g 'AON 0I-¥
~96I 'gg "aoCE 8-V ~961L 'gI "°,aO I-K g96[ '9I "ao(I 9-V g96I '6 "A°N ~ V
~96I '91 "~nv I*-V g96~ '9 "aa(I ~-V
~96~ '6 '~tcI°s ~-V g96I 't ~aa~ I-V
o~(I xopuI
IXqffV&
• sda ~8_ = of "uot.~aunj -dals c~i.un apt.sDsa H s aoj alst.adoadds f/0f aAana aql ol paasdmoa ss (i aIqa&) s~Iaoqs doop x,.s ao 3 (of)o~/(f)o~ uot.laun3 aqc~ s,~oqs SI oan~ld "aaanos aq~ ~v oauapuadap omt.l aSsaoAs iisaoAo oql aapuaa I[t.,~ 'smnalaads paAaosqo aqc~ moaj £ilsluam~.aadxa paA!aa p ss
~6][ S~CL~V~I ~Sa~I~S 'IVffOqD (INS qV~OID~t~t
dnoa~ #sag oqqt qtvq~ oanc~voj ~utyoaoc~ut. aqc~ o~o N 'suo~.c~om int.c~t.u.t pun sapn}t.idms oa~,x jo stsnq oq~ no papanas~.p ss~a qa~.qat uoi.~nlos q~ctaaoSjt.p s £q pot.usdmoaos ssa~ uloqq~
~o ouo qana "suo!c~nloa Saq~acuuaSs snotaoad oqc~ moa~ snoDqo st ss 'vc~vp oq# ~o suot.a -~#aadaoc~m. o[qt.ggod oe,~a o# puodso.taoa ~ou op guot.}nlog oA~4 osoq,L "(t-a '0t-V '9-g 'g-V '~e-V 'IW) ~InvJ ~utddt.p og~e s uo uot.c~oua dt.is-dt.p s pun (~-g 'I-~¢ 'g-V 'g-V 'g-V) qqn~t isat.aaoa s uo uotq~om dt.is-dt.p ¥ :s~iaoqs doap oq~ ao t asoddn suot.cmIOS ~o sod£# o~a&
• m.oaoqc~ ~mavodds suo~.c~aun t at.ac~ocuouo~m aq# jo ssouonbmn-uou oq# moa~ s~Insoa #t. pun '(0I) o# (g) suot.#vnbo to oauonbosuoo ~ooa~.p s s~. ~t.q& "soa~±a d a°t uao#c~d uot.#m.psa omss oq# aa!$ iiFa qatqa~ ~atvd ~utpuodsoaaoa oaom ao ouo oq Snm oaoqc~ (y '{?) uoDnios qaso ao~ '[naauo~ u I
• snoDqo st (L) su°13vnb° oc~ £c~Vs .l.Xtu!s aq, L "sooa~op m. possoadxo oar SOlSUV ii s
'0 = (x)v + (0~t + x)v
(0 - OgI !06 'e,~e)V = (0 !06 'e.t~)V
(0 - 06 !~I'- '06)V = (0 '.0 '~v)V
(06+0'.06'06)V-- = (0 -- 06 !06'0)V = (eA7+O!9t7'O)V = (O!O'O)V
'(St) o# (8) suot.#snbo cuoaj pug oA~ 'X pus , sc~uamolO q~D~ oaanos #uomaaNdst.p n moat v., oa~,oSaacuo to o[Suv q~Fa sooaSap 0 to q:mln./zn us ~n popaoaaa Oanax d s to opn3t.iduls isa#aods oq# (0 "¢ '~) V ~q ~m.c~ouo(i "soas.~a d a°J suaac~:~sd uo!~st.psa aq~ ~to suot.:~sioa Sac~omcu~s oq# m. poc~aOl~ -oa st. s/.q& "onbNn clou oas suot.~nlos oq~ 'utsSs oaai_ I "(g961) aunaa puv dosig to ~qc~ qc~t.~ sooaSs #In~oa ano ~'-V to osva oq~ u I "guo!#nIos iva#aods pus uot.c~om-ist.~t.m " uoom -aq pom.~qo sww c~uamooa~v iinj s sassa osolt9 ~ iis u I "ao~.iaso poqt.aosop mna$oad om.qasm ocgsodtuoa ano Sutsn 'sn £q pomyNo oao~a 'm21 00L-00g oSu~z q#dop oq~ m. s:,iaoqs 6 ~m.pnlam. 'osoqc~ jo nOaOla "poq#oua uo!~om im.~N~, aq# £q poutyNo uo.tqmlos isuo~y.ppn u~ pus poq#om [~a~aods oq# Sq pom.s#qo suo~.anios ou~id-c~ins ~ gI s#uosoad I o[qs,L
• oSvaoAoa isonmt.zs #uot.a!ttns v qc~D~ 3.t punoas suo~.c~nc~s 0I ~o aSnaoas us jo smna#oods aq~ moat pat.pn#s uooq svq #uoao qan~ "it.zvaa pu~ nao d 'usdsf ,sAsr 'sust.asiA ~ 't.!~.~ I #s s:,[aoqs 6 1 o Spn#s oqc~ papnlauOa oAsqo~a '£pn~s st.q~ ao~ popuo~m. S~UOAO gf JO IV#O~ V jo #n O "L-9 o~uva apn#~.u~m 900 oqc~ ut. ~iooqs doop £aOa 10 £pms o~t.~asdmoa s ao~ posn oao.~ ~N3A3A oq# lo n#n(i
• inJ~m.usom oaom puv aot~o q#oq sl. uot.~vzt.inuot~oa oq# 'oaaq~ ~vq~ oaotlo q oa~ oam.s s~iaoqs doop q~I.~ po#av~s oaw[ oak "UOI~Oa llOAI~ S O~ r gJ0#0LlI~a~gd 10 Clr0g S tO #llOllIU~t.gsn 01.[q r 'gI. ~q~qc~ 'so!pn#s oaanos isuo~.~aa .lO t st. tu~a:~oad ano jo uot.gvo.qdds snot.Aqo #sore aq~ L "ga/ao,/~ daap fo @n~e ~)qolD (~)
~ "~O pus
oq# moaeI "ao#s I anoq u~ ~o~:ut~ ~/to os~qd-Xat.V aq~i, "a.m aof~m aq~ ~uois ov.i_ I t[a~a:t oc~ sanoq {g puods [it.~ ~/jo ossqd-Xa W oq# 'ao~o~ao H "~ocmm.m 0~ cmoq~ ut. oau~c~!p s~.q# sao~oa ~/ "sanoq L ~noqs s~. oou~#s.~p ~nq# ao~ om~.~ [oasa~ ~.msuns# ~m.puodsoa -aoa oR& "009 ~noqs st. Xaoqd~.aod s,usoao oR# moa~ oi! H o~ oausc~st.p o~aaas oqc~ :#ao[oad oqc~ o# c~usaolOa oar ~oas~a oasjans o[~mam pus soas~a .tmsun~# 1o saint.# io~sa# o~t.#SlO H
• oaanos l.msuns# oq# jo sao#omsasd o O 1o smao~ ut. po~adao~ut uoqa pus punoj oq IV.At s~uomo[a ~invj pus suot.#aun~ om n 'sot~t.M~aaa~.p 'suao##sd uot.#s/.psa a~.oq& "uoI.3sc~ Isa~uoa oqc~ c~ poz~.[snbo pu~ poz£i~u~ oq IID~ soAma~
VOIHaI1~V ~IO X&XIOO~ ~IVOIDO~lO:~Ia~ XH~ ,frO NI&XTIfla 996I
: ~mami[oj aqc~ sc~aoddns uosDa £q pac~uasaad s~sp aqa ~sqc~ aao~oaot D papniauoa s.~ c~ I • £[aaF~aodsoa ~uaa aad g6 pus ~noa aod g8 jo so~3t.asiod oc~ spuods
-oaaoa s~.q& "snao 5 oassans s aoj 03 ~noqs pus m:, I 0.e9 jo ~Ddop ISaOj s ao 5 L sI ~nba c~I • { I - a["~P]g } £q uoa!~ s! d ismaa}xo aq& "o06 jo o[~us d~.Is s pus o.e~ 5o oI~us d~.p ~ o~ s£s~aIs spuodsaaaoa £~.aslod [suioa~xo aq& "6[ °an~.<I ui. u~tsoqs oas salnsoa oq& "soi~uv di[g pus dip jo p,.a$ oa~.c~vc~uasaadaa s ao 5 pa:mduioa uooq s~q (y '~)d uoDaun5 oq&
(9[) "(Y'9)J = ('~ + OgI'9)d = ('( -- 0gI'~)d = (~('9 -- 08[)d
aam.s o08[ ~ '~ ~ 0 '006 ~ ~ -~ 0 osooqa ocl c~ua~.a~ns s.~ ~I (t796I aoP~.a~asIt pun uioqsual/V-ua~t)
u.~s y ms 'I ,~ ~us~ + ~2 ~us~ a N (~I) ~ ~ui.s ,~ ~ui.s i/,x" = ,~ usc~ - - ~N - ('~ '~)J -- ap T ,
'd a~uaoaod £~.as[od oq~ ao~ a~.aa~ pu~ o N < qN ~q~ ouinss~ Xsm o~ 'ousid oous~s!p papua~xo oq~ uo Xdnoao £aq~ qo.N~ ~oa~ aq~ o~ isuo!~aodoad aq o~ (suo~.ssaadtuoo ao) suoD~Ni.p ~o aoquinu oq~ ~ui)is~ pu~ s~aa~ a~.aq~ ~o runs at D ocl oA*.q~sIoa soloa~.a o~c~ oW~ ~o ~oa~ uouiuioa o1I, 1 ~m3ooi~a±~ "£[oA~.c~aodsoa 'ouNd £a~a~[~.xn~ aqc~ pun ausld-cqns 5 aqcl 5o saI~V dip ag~ oas ,~ pun ~ aaoql~ ,~ u~c~ { = ~/sn.,psa jo aoq~o aq~ pras ~ us~ { = .t sm.psa jo ouo 'saiaa~.a isuo~o~I~aO oa~ 5o ~s.ts*IOO ad£~ aaoqs oq~ 5o aaanos aapao puoaos s moa 5 saavl,a d a°J sam.[ lspou aq~ c~sqc~ uatou~i-iioea s~. ~. 'aattc~an d
• ausld aausc~st.p popua:~xa s,Xlaa~; a uo Lg'~ > t P [ > 96"I aauaH • sq~dop oaaz c~s o~9I = v.z o:~ q~dop Isoo5 auioa~xo cls age[ = v.~ uioaj £asa og0I = V aoJ soi~us jjo-a.,tm (8e6i) suios~.l t oc~ ~ui.paoaag "£sa aAs,~ d oqc~ 5o ai~us jjo-a:,is ~ aqc~ s~. (V)> = v? oaaq.,a v.~ ~oa = p sm.psa ~o aIaa~.a s m.tI,~.~ts o~.i IV..~ s~m.od poAaosqo aqc~ I[v c~sq~ oai.~ou a~a 'o90I usqc~ ssa I aas qa!tpa saauscls~.p isac~uoa~.do aoj slsu$~.s oasis- d oc~ SOA[asano ~ui.~a*.ac~solI "~asqa aaus:~s~.p popua~xo X[aoX a s no pocno[d uooq oasq c~uaao uaa~$ s UlOa 5 suo~/lom-asa 9 paaaasqo oqcl asqa ~xou ouinss v .~ OlSt, s d~.p s pus ',~ aiSus &.i s s £q pam.m -aoc~op s~. qa~.qax jo rJot.c~s~uo~.ao oq~ '~[ns 5 asusid s no uo~.~SOOlS.~ p :~**auiaaNds~ p s £laulsn 'aapao puoaos o~tc ~ 5o aaqc~sa cmq aopao oaoz lo ~ou s, oaanos aqc~ qsqc~ 's~.soqcmdAq s,.qq o~ £asac~uoo 'ouinsss sn cla~ I "s:,iaoqs auios ao 5 aaanos aqc~ c~s odsqs 50 aSusqa s 5o £c~.p.q -tssod s soanpoa~m, raos~.a~t 'soaanos ,,aa~.so[duq-i[%, ao ,,oa~.soidxo-i[s,, uioa~ soamasdop u.tsldxo O,L "g96I-g_e6[ po~.aad oq} u.~ s:,iaoqs g9 jo so~.a~.aNod uoF~om ~sag jo noF~nq~.ac~s~.p oq~ uo ~saa sc~r.Iotun~as st.H "oa,.soidtui " ao oa~.soldxa £Dusm.uiop ss poD~.sssia aq oc~ c~q~no sosi~nbqc~aso c~sqc~ pasodoad ssq aq 'sc~sp 5o soidmss u!sc~aaa ~u!u!uisx~ -tuns a!aq~ 5o oSsquaazod s ss passaadxo saoqmnu am aqc~ jo aa~saa~ atlc~ ss £c~.asiod ottc~ pou~ap pus c~uoao noa~ s 5o (~N) suotssasduioa 5o aoqmnra oq~ pus (PN) su°~.~s:~Slt.P 5 ° aoqmnu oq~ pa~unoa ssq oi_ I "£aooqc~ uo.~w~u-asag u., ctdoauoa injosn v paonpoac~m. (L96I) u°sDEt
• s~sp £~!aNod uo.~oui-~sag jo uot.~sc~oadaac~m.aa
uioa 5 samoa 006 = Y 'ogt~ = ~ uoF~nIos oq:~ jo oansu.vJ~op aqc~ ao 5 c~aoddns isuoD!ppv '@96[ ) suias'~.II 5 ° s~ui.pug aa,.iasa q~.~ c~uauiaaaSs
u.~ s.~ oiduiss ~uasoad aqc~ ui. s~[ooqs doap ao 5 uoDoui d~.Is-d~.p oqc~ 5o aausm.mop oq& • SIOliSasd o~ asaqc~ uaa.~c~
-oq uoI$os is,ao~snba oqc~ oc~ pauguoa oas dnoa$ puoaas aqc~ jo ~.aoj oq~ oi.N~a naoa~.ads 9 5o a!doa& aq~ 5o q~nos oq~ o~ pun aoaus D jo a~.doaz aq~ 5o q~aou aqc~ oc~ .,ao 5 s~,. ssq
L~6[ gNH~Vd ~gXH~g 'IV~OqD (INV ~IVi~OIDN~[
s~aaj~a asaq~. 5o amo S "uo~.~Ouovo pu~ _~auonbaa~ 'q~dap s,oaanos aq~ uo spuadap q~dap u.~ sa~u~qa o~ suaa~d oq~ ~o _,~.AD.~suas aq~ ~sq~ pu~ q~dap s,oaanos aq~ jo aDsou~s!p st saAs~ q~.ai_~_ [ pu~ aAoq q~oq jo uaa~d uot.~s~.psa oq~ ~q~ puno~ oA~q (1e96I) aopw, Ia~ H pu~ maq~ua~-ua~ "~o}Tw, 7~Taad~ 7~pou~ ,uo~f uo.~Tvu.~u~,~aTap ~tTda o ( ~)
"adRq. (osaaaaa
ao) IqSmaou oqc~ jo s~ln~ J a~oqs q~Dt pa~!aossqs a.m suo{~Aaosqo oq~ jo £~t.ao[~m g (g) "OO.IIlO~
aq~ jo ~uomuoa!Auo aq~ oc~ pa~laa aa~ suoty~aoist.p a~aqs jo suo!'1~c~uotao [s~Asds oq~ L (I)
os~qd ga~.v aq~ c~g (-'f~) soA~ea t{~t.o[gg~[ jo uao~c~gd um.c~s~.p~a oq~ moa~ uol, tgm.mao~op tDdo([ '0E "oI~I
),,130bl01:t'41,,,1'~ SGI -4"111:tl3>1
o06 \ o06 ""
))// ?2- o0 o0
"(0 = t/'o~0~ = "~*~V) umA~OOlS~.P a~oqs oa~ans s ~o ~o~.~um.ao aq~ tm Xt~.a~[od oA~a- d oqt ~o oo~ap~odop oq~ "6I "oI~I
tX'~) d O~ O~ Ol 2. c3 ~ ~ l
~ ~'
;_< _~
i" I / oo "/o E~J6 "/,06 %ll % 0~3
39VLN33~3d ALII:IWIOd
¥OlE~tIAI¥ ~O X~tlOO~ qVOIDOqO~%SI~I~ ZH~ ~IO i~I~fiIqqflE ~6[
jo sapom aoq$!q jo smnac~aads pacmdmoa (L96[) aopt.,~IaSH "sq~dap aaanos am[[sqs ~qs Iopom qla~a pla!qs ~ ao/006 = '( oel~ = ~ uo.~qscmolao ogc~ jo ~ql moa/oiqsqs!n~m.c~s!pm " st. c~qsq~ uaocF~qsd uoTc~t.p~a s s~q 006 = ~ 'o08 = ~ jo raoDqsc~uoTao ms qID~ aaanos z~ags s !-sql- u~aoqs oasq (~7) uot.c~vnbo uo pos~q suot.~[nais 0 "SlV~laas oava~- duo pos~q '~oDvu -~.maolop qc~dop ~DOgfl oqc~ scar 3 osis qot.q~,a 'm~ I .eg jo q~dop s aoAvj suoTqmAaosqo 'aao H • so~u~qa qc~dop-oaanos oc~ snaa~c~d uo!l~.p~a oqc~ ~o £c~.aT~.~suos oqc~ £ia~Ol a aaq~sa ol~a~s
"0g = -~ 'aag 0II = ~Z 'aos 09 = °,E oaqs (096I 'uqsmI~.O) sc~u~lst, oa l~luomnac~sui "o~.~a [sa~aods I~spom s moaj uo.~u!maolop g~do G "gg "o~
93S '(]OIW3d C)~'I Ogl 001 08 09 0t7 Og
g'9~l,N 1i3 9'61 gt,£O
i*961 ' Ig 4aJOl~l' oaS- opuoB
(V-81~ VN3(1VSVd) a3A~13980, e,
( ~,100t:,= q)
ogl£='( ' o06=~ (o£6g =qlnw!zv) O31V7~37V9
0 , I00'
I0' 'ID l'tl -I
l-
l=,, .-I
I' o
o
I
• tt~ UO ~n.tp*.a soAs~a q~t.oiXs K l~0~gn~a alnvoao oc~o K 'qsuopqss~ d c~ uoBaaa!p A4-E qc~l~ sapTam.oa soav~ jo q~qsd o[aa D c~soa~ oams ooat-HS, s.t mlsa~oms~.o 9 .(s,~/) opom q~.aIX~ K aoq~!q ptmaos ~ Xq papaaoacI (~/) oa~a q~.olX~s~t at.uqsoao i~luom~spun~ ¥ "Ia "rag
g9 " ~
Og-giz-£O 9961 Ig qaJo~]
w~ gz£=q V3s-vaNV8
v
/',A- 3 VN3C]VSVd H~ gf~
696I ~Ha~£va 99K~I~L9 rlVgO~IO (INIV ~IVKOID0t~
suapssv d '£~OlOUqao & jo o~n.aNsu I ~.uaop.Is O 'u0~ -vc~aoss~.G I~ao~ao(I '~apg~R paL*w) u~a?s'ac~ a*/~ u.z uo.,~fi~do~d aa~ca aa~f~n~ "(g96D "~ '~ 'a°pu~xaIv
"88-gL 'gL-~g, '?~ "~s'uI "~a?g "5"q~var "ll~'~t %96I '9t ounr ~o a:,isnbq~a~a vav2t.'t.N oq~ moa~ S0ASeA D ~o uo~.qtv~vdoad pu~ uoDvaouo O '(9960 '3t 't.:'IV
"0ITL-6gL '~9 "~a~/"zldoa D "1° 'soAs~ oAo, I pu~ soav~ q~t.OlKS H ocl pa.qdd~ uot.avzt.ivn:bo os~qd jo poitclom s £q msVmqaom os[~nbq~a~o jo £pncl~ "(0961) "15 'PlV
• sotu~.~ [oava:~ oav~a-Xpoq ot D jo ~m.mmva~oad oqcl ttcO.m sn podDq o~n~t:~su I nu~mz!oA~ ati1 jo ~.uoqsmvt ~ iosqa!iA~ "a(i "UoDvaHqnd jo aausApv u~. salnsoa s~q sno¢ su!~sa*unu~ -moa aoj 'pmais I opolpd 'X~.saoAV*fl ~aoalt jo aopla:~a~ H "O P~.A~G aosso~oad ~lU~q~ 0% qs~.~ o?A
"Pi~IO~IIKII-Vq~[A :~ao,~oacI s,dauo~ v s~ao!oad qaa~osoH poau~apv oqc~ 1o ~ascI sv 'elVS~I '~1¥O 'qoavoso~I aavdsoaov ~o oaNo uvodoan a oq~ q~noaqc~ ~,~6-(as0) [9¢IV ~a~a~u°o aopun s~t.aoc~vaoqv,I qaasosal:I o~p~.aqmv O aaa%I a!v aq~ £q poaosuods ttgaq svq qaas~soa s.ttt&
sm~va~vo~a~ao,vxa v
• soAva~ aavlans ~o soF~sa ispom ivacDads moaj oiqvaoAoaoa st. qc~dop s,aaanos 9q& (9) • oao~paosIo c~usuWo p s~. oA*.c~snao~is c~sa~ oq~ OlN~a og'gg > °PmF~wI >
o~'~- ouoz ist.aoc~nbo oq% jo i~at.d£~ st. oAt.~uao~i~ puooos o~[# ~q# so, solOns £IOAD -vC~llO% Oldm~s ~uosoad an 0 • (ogtr = ~ '006 = Y) "og~r ~v Sut.ddt.p c~in~ ~ ~ uo d~.is-d~.p s pu~ (°06 = e '006 = X) ~Inv~ Isa~3a eA s no dt.is-d~.p ~ :%u~ra.mlop oa~ suot.c~qm~uot.ao oa~/L "(I oIqS/L) "s:'Iaoq s doop poz£Ivuv c~som o~ uommoa s~. uot3s~uo~.ao d~.is-dt.p V (1~)
• (gI oan~.¢I) anaao Xoqc~ qa~.gea ut uot~oa oq~ lo oan~lsu~t.s v £aava OSlV Lyre s)iaoqs daap jo suot 3 -ounj am~.& "c~uouodmoa uo~.c~aun~-sc~io p v uty~toa £sm s~Iaoqs daap jo c~vq/L "uot~ -aunj dec~S4lUn v jo ~[~ q~t.~ spaoaav s>iaot[s ~OliSqs ~o aa~avavtia i~aodmoc~ 9q& (g) • q~dap s,oaanos oq~ no spuadap uo~3vaois!p aq~ jo az~.s aq/L "uo~.~vao[s!p av~qs ac~t.u~
jo cmqc~ oq oc~ stuoas sttc~do p ~o o~usa opD~ s c~s soaanos jo a~avavqa isBsds oR& (g) "mo~sLs
0-q~.t[ 'at.doa:~ost 'avom.[ ~ sv oA~t~aq qq~a~ X axi% jo 9Durra aoddn ~q% puv ~snaa oq& (i) : suot.~dmnssv sm aOltOX o~ ~aoddns soAvav aavjans puv £poq jo plag uot.c~vt.pva
a~j aqc~ ~o sosXIsu~ i~ac~aods oqc~ £q o~aoqc~tq pau!~cNo s~ins%i "sc~tgAa atms~os jo aoqmnu usoa~ ~ ssoaoad o~ x~.i~.qs oqc~ uo puadop IID~ sot.pn~s mstusqaom aaanos ~o oanan~ oR&
~lOlSnqo~o 0
• sgmt.c~ [aAvac~ oa~-Xpoq jo ash oqc~ q~noaq} poAt.aep q~dop oq~ qc~,.~ ~uoc~s~.suoo st. qa,.qa~ mN Og q: m~I 001r jo q:ldgp IVaOj v no aoaSv sassa qc~oa "o*0 - 006 = 0 jo q~nmt.z~ uv q~t?a o0 = '~ 'oel~ = ~ uoDvc~not.ao oqc~ jo c0aqc~ o3 ua~c~vd ~UOlSat.nbo us aonpoad ilPa 'o*0 = 0 qcmmtzv us qc~t.A~ oglg = "{ '006 = ~ suo~.}vc~not.ao oR% cmqc~ (L uot~nbo) aot.iavo poat.c~on oBA "suaoc~ -~d uot~m.p~a poAaosqo oqc~ o~ c~g c~saq v oAs~ oglg = X '006 = 9 ~o~.~nlos oq~ ~vqc~ uoqa punol s~a ~I 'S~NA~3A 9qc~ no pewoooa saA~l d jo sapnc~!idm~ I~a~aads moal (~96I) moq~uel?~-uaIt pus ~uoK dq pamtuaa:~gp u~oq s~ t ~iaoqs ~o S ~pus~[ o N jo mst.u~qaom oaanos oq& • ~//~/jo ot.c~sa isa}aads s moaj q~dop s,oaanos oqc~ aaaoaaa oc~ pasn aa~ :,[aoqs doop ~ moaj s[suSt.s oAs~ oaS~ans po,.aad-Suo I eaoq~a 'gg puv [g soanS~I m. u~otis st. oldm~xo u V "q3d~p [saoj oq~ jo uot.c~smy, iaa~gp aqc~ ao~ ioo% inpsn s ss aaaos ~sm soa~ea oao~ I pus q~tolgs E ~o sopom aoq~tq ~o suo~.#mqqmoa snou~A Jo Sot3~a Isa~oods "qL pl_tv .sL soan$~.~I m. poc~uosaad aa~ suo.v~slnalva st.q uo passq sc~insoa OUlO~ "[opom q~a~o aa~ds-jiv q paaoAvi,.~inm v m. suoD~aOOlS~.p-avoqs c~m.od moq saava~ aaoq pns q~DiAv~
YOI~atlAI¥ dEO X&~IOO~ "IVOIDO'IOI%~IX~ XHff~ ¢IO NIGXq'ID_~ 0~6I
"~L-8~ '6. e "gfiydoaD "ddv pus a~n d 'suoDnIos ouvId ~In~J oiq~!ioa omo9 @96I) "~I V '~mos%r~ '0I-I '~e ua~u.~lapWoWa A '~ohw~pofi( 1 "~u I .~,~ldoa D pus
• ,o.wa?a/~ 'qadap [~aot Xuu jo soAv~ a~mstos Xi!po q ao~ soaano--(V -- .,) "(896[) "I=1 "V 'vua°sq.I~I 'g9I-~I 'x-I-~89L "sq~I unH ~OlI.~2A 'm~.~umlaald aa~no~ ~of aaua~afuo D
DVIS~rA "a°~d 's°~Im~bq~avo ~o[[~qs I[~ms ao~ uot~oa ooanos OLI~ Jo suo.isLtom.i(i (~96I) "¢[ 'ssoacI 9[g-60~ '[~' "~suI "~a~t
• 57~a~Ig "lln~I 'sosi~nbq~a~o snaoj-doop moaj os[nd ~ jo s.~sXi~u~ maojoAnAk "(~96I) "3I 'vamtvs~3~ "L~-I~g~ '~ "F "~thld°aD '~d pu~ d ~ '~ 'dd jo ~oultj~ oq& "(~96I) .moqsm.~q~ "IN pu~ "H 'sLoajjof
• uopuo~I 'I'M '°sn°H uo~.qan~ 'oauo.~o S jo ~uomoauv~pv oq~ aoj uoD%moss V qsD!a H oqc~ ~o 00~O '~alqv £ lva.*go~omz*a ~ '(826[) uolina 'X 'N ptm "H 'sdoa~of
-.ws" y~av,g fo "f 'suo.~suom.~p oaanos pus aln~j o~I~nbq~a~o 'opn~.~u~ui o~ivnbq~an ~ "(2960 3I 'np.tI .l~gH-6ilr L '~ .~su I "sa~t "13g~.w;g "lln~i 'I,96[
'gg Xannun r 3o o~InnblDano qsn N npu!H oq~ 30 UlSt.unqaoiN '(9961) ~ansna.~H "& pu~ "V 'Dn£~POH "L9L~-I2L~ 'L9 'sa~/ "*ldoa D "g 'soan~a AS' pun d ou~[d jo suoDaolJOa [nasna o "(g96I) "V "N 'I[°:~SnH
'l~g-L[ '~ "uev • aos" "ms.za~ "lln~ 'n.~po}~ poaodnI.I~injA ~ u.t so~A aanjan ~ jo uo.tsaods!([ oq& '(~26I) 'V "N '[[mtSnlt
"g~9-619 'ge "m V "aos' "zus.*as' "llnff 'uln.tpoui snoouo~omoq vut. uoDom 3o uoDaoa -t.p pun d.Ip £ana~.~qau 3o ~In~ 3 ~ uioa3 SOan~ q~Z.OI£n ~ 30 uao~nd uoD%Ip~H "(g96I) "V "K '[I°~IS~H
"g6g-LL?, '~e~ "mV "aos" "vzZzas" "llnff 'mn~.pom poaoXnI-Dinm n u.i saaanos ]u.md moa 3 soa~a oan/ans jo uao%vd uolav.~pn H "(f96[) 'V 'N '[[°~ISnH
'0g9-Lg9 '~ "mv 'aoR "Ms}as' "lln~/'oands-j[~t I at.asvio poaoX~I.Ialnm n ut soaanos po.~anq moa 3 soa'~a oaorI pun q~t.o[£nE "I 're.pore a.,~snIa poao£nlDinm m saan~a oa~jan ~ "@960 'O "(7[ 'a°P[.a~IanII
"(ssoad u.0 "m V 'oos' "Ms}a s, "llnff 'siopoui q#a~o poaods[ ounId ui soaanos ~m.od moa 3 so.zana Ina~oods pus ~a~aods opom aoq~.i H "g 're.pore a.t~snIo poao£niDinm u.[ saanea oa~3an ~ '(L960 "D "(2 'aopta~Ia~H
'~9I-6g[ '9g "~suI • salt "bZll,W,g flnff 'qd~a~omst.os aDou~vmoaaaaIO oq~ jo daooq~ oq~ uo o~ou V '(g26I) '& 'v'In~tflnH
"622-g29 '0~ • vz V "oo~ "ms}as" "fln~I 'sqdna~oms!os po.Iaod-2uoI i~auoult.aodxo otuos no saaoda~i '(096I) "~ 'unmI.~©
"2g-6 'L~ "u~V "aos' • ms.zas' "fin H 'oaanos o~Innbqaauo oqa c~n o~ttnqa omnioa 3o oauoaanaao oqc~ u O "(L96I) "¢I "d 'uos!aa
"0gS-~0~ '~S "mv "aos' "z~s.zas' "lln~r '596I '9 £In£ J ° o~tvnbtDan° qsn~ nptt.~ H oqa jo tus.mnqaom oaanos oq,~ pnn soa~a q~t.oi£~I olau~m 30 uao~nd uot]~.pn1:I "(~96[) ouna{t "~ "f pu~ "H 'a°Punqo
"ggg-gLg '~7, va~770 sqo uo.,u.~moq "qn d '896I '0I Xlnf 3o o:innblDxeo n~sniV ~s~oti~tlOS oq~ uloaj SOA~ q~.toIdv H 3o itao:~nd uoDnipv ~ '([96[) "~ '£ 'ouna~t
"oo S "Ms.*as" "lln~I 'q~an~ aq~ 3o sopom Ivmaou p~v SaA~A £poq 'somI.~ IoaVa/L '(~96[) "N "f 'ouna~[ "L2g-L~g ' I'd "~uV "oos" "Ms}as" "lln,ff
'oaoqd~ ~ uo SOAV3A ~anjan~ Jo a3.tqs os~qd an[Oc[ oq: L "([96[) dos[v '~ "~I pu~ ojn K "~[ "K 'f '°unaa • (ssoad m.) '£aooq& i~a.mdltdooo o0 suoD~a.qddn
sa! pus spnd(I s,uooa O jo suo.Isundx~ ao~aoauo~.I a '(L96I) q~ut~ cgf naan S pun "g 'txloqnnoJ/V-uoa "2g}-I0> 'I~ "v~V "aos' "*us}as'
lln~/ 'soaanos ~utAom oa!ug moa 3 soan~ oanjans atms~os 3o uot)v!pnlt "(I96I) 'V 'tu°q~u°N-u°a "ggg2-LOg2 '89 "sa~/"gdoa D 'F 'soa~ oanjans
po!aod-~tm I jo smna]aods moa 3 ms.m~qaoui oaano~ (g96I) ~9s~Io& "N "IN pun "V 'm°qnu°]/~-u°N "2ga-g0g 'e~ "u, V "aos' "Ms.*as' "ling 'goan~ £poq almS.lOg potaod-~o I 30 smna~
-aads moa3 sotpn~s oaanos ao 3 oanpoaoad V "(996I) ~ttO,L '~I "& pun q%tulS "2A "S "g 'uloqnuoIN-llaE 0g9g-g09g '69 "sa~/"'qdoa D "2? 'q~a~[E pa~j!avaas anti n u~ sooanos ~ut.od anlod!p po~.anq
UlOa 3 soavea oanjans a.[msms jo suao~nd uotan.~pn~ '(~96[) aopta~Ianlt "O "G pun "V 'moqnuojN_-noa '80I-2~ 'x- [-2S~L "sq~I unH ~aOlI.DA 'ms.~UmlOa,1/f ao.mos" ,wf
aaua'~afuoD DVIS',gA "OO~d 'SlnU~t.s a.~ms[.os poanlos.~ UlOa 3 so~.pn~s oaano S '(996I) 'V 'moqnuoN-u°a "I29~-II~9~ '0L "sa~/"~ldOa D "I' '°Duntu aad
-dn oq~ ul soavax oanjans a~tUSlOS 3o soni~ A 0 pu~ uo.v~nuo~n poaaosqo "(996I) "V 'moq~u°IN-U°a "SI~Iq-IH~I '0L "sa~/ "~ldoa D "F '°F~umxI aoddn oqc~
u.~ d~aouo a!ms~.os jo uoDnnuo~a v '(996I) nnaqmnqaaV a 'O pu~ moqnuol/q-uo a "V '"I "(2 '~ossopuv '~LI9-g9 I9 '0L "sa~/"~tdOaD "I'
'o:tnnbtDano doop n £q pa~taxo suot.lni[.~aso oaaj ~o uoDnaaosqo "(296I) °unaa "K T pus ":~ "~I 'doslv
"996I 'L ~taavl/V POa!Ooaa adt.aasnu~1~
~iavus I ~ ,LOAOH~I
aa~ala~ ao amflmlmS~ I ~sv~VZlapA aH~L
~OI~LVI~XH~L¥~ (]aI'I~Ig v aO ~iVXI~LHV~IX('I
'(avu~taeff "A "~i 'u~ma~.~qo) 6 x.tpueddv 'Tuau~aao~duff a.*u,s.*aS fo laU~d v uo ~oda~I 'soAu~ q~!oi£~lI ~o osues [%~%tu.1 io uo.t~uut.mae~ap oqc~ o~ po.t[dd~ vaubt.ultoe~ ~u.tduqs osind pu~ uot.~zt.I~nb X "(6~6D 'F '£e:;lnJ~
"daoo IUO~.ultvo~°oO atkL '~-99 "o1~ ~2oda~i 2va.Zu~laa£ 'se[q~c~ i~a*flo[oms.tos uo[in E pu~ sXoajga F po<mlOdaO~U I '(~96[) "S "H 's!A~aj,
"99~'47~9) '69 "sa~ "ydo~ D • f 'S0AV~ oo~jans otmstos ~o uoi.c~zt[~nbo opn%iidlliv Xq so~i~nblt~a~a pli~ suot.so[dxo ~o sae~ -mva~d eoanos ~o uo!~m.mzv~v(I "07961) avp!a~Ia~ H "O "(i[ puu moquue~v-ue ~ "V "h! 'IK 'z9vs[ o&
"~9L-I~L '~ "u~V "aos "u~s.~aR "fln~I 'sq~d eidvqnm JOAO saa'g~ t[~toi£~gH pu~ Oao~I OI~U~m Jo ~ot~taOlO A "(g96t) motI~UOlAI-uoE "V pu~ "N "7A~ 'z.°.s~io&
"OLIg-L~Ig '0L "salt "~ldoa D "£ 'sivu~.s oAg~-Xpoq poc~ I -os.I jo sulna~aods llioa~ se~i~nbq~a~a doop jo m%m~qaOl/V "(g96i) uloq~ua]A!-UO~[ 'g pu~ "'I "& '~llo~L
"Igg-L~g 'gg9 "qnd uo1~u.~lSVA4 fo • ~s.u I a*.~au~v o 'oan~ana~s IU~llOUDUOa ~o soi.pn~s uo!soidx ~ "(I96I) ao£o~ 'K 'H pug "9 "F '~a~'qu!o~S
"9S~-LLI, 'II 'f "sfiydoaD '~;d P~[v (If; '8"~ 'rid ~o som~ 3, oq~ L "(996I) '~ 't.uoqsm.~qS "gV-gg '~ "lsuI "ga~t
"bglav,g "l,n~t 'maoJsuvaa aot.ano~ jo suborn Xq soav~a oa~jans posaodstp Jo st.sXI~n V "(gg6I) 'X '9ass
WDIH~tlAIV elO X/LHIOO~ 'IVOIBO'IOY{SIX9 XH~ ¢IO N!Ia~i'I~IflK ~6]~