cats_v312.ps

最大似然估计算法

2D7CAB2D>I<EE07E0EE1FF8EE7C1CEEF80E923801F03E923803E07F17FFED07E116C117
FE92380FC0FC177817004B5AA4153F93C7FCA45D157EA491B61280A3DA00FCC7FCA31401
5DA414035DA414075DA4140F5DA5141F5DA4143F92C8FCA45C147EA45CA45C1301A25CA2
EA1C03007F5B12FF5C13075C4848C9FC12F8EA601EEA783CEA1FF0EA07C0305A7BC530>
I<14FE137FA3EB01FC13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CED
3FC090393F81FFF0913887C0FC91380E007E023C133ED97F70133F4A7F4A14805C13FF91
C7FC5BA24848143F17005BA200035D167E5BA2000715FE5E5B1501000F5DA24913035E00
1F1607030713064914E0150F003FEDC00E170C90C7141CEE80184816381730007E167017
E000FE91380781C0EEC38048913801FF000038EC007C30467BC438>104
D<141E143F5C5CA3147E143891C7FCAE133EEBFF803801C3C0380781E0380601F0120E12
1CEA180312381230A2EA700700605BA2EAE00F00C05BEA001F5CA2133F91C7FCA25B137E
13FE5BA212015BEC03800003140013F01207495A1406140E140CEBC01C141814385C0003
5BEBE1C0C6B45A013EC7FC19437DC121>I<163C16FEA21501A316FCED00701600AE15FC
EC03FF91380F0780021C13C091383803E0147014E014C01301EC8007130314005B010613
0F130E010C14C090C7FC151FA21680A2153FA21600A25DA2157EA215FEA25DA21401A25D
A21403A25DA21407A25DA2140FA25DA2141F5DA2143F001C91C7FC127F48137E5CA24848
5AEB03E038F807C038781F80D83FFEC8FCEA07F0275681C128>I<01F8EB03FCD803FEEB
1FFFD8071F90387C0FC03B0E0F80E007E03A0C07C3C003001CD9C7007F001801CE130100
3801DC80003013D8EB0FF800705B00605BA200E0491303D8C01F5D5C12001607013F5D91
C7FCA2160F495D137E161F5F13FE49143F94C7FC187000014B136049147E16FE4C13E000
0317C049150104F81380170300071700495D170EEE781C000FED7C3849EC1FF0D80380EC
07C0342D7DAB3A>110 D<141C147EA314FE5CA313015CA313035CA313075CA2007FB512
FCB6FC15F839000FC000A2131F5CA3133F91C7FCA35B137EA313FE5BA312015BA312035B
A21570000714605B15E015C0000F130101C013801403EC070000071306140E5C6C6C5A00
0113F03800FFC0013FC7FC1E3F7EBD23>116 D<013E1738D9FF80D901C013FC2603C3C0
903907E001FE380703E0380601F0000E150F001C16C0D8180316000038187E0030031F14
3E00705ED86007171E5C163FD8E00F92C7121C00C049160CEA001F4A49141C047E141813
3F91C7FC04FE1438491730017E5CA20301157001FE1760495C19E019C0A2494948130119
8018031900606D0107140670130E017C010F5C017E010C1418013ED91CFC13386DD9387E
13F0903B0FC0F01F01C0903B03FFC00FFF809028007F0001FEC7FC3F2D7DAB46>119
D E
%EndDVIPSBitmapFont
/Fl 134[44 4[28 39 39 1[50 50 50 72 28 44 1[28 50 50
1[44 50 44 50 50 6[55 2[83 3[50 61 4[83 55 1[44 1[72
72 4[61 61 7[50 50 1[50 2[50 50 50 50 1[25 33 25 41[50
2[{TeXBase1Encoding ReEncodeFont}40 99.6264 /Times-Italic
rf
%DVIPSBitmapFont: Fm cmsy10 12 4
/Fm 4 113 df<007FB912E0BA12F0A26C18E03C04789A4D>0 D<0060160600F8160F6C16
1F007E163F6C167E6C6C15FC6C6CEC01F86C6CEC03F06C6CEC07E06C6CEC0FC06C6CEC1F
80017EEC3F006D147E6D6C5B6D6C485A6D6C485A6D6C485A6D6C485A6D6C485ADA7E3FC7
FCEC3F7E6E5A6E5A6E5AA24A7E4A7EEC3F7EEC7E3F4A6C7E49486C7E49486C7E49486C7E
49486C7E49486C7E49C7127E017E8049EC1F804848EC0FC04848EC07E04848EC03F04848
EC01F84848EC00FC48C9127E007E163F48161F48160F00601606303072B04D>2
D<49B4FC010F13E0013F13F8497F48B6FC4815804815C04815E04815F0A24815F8A24815
FCA3B712FEA96C15FCA36C15F8A26C15F0A26C15E06C15C06C15806C15006C6C13FC6D5B
010F13E0010190C7FC27277BAB32>15 D<1B0C1B1E1B3EA21B7CA21BF8A2F201F0A2F203
E0A2F207C0A2F20F80A2F21F00A21A3EA262A262A24F5AA2621903A24F5AA24F5AA24FC7
FCA2193EA261A261A24E5AA24E5AA24E5AA24E5AA2010C4CC8FC133C017C163EEA01FE00
035F487E001E5F00387FD8707F4B5A00E07FD8003F4B5A80011F4B5AA26E4A5A130F6E4A
C9FC13076E143E13036E5C13016E5C7F6F5B027F1301A26F485A143F6F485A141F6F485A
140F6F48CAFC1407EDFC3E14035E15FE02015B15FF6E5BA26F5AA26F5AA26F5AA26FCBFC
150E4F647A8353>112 D E
%EndDVIPSBitmapFont
/Fn 105[50 1[44 44 24[44 50 50 72 50 50 28 39 33 50 50
50 50 78 28 50 28 28 50 50 33 44 50 44 50 44 3[33 1[33
61 72 72 94 72 72 61 55 66 1[55 72 72 89 61 1[39 33 72
72 55 61 72 66 66 72 5[28 28 50 50 50 50 50 50 50 50
50 50 28 25 33 25 2[33 33 33 1[83 3[33 29[55 55 2[{
TeXBase1Encoding ReEncodeFont}78 99.6264 /Times-Roman
rf /Fo 134[50 1[72 50 55 33 39 44 1[55 50 55 83 28 2[28
55 50 33 44 55 44 55 50 6[66 1[72 100 72 1[66 55 2[61
78 1[94 4[78 1[61 66 72 72 66 72 13[50 50 50 50 28 25
33 3[33 33 36[55 55 2[{TeXBase1Encoding ReEncodeFont}48
99.6264 /Times-Bold rf /Fp 134[72 3[80 48 56 64 1[80
72 80 120 40 2[40 80 72 48 64 80 64 1[72 12[96 80 104
1[88 112 2[96 2[56 2[88 2[104 13[72 72 72 72 72 49[{
TeXBase1Encoding ReEncodeFont}32 143.462 /Times-Bold
rf /Fq 134[60 3[60 1[47 3[60 60 93 33 2[33 7[53 9[113
3[66 8[47 20[60 2[60 60 60 3[30 44[{TeXBase1Encoding ReEncodeFont}17
119.552 /Times-Roman rf /Fr 134[86 1[124 2[48 67 57 2[86
86 134 48 2[48 2[57 76 86 2[76 10[124 1[105 96 15[115
1[124 6[48 6[86 1[86 2[43 46[{TeXBase1Encoding ReEncodeFont}23
172.188 /Times-Roman rf end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%PaperSize: A4

%%EndSetup
%%Page: 1 1
1 0 bop 554 955 a Fr(Create)44 b(and)g(Analyse)g(T)-6
b(ime)44 b(Series)f(:)54 b(CA)-19 b(TS)1391 1162 y(softw)n(are)45
b(V3.1.1)1555 1461 y Fq(Simon)30 b(W)-5 b(illiams)1619
1695 y(July)29 b(11,)g(2005)324 2143 y Fp(1)143 b(Intr)m(oduction)324
2366 y Fo(cats)23 b Fn(is)g(a)h(program)f(to)h(use)f(Maximum)f(Lik)o
(elihood)g(Estimation)f(to)i(\002t)h(a)g(multi-parameter)324
2487 y(model)d(to)g(a)h(time)e(series)i(\(such)f(as)h(continuous)e
(GPS\).)j(The)e(routine)g(solv)o(es)f(for)i(all)g(param-)324
2607 y(eters)32 b(simultaneously)-6 b(,)30 b(b)n(ut)i(in)f(tw)o(o)h
(parts)f(to)h(increase)g(speed;)j(the)d(linear)g(part)g(includes)324
2728 y(an)f(of)n(fset)f(and)h(slope,)h(the)f(possibility)d(of)j(abrupt)
g(steps)f(\(as)h(from)g(earthquak)o(es\))g(and)g(si-)324
2848 y(nusoidal)d(terms)h(\(for)h(e)o(xample)f(annual)g(and)h
(semiannual)e(terms\),)j(while)e(the)g(non-linear)324
2968 y(part)c(solv)o(es)e(for)i(se)n(v)o(eral)f(speci\002c)h(noise)g
(models)e(and)i(combinations.)469 3197 y Fm(\017)49 b
Fn(White)24 b(noise.)469 3400 y Fm(\017)49 b Fn(Po)n(wer)n(-la)o(w)24
b(noise)g(\(otherwise)h(kno)n(wn)e(as)i(fractionally)f(inte)o(grated)g
(noise\))469 3603 y Fm(\017)49 b Fn(First-Order)24 b(Gauss)f(Mark)o(o)o
(v)g(noise)g(\(equi)n(v)n(alent)f(to)h(autore)o(gressi)n(v)o(e)f
(AR\(1\))i(noise\))469 3807 y Fm(\017)49 b Fn(Band-pass)25
b(noise)f(\(See)i Fl(Langbein)e Fn([2004]\))469 4010
y Fm(\017)49 b Fn(Generalized)25 b(Gauss)f(Mark)o(o)o(v)g(noise)g
(\(See)i Fl(Langbein)f Fn([2004]\))469 4214 y Fm(\017)49
b Fn(V)-11 b(ariable)25 b(white)f(noise)g(\(i.e.)31 b(using)24
b(the)g(formal)h(errors\))469 4417 y Fm(\017)49 b Fn(Step-v)n(ariable)
24 b(white)h(noise)f(\(i.e.)32 b(a)25 b(change)g(in)g(the)g(scale)g(of)
g(white)f(noise)h(between)568 4537 y(tw)o(o)f(epochs\))469
4741 y Fm(\017)49 b Fn(T)m(ime-v)n(ariable)37 b(white)g(noise)h(\(i.e.)
72 b(an)38 b(e)o(xponential)f(decay)i(in)f(the)g(scale)g(of)h(the)568
4861 y(white)24 b(noise\))1918 5251 y(1)p eop
%%Page: 2 2
2 1 bop 470 548 a Fn(The)28 b(background)f(to)h(this)e(program)i(can)g
(be)g(found)f(in)h(the)f(follo)n(wing)f(papers,)j Fl(Lang-)324
668 y(bein)20 b(and)g(J)n(ohnson)g Fn([1997],)h Fl(Zhang)f(et)h(al.)29
b Fn([1997],)21 b Fl(Mao)g(et)f(al.)29 b Fn([1999],)22
b Fl(W)-5 b(illiams)18 b Fn([2003],)324 789 y Fl(W)-5
b(illiams)20 b(et)j(al.)30 b Fn([2004])22 b(and)h Fl(Langbein)f
Fn([2004].)30 b(The)23 b(program)f(is)g(command-line)g(orien-)324
909 y(tated,)g(so)g(it)f(does)h(not)g(require)g(an)o(y)f(other)h
(\002les)g(e)o(xcept)g(for)g(the)g(time)g(series)g(\002le)g(in)g(order)
g(to)324 1029 y(run.)43 b(F)o(or)29 b(the)g(po)n(wer)n(-la)o(w)g(noise)
f(models,)h Fo(cats)g Fn(uses)g(the)g(fractional)g(dif)n(ference)h
(method)324 1150 y([)p Fl(Hosking)p Fn(,)25 b(1981])g(for)h(creating)f
(the)h(co)o(v)n(ariance)f(matrix.)32 b Fl(Zhang)25 b(et)h(al.)32
b Fn([1997])26 b(and)f Fl(Mao)324 1270 y(et)c(al.)29
b Fn([1999])22 b(used)f(an)g(approximate)g(co)o(v)n(ariance)g(matrix)g
(for)h(\003ick)o(er)g(noise)f(deri)n(v)o(ed)f(from)324
1391 y(an)j(algorithm)f(described)i(by)f Fl(Gar)l(dner)g
Fn([1978])g(for)g(simulating)f(such)h(noise)g(\(H.)g(Johnson,)324
1511 y(pers.)43 b(comm.,)29 b(1996\).)43 b(The)28 b(constants)g(in)h
(this)f(matrix)g(were)i(chosen)e(so)h(that)f(the)h(po)n(wer)324
1631 y(spectrum)35 b(of)h(\003ick)o(er)g(noise)f(and)h(random)f(w)o
(alk)g(noise)g(cross)h(at)f(a)h(period)g(of)g(one)f(year)324
1752 y(when)26 b(both)g(ha)n(v)o(e)g(a)h(sampling)e(interv)n(al)h(of)g
(one)h(day)f(and)h(equal)f(amplitude)f(\()p Fk(b)3135
1767 y Fj(\000)p Fi(1)3261 1752 y Fh(=)31 b Fk(b)3409
1767 y Fj(\000)p Fi(2)3504 1752 y Fn(\).)324 1872 y(This)k(earlier)i
(co)o(v)n(ariance)e(matrix)g(is)h(not)f(e)o(xactly)h(the)g(same)g(as)g
(that)f(deri)n(v)o(ed)g(from)h(the)324 1993 y(abo)o(v)o(e)25
b(transformation)h(matrix.)35 b(The)27 b(major)f(dif)n(ference)h(is)f
(in)g(the)g(scaling)g(of)h(the)g(ampli-)324 2113 y(tude.)j(The)24
b(scaling)f(between)h(the)f(\223ne)n(w\224)h(and)g(\223old\224)g
(amplitudes)e(can)i(be)g(estimated)f(from)324 2233 y(their)h(respecti)n
(v)o(e)g(po)n(wer)g(spectrum)h(equations.)k(That)c(is)1087
2498 y Fk(P)1150 2513 y Fg(ol)q(d)1329 2498 y Fh(=)1498
2431 y Fk(b)1539 2395 y Fi(2)1539 2455 y Fg(ol)q(d)1636
2431 y Fk(f)1695 2395 y Fj(\000)p Fi(1)p 1498 2475 291
4 v 1570 2567 a Fh(2)p Fk(\031)1678 2538 y Fi(2)3445
2498 y Fn(\(1\))1051 2746 y Fk(P)1114 2761 y Fg(new)1329
2746 y Fh(=)1998 2679 y Fk(b)2039 2643 y Fi(2)2039 2703
y Fg(new)2171 2679 y Fk(f)2230 2643 y Fj(\000)p Fi(1)p
1498 2723 1327 4 v 1498 2816 a Fk(\031)1557 2741 y Fm(p)p
1640 2741 1185 4 v 75 x Fk(f)1688 2831 y Fg(s)1747 2816
y Fm(\002)e Fh(24)e Fm(\002)i Fh(60)f Fm(\002)g Fh(60)g
Fm(\002)h Fh(365)p Fk(:)p Fh(249)324 3001 y Fn(therefore)999
3164 y Fk(b)1040 3179 y Fg(new)1200 3164 y Fh(=)1314
3097 y(\()p Fk(f)1400 3112 y Fg(s)1459 3097 y Fm(\002)f
Fh(24)g Fm(\002)h Fh(60)e Fm(\002)i Fh(60)f Fm(\002)g
Fh(365)p Fk(:)p Fh(249\))2575 3061 y Fi(1)p Fg(=)p Fi(4)p
1314 3141 1371 4 v 1903 3159 a Fm(p)p 1986 3159 108 4
v 82 x Fh(2)p Fk(\031)2722 3164 y(b)2763 3179 y Fg(ol)q(d)2859
3164 y Fk(:)559 b Fn(\(2\))324 3380 y(When)25 b(the)f(sampling)f
(frequenc)o(y)i(is)g(once)g(per)g(day)f(then)1558 3589
y Fk(b)1599 3604 y Fg(new)1760 3589 y Fh(=)j(1)p Fk(:)p
Fh(7440)g Fk(b)2203 3604 y Fg(ol)q(d)2300 3589 y Fk(:)1118
b Fn(\(3\))324 3798 y(Therefore,)30 b(v)n(alues)e(quoted)f(for)i(the)f
(amplitude)f(of)i(\003ick)o(er)g(noise)f(in)g(papers)h(that)f(use)g
(the)324 3919 y Fl(Zhang)k(et)g(al.)52 b Fn([1997])32
b(co)o(v)n(ariance)g(matrix)g(must)f(be)h(scaled)g(before)h(being)f
(used)f(in)h(an)o(y)324 4039 y(studies)23 b(using)h(the)h(ne)n(w)f
(matrix.)470 4159 y(In)j(the)f(formulisation)f(used)h(in)g(this)f
(program,)i(the)f(system)g(is)g(scaled)g(so)g(that)h(for)f(an)o(y)324
4280 y(spectral)e(inde)o(x,)f(the)h(po)n(wer)g(spectra)g(cross)g(o)o(v)
o(er)f(at)h(the)g(same)g(frequenc)o(y)g(gi)n(v)o(en)f(the)h(same)324
4400 y(sampling)j(frequenc)o(y)i(and)h(the)e(same)h(size)h
Fk(\033)t Fn(.)43 b(F)o(or)30 b(daily)e(sampling,)h(the)g(cross)g(o)o
(v)o(er)f(fre-)324 4521 y(quenc)o(y)34 b(is)g(about)h(120)f(days.)61
b(This)34 b(also)g(means)h(that)f(for)h(spectral)g(indices)f(other)h
(than)324 4641 y(random)29 b(w)o(alk)h(and)g(white)f(noise)h(the)g
(scaling)f(parameter)h(changes)g(with)f(dif)n(ferent)h(sam-)324
4761 y(pling)c(frequencies.)37 b(This)27 b(must)e(be)j(tak)o(en)f(into)
f(account)h(when)g(comparing)f(results)g(from)324 4882
y(daily)c(solutions)e(to)j(those)f(from)g(weekly)h(solutions)e(or)h(if)
h(the)g(data)f(has)h(been)g(decimalised.)324 5002 y(F)o(or)d(instance,)
h(gi)n(v)o(en)d(\003ick)o(er)j(noise)f(and)g(a)h(sampling)e(interv)n
(al)g(of)h(2)g(days,)h(the)f(\003ick)o(er)h(noise)1918
5251 y(2)p eop
%%Page: 3 3
3 2 bop 324 548 a Fn(parameter)30 b(will)g(be)g Fh(2)1111
512 y Fi(1)p Fg(=)p Fi(4)1251 548 y Fn(times)g(smaller)f(than)h(the)g
(daily)g(v)n(alue.)46 b(John)30 b(Langbein)f(uses)h(a)324
668 y(dif)n(ferent)c(scheme)g(again)g(so)h(that)f(\003ick)o(er)h(noise)
f(amplitudes)f(from)h(this)g(program)g(will)g(be)324
789 y(4.3717)e(times)f(lar)n(ger)j(than)e(his)h(results.)324
1128 y Fp(2)143 b(The)35 b(T)m(ime)g(Series)f(File)324
1352 y Fn(There)g(are)h(currently)f(tw)o(o)g(accepted)h(formats)e(for)i
(entry;)j(a)d(\223cats\224)f(\002le)h(and)f(a)h(\223psmsl\224)324
1472 y(\002le.)h(In)27 b(the)g(future,)g(other)f(formats)g(may)h
(become)f(a)n(v)n(ailable.)36 b(Users)26 b(are)i(free)f(to)g(suggest)
324 1593 y(ne)n(w)i(formats)g(\(writing)g(the)h(code)g(w)o(ould)f(be)h
(e)n(v)o(en)f(better)g(-)h(see)g(read)p 2841 1593 30
4 v 37 w(series.c)f(in)h(the)f(lib)324 1713 y(directory)24
b(for)h(e)o(xamples\))324 2008 y Ff(2.1)119 b(\223cats\224)28
b(\002le)j(description)324 2196 y Fn(The)c(data)g(\002le)h(is)e(f)o
(airly)h(free)h(format)f(consisting)e(of)i(tw)o(o)g(parts,)g(header)h
(information)e(and)324 2316 y(the)j(time)g(series.)46
b(The)29 b(header)i(information)d(is)h(basically)g(a)h(list)f(of)h
(parameters)g(rele)n(v)n(ant)324 2436 y(to)35 b(the)g(GPS)h(site)e(the)
i(time)e(series)h(comes)g(from.)62 b(The)35 b(header)h(information)e
(\(plus)g(an)o(y)324 2557 y(line)24 b(you)h(w)o(ant)g(to)g(eliminate)f
(from)h(the)g(processing\))f(starts)h(with)f(a)i Fh(#)f
Fn(symbol.)30 b(The)c(only)324 2677 y(header)k(information)e(rele)n(v)n
(ant)h(to)g Fo(cats)h Fn(is)f(the)g(list)g(of)g(of)n(fsets.)45
b(The)29 b(data)h(set)f(consists)g(of)324 2798 y(se)n(v)o(en)24
b(columns)g(\(no)h(particular)g(format\))h(corresponding)e(to,)h(in)g
(order)l(,)h(time)e(\(in)h(decimal)324 2918 y(years\))31
b(north,)h(east,)g(up,)g(north)e(error)l(,)j(east)e(error)l(,)i(up)d