RDA I S T GE OF5 OHYSICS HONOLULU INCIDENT … · theory and a progam lstng,with example. ae...

,R -A19 65 GEERAIONOF ERTICALLY INCIDENT SEISMOGRAS(U) HAWAII /

RDA I S T OF5 GE OHYSICS HONOLULU L N FRAZER ET AL. SEP 85

UNCLASIFIEDHIG-CONTRIB-1643 NOMR4-82-C-0388 /811 N

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I. REPORT NUMMER 1. OVT ACCI|ON NO 1 . RECIPIENT'S CATALOG NUMBER

BIG Contrib. 1643 ____________5__In 4. TITLE (an Subtil) S. TYPE OF REPORT A PERIOD COVEREDO)(D Generation of vertically incident seismograms.

S. PERFORMING ORG. REPORT NUMBER

In 7. AUTHOR(q) 8. CONTRACT OR GRANT NUMBER(s)

L. N. Frazer, D. L. Bates, and A. J. Rudman N00014-82-C-0380<dS. PERFORMING ORGANIZATION NAME AND ADDRESS I0. PROGRAM ELEMENT. PROJECT, TASK

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Published in Geological Survey Occ. Pap. 49, Geophysical Computer Program 10,Dept. of Nat'l Resources, State of Indiana, Bloomington, Indiana, 62 pp., 1985

is. KEY WORDS (Continu an rev e red It 0eeaid w i60 Id luSiI' by wleb nambw)

"', Algorithm

SeismogramsFORTRAN 77

* Vertically incident waves

-JL.. 20. ABSTRACT (Contnie an reverse @I#d It neeosee And Idetbllby Nbohl ml.)

-An algorithm for synthetic seismogamsfollowing the method of Kennett (1981) hasbeen Implemented in FORTRAN 77. Compu-tations proceed in the frequency domain andthen are Fourier inverted. Reflections ofnormally incident waves and their multiplesae plotted on a Veuatec plotter. Theagorithm allows easy adjustment to other

DO i j'Is 1473 EDITION OF I NOV 55 IS OBSOLETE UclassifiedS/N 0102-014-6601 I

SECURITY CLASSIFICATION oI THIS PAGE (Mm Dole BtaNe..

"ONE.

UnclassifiedSIC.UqITV CLAS aP0SAThW OF TNIW1 PAGg(Wh. Doe t-s)

-plotting protocol.. A brief outline of thetheory and a progam lstng,with example.ae included.

Unclassified-ICUNITY CLASSIFICATION OP THIS PASGflh@ 0l0t XnteWe

Generation of Vertically IncidentSeismogramsBy L. NEIL FRAZER, DAVID L. BATES, ad ALBERT J. RUDMAN

* DEPARTMENT OF NATURAL RESOURCESGEOLOGICAL SURVEY OCCASIONAL PAPER 494

. . . . . . . . . . . . . . . . . . ........ ...............

8510 07 049

SCIENTIFIC AND TECHNICAL STAFF OF THEGEOLOGICAL SURVEY

JOHN B. PATrON, State GeologistMAURICE E. BIGGS, Assistant State Geologist

MARY BETH FOX, Mineral Statistician

COAL AND INDUSTRIAL MINERALS SECTION GEOLOGY SECTIONDONALD D. CARR, Geologist and Head ROBERT H. SHAVER, Paleontologist and HeadCURTIS H. AULT, Geologist and Associate Head HENRY H. GRAY, Head StratigrapherDONALD L. EGGERT, Geologist N. K. BLEUER, Glacial GeologistDENVER HARPER, Geologist GORDON S. FRASER, Glacial GeologistNANCY R. HASENMUELLER, Geologist EDWIN J. HARTKE, Environmental GeologistWALTER A. HASENMUELLER, Geologist CARL B. REXROAD, PaleontologistNELSON R. SHAFFER, Geologist SAMUEL S. FRUSHOUR, Geological TechnicianCHRISTOPHER R. SMITH, Geologist

GEOPHYSICS SECTION

MAURICE E. BIGGS, Geophysicist and HeadDRAFTING AND PHOTOGRAPHY SECTION ROBERT F. BLAKELY, Geophysicist

WILLIAM H. MORAN, Chief Draftsman and Head JOSEPH F. WHALEY, GeophysicistBARBARA T. HILL, Photographer SAMUEL L. RIDDLE, DrillerRICHARD T. HILL, Senior Geological Draftsman THOMAS CHITWOOD, Geophysical AssistantROGER L. PURCELL, Senior Geological DraftsmanKIMBERLY H. SOWDER, Geological Draftsman PETROLEUM SECTIONWILBUR E. STALIONS, Artist-Draftsman G. L. CARPENTER, Geologist and Head

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EDUCATIONAL SERVICES SECTION JOHN A. RUPP, GeologistJOHN R. HILL, Geologist and Head DAN M. SULLIVAN, Geologist

JERRY R. BURTON, Geological AssistantJAMES T. CAZEE, Geological Assistant

GEOCHEMISTRY SECTION SHERRY CAZEE, Geological AssistantR. K. LEININGER, Geochemist and HeadLOUIS V. MILLER, Coal Chemist PUBLICATIONS SECTIONMARGARET V. ENNIS, Instrumental Analyst GERALD S. WOODARD, Editor and HeadJOSEPH G. HAILER, Geochemist/Analyst PAT GERTH, Principal Records ClerkJIM J. JOHNSON, Electronics Technician BARBARA A. SEMERAU, Senior Records Clerk

AUTHORS OF THIS REPORT: L. Nei Frazer and David L. Bates, Hawaii Institute ofGeophysics, University of Hawaii at Manoa, 2525 Correa Road, Honolulu, HI 96822; AlbertJ. Rudman, Department of Geology, Indiana University, Bloomington, IN 47405.

Generation of Vertically IncidentSeismogramsBy L. NEIL FRAZER, DAVID L. BATES, and ALBERT J. RUDMAN

GEOPHYSICAL COMPUTER PROGRAM 10

DEPARTMENT OF NATURAL RESOURCESGEOLOGICAL SURVEY OCCASIONAL PAPER 49

PRINTED BY AUTHORITY OF THE STATE OF INDIANABLOOMINGTON, INDIANA: 1985

STATE OF INDIANARobert D. Orr, Governor

DEPARTMENT OF NATURAL RESOURCESJames M. Ridenour, Director

GEOLOGICAL SURVEYJohn B. Patton, State Geolst

For sale by Publications Section, Geological Survey, 611 North Walnut Grove,Bloomington, IN 47405

Price $2.50

I!

To the Geophysics Community relatively small laboratories, do not alwaysThis report is one of a series of Geophysical have access to such programs. We also solicitComputer Programs that are being published programs implementing new geophysical pro-in the Indiana Geological Survey Occasional cedures, but we anticipate that such materialPaper Series. Members of the Geophysics will be made available only rarely. Neverthe-Section of the Indiana Geological Survey, less, even large laboratories with extensivewith the advice and counsel of an advisory computer libraries may welcome a study ofboard,* select and edit submitted papers. the other fellow's approach. In the sameReaders are invited to submit programs and spirit, we hope that geophysicists will sharemanuscripts to the Geophysics Section. The both their new and standard programs.primary purpose of this series is to make The format for this series is intentionallyreadily available those programs that deal kept simple to encourage others to submitwith established geophysical computations. manuscripts. It should contain: (1) a state-

Although the editors of some journals ment to establish the purpose of the programsolicit only new approaches, we seek to and some discussion of applications; (2) apublish programs that also deal with standard brief summary of the theory that underliesand classic problems. Our experience has the algorithm; (3) a discussion of theshown that geophysicists, working alone or at programs, perhaps with the aid of a flow

________diagram-, and (4) presentation of a test case.

*NomanS. eidllZenthExporaionCo. In.;Responsibility for distribution of the

Sigmund Hammer, University of Wisconsin; Judson prassm byrd the Indiad Geloiale SurleyMead, Indiana University; Franklin P. Prosser, Indiana asuebyteIdnaGogilSrv.

*University; and Joseph E. Robinson, Syracuse -Albert J. Rudman and Robert F. Blakely,*University. editors

INDIANA GEOLOGICAL SURVEY GEOPHYSICAL COMPUTER PROGRAMS

No. 1 "Fortran Program for the Upward and Downward Continuation and Derivatives of PotentialFields" (Occasional Paper 10)

No. 2 "Fortran Program for Generation of Synthetic Seismograms" (Occasional Paper 13)

No. 3 "Fortran Program for Correlation of Stratigraphic Time Series" (Occasional Paper 14)

No. 4 "Fortran Program for Generation of Earth Tide Gravity Values" (Occasional Paper 22)

No. 5 "Fortran Program for Reduction of Gravimeter Observations to Bouguer Anomaly" (OccasionalPaper 23)

No. 6 "Fortran Program for Correlation of Stratigraphic Time Series. Part 2. Power Spectral Analysis"(Occasional Paper 26)

No. 7 "Application of Finite-Element Analysis to Terrestrial Heat Flow" (Occasional Paper 29)

No. 8 "Generation of Synthetic Seismograms for an Acoustic Layer over an Acoustic Half Space"(Occasional Paper 35)

No. 9 "Computer Calculation of Two-Dimensional Gravity Fields" (Occasional Paper 40)

No. 10 "Generation of Vertically Incident Seismograms" (Occasional Paper 49)

Cost of Nos. 1 through 5 is $1.00 each + 50-cent mailing fee (third and fourth class) or 80-cent mailingfee (first class).

Cost of Nos. 6, 7, and 9 is $1.50 each + 50-cent mailing fee (third and fourth class) or 80-cent mailing*fee (first class).

Cost of No. 8 is $2.00 + 50-cent mailing fee (third and fourth class) or 80-cent mailing fee (first class).

Cost of No. 10 is $2.50 + 50-cent mailing fee (third and fourth class) or 80-cent mailing fee (first class).

'.,S,,'. , . . , , : ...... . . , ,, . ' . . ,, ,

ContentsAbstract ............ .............................................. 1......Introduction I............................................ 1Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Sum m ary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

iterature cited .......................................... 5Appendix 1. Generalized description diagram of Programs VISP and PLTVISP ............ 6Appendix 2. Glossary of variables used in Program VISP ........................ 7Appendix 3. FORTRAN 77. Program VISP and Program PLTVISP .................. 10Appendix 4. Input records and output plots for 12 tests .................... 41

IllustrationsPage

Figure 1 Graphic representation showing the first few terms of equation 9 forreflection and transmission matrices of superposed media and show-ing schematically the interactions undergone by the waves with theregions z, < z < z 2 and Z3 < z < Z2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 (Test 1) Output plots generated by Program VISP. A, input data: veloc-ity (CL), Q (QL), and density (RHO); B, synthetic seismogram gen-erated from input data ...... ............................... 4

--. 3 Velocity models for Tests 2-13 (appendix 4). A, one-layer; B, two-layer;

C, six-layer ......... .................................... 41

4 (Test 2) Reflection from a single layer (fig. 3A) for A, Q = 1500 and B,Q-5 ......... ....................................... 43

5 (Test 3) Reflections from a two-layer model (fig. 3B) for A, full-response option and B, one-multiple option ..... ................... 45

6 (Test 4) Reflections from a one-layer model (fig. 3A) used to displayfilter options. A, band pass of 10-50 hz; B, band pass of 10-500 hz;C, D, E, and F, high and low cut with minimum and zero phase; G,band pass with 6-db slope versus 96-db slope used in A ............... 46-47

7 (Test 5) Reflections from a two-layer model (fig. 3B) with amplitudescale (ASC) 1 ......... .................................. 49

8 (Test 6) Full response from a two-layer model (fig. 3B) for A, no AGC;B, AGC with window - 10 msec; C, AGC with window - 60 rnsec; D,AGC with window = 500 msec ...... ......................... 50-51

9 (Test 7) Variations of computational frequency (NW) for a single re-flector model (fig. 3A) for A, NW - 16; B, NW - 64; C, NW - 256 ......... 54

10 (Test 8) Variation of record length (TSEC) for a six-layer model (fig.3C). A, TSEC - 500 and B, TSEC - 2000 .... .................... 55

11 (Tests 9 and 10) Arrival times and amplitudes for a six-layer model (fig.3C) for A, reflection coefficient; B, vertical displacement; C, pressure ...... .57

.- - ., , - ,- ,,.- . .- . . . ,- . .. • • . . . .. . . - .. .- .. ., ... ... . - ,..-. ..- , .- .- ,. . -. -. . .:

Illustrations Pg

Figure 12' (Ts 11 Pimary elecioso a sxlyrmodel(fg3Cfoareceiver at the top of layer 4. .. .. .. ... .... ... .... .. . ..... 59

v13 (Test 12) Generation of interpolated layers with uniformly increasingvelocities. .. .. .. ... .... .. . .... .. . .... ... ... .... 61

TablesPage

Table 1 Input data used to generate a typical synthetic seismogram (fig. 2) .. .. .. .. ... 5

2 Input data used to test high Q (fig. 4A). .. .. .. ... ... .... .. . .... 42

3 Arrival times of reflections and multiples for a two-layer model (fig. 5) .. .. ... 44

4 Input data used to test a full response (fig. 5A) .. .. .. .. .... .. . ..... 44

5 Input data used to test a 10-50 hz band-pass filter (fig. 6A). .. .. ... ..... 48

6 Input data used to test a high-cut filter with zero phase (fig. 6C). .. .. .. .... 48

7 Input data used to test automatic gain control (fig. 8C) .. .. ... .. . ..... 53

8 Input data used to test computational frequencies (fig. 9C). .. .. ... ..... 53

9 Input data used to test record length (fig. 10A) .. .. ... ... .... ... .. 56

10 Observed and predicted times and amplitudes of reflection coefficientsfor a six-layer model (fig. 11A) .. .. ... ... .... .. . .... .. . .. 56

11 Input data used to test times, amplitudes, and polarities of reflections(fig. 11A). .. .. .... .. . ... .... ... .... ... .... .... 57

12 Arrival times for a buried receiver (fig. 12). .. .. .. .... .. . .... .... 58

13 Input data used to test receiver depth (fig. 19) .. .. .. .. . .... .. . .... 60

14 Input data used to interpolate layers (fig. 13). .. .. .... .. . .... .... 60

15 Input data used to generate a six-layer model using absolute depths (fig.3c) .. .. .. .. .... ... .... ... .... .. . .... .. . ..... 62

-U-

,--A %. P .

Generation of Vertically Incident SeismogramsBy L. NEIL FRAZER, DAVID L. BATES, and ALBERT J. RUDMAN

Abstract tions proceed in the frequency domain toAn algorithm for synthetic seismograms permit inclusion of attenuation by a complexfollowing the method of Kennett (1981) has velocity. The plane-wave components arebeen implemented in FORTRAN 77. Compu- related to reflection and transmission withintations proceed in the frequency domain and the layers by a standard filter theorythen are Fourier inverted. Reflections of approach following the method of Kennettnormally incident waves and their multiples (1981). An expansion of the response into aare plotted on a Versatec plotter. The power series permits the user to choose aalgorithm allows easy adjustment to other complete-response seismogram or to designateplotting protocols. A brief outline of the the number of multiples to be used. The finaltheory and a program listing with examples seismogram is constructed by Fourier inver-are included. sion.

The algorithm presented here, ProgramIntroduction VISP, is modified from Kennett for the caseThis report concerns the generation of of horizontally layered media bounded on topsynthetic seismograms for vertically incident and bottom by half spaces. This code doeswaves on a multilayered horizontal medium. not include a free surface, and therefore theSuperposition of plane waves allows the ringing effect of surface multiples is notsimulation of a localized source. Computa- included.

TheoryIn wave propagation in the presence of depends on the Q of the medium. Theabsorption, solution to the wave equation absorption model is an exponential decayleads to a complex velocity V(w) that with distance

A = Aoe-az

where a is related to frequency w and Q

2cQ(2)

and c is the phase velocity.A plane compressional wave normally of displacement and stress determines the

incident on two semi-infinite layers generates amplitudes of the waves in terms of the re-a reflected and transmitted wave. Continuity flection and transmission coefficients R and T

pjvj - Pj+IVj+T 2 pjvjR= T=

PJvj + Pj+1~j+l pjvj + Pj+lVj+l(3)

2 r.

2 GENERATION OF VERTICALLY INCIDENT SEISMOGRAMS

where pj is the density of layer j and vj is the spaces, a matrix representation of the upgoingcompressional velocity, and downgoing wave fields U and D is given

' For n layers sandwiched between two half by

(?' - QI Q2 ... Qn ( 2 (

-22,D I Dn+ i-- 1) (4)

Q is a wave propagator related to a matrix of cients R and T (Kennett, 1981, equationthe total reflection and transmission coeffi- 3.81)

Q TU -RDTDl RU RDTD:

-TDRu T D - 1

(5)

R\ 2 R13

T2

+ T12 R3R 2 3 T12 . ..

t 0 Un "0 T U D U "0 D0 ...

z"

,- T"U where the subscripts U and D refer to

computations for upgoing and downgoingZ2 waves.

02z 3 JR T3 R -To illustrate the significance of the total3 + \ 23 reflection and transmission coefficient, first

\ To To2 To +. consider two layers sandwiched between half13 spaces (fig. 1). Then the overall response interms of reflection and transmission proper-

" ' : ties isFigure 1. Graphic representation showing the first fewterms of equation 9 for reflection and transmissionmatrices of superposed media and showing schemat-ically the interactions undergone by the waves withthe regions z, < z < z2 andz 3 < z < z2 .FromKennett (1981).

RD 3 RD 12 + TU2D 3 [I - RuRD231- 1 TD 12

TDI3 = 2 3 - Ru 2 D2 3 - 1TD12

RU 3 = U2 13 + T2 3 RU 2 - RD Ru 12] -1 "U23

TU13 =u - D RU ] - U

(6)

.. " .. , ........ .. .. .-


COMMON ICHAR IITINE,IDATE,IQBT,TITLE9 WRITE(6,'(1X,"VISP OCEAN CRUST N)ODELING PROGRANM",8X,

AIO,2X,AIOIII)') ITIME,IDATE%%RITE(6,'(" EPS = ",F6.4," SIG'A =",F5.2,3X,"YSIDE=",F5.2,+3X,"TLNTH =", F'S.2,/)' )EPS,SIGMA,YSIDE,TLNTH%NRITE(6,'(" LAYERf",lx,"VELOCITY",4X,"Q",5X,"DENSITY",IX,-'THICKNESS",7X, "DEPTH",/,9X,"KMISEC",2X,"KM/SEC",3X,"GRMISEC",+ 5X, ":'W", 13 X, "NI")WRITE(6,'(" 1 ",F8.2,F9.1,F8.2)') CL(1),QL(i),RH-O(l)TTUI' = 0.0DO 40 1=2,NL-l

%ARITE(6, '( IX,14,IX, F8.2 ,F9. 1,F8.2, lX,F9.2,F10.2,* " ~~~TO", IX, F7.2)' ) I,CL(I) ,QL(I) ,RHO(I) ,T(1) ,TTOT,TTOT+T( 1)

TT(YT = TTCYT+T(l)40 CONTINUE

%NRITE( 6, '(lX, 14,IX, F8 .2, F9 .1, F8 .2, F20 .2,"TO INFINITY")') NL,CL(NL),QL(NL),RHiO(NL),TTOT

RET URNEND

C---------------------------------------------------------------CC SUB3ROUTINE PLTARMI

SUBROUTI[NE PLTARVIICONITvON / NUMI / CL(200),QL(200),RHiO(200),T(200),EPS,S[GMA,+ CRUST,NL,NTRACE,LOBS,NW,TSEC,TSC,ASC,NvIULT,

TLAG,YSIDE,TLNTHCOMMON / CHAR / ITIMNE,IDATE,IOBT,TITLECOMMON /FILTDT/ Fl10),IDB(10),IFILTYP(10),NFILT,MNPHASE,-FFI(I0)

CO)MMON /ARIIAGC,WINDOWLOGICAL MIPHASECILARAC TER*80 TITLE(ILARACTER*10 ITIME, IDATE, LINECHARACTER*1 IOBTNFILT =0READ(, '(A2)' ) %WREA-D(l,*) NTRACE,NW,T'SEC,TSC,ASC,NMULT,IAGC,

*V I NDOWWRITE(6, 101)

101 FOR.VAT(//,IX,"NTRACE",lX,"# FREQS",1X,"TC'NIECS)",1X,"IN/MNSECS",* IX,"ARP-SCL", IX, "VRLTPL",lX, "AGC", iX, "WINDOW")WH lI'E( 6, 102 )NTRACE ,NW, TSEC, TSC, ASC, NMULT ,IAGC, WINDOW

102 FOR.MAT(3X, 12,4X, I4,3X,F6.0,4X,F4.3,6X,F4.1,4X, I2,3X,- -13,2X,F4.0)

IF (NTRACE .GjT. 10.0) CALL TERMIN(27,0)IF ((NW.NE.16) .AND. (NW.NE.32) .AND. (NW.NE.64) .AND. (NW.NE.128)* AND. (NW.NE.256) .AND. (NW .NE. 512)) CALL TERMIN(23,NW)

IF (TSEC .LT. 1.0) CALL TERMIN(25,NINT(TSEC))IF ((TSC.EQ.0.0) .OR. (TSC*TSEC.GT.YSIDE)) THEN

[SC =YSIDE/TSEC

APPENDIX 3 15

IF (NINTLAY+I .Gr. NL) CALL TERMIN(4,MLKR)TINTLAY = RHO(IIF (TINTLAY .LT. 0) THEN

TINTLAY = -TINTLAY-CRUSTIF (TINTLAY .LT. 0) CALL TERMIN(5,MLNR)

END IFCRUST =CRUST+TINTLAYINCRCL =(CL(I+NINTLAY)-CL(I-1))/(NINTLAY+l)INCRQL =(QL(I.NINTLAY)-QL(I-1))/(NINTLAY1l)IF (RHO(I+NINTLAY).EQ. -1) RHO(I+NINTLA)(CL(I+NINTLAY)+1.5)/3INCRRHO = (RHO(I+NINTLAY)-RHO(I-1))/(NINTLAY+1)DO 25 J=i,NINTLAY

CL(J+I-1) = CL(I-1) + J*INCRCLQL(J+I-1) = QL(I-1) + J*INCRQLRHO(J+I-1) = RHO(I-1) + J*IN.CRRHO0T(J4I-1) = TINTLAY/NINTLAY

25 CONTINUEI = I+NINTLAY

ELSE.4 IF (RHO(I .EQ. -1) RHO(I)=(CL(I)+1.5)/3

IF (T(I) .LT . 0) THENT(I) = -T(l)-CRUSTIF (T(I) .LT. 0) CALL TERMIN(5,MLNR)

END IFIF (I .LT. NL) THENCRUST =CRUST+T(I)

ELSET(I) 10000

END IFI = 1+1

END IFIF(I.LT.NL)GO TO 20IF(RHiO(I).EQ.-1) RHO(I =(CL(I)+1.5)/3DO 30 l=2,NL

IF ((CL(I).LE.0) .OR. (CL(I).GE.10)) CALL TERMIN(11,I)IF (QL(I) .LT. 0) CALL TERMIN(12,I)IF( ((RHO(I) .LE.0) .AND. (RHO(I) .ME.-1)) .OR. (RHOCI) .GE. 10))

*CALL TERMIN(15,I)*30 CONTINUE* END

7, ~ ~ -----------------------------------------------------------....CC SUBROUTINE PRTMLDACC...............................................................

SUBROUT INE PRTMLDACHARACTER080 TITLEC2IARACTER10 ITIME, IDATECHARACrERI lOBTCOMMOIN N UM /CL(2OO),QL(200),RHO(200),T(200),EPS,SIG

4 ,

+ GRUST,NL,NTRACE,LOBS,NW,TSEC,TSC,ASC,NMULT,+ TLAG,YS IDE,TLNTH


END

C -----------------------------------------C SUBROUTINE MDLINCHC ----------------------------------------------------------

SUBROUTINE MDLINCHCHARACrER*80 TITLECHARACER*10 ITIME, IDATECHARACrER*1 IOBTCOMMON / NUM / CL(200),QL(200),RHO(200),T(200),EPS,SIGMA,+ CRUST,NL,NTRACE, LOBS,NW,TSEC,TSC,ASC,NMULT,+ TLAG,YSIDE,TLNTHCUON / CHAR / ITIME,IDATE,ItOBT,TITLEREAL INCRCL, INCRQL, INCRRHO,TINTLAYTINTLAY=0.0ILNR=0

CC READ IN TITLE AND WRITE ITC

READ( 1,100 )TITLE100 FORMAT(A)

WRITE(6,200 )TITLE200 FORMAT(///,1X,A)

NL=-1ILNR = ILNR+lDO 10 1=1,200

NL = NL+IIF (NL .EQ. 0) THENREAD(1,' (A2)')WWWREAD(l,*) EPS,SIGMA,YSIDE,TLNTHREAD(l, ' (A2) ' )WWW

ELSEREAD(1,*) CL(NL),QL(NL),RHO(NL),T(NL)IF(CL(NL).EQ.9999)GO TO 15

CC ... INTERPOLATED LAYERSC

IF (CL(NL) .EQ. 0) NLfNL+NINT(QL(NL))-iIF (NL .GT. 200) CALL TERMIN(I,ILNR)

ENDIF10 CONTINUE

15 IF ((CL(1) .EQ. 0) .OR. (T(1) .LT. 0)) CALL TERMIN(3,1)NL = NL-1CRUST = 0MLNR= 11=2

CC ... EXPAND INTERPOLATED LAYERS AND CONVERT ABSOLUTE DEPTHS TO THICKNESS.C

20 MLNR = MLNR+ 1IF (CL(I) .EQ. 0) THENNINTLAY = NINT(QL(I))

S' ', " % :, . ". ' . . .. " " , ,, "-.-

APPENDIX 3 13

C --- - - - - - -

"' CCC THE CODE HAS A MAIN PROGRAM THAT CALLS 6 SUBROUTINES. THESEC SUBROUTINES, IN TURN, CALL 6 OTHER SUBROUTINES. OUTPUT CONSISTSC OF A BRIEF LINE PRINTER SUARY OF THE INPUT PARAMETERS AND AC PLOT OF THE SYNTHETIC SEISMOGRAM AND LAYER PARAMETERS (VELOCITY,C Q AND DENSITY).CC ACTION OF PROGRAM:C--------------------

C THE PROGRAM READS AND CHECKS THE MODEL PARAMETERS. IN ALL CASES IT THENC PLOTS THE PARAMETER VALUES AS THEY VARY WITH DEPTH. THEY ARE PLOTTED ONC THE SAME GRAPH, WITH VALUES OF Q REDUCED BY 1000. THE Y AXIS FILLS THEC PAPER WIDTH AND HAS VALUES 0 - MAX PARAMETER VALUE. THE LENGTH OF THE XC AXIS IS DEPENDENT ON BOTH THE TOTAL THICKNESS AND THE NUMBER OF LAYERSC REQUESTED IN THE MODEL.CC THE MODEL USES THE THEORY OF B.L.N.KENNETT (ADVANCES IN APPLIEDC MECHANICS, VOLUME 21, PP.79-167, ACADEMIC PRESS, 1981) TO COMPUTEC RESPONSE OF MODEL FOR SELECTED FREQUENCIES (SUBROUTINE EXEMODL)C 2*PI/TSEC ..... ,NW*2*PI/TSEC. THE RESPONSE VALUES ARE THENC FOURIER TRANSFORMED TO THE TIME DOMAIN AND PLOTTED.C IF NO TIME SCALE FACTOR IS SPECIFIED (OR IF THE ONE GIVEN ISC INAPPROPRIATE), A VALUE OF I MSEC PER INCH OR LESS, IF NECESSARY, IS USED.C TRACES ARE SPACED 0.65 INCHES APART AND ARE SCALED TO A MAXIMUM MAGNITUDEC OF 0.5 INCHES, UNLESS AN ASC VALUE IS DESIGNATED (OTHER THAN 1). IN THATC CASE, PEAKS ARE TRUNCATED AT 0.5 INCHES.CC- -------------------------------------------------------------------------C ------------------------------------------------------------------------

CC MAIN PROGRAMCC -TST- ( - - - - - - - - --UT- - - -

PROGRAM TEST (OUTPUT,TAPE6=OUTPUT)CHARACTER* 80 TITLE

CHARACTER*10 DATE,TIME, ITIME, IDATECHARACTERS1 I OBTCOION / NUM / CL(200),QL(200),RHO(200),T(200),EPS,SIQGMA,+ CRUST,NL,NTRACE,LOBS,NW,TSEC,TSC,ASC,NMULT,+ TLAG,YSIDE,TLNTHCOMMfVON / CHAR /ITIME,IDATE,IOBT,TITLECOMMON /AR/IAGC,WINDOWOPEN (UNIT=1,STATUS= 'OLD' ,FILE= MDL )ITIME=TIME()IDATE=DATE()CALL MDLINCHCALL PRTMLDACALL PLTARMICALL EXlEMDLIF(IAGC.EQ.1)CALL AGCFREQCALL WRTPLT

N.

%-

_P:..,.'.' . :- . .', -" ,:.,.' ,;. ,'. ,: ;:. .'-'., ,.'.,. . , -. ,-: - '''":''".'"-", r.- ",, ' , "., ' ... '". , : . -'


C AMPLIFY ALL EVENTS AND CREATE A RINGING EFFECT. TOO LARGEC A WINDOW EFFECTIVELY CANCELS THE AGCACTION.CC 8) CAPTIONS (NOT READ BY THE COMPUTER)CC 9) PARAMETERS SELECTING DETECTOR AND LAYER TO PUT ITC LINELOBSCC WHERECC LINE - IS EITHER "REFLECTION", "VERTICAL" OR "PRESSURE"C DEPENDING ON RECEIVER TYPE DESIREDC LOBS - IS LAYER NUMBER TO PLACE RECEIVER (NUMBER MUSTC BE IN COL 28)CC IF THE RECEIVER CHOICE IS THE REFLECTION COEFFICIENTC ONLY LAYER I MAY BE DESIGNATED. THE CALCULATION ISC IMADE AT THE BASE OF THE HALF SPACE. IF THE RECEIVER ISC DESIGNATED AS VERTICAL(DISPLACEMENT) OR PRESSURE, THEC RECEIVER IS AN OBS OR BOREHOLE INSTRUMENT AND MUST BEC PLACED IN LAYER 2 OR GREATER (NOT LAYER 1). THE OBSC IS AT THE TOP OF THE LAYER SPECIFIED,BUT WITHIN THEC LAYER. FOR EXAMPLE, AN OBS IN LAYER 2 IS AT THE TOPC OF LAYER 2, ESSENTIALLY ACROSS THE INTERFACE FROM THEC STANDARD REFLECTION COEFFICIENT CALCULATION INC LAYER 1.CC 10) CAPTIONS (NOT READ BY COMPUTER)CC 11) IF THE PLOT IS IS TO BE FILTERED, THE FILTER PHASE IS GIVENC IPHASECC IPHASE - IF "0" THE FOLLOWING FILTER(S) IS ZERO PHASE,C IF "1" THE FILTER(S) ARE MINIMUM PHASECC 12) SUBSEQUENT DATA LINES (UP TO 10) ARE FILTER DEFINITIONSC IFILTYP,IDB,FF1CC WHERE:CC IFILTYP - I = HIGH CUT (LOW PASS) BUTTERWORTHC 2 = LOW CUT (HIGH PASS) BUTTERWORTHC 3 = NOTCH FILTERC IDB - DECIBEL REDUCTION WHERE POLES = DB/6 + IC FFI - CUT-OFF FREQUENCY IN HZCC IF A BAND PASS FILTER IS DESIRED, TWiD DATA LINES AREC READ IN CONSECUTIVELY: ONE GIVING THE HIGH CUT VALUESc THE OTHER THE LOW-CUT.

C IF A NOTCH FILTER IS DESIRED, INPUT IS SIMILAR TOC BAND PASS (SEE ABOVE), EXCEPT IFILTYP = 3 FORC BOTH INPUT LINESCC USING THE PROGRAM:

,I

I , , M . ;. . ..<. . . :. . :. . . . / -, . . . , . . , ,. . -... ., .,- -. .,.,.., . ,, -..,-,-, .,'.

APPENDIX 11

C TO ZERO. THE FINAL LAYER IS THE BOTTOM HALF-SPACE AND IS IDENTIFIEDC BY A THICKNESS T SET EQUAL TO ZERO. A FLAG OF 4 CONSECUTIVE 9999'SC CLOSES OFF THE LAYER PARAMETER INPUT.C

C FOR EACH LAYER, OTHER THAN THE FIRST, IF RHO IS GIVEN AS A -1, AC DEFAULT VALUE OF (CL+1.5)/3 IS TAKEN.CC EXTRAPOLATION - IT MAY BE DESIRED TO HAVE LAYER PARAMETERS CHANGEC SMOOTHLY FOR A CERTAIN REGION. TO AVOID HAVING TO HAND CALCULATE ANDC INPUT VALUES FOR SUCH A REGION DIVIDED INTO A DISCRETE NUMBER OFC LAYERS, IT IS POSSIBLE TO REQUEST THAT BETWEEN THE PRIOR AND NEXTC FULLY DESCRIBED LAYERS THERE WILL BE N LAYERS OF EQUAL THICKNESS ANDC WITH PARAMETERS COvPUTED BY LINEAR EXTRAPOLATION BETWEEN THE VALUESC FOR THE PRIOR AND NEXT LAYERS. THIS OPTION IS REQUESTED BY ENTERINGC A LINE OF THE FORMAT 0,N,T WHERE THE 0 IS AN ESCAPE VALUE FOR THEC NORMALLY EXPECTED CL, N IS THE NOS OF LAYERS TO BE INSERTED, TC IS THE TOTAL THICKNESS OF THOSE LAYERS, AND THE "1" IS A DUMMY.C FOR EXAMPLE,THE VALUE OF CL FOR THE 2ND INTERPOLATED LAYER WILL BE:C CL(PRIOR) + 2*(CL(NEXT) - CL(PRIOR))/(N+I)C AS A USEFUL GUIDE, IF YOU WANT EACH LAYER 1/4 WAVELENGTH THICK (ATC THE HIGHEST FREQUENCY TO BE USED), CHOOSE N = TOFW*4/(CL*TSEC)CC ABSOLUTE DEPTH - NORMALLY T SHOULD BE A POSITIVE VALUEC SPECIFYING THE THICKNESS OF THE LAYER. IF, HOWEVER, IT IS PREFERLDC TO SPECIFY THE DEPTH BELOW THE HALF SPACE TO WHICH THE LAYER WILLC EXTEND (ITS STARTING POINT WILL OF COURSE BE IMMEDIATELY BELOW THEC PREVIOUSLY DESCRIBED LAYER), A NEGATIVE VALUE CAN BE GIVEN, WHOSEC MAGNITUDE WILL INDICATE THAT ABSOLUTE DEPTH. THIS OPTION CAN ALSO BEC BE USED WITH EXTRAPOLATED LAYERS.CC 6) CAPTIONS (NOT READ BY COMPUTER)CCC 7) INPUT PARAMETERS FOR COMPUTATIONAL PURPOSES IN FREE FORMAT ARE:C NTRACE,NW,TSEC,TSC,ASC,NMULT, IAGC, WINDOWCC WHERE:CC NTRACE -NUMBER OF TRACES PLOTTED AS DUPLICATES ON THE SYNTHETICC NW - NOS OF FREQUENCIES (116, POWER OF 2) TO BE USED IN FOURIERC TRANSFORM TO TIME DOMAIN.C TSEC - MSECS OF TIME SERIES (STARTS AT -1, -5 OR -10 MSECSC DEPENDING ON THE VALUE OF TSEC). TSEC SHOULD BE MOREC THAN TIME FOR 1-3 REFLECTIONS FROM BOTTOM INTERFACE, DEPEND:NGC ON WHETHER YOU ARE REQUESTING PRIMARIES ONLY OR FULL RESPONSE.C TSC - TIME SCALING FACTOR(IN/MSEC).IF TSECOTSCIYSIDE,THEN IFC TSC IS POSITIVE,A VALUE OF TSC IS COMPUTED = YSIDE/TSEC, WHILEC IF TSC IS NEGATIVE,PLT IS TRUNCATED AT YSIDE/TSC MILLISECONDSC ASC- AMPL SCALE FACTOR (DEFAULT = il.0). IF i 1, SIGNAL ISC AMPLIFIED, BUT THE PLOT IS CLIPPED AT 0.5 INCHES AMPLITUDE.C NMULT -NOS OF MULTIPLE REFLECTIONS TO BE COMPUTED.C VALUE 1 0 IMPLIES FULL RESPONSE REQUIRED (BY MATRIX INVERSION).C IAGC- SET = TO 1 IF AUTOMATICGAIN CONTROL IS DESIREDC WINDOW - LENGTH OF AGCWINDOW IN MSECS. A SMALL WINDOWC (RELATIVE TO EXPECTED TIME INTERVALS OF REFLECTIONS) WILL

- . .. .,.. . . , ,. . .- . . . .., . ,. . . . • . , , - , : . . , , . .. -. .. ,,..'.-, ,. ;


Appendix 3. FORTRAN 77. Program VISP and Program PLTVISP

CCC PROGRAM VISPcC (VERTICAL INCIDENT SEISMOGRAM PROGRAM)CC BY L.N. FRAZER, D.L. BATES & A.J. RUDMAN JULY 1983CCCC USES I/O STREAMS AS FOLLOWS:

C 1: INPUTC 6: OUTPUT, INCLUDING ERROR MESSAGESC 4: STORED ON FILE PLTIN FOR PLOTTING BY PROGRAM PLTVISPCCC FORMATS AND DESCRIPTIONS OF INPUT FILE:C --------------------------------C A) DATATYPES - ALL DATA IS ACCEPTED IN FREE FORMAT, WITH ANY EMPTY FIELDSC BEING READ AS 0.CC B) DATALINES - USEABLE DATALINES ARE INTERSPERSED WITH CAPTIONS-LINESCC 1) TITLE (ALPHA-NUMERIC)CC 2) CAPTIONS (NOT READ BY COMPUTER)CC 3) EPS,SIGMA,YSIDE,TLNTHCC WHERE:CC EPS - PARAMETER GOVERNS VARIATION OF VELOCITY WITH FREQUENCY WC SIGMAA - PARAMETER GOVERNS VARIATION OF VELOCITY WITH FREQUENCY WC YSIDE - MAXIMUM INCHES PERMITTED FOR LENGTH OF SYNTHETIC PLOTC TLNTH - FIXED LENGTH OF PARAMETER PLOT(IN INCHES)CC 4) CAPTIONS (NOT READ BY COMPUTER)CC 5) CL,QL, RHO,TCC WHERE:CC CL - IS COMPRESSIONAL VELOCITY OF LAYER IN KM/SECC QL - IS COMPRESSIONAL Q FACTORC RHO - IS DENSITY IN GM/CCC T - IS THICKNESS IN METERSCC ALL SUBSEQUENT DATA LINES ARE READ AS DESCRIPTIONS OF CONSECUTIVEC LAYERS OF THE MODEL (UP TO 200). THE FIRST LAYER IS THE UPPER

4 C HALF-SPACE (CORRESPONDING TO AN OCEAN LAYER) WITH THICKNESS SET

i'...

* L . .. . -k b % M 4-*- .0 . .o,

APPENDE 2 9

RVRB2EW RVRB2*EWIGH*TUSC FFT variableSIGMA Parameter used in computing variation of velocities with WSIGN! FFT variableSQREFT Square of amplitudeSQREFW Frequence equivalent of SQREFT

.. T Array of thickness (in meters), one for each layerTD Downward transmission coefficients for current interfaceTDON Downward transmission coefficients from ocean bottom to

lower half spaceTDONP New value of TDONTDOR Downward transmission coefficients from ocean bottom to

receiverTEMP Temporary variable for truncationTEST Temporary variableTINTLAY Thickness of each interpolated layerTITLE String used for plottingTLAG Time plots will begin at -TLAG msecTLNTH Fixed length of parameter plot (in inches)TSC Time-scaling factor in inches/msecTSEC Number of msec of time seriesTTOT Total thickness (in meters)TU Upward transmission matrix for current interfaceTUNO Upwards transmission matrix from lower half spaceTUNOP New value of TUNOUNIT CIMPLX (1.0, 0.0)W Current frequency in KHzWARNED Logical variableWIGH Phase lag associated with propagation through vertical

distanceWINDOW AGC window length in mseeWW AGC filterWWW Ruse to read past a cardY Common factor used in routine REFLYSIDE Max length of plot (in inches)

.J.

r-

8GENERATION OF VERTICALLY INCIDENT SEISMOGRAMS-sISTEP FFT variableITIME Current timeITW2 Number of points in AGC filter1W Frequency loop counterJ Miscellaneous loop counterL FFT variableLINE String to hold lines read from input file (allows free

format). (See IOBT.)LOBS Layer in which OBS located (1 if no OBS)LX FFT variableM FFT variableNAXABSV Filter variableMD (See Kennett, 1981, p. 106, equation 3.38.)%lPHASE Flag: If set, Minimum-phase filter required;

otherwise, Zero phase%ILNR Counter of model file input lines, used in error messagesMU (See Kennett, 1981, p. 106, equation 3.38.)NINTLAY Number of interpolated layers requestedNFILT Number of filters requestedNL Total number of layers in model including bounding half

-WV spacesNIULT Number of multiple reflections to be calculatedNT Number of time steps (= NW*2)NTIRACE Number of traces to be plotted on the seismogramNW Number of frequencies to be calculatedPI 3.141592653POLES Filter variablePR Value of pressure recorded at OBSPRESSFA Pressure related variable for given layerQL Array of P-wave Q values, one for each layerR Filter variableHCOEFF Reflection coefficient or OBS response for current

frequency W and slownessRD Downward reflection matrix for current interfaceHDON Downward reflection matrix from ocean bottom to lower

half spaceRDONP New value of RDONREFT Reflection coefficient (or OBS response) in time domainREFW Reflection coefficient (or OBS response) in frequency

domainRHO Array of densities, one for each layerlutOl Density of layer above the current interfaceR102 Density of layer below the current interfaceRTBI Temporary variable

RTB3 Variable in computation of RCOEFFRU Upward reflection coefficients for current interfaceRUNO Upward reflection coefficients from lower half space to

ocean bottomRUNOP New value of RUNO

* RURO Upward reflection coefficients from receiver to oceanbottom

RVRBI Effect on downward waves of all multiples in current layerRVRHIEW RVRBl*EWIGfI*TD0NHVRB2 Effect on upward waves of all multiples in current layer

I',

-J

GENERATION OF VERTICALLY INCIDENT SEISMOGRAMS 7

Appendix 2. Glossary of Variables Used in Program VISP

(Variables in the plotting Program PLTVISP are not listed here)

A Dummy argument in multiple computationAA FFT variableALl P-wave slowness of the layer above the current interfaceAL2 P-wave slowness of the layer below the current interfaceASC Amplitude scaling factor for tracesB Dummy argument in multiple computationBI AGC filter variableBEX Numbers smaller than exp (-BEX) taken to be zeroCO CMPLX (0.0.0.0)C1 CMPLX (1.0.0.0)

CL Array of P-wave velocities, one per layerCRUST Total thickness of layers, excluding first and lastCTEMP FFT variableCW FFT variableCX FFT variableCURRMIN AGC filter variableDELFREQ Frequency increment in filteringDELTAT Time incrementDET Temporary variable in multiple computationEIW CPLX(EPS,-W)O*SI(DAEPS Parameter governing variation of velocities with

frequency WEWIGH EXP(WIGH)EWRD EWIGHSRDEWRUNO EWIGH*RUN0F1 Cut off frequency in KhzFF1 Cut off frequency in HzFACTOR Filter variableFILT Digitized filterFILTI Second copy of filterFRSTTIM Logical variableGL Z-omp of P-slowness vectorGLI Z-comp of P-slowness vector in layer above current

interfaceGL2 Z-comp of P-slowness vector in layer below current

interfaceMiscellaneous loop counter

IAGC Flag for AGC filterIDATE Current dateIDB DB reduction for notch filter, or =6*POLES-I for

ButterworthIFILTYP Type of each filter requestedIL Layer loop counterINCRCL Incremental value of CL through interpolated layersINCRQL Incremental value of QL through interpolated layersINCRRHO Incremental value of RHO through interpolated layersINDEXI Filter variableINDEX2 Filter variableIOBT Character for type of OBS response: reflection/

vertieal/pressure" IPHASE Flag: 0 for zero phase and I for minimum phase

- 'Mr


Appendix 1. Generalized Description Diagram of Programs VISP and PLTVISP

Program VISP

Subroutine Comments

1. MAIN Calls six subroutines listed below.

2. MDLINCH Reads model parameters and interpolates layer parameters. Calls

TERMIN for error stop.

3. PRTMLDA Writes model parameters.

4. PLTARMI Reads and writes computational parameters, user options, and filterspecifications. Calls TERMIN for error stop.

5. EXEMODL Main computation subroutine for a given frequency: Computesreflection coefficient for all layers (for user-designated number ofmultiples). Options for pressure or vertical displacement. Repeats forall frequencies and then filters. Finally, transforms to time domain.

The above computations involve calls to five subroutines: PARMGEN(computes vertical slowness), REFL (computes reflection coefficientfor a single interface at a single frequency), REVERB (selectsmultiple computations), FILTER (filters amplitudes), and FFT (fastFourier transform).

6. AGCFREQ Simulates automatic gain control in frequency domain for specifiedwindow. Calls FFT.

7. WRTPLT Writes header and seismogram amplitudes on file for plotting byProgram PLTVISP. (See table below.)

Program PLTVISP

Subroutine Comments

1. MAIN Calls four subroutines listed below.

2. READINP Reads data generated by Program VISP.

3. INITPLT Plots major headings.

4. PARMPLT Initializes plot parameters and plots axes and model parameters.

5. RSPMDL Writes filter, AGC, and multiple specifications. Plots seismogram tracesand axes.

jIv4"

LITERATURE CrD 5typical field records As a demonstration, a plots for 12 other test cases used tomodel that simulates a continuous velocity demonstrate the user options.log with 123 layers was used to create Test 1(fig. 2). A CDC Cyber 170/855 computer atthe Indiana University Wrubel Computing Literature Cited

* Center generated the output data in 13.6 Kennett, B. L N.seconds with a 71300 octal field length. Table 1981 - Elastic wave propoption in stratified1 lists the input data used to generate figure media, in Advances in applied mechanics:2. New York, Academic Press, Inc., v. 21, p.

Appendix 4 lists the input data and output 79.167.

* ., Table 1. Input data used to generate a typical synthetic seismogram (fig. 2)

TEST 1 - DSYN. SYNTHETIC SEISMIGRAM.EPS SIGMA YSIDE XSIDE0.001 0.1 40. 12.0CL QL RHO THICKNESS1.5 2000. 1.1 0.1.9 22. 2.2 10.2.1 22. 2.2 102.0 22. 2.2 102.2 22. 2.2 102.1 22. 2.2 102.8 25. 2.5 10

29 2. 2 10

2.7 23 2.42.6 23 2.4 102.7 23 2.4 102.8 23 2.4 102.6 23 2.4 10

1.5 20 2.2 0.9999 9999 9999 9999#TRC #FREQ T(NSEC) IN/N5EC AMP-SCALE MLTPL AGC WINDOW5 512 2000. .006 1.0 -1 1 400

DETECTOR TYPE DETECTOR LOCATIONREFLECTION LAYER 1FILTER PHASE1 (MINIMUM PHASE)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY1 72 702 72 30

4'


VISP; PLOTS OF PARAMETERS TEST I - OSYN. SYNTHETIC 5EIS1OGWM.REFL.ECTION COEFFIINT

AT 055IN LAME I AT .0 M OPT"FQ(Q1IUI. SIZ 'II'SECS3.Z000

TEST I - 053W. 5Th',tTIC 5EI5PGRAfl. MIN . .50 MZ MIAX *Z2U.30 4Z

FULL RESPONSE tALL MULTPLES)

AGC IjINOOM - 400.'lS

4 --- F ILTERS x MINIMUMq PHASE---

101 CUT AT 70. H1Z;?Z 06SLPLIKM/SEC) X1. .010 RHlO (11/C L 0, CU T AT 30. 91Zs?2 30 SLOPE

1 3 0 33 1 3

. .. .....

3 1

Figure~ ~ ~ ~ 2.(et1 uptposgnrtdb rga IP ,iptdt:vlct C)

Q0 Q) n est R O;B ytei esormgnrtdfo nu aa

Signficat prameersare iste abve te sismoram

SUMMARY 3

where, for example, the coefficients RD1 are adjusted for travel through the layer by E =for the interface at Z2 , and the coefficients eiwd/c, where d is layer thickness. Hence-RD23 are for the interface at Z3 , but are

Ir'D2 3 = ERD2 3E ITU2 3 = ERu2 3 E T D23 = ETD 2 3 'T23 = ETu2 3

D D U U (7)

Kennett (1981) pointed out that the power seriesbracketed quantity may be expanded as a

[I - A] I + A + A2 + ...~(8)

I'.' Therefore,

RD 1 3 = RDI2 + TuI2RD23TD1 2 + Tu2RD23Ru12R2 + . .+

(9)

which is represented schematically in figure 1. beginning of Program VISP detail, card byRD12 is the reflection from the upper region. card, the input data required to generate anReading from right to left, TU 12 RD 23 TD12 output.represents a transmission back up through the User's options include an output plotupper zone. TU 12 RD23 RU 2 RD2 3 TD1 2 (seismogram) of the reflection coefficientrepresents a reverberation within the layer. (pressure of the reflected wave divided by the

The total response (equation 6) includes all pressure of the incident wave), pressure, orinternal reverberations, and the bracketed vertical displacement. The receiver may be atquantity is termed the reverberation operator. the top of any of the layers except when aNote that the reflection-transmission coeffi- reflection coefficient is requested; then thecient may be calculated iteratively by adding receiver is just above the first interface.a layer at each stage, beginning at the top or Seismograms may be filtered by using athe bottom of the stack of layers. Computa- Butterworth-type high-pass, low-pass, ortion of the response of the model proceeds band-pass filter. The filter slopes and thefor selected frequencies and is finally Fourier phase characteristics (minimum or zero) aretransformed to the time domain and plotted, specified in the input. The user may

4uniformly amplify the signal (ASC) orSummary optionally select a simulated automatic gainThe algorithm for Program VISP and Program control (AGC). The final seismogram mayPLTVISP (appendix 1) presumes an incident display primary reflections only, primariesplane wave originating at the base of, but and a selected number of multiples, or awithin, the upper half space. The two complete response.programs are written in FORTRAN 77, and Besides computational parameters, the userthe codes are listed in appendix 3. Only one must read in the following model parametersinput file is required to run Program VISP. for each layer and the top and the bottomOne output file is generated for plotting. half space: velocity, Q, density, and thickness.Program PLTVISP plots the output on a If a negative one is read in for the density, aVersatec plotter by using standard calcomp default value of (velocity + 1.5)/3 iscalls. A glossary of constants and variables is calculated. Program VISP successfully gener-in appendix 2. The comment cards at the ates synthetic seismograms that simulate

::!I

,i

% ; %" %, . .' . ' . , ,.. .. . . .

APPENDIX 3 1

ELSEIF (TSC.LT.O.0) THENCC ... IN THIS CASE DO14T PLOT ALL.

TSC = -TSC

ENDIFIF (ASC .EQ. 0.0) ASC=1.0IF ((ASC .LT. 1.0) .OR. (ASC .GT. 100)) CALL TERMIN(29,D)

CC LOOK FOR OBS OPTIONS

* READ(l, '(A2) ')WWWREAD(1, '(A11,16X,11)')LINEpLOBS

WRITE(6, 103)LINE,LOBS103 FORMAT(/,iX, "DETECTOR TYPE IS ",A," IN LAYER V",13)

IOBT=LINE(1:1)IF ((IOBT.EQ.'V') .OR. (IOBT.EQ.'P')) THEN

IF ((LOBS.LT.2) .OR. (LOBS.GT.NL)) CALL TERMIN(31,O)ELSEENDIF

CC NOW READ FILTER PARAMETERSC - - -- - - -- - - -- - -

C

READ( 1, '(A2) ')WWWREAD(1,*) IPHASEIF( IPHASE.EQ.0)THENWRITE(6, '(lX, "FILTER-PHASE")')WRITE(6, '(1X,11,"(ZERO PHASE)")' )IPHASEMPHASE= .FALSE.

ELSE IF( IPHASE.EQ. I)THENWRITE(6, ' (X,"FILTER-PHASE")')WIITE(6,'(lX,JI,"UWINIMUM PHASE)")')IPHASEMPHASE= .TRUE.

ELSEIF( IPHASE.NE.0.AND. IPHASE.NE. 1)THENWRITE(6,'(lX,"NO FILTERS")')GO TO 15

ELSEEND IFWRITE(6,'(//,1X,"FlLTER TYPE",2X,"DB SLOPE",2X,

+ "CUT-OFF FREQUENCY")'READ(l,'(A2))WWDO 10 1=1,15

READ(1,*,END=15) IFILTYP(I), IDB( I),FFI( I)IF(IFILTYP(I).EQ.1)00 TO 11IF(IFILTYP(I).EQ.3)GO TO 41

kV GO TO 2 111 WRITE(6,104)IFILTYP(I), IDB(I),FFI(I)

104 FOHMAT(lX,I1,"(LOW PASS)",4X,13,IOX,F4.0)GO TO 31

21 WRITE(6,105)IFILTYP( I), IDB(I),FF1(I)105 FORMAT(11,"(HIGH PASS)",3X,13,1OX,F4.0)

I00 GTO 31I'. 41 WRITE(6,106) IFILTYP( I), IDB(I) ,FF1( I)


106 FORMAT(1X,I1,"(NOTCH FILTER)",3X,13,10X,F4.0,3XF4.0)31 NFILT=NFILT+l

Fl(NFILT) = FF1(NFILT)*.00110 CONTINUE15 IF (NFILT .GT. 10) CALL TERMIN(30,NFILT)

CLOSE(UNIT=1RETURNEND

C-----------------------------------------------------------CC SUBROUTINE EXEMODLCC ----------------------------------------------------------

SUBROUTINE EXEMODLCOMMON / NUM I CL(200),QL(200),RHO(200),T(200),EPS,SIGMA,+ CRUST,NL,NTRACE,LOBSNW,TSECTSC,ASC,NMULT,+ TLAG,YSIDE,TLNTHCOMMON / CHAR / ITIME,IDATE,IOBT,TITLECOMMON /FILTDT/ FI(10),IDB(10),IFILTYP(10),NFILT,MPHASE,+ FFI(10)

CHARACER*1 IOBTCHARACTER*10 ITIME,IDATECHARACTER* 80 TITLECOMPLEX GLI,GL2COMPLEX EIW,WIGH,RCOEFF,C0,C1,AL1,AL2COMPLEX EWIGH,RVRBI ,RVRB2COMPLEX EWRUN0, EWRD, RVRBIEW, RVRB2EWCOMPLEX RTB1,RTB2,RTB3,Tr'NP,TUNOPCOMPLEX RDONP,RUN0P,RDON,RUN0COMPLEX TDON,TUNO,RD,RU,TD,TUCOMPLEX MU,iMD,RURO,TDORCOMPLEX PRESSFA,PR,UNIT,REFW(1024)CO ON /TS/ REFT(1024)DATA PI/3.141592653/DATA BEX/-20.0/DATA CO/(0.0,0.0)/, CI/(1.0,0.0)/

CC INITIALIZE BEGINNING OF PLOTCC

NT = 2*NWIF (TSEC .GT. 150.0) THENTLAG = 10.0

ELSEIF (TSEC .GT. 90.0) THENTLAG = 5.0

ELSETLAG = 1.0

ENDIFUNIT = C1

CC LOOP OVER ALL FREQUENCIESC

mb4-.

B-

APPENDIX 3 19

DO 1 WO ,N-

EIW = WMLX(EPS,-W)**SIGIAALI = aCPLX(I.O/CL(l ) ,O.G)O(OWLX(O.5/QL(1) ,O.O)/EIW+CI)RHOl = RHO(1CALL PARMGEN(AL1,GLI)

CC LOOP OVER ALL LAYERS

DO 15 IL=1, NL-1AL2 aW~1LX(1.O/CL(IL+1),O.)

+ (CN1LX(O.5/QL(IL1),O.O)/EIW + Cl)RH02 =RHO(IL.1)

CALL PARMGEN(AL2,GL2)CALL REFL(RHiO1RH~O2,GL1,GL2,RU,RD,TU,TD)IF (IL .EQ. 1) THENRDON=RDRUNO =RUTDON=TDTUNO =TUMD =CO

ELSEWIGHi = CPLX(O.O,W'T(IL))*GLIIF (REAL(WIGH) .GT. BEX) THEN

EWIGHi CEXP(WIGH)ELSEEWIGH =CO

END IFEWRD=-EWIGH*RDEWRUNO=EWIGHi*RUNORTB1=EWRUNO*EWRDIF (NMULT .LT. 0) THEN

CC ..COMPTYE ALL MULTIPLES RVRB2=1+EWIGHRD*RVRB1*EWIGHiRUNO.C

CALL REVERB(RTB1 ,RVRB1)RTB1=RVRB10EWRUNORTB2=EWRD*RTBIRVRB2=UNIT+RTB2

ELSECC ..VALUIE FOR NO MULTIPLES.C

RVRBI=UNITRVRB 2 =UN ITIF (NMULT .GT. 0) THEN

Cc .. .COMPUTE FINITE NUMBER OF MULTIPLES.

* CC

DO 20 1=1, NMULTRTB2=RVRBlORTBI

4 'j

.4,20 GENERATION OF VERTICALLY INCIDENT SEISMOGRAMS

RVRBI=UNIT+RTB220 CONTINUE

RTBl=EWRD*EWRUNoDO 25 1=1, NMULTRTB2=RVRB2*RTBIRVRB2 sUN IT+RTB2

25 CONTINUEENDIF

ENDIFRTB1=EWIGH*TDONRVRBl1EW: RVRB1 RTB 1

C .. .TDON=TD*RVRBI*EWIGHi*TDON.C

TDONP=TDORVRB1EWRTB1=EWIGHTU

C RVRB2EW=RVRB2*RTBI

C .. .TUNO=TUNOORVRB2*EWIGH*TU

TUNOP=TUNO RVRB2EW~ * RTBI=EWRD*RVRB1EW

4. cC ... .RDON=RDON+TUNO*EWIGHi*RDRVRB1*EWIGH*TDON.C

RTB2 =TUJN0 RTB IRDONP= RD0N+RTB2RTBI=EWRUND*RVRB2EW

C ... RUNO=RU+TDEWIGI*RNO*RVRB2*EWIGH*TU.

RTB2=TD*RTB1RUNOP=RU-RTB2TD0N=TDONPTUNO=TUNOPRDON=RDONPRUNO=RUNOP

END IFTEST =CABS(TDON)

*.1 CC ... EXIT LAYER LOOPc

IF((TEST.EQ.O.0).OR.(ALOGIO(TEST).LT.-8))GO TO 30IF (IL .EQ. LOBS-I) THEN

RU;RO=RUNOTU R=T[)oN

klNTUG N=UN ITTLN = UN ITRUNO CORDON = CO

PRESSFA =RHO(LOBS)0(1.0-(4.0/3.0))

c ... .THE 085. SITS IN THE UPPERMOST PART.

(4' i17J -GL2

APPENDIX 3 21

MD = GL2END IFALl = AL2RHOI = RHO2GLI = GL2

CC ... END OF THE LAYER LOOP.

15 CONTINUE30 CONTINUE

IF (LOBS .GT. 1) THENCC ... IF AN OBS MOTION IS ASKED FOR THE INCIDENT PRESSURE WAVEC ...IS A DERIVATIVE OF A DELTA FUNCTION. IF AN OBS PRESSUREC ... IS ASKED FOR, THE INCIDENT PRESSURE WAVE IS ASSUMED TO BEC ...A DELTA FUNCTION.C

RTB1 =RURO*RDONIF(NMULT.LT.0) THEN

CALL REVERB(RTBI ,RTB2)ELSE

RTB2=UNITIF(NMNULT.GT.0) THEN

DO 40 I=I,NMULTRTB2=UN ITRTB1*RTB2

40 CONTINUEENDIFENDIF

CRTB1=RTB2*TDORRTB2=RDON*RTB1PR=PRESSFA*(RTB2+RTB1)RTB2=MU*RDONRTB2=MD+RTB2RTB3=RTB2*RTBI

C

C ADJUST FOR RECEIVER TYPECC

IF( IOBT.EQ. 'V' )THENRCOEFF = RTB3/RHO(I)

ELSECC ... PRESSURE.C

RCOEFF = PR/RHO(1)ENDIF

ELSERCOEFF = RDON

ENDIFf* ROEFF = RCOEFF CMPLX(50.*(I+COS(PI*IW/NW)),0.) *

+ CEXP(CMPLX(0.0,W*TLAG))REFW(IW+I) = RCOEFF

CC ... NEGATIVE FREQUENCIES ARE COMPLEX CONJ.

-4,.


CREFW(NT-IW+1) =COIIJG(RCOEFF)

CC ... END FREQUENCY LOOPC1 t0 CONTINUE

CC ... DC AND NYQUIST FREQUENCY SET = TO 0C

REFW(I) = CoREFW(NWI) = REFW(l)CALL FILTER(REFW,NW,TSEC)

CC ... TRANSFORM TO TIE DOMAINC

CALL FFT(NT,REFW,-1.)DO 35 1=1, NT

REFT(I) REAL(REFW(1))35 CONTINUE

RETURNEND

C SUBROUTINE PAIMGENCC -------------------------------------------------------------

SUBROUTINE PARMGEN(ALGL)COI'vLEX ALGLGL = CSQRT(AL*AL)IF (AIMAG(GL).LT.o.0) GL=-GLRETURNEND

C-- ------------------------------------------------------

CC SUBROUTINE REFLCC -----------------------------------------------------------

SUBROUTINE REFL(RHOI ,RHO2,GL1,GL2,RU,RD,TU,TD)

C ... COMPUTES REFLECTION COEFFICIENT RU,RD,TU & TD FOR GIVEN LAYERC ... INTERFACE PARAMETERS. THE REFLECTION/TRANSMISSION COEFFICIENTS AREC ... RATIOS OF DISPLACEMENT POTENTIALS. IN THE KTH LAYER, THE DISPLACEMENTC ...VECTOR U(K) IS GIVEN BY:C U(K) = GRAD(PHIU(K)+PHID(K))/(I*W) +C CURL CURL(ZHAT(PSlU(K)*PSID(K))) /(W*W*P)C ... IN WHICH PHIU AND PHID ARE THE POTENTIALS ASSOCIATED WITH THE UP ANDC ...DOWN GOING P-WAVES RESPECTIVELY. ZHAT IS A UNIT VECTORC .. POINTING IN THE POSITIVE Z DIRECTION, I.E. DOWNWARDS.C ...THEN, FOR EXAMPLE, THE DOWNWARD TRANSMISSION COEFFICIENT FOR P WAVES

m ,

APPENDIX 3 23

C ...FROM LAYER 1 TO LAYER 2 IS TPP12 = PHID(2)/PHID(I).C

COMPLEX GLI,GL2CMPLEX RU,RD,TU,TD,COCOMPLEX Y

CC ... NOTE THAT: GL=1/ALPHAC

DATA CO/(0.0,0.0)/Y = RHOI8GL2 + RHO2*GL1TD = 2.0*RHOI*GLI/YRD = (RHO2*GLI - RiIO1WGL2)/YTU = 2.0*RHO2*GL2/YRU = -RL)

RETURNEND

C --------------------------------------------------------CC SUBROUTINE REVERBCC-------------------------------------------------------------

SUBROUTINE REVERB(A,B)CXMLEX A,B,X,YDET,C0,C1LOGICAL WARNEDDATA CO/(0.0,0.0)/,C1/(1.0,0.0)/,WARNED/.FALSE./IF (ABS(REAL(A))+ABS(AIMAG(A)).LT. 1.OE-12)THEN

IF (.NOT. WARNED)THENWRITE(6,'(/,"OO*MULTIPLES IGNORED WHERE MAGNITUDE i E-12")')WARNED = .TRUE.

ENDIFCC ... IGNORE MULTIPLES, TO AVOID UNDERFLOW PROBLEMSC

B = C1ELSEX = 1.0 -AY = 1.0DET = X*YB = Y/DET

ENDIFRETURNEND

C------------------------------------------------------------CC SUBROUTINE FILTERCC----------------------------------------------------------


SUBROUTINE FILTER(REFW,NWTSEC)LOGICAL MPHASELXSINON /FILTL'F/ FI(IO),IDB(10),IFILTYP(IO),NFILT,NPtiASE,

+ FFI(10)REAL MAXABSVLOGICAL FRSTTIMCOMPLEX FILT(1024), FILTI(1024), REFW(1024)DATA PI/3.141592/DATA FRSTTIM/.TRUE./IF (NFILT .EQ. 0) RETURN

CC ..... GENERATE FILTER .....C

IF (FRSTTIM) THENCC ... INITIATE FILTER IN POSITIVE FREQUENCY DOMAIN. NEGATIVEC ... FREQUENCIES BECOME COMPLEX CONJUGATES OF POSITIVE FREQUENCIESC ... AND CAN BE COMPUTED WHEN NECESSARY.C

DO 10 1=1, NW+lFILT(I) = CIPLX(1.0, 0.0)

10 CONTINUECC ... SMEARING RANGE

4 CDELFREQ z 0.0

IF (MPHASE) DELFREQ=2*PI/TSECDO 15 1=1, NFILT

IF (IFILTYP(U) .EQ. 1) THENCC ... LOW PASS BUTTERWORTH FILTERC

POLES = FLOAT(IDB(I))/6 + IR = I/((FI(I)-DELFREQ)*TSEC)DO 20 J=l, NW+1

FILT(J) = FILT(J)/SQRT(I+((J-I)*R)**POLES)20 CONTINUE

ELSEIF (IFILTYP(I) .EQ. 2) THENCC .. .HIGH PASS BUTTERWORTH FILTERC

POLES FLOAT(ID(I))/6 + IFACTOR 1/((FI(I)+DELFREQ)*TSEC)L)0 25 J=i, NW+I

R = ((J-I)FACTOR)**POLESFILT(J) = FILT(J)OSQRT(R/(I+R))

25 CONTINUEELSE

CC ... NOTCH FILTERC

IF(I.EQ.2)GO TO 26INDEXI = IFIX((FI(i)-DELFREQ)*TSEC) + IGO TO 27

26 INDEX2 = IFIX((FI(I).DELFREQ)*TSEC) + 2

. 6

I- . ' ',.- 3 ' =, '" " ,-, - ,. , . - ,, -, - . , - ., ,- . . . . . . . . . _ .,,. ... . .

,I . ., . ,., , .: .. .. . : . . . . .-. . . ., . . . .: , .. ..

APPENDIX 3 25

IF (INDEX2-INDEXI .LT. 16) THEN,.-'" WRITE(6,'(" *** FI(I) TOO CLOSE TO FI(2) IN NOTCH - NO

+ "FILTERING DONE ***"))RETURN

ENDIFCC ... IDB REDUCTION

GO TO 29

27 R = 1 - 10*°(-(FLOAT(IDB(I))/20))CC ...INEILS DESIGN

IF(I.EQ.1)OO TO 28C

29 DO 30 J=INDEXI, INDEX2FILT(J) = FILT(J)*

+ (1 + R*(OUS(2*PI*(J-INDEXI)/(INDEX2-1 EXI))-I)/2)30 CONTINUE28 ENDIF

715 CONTINUE

IF (MPHASE) THENCC ... SET A(W) = LN F(W)C

DO 35 1=1, NW IIF (REAL(FILT(I)) .EQ. 0.0) THEN

FILT(I) = CMfLX(-30.0, 0.0)ELSE

FILT(i) = CMPLX(ALOG(REAL(FILT(1))), 0.0)ENDI F

35 CONTINUECC ... NEGATIVE NEEDED FOR FFTC

DO 40 I=NW+2, NW240 , FILT(I) a CONJG(FILT(NW*2-1*2))40 CONTINUE

CC ...A(T) = INVERSE FFT A(W)C

CALL FFT(NW*2,FILT,-.0)C ... B(T) = A(T)*G(T)

DO 45 1=2, NW+IC ... G(T)

R = (I+COS(PI*(l-1)/NW)) /2C ... NW+I VALUE = 0

C ... 1 ST VALUE UNCHANGEDFILT(NW*2+2-1) = ROFILT(NW*2+2-1)

C ...2 & NW*2 VALUE NEARLY = 045 CONTINUE

C ...lNW' 1VAL = 0 IS USED HEREDO 50 I=l, NW

FILT1(I) = FILT(I)50 CONTINUE

-


C ... C(T) HAS INVERTED 2 HALFDO 55 I=NW+t, NW*2

FILTI) = -CONJG(FILT(I))55 CONTINUE

C ... B(W) = FT B(T), C(W) = FT C(T)CALL FFT(NW*2,FILT,1.0)CALL FFT(NW*2,FILT1,I.0)MAXABSV = 0.0

C ... F'(W) = EXP(B(W)+C(W))DO 60 1=1, NW+l

FILT(I)=CEXP(FILT(1) + FILT1(I))

MAXABSV = AMAXi(CABS(FILT(1)),MAXABSV)60 CONTINUE

DO 65 1=1, NW+IC ... NORMALIZE

FILT(I) = FILT(I)/IMAXABSV65 CONTINUE

END IFFRSTTIM = .FALSE.

ENDIFCC ..... ACTUAL FILTERING FOLLOWS .....C

C .. .MUL-IPLY BY POSITIVE FREQ FILTERC

DO 70 1=1, NW+1REFW(I) = REFW(I) * FILT(1)

70 CONTINUEC

C ... NEGATIVE FREQUENCY ARE CONJUGATESC

DO 75 I=NW+2, NW*2REFW(I) = CONJU(REFW(NW*2-I+2))

75 CONTINUERETURNEND

C - ----------------------------------------------------------CC SUBROUTINE FFTCC ---------------------------------------------------------

SUBROUTINE FFT(LX,CX,SIGNI)COMPLEX CX(LX),CTEMP,CWJ = 1SC = SQRT(I./FLOAT(LX))DO 3 I=1,LXIF(I.GT.J) GO TO ICTE P = CX(J)*SC

CX(J) = CX(I)*SCCX(i) = C(.'EN

I M = LX/22 IF(J.LE.M) GO TO 3

• € ' -,' "" ", '. ": -' ", , .- : ..." . ......."-. ,, .-"," ,, •"; " ""'.''".,,. , . , """ "". """"" , . .

APPENDIX a 27

jzj - MM =M/2IF(M.GE.1) 00 TO 2

3 J J +ML= 1

4 ISTEP = 201DO 5 M*1,LAA = 314159265358979.D-1451Q41(M-1)/LCW = Q.FLX(ClOS(AA),SIN(AA))DO 5 I=M,LX,ISTEPCTEWP = CVPCX(14L)CX(I.L) zCX(I) - CTEP

5 CX( I) a CX( I + CTEMPL aISTEPIF(L.LT.LX) OD TO 4RETURNEND

C C-----------------------------------------------* C

C SUBROUTINE WRTPLTCC -----------------------------------------------

SUBROUTINE WRTPLTCMMON / NUM / CL(200),QL(200),RHO(200),T(200),EPS,SICNAk,+ CRUST,NL,NTRACE,LOBS ,NW,TSEC,TSC,ASC,NMULT,+ TLAG,YSIDE,TLNTHCOMMON /TS/ REFT(1024)COMv14/AA/ IAGC, WNDOWCOMMON IFILTUF/ F1(10),IDB(1O),IFILTYP(10),NFILT,NPHASE,

+ FF1(10)COMMON / CHAR /ITIME,IDATE,IOBT,TITLECHARACTER 1. I OBTCHARACFER010 ITIME,1DTECHARACrER080 TITLEOPEN(UNIT=4,FILE='PLTIN' .STATUS='NEW')IF( IOBT.EQ. 'P' )THEN

ELSE IF(IOBT.EQ.'V')THEN

ELSEI NUW z3

* END IFI' NT2NW

WRITE(4,1001)TITLE1001 FORMAT(A)

WRITE(4,999)NTRACE,YSIDE,NW,TLNTI4,NL,NFILT,MPHASE999 FORM&T("NTRACE=", I4,",YSIDE=",F5.2,".NWfi,15,",TLNTH=",

*FS .2 ,".NL=",13,",NFILT= ,13,",WHASE=",L2)WRITE(4,989)TSEC,TSC,TLAG,ASC

989 FORMAT( "TSEC=".F1O.0, ",TSC=",F1O.S,",TlAG=-",F1O.0,",ASC=",F1O.5)DO 5 Iz1,NFILT


WRITE(4,995)IFILTYP( I),IDB( I),FFI( I)995 FORMAT("FILTER TYPEm",12,1X,"DB-SLOPE=",13,lX,

*"CUTF-OFF FREQUENCY:",F5.1)5 CON4TINUEWRITE(4,987)INUM,LOBS,NMULT,CRUST, IAGC,WINDcOV

987 FORM4T(lX,"IOBT=",I1,",LOBS=",13,",NMULT=",IS,",CRUST=",FlO.5IAGC= ",13, ",WINDOW",F7 .2)

DO 6 lIl,NL

+CL(I) ,QL(I) ,RlHO(1) ,T( I)6 CONTINUE

DO 10 I=1,NTWRITE(4,'("REFT=",1X,F20.14)')REFT(I)

10 CO)NTINUERETURNEND

C-----------------------------------------------------------

C SUBROUTINE AGCFREQCC----------------------------------------------------------

SUBROUT INE AGCFREQDIMENSION SQREFT(1024),BB(2)COMPFLEX SQREFW(1024), WW(1024)CXJfvIN / NUM / CL(200),QL(200),RHO(200),T(200),EPS,SIGvA,

+ CRUST,NL,NTRACE,LOBS ,NW,TSEC,TSC,ASC,NMUJLT,+ TLAG,YSIDE,TLNTHCOMMON / CHAR / ITIME,IDATE,IOBT,TITLECO'I142N /TS/ REFT(1024)COMtMtON/AR/ IAGC,WINDOWDATA Pi/3.141592653/

* CC .. SQUARE TRACE AMPFLITUDES AND MAKE COMPLEXC .... INITIALIZE FILTER TOD COMPLEX ZEROC

SUN5Q-0o.0NT =NW*2DO 330 1 = 1,NT

SQREFT(I) =REFT(I)OREFT(I)V SUMSQ=SUMQ+SQREFT( I)* -S. SQIIEFW(I) =CMPLX(SQREFT(),0.0)

WW(I) a LWWILX(0.0,0.0)

30CONTINUEc NDTOTH INUTIESRECCODTOTHINUTIESRE

* * ASQSU~Q/NBOI/AVSQQWDOS331I.O/AVS

* ~ ~ ~ D 331F~l = SREW(18cTS

331 CONT INUE

APPENDIX 3 29

C .... 0OSTRUCr AOC FILTER IN TIME DOMAINc ...."WIN4DOW" (READ 1I4 BY USER) IS FILTER LENGTH IN NSECSC

DELTAT = TSEC/NTITW2 z NINT((WIND(OV/DELTAT)/2.0)

DO 340 1 a 1,ITW2+1JW z= NT'1-I+0$Pl(-I/TW),OOJ) = WV(I)

* ~ ~ W 34 OONINU34C ONIU

C DTI4T ILEc CNIINTEFLE

SLFL=.DO 31 L-0.TDO341IL=SWFINTVISU*~SNI 34 OONTINU

34 ONTI=NE LMIBOS 34 INTMI

WW( I)=WW( I)*BOOST*342 CONTINUE

CC ... TRANSFORM TO FREQUENCY DOMAIN AND FILTERc

CALL FFT(NT,SQ~EFW,+1.0)CALL FFT(NT,WW,+1.0)DO 350 1 1I,NF

SQREFW(I) = SQREFW(I)OWW(I)350 CONTINUE

CC ... TRUNCATE DC COMPONENT TO 5 SIGNIFICANT FIGURES

* CTENP=REAL(SQEFW( 1))ENOODEC 14,345 ,BB)TEWPDECODE( 14 ,345,BB)TEMPI

345 FORMAT(1E14.5)SQREFW(1) = akVLX(TE*1I,0.0)

CC ... RETURN4 TO TIME DOMAINC

CALL FFT(NT,SQREFW,-1.0)CC RESTORE TINE SERIESC

SLmsQF = 0.0DO 346 lz1,NT

* SLN5QF = SUi.5QF + SQREFW(I)*02346 CONTINUJE

AVSQF =SUNSQF/NTBOOST = AVSQ/AVSQFDO 347 I=1,NT

SQREFW(I) aSQREFW(I)OBOOST347 ONITINUE

* C


C APPLY AGC-' C

CURRMIN = REAL(SQREFW(l))V DO 360 1= 2,NT

CURRMIN = AMINI(CURRMINREAL(SQREFW(I)))360 CONTINUE

DO 380 I = I,NTIF (CURRMIN.LT.0.0) THEN

REFT(I) REFT(I)/SQRT(REAL(SQREFW(I)) + ABS(CURRMIN*2.0))ELSE

REFT(I) = REFT(I)/SQRT(REAL(SQREFW(I)))ENDIF

380 CONTINUERETURNEND

C-----------------------------------------------------------------CC SUBROUTINE TERMINCc-------------------------------------------------------------------

SUBROUTINE TERMIN(NERR, LNR)

CXOfNON / NUM / CL(200),QL(200),RHO(200),T(200),EPS,SIGMA,+ CRUST,NL,NTRACE, LOBS,NW,TSEC,TSC,ASC,NMULT,+ TLAG, YS IDE,TLNTHCOMMON / CHAR / ITIME,IDATE,IOBT,TITLE

. IF (NERR LT. 10) THEN* ." WRITE(6,'(/" 000 ERROR IN MODEL FILE LAYER: ",14)') LNR

ELSEIF (NERR .LT. 20) THENCALL PRTMLDAWRITE(6,'(/" 0*s ERROR IN PROCESSED LAYER: ",14)') LNR

ENDI F

IF (NERR .EQ. 1) THENWRITE(6,'(" TOO MANY LAYERS IN MODEL: ",16,", MAX=200")') NL

ELSEIF (NERR .EQ. 3) THENWRITE(6,'("CL CANNOT BE 0 AND H CANNOT BE -VE FOR FIRST

+LAYER")')ELSEIF (NERR .EQ. 4) THENWRITE(6,'("LAST LAYER CANNOT BE AN INTERPOLATED LAYER")')

ELSEIF (NERR .EQ. 5) THENINRITE(6,'("ABSOLUTE DEPTH GIVEN IS LESS THAN THE CURRENT DEPTH")')

ELSEIF (NERR .EQ. If)THENWRITE(6,'("CL NOT IN RANGE 0 1 CL 1 10")')

ELSEIF (NERR .EQ. 12)THENwRITE(6,'("QL i 10O")')

ELSEIF (NERR .EQ. 15) THENW'RITE(6,'("RHO NOT IN RANGE 0 1 RHO 1 10")')

ELSEIF (NERR .EQ. 21) THENWRITE(6,'(/" *00 TOO FEW (OR TOO MANY) VALUES ON ONE LINE "

+ "OF MODEL FILE -"/" CHECK FOR / AT END OF INTERPOLATED LAYER ",

t.

%-

i '' "".. -, . -' '' '". - * , '. - - ' , " " . .' . ' . . " . " ."- " - . " ' " " - . . " ' ' . .. -. . . . . . . .


Test 3. Multiples

Two layers, 75 and 100 m thick, are through M4 identify the "peg-leg" nult'ples.sandwiched between half spaces (fig. 3B). Q Figure 5A demonstrates the .omplete-200 and density = 1.1 for all units. The response option; the clipping occurs because100-meter-thick layer has a velocity of 3.0 of a large amplification option (ASC = 100).km/sec; the other units have a velocity of 1.5 Figure 5B shows the seismogram for the samekm/sec. The seismogram consisted of the model but for a user option of only onetime-domain reflection coefficient plotted multiple. Note that no reflections arewithout filtering, observed beyond the first multiple arrival at

A series of tests were run with options 234 ms. Arrival times, amplitudes, andbeginning with "primaries only" to options polarity in figure 5 are consistent with thosefor a selected number of "multiples" and predicted by hand calculations based onfinally a "complete-response" seismogram reflection-transmission coefficients. Table 3(fig. 5). R1 and R2 identify the reflections summarizes the results.from the top of the two reflectors. MI

Table 3. Arrival times of reflections and multiples fora two-layer model (fig. 5)

Reflector Primary One Two Fullindex only multiple multiples response

Ri 100 ms 100 ms 100 ms 100 ms

R2 167 ms 167 ms 167 ms 167 msMI - 234 ms 234 ms 234 ms

M2 - - 300 ms 300 ms

M3 - - - 367 ms

M4 - - 434 ms

Table 4. Input data used to test a full response (fig. 5A)

TEST 3- D2L. FULL RESPONSE OPTION.EPS S I(M YSIDE XS IDE0.001 0.1 40. 6.CL QL RHO THICKNESS1.50 200. 1.1 0.1.50 200. 1.1 75.3.00 200. 1.1 100.1.5 200. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(MVBEC) IN/INSEC AMP-SCALE MLTPL AGC WINDOW5 512 1000. .006 100.0 -1 0 0

DETECTOR TYPE DETECTOR LOCATIONREFLECTION LAYER IFILTER PHASE2 (NO FILTERS)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY

• - , ..

APPENDIX 4 43

TEST 2 - OIL. HIGH 0 (=1500) TEST 2 - OIL. LCW 0 (=5JREFLECTION COEFFICIENT REFLECTION COEFFICIENT

AT 055 IN LAYER I AT .0 M DEPTH AT 055 IN LAYER I AT .0 M DEPTHFREQtNW)= 512 TrISECS]=2000 FREO(NW]= 512 TIMSECS)=200,0

MIN = .50 HZ MAX =256.00 HZ MIN = .50 HZ MAX =256.00 HZ

--PRIMARIES ONLY PRIMARIES ONLY

NO ASC. ASC = 1. NO AGC. ASC = 1.

NO FILTERS NO FILTERS

"25n

W' 5

or ,500

55,' 550

60, 600

4 ¢ 650

e0r 000- 0 00

M ,, 050

957 95CM50 FTI Or 0

7:o1o00 1 00

1150 1150,t* m m @@

IZ1 1200-

13co 1300007'" I050"

- A 3- I - 35 0

1400 1400"

14-0 1450-

:500k 1500

157 C 1550-OCI@-. 1600

: -A 1050 B17"C0 1500.

A170000- 000

100- 1050

0900 .900

050 050990- 990

Figure 4. (Test 2) Reflection from a single layer (fig. 3A) for A, Q - 1500 and B, Q - 5. Arrow identifies reflec.tion from change in Q at upper half space.

_ . _ . . . , " . .. , . . . . . .- - • + , -


Test 2. Attenuation Factor Q

A layer 1000 m thick was overlain by a half to 20 msec, with a width of about 150 msec

space with an identical velocity (1.5 km/sec) for a Q of 5 (fig. 4B). As expected, low Q

and underlain by a half space with a velocity emphasized lower frequencies.of 3.0 km/sec (fig. 3A). All units had a A change of Q from 15 in the top half

constant density of 1.1 gm/cc. No filter was space to 1500 in a layer 1,000 m thick (but

applied. The seismograms consisted of a plot with no change in the user-specified velocity

of reflection coefficients for primary arrivals between these two regions) yielded a small

only. A wide frequency range of 1-512 hz was pulse at zero time. (See arrow in fig. 4A.) This

invoked to study the waveforms better. is consistent with our algorithm, which brings

The Q of rocks for seismic energy is of the in attenuation changes through a complex

order 50, although poorly consolidated velocity.materials may be lower. In this test Q was The following records (table 2) were used

-. varied from 5 to 2000. For Q values above 50, as input to Program VISP to generate figure

the response was essentially a spike with a 4A. The same records were used to generate

width of less than 10 msec. Figure 4A figure 4B, except that QL values were all set

illustrates a Q of 1500. For Q values of 20 or equal to five.less, the pulse width of the response increased

Table 2. Input data used to test high Q (fig. 4A)

TEST 2 - D1L. HIGH Q (=1500)EPS SIGM4A YS IDE XSIDE0.001 0.1 40. 6.0CL QL RHO THICKNESS1.5 15. 1.1 0.1.5 1500. 1.1 1000.3.0 1500. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(MSEC) IN/MSEC AMP-SCALE MLTPL AGC WINDOW5 512 2000. .003 1.0 0 0 0DETECTOR TYPE DETECTOR LOCATION

REFLECTION LAYER I

FILTER PHASE2 (NO FILTERS)FILTER-TYPE DB SLOPE Cur-OFF FREQUENCY

KF.7

L j, o , , , , , ~~~~~~~~~..... . ......... .. .... ,. . .................. ..... . . .. •.... .... ,...... ..... ,:. . .-. ,

GENERATION OF VERTICALLY INCIDENT SEISMOGRAMS 41

• Appendix 4. Input Records and Output Plots for 12 Tests

Thirteen tests were run to demonstrate the following test cases is related to one of these

reliability of the options available to the user three models, although the velocity, Q, andof Program VISP. Test 1 consisted of a model (or) density may be varied. Program VISP hassimulating a standard field record (fig. 2). In detailed comment cards at the beginning thatthe remaining 12 tests, three basic models explain the various user options tested in this

- were used: (1) one-layer, (2) two-layer, and appendix.(3) six-layer (figs. 3A-3C). Each of the

CL U(M/SECJ CL (KM/SEC) CL (KM/SEC)

1 2 3 1 2 3 1 2 37"t" ."m" [|I .. ... h* ~ ~~...... ,I I ....,, I ......... l..... ....

M aU

I|

M rn M-44

U) LO~ LO I

U!

a" I" .......... .... . .... ... '

'-."Figure 3. Velocity models for Test 2-13 (appendix 4). A, one-layer; B, two-layer;

C, si°,e

:'I

4 . .. . . . ., ,( . .... . ; . . , . . . . , " '." "- - . . . ' . '. . . . ,, ,X 'k ' . ' '' .'.

."-.4.-- --.- ,, , ', . .'a .. ', ,,' " ,,€'' .. ,. .. " - ,,; , .. .' -. "- " ''' :' i. . i , '" " ,ie-.-...m'" " "..,,.. ., .

40 GENERATION OF VERTICALLY INCIDENT SEISMOGRAMIS

IF (MDD(IXRANGE,100) .EQ. 0)+CALL NUNUER(X-0.15,Y+YOFFSET,0.055,FLOAT( IXRANGE) ,0.0,-1)CALL PLOT(X,Y,INKOFF)CALL PLOT(X+0.75,Y,INKO4)IF (I.EQ.0) CALL SYMBOL(XO+TLNTH/2-0.4,Y-0.7,0.16,

+ "ETERS",0.0,6)

Y= Y + 7.0 - 0.4x = xo

C PLOT MO)DEL PARAMETERS

DO 170 1=1,3IF (PMAkX(I) .NE. PMIN(I))GO TO 55

YSC =0.0Y1 YSTRIP/2

GO TO 6555 YSC = YSTRIP/(PNIAX(I)-PMIN(I))

Yl = 0.0

65 YI =YO +0.2 + (I-1)*(YSTRIP+0.2) + 0.1IF ((I.EQ.i) .OR. (I.EQ.5))+ CALL PLOr(XO,YI+(PARM(l,I)-PMIN(I))OYSC+YI,INKOFF)X = XO+0.75LIMIT=NL-1DO 180 J=1,LIMIT

IF ((J.NE.1) .OR . ((I.LT.2) .OR. (l.GT.4)))GO TO 75CALL PLOT(X,YI+(PARM(2,I)-PMIN(I))*YSC+Yl,INKOFF)

GO TO 8575 CALL PLOT(X,YI+(PARM(J,I)-PMIN(I))*YSC+Yl,INKON)

CALL PLar(X,YI+(PARM(J+1,I)-PMIN(I))*YSC+YI,INKON)85 IF (J.LT.NL-1) X=X + T(J+1)*(TLNTH-1.5)/IXRANGE180 CONTINUE

X = XO'TLNTHCALL PLOr(X,YI+(PARM(NL,l)-PMlN(l))*YSC+YI,INKON)

+1"CL (KW/SEC) ",90.,12)IF( I.EQ.2)CALL SYMBOL(XO-0.6,YO+( I-iP*(YSTRIP+.2)+.3, .1,+ 11QL*",90.,12)IF( I.EQ.3)CALL SYNUOL(XO-0.6,YO+( I-i)*(YSTRIP..2)+.3, .1,

CALL NUNUER(XO-0.6,YO+1 .96,0.10 ,PARMPY,90.0 ,3)170 CONTINUE

XO = XO+TLNTH+2.5RETURNEND

APPENDIX 3 39

A'10 CALL PLOT(X.Y,INKOFF)IF(J.EQ.2)CALL PLOT(X4.10(12-1),Y,INKON)CALL PL0T(Xe0.*(1*2-I),Y,JNKON)CALL NUISER(XeXOFFSET,Y,0.1 ,FLOAT(PMIN(J)) ,90.0, -1)CALL PLOT(XY, INKOFF)ISTART=PMIN(J)+lISTOP=PMAX(J)DO 130 K=ISTART,JSTIOP

DO 140 L=1,10Y = Y + YSTRIP/((PMAX(J)-PMIN(J))*10)CALL PLOT(X,Y, INKON)IF(J.NE.2) CALL PLOT(X+0.05*(1*2-1),Y,INKON)CALL PLCYF(X,Y, INKOFF)

140 CONTINUECALL PL0r(X.0.1*(1*2-1),Y,INKON)

IF( J .NE.2)+ CALL NUMBER(X+XOFFSET,Y-0.1,0.1,FLOAT(K),90.0,-1)

IF(J.EQ.2.AND.K.EQ.PMAX(2))+ CALL NUMBER(X+XOFFSET,Y-0.1 .0.1 ,FLOAT(K) ,90.0, -1)

CALL PLOT(X,Y, INKOFF)130 CO~NTINUE

20 Y= Y+0.1120 COlNTINUE

X = X+TLNTHY = YO + 0.2

~110 CNTINUJE

C PLOT X AXIS

X = XOY = YO + 0.2I1=0YOFFSET = -0.1+0.25*(102-1)CALL PLOT(X,Y, INKOFF)X = X+0.75CALL PLOT(X,Y,INKON)DO 160 N=1,IXRANGE,10

J=N-1IF(MOD(J,100).NE.0)OO TO 30CALL PLOT(X,Y'0.*(1*2-1),INK0N)CALL NUMBER(X-0.05,Y+YOFFSET,0.055,FLOAT(J), .. ,-i)

0O TO 4030 CALL PLOT(X,Y.0.05*(12-1),INKON)40 CALL PLOT(X,Y,INKOFF)

X = X +(TLNTH-1.5)/IXRANGE*1OCALL PLOT (X,Y,INKON)

160 COlNTINUECALL PLOT(X,Y+0. 1*([12-1), INKON)


INKON2INKOFF=3

N YO=0. 5Xo = XO+2.0PAMMAX =ABSPARM(1,2)DO 50 I= 2,NL

'SPARMAX =AMAX1(PARMAX,ABSPARM(I,2))50 CONTINUE

IF(PARMAX.LT.100.0) PARMPY = 1.0N IF(PARMAX.GE.100.0.AND.PARMAX.LT.1000.0) PARMPY = 0.1

IF(PARNIAX.GE.1000.0.AND.PARMAX.LT.10000.0) PARMWY 0.01IF(PAIRMAX.GE.10000.0) PARMPY= 0.001DO 60 lzl,NLDO 70 J=1,3,2

PARM(I,J) =ABSPARM(I,J)70 CONTINUE

PARNI(1,2) = ABSPARM(1,2)*PARMPY60 CONTINUE

DO 80 1=1,3PMAX(l) =0PMIN(I= 1000

S0 CO~NTINUEPMINMi = PARM(1,I)DO 90 I=2,NL

DO 100 J=1,3PMAX(J) = NAX1(FLOAT(PMAX(J)),PARM(I,J)+0.999)PMIN(J) =MIN1(FLOAT(PMIN(J)) ,PARM( 1,J))

100 CONTINUE90 CONTINUE

YSTRIP =1.0IXRANGE =CRUST+0.99

CC PLOT Y AXIS

x = xoY =Yo+0.2DO 110 M=1,2

I =M- 1XOFFSET =0.12+0.30(102-1)CALL PLCOr(X,Y, INKOFF)DO 120 J=1,3

Y = Y+0.1IF(PMIN(J).NE.PMAX(J))GO TO 10

Y = Y + YSTRIP/2CALL PLOT(X,Y, INKOFF)CALL PLOT(X+0.10(12-1),Y,INKON)

CALL NUNMER(X4XOFFSET,Y,0.1 ,FLOAT(PMIN(J)) ,90.0, -1)

GO TO 20 YTI/

i-

APPENDIX 3 87

C PLOT TIME SERIESC --- - - - - - -

CCURRMAX = ABS(REFT(1))

NT=NW 2DO 290 I=2,NT

CURRMlhX = AMAXI(CURRMAX,ABS(REFT(I)))290 CONTINUE

X = XOY = YO - 2.0

CC EFFECTIVELY A NULL TRACE (NOISE)C

IF (URM.LT.0.1) CUEBMAX=-i0.0

CALL PLOT(X,Y+AY,INKOFF)CC ALLOWS FOR TRUNCATED TIME SERIES (TSC 1 0)C

NPTS = NW*2*AMIN1(1.0,YSIDE/(TSECOTSC))) ~ YSC = NPTS*TSECOTSC/((NPTSI)NW2)DO 310 I=1,NPTS

IF(.NOT. ASC.EQ.1.0) GO TO 55x(I) = X+(I-1)*YSCYY(I = Y+AY+REFT(I)/(CURRMAX*2)CALL PLOT(XX(I),YY(I),INKON)

GO TO 31055 XI AMIN1(ABS(REFT(l))*ASC/(CURRMAX*2), 0.4)

IF (REFT(I) .LT. 0.0) Xl=-X1xOC(I) = X+(I-1)*YSCYY(I = Y+AY+XlCALL PLOT(XX( I) ,YY( I), INKON)

310 CONITINUE300 CONTINUE

RETURNEND

C------------------------------------------------------------CC SUBROUTINE PARMPLTC

CSUBROUTINE PARMPLT

COMMOEN/ PLTPAR /NTRACE,YSIDE,TSEC,TSC,TLAG,ASC,REFT(1024),NW* ,IOBT,LOBS,NMULT,NL,CL(200),QL(200),RHO(200),T(200),TLNTH,XO* CRUST ,IAGC, WINDOW, NF ILTCOMMOfN/ FILTDT /IDB(10), IFILTYP(10) ,WFIASE,FF1(10)REAL ABSPARM(200,3), PARM(200,3), TLNTHEQUIVALENCE (ABSPARM(l,1),CL(1))INTEGE.- PMAX(3),PMIN(3)


Y = YO - 2. 41=0XOFFSET = 0.07+0.3*(1*2-1)CALL PLar(X,Y, INKOFF)DO 270 M=1,IYRANGE

J=M-1IF(.Nar.IW3D(J-1,MDDF) .EQ. INT(TLAG)-l) GO TO 50

C CALL PL0T(X,Y+0.1*(I*2-1),INKON)

C CHANGE SIZE OF CHARACTERC

IF(TSC.LT.(.01))OO TO 49CALL NUN3ER(X-0.07,Y+XOFFSET,O.055,FLOAT(J)-TLAG,0.,-l)GO TO 50

49 CALL NUNBER(X+.03,(Y+i(OFFSET)-.05,0.055,FLOAT(J)-TLAG,90.,-1)50 IF(.NOT.NI)D(J,(MODF-1)/10+1).EQ.0) GO TO 51

CALL PLOT(X,Y+0.070(12-1),INKOI)51 CALL PLOT(X,Y,INKOFF)

IF(.NOT.IYRANGE.LE.20)GO TO 52DO 280 K=1,10X =X + TSCOO.1CALL PLOT(X,Y, INKON)CALL PLOT(X,Y.0.05*(1I2-1),INKON)CALL PLOT(X,YINKOFF)

280 CONTINUEGO TO 270

52 X = X+TSCCALL PLOT(X,Y,INKON)

270 CONTINUECALL PLaT(X,Y+0.1*(1*2-1),INRON)

IF(TSC.LT.(.01))OO TO 53CALL NUMBER(X-0.07,Y+XOFFSET, .055,FLOAT(IYRANGE)-TLAG,0.0,-l)

GO TO 5453 CALL NUMBER(X+.022,(Y.XOFFSET)-.05,.055,FLOAT(IYRANGE)-TLAG,

$90., -1)54 Y = YO - 1.4

X =X0+IYRANGE*TSC/2-1.5CALL SYMBOL(X+.75,Y-1.5,.15,"TIME IN MSEC -,0.0,13)

CC PLOT X AXISC-- - - - -C

Y = YO - 2.0CALL PLOT(XO,Y, INKOFF)CALL PLOT(X01Ye0.4+YS,INKON)

C* C

*. A

APPENDIX 8 86

33 CALL SYMBOL(X0+1.8,6.5,.1,"---FILTERS = ZERO PHASE---",90.,26)34 DO 101 I=1,NFILT

IF(IFILTYP(I).NE.1)OO TO 35CALL NUhBER(XO+1.9*I1,7.5,.1,FFIl),

9O. ,0)CALL NU[MER(X+1.9.I*.15 ,8.3,.1,PLOAT(IDB(i))s

9 ,-90.CALL SY!MOL(X+1.9+I*.15,6.5, .1*"HIGH CUTr AT HZ; DB SLOPE",90.,33)

35 IF(IFILTYP(I).NE.2)OO TO 36

CALL NUMBER(X041.9+10.15 S.3,.l,FLQAT(ID(I)) 9 0. ,-

CALL SYMBOL(XO+1.9+1*.15,6.5, .1"LOWV CUTI AT HZ; DO SLOPE",90.,33)

36 IF((IFILTYP(I).NE.1).AND.(IFILTP().E.2 ))GO To 3 7

(J0 TO 10137 IF(I.EQ.2)GO TO 101

A> CALL SYIMOL(X+1.9+I*.15,6.5,.l.

*"NOTCH 1)8 FREQUENCY RANGE - Z",90.,95)CALL NUMBER(XO+1.gI'*.15,8.9,.1,FFIl(),

9 0. ,-l)CALL NUMBER(XO+1.9+I's.15 ,9.4,.1,FFI(

2),9O. ,-1)101 CON4TINUE31 IF(IAGC.NE.1)0O TO 12

CALL SYMBOL(X0+1.4,6.5,.l,"AGC WINDOW MSECS",90.,24)CALL NUNSER(XO+1.4,7.8,.I,WINDOW,90. ,0)

00 TO 3012 CALL SYMBOL(XO+1.4,6.5,.1,"NO AGC. ASC = ",90.,14)

CALL NVUER(XO+1.4,7.9,.1,ASC,9 0. ,0)

30 XO = XO+3.0

xsc 0.30

C FOR TRUNCATED TIME SERIESC

MYANGE = AMIN1(TSEC,YSIDE/TSC) -0.01 +1

CC (TSC 1O)

-. C

* IF (IYRANGE .LE. 10) MDDF1lIF (IYRANGE.LE.20)IMVDF=2IF(IYRANGE.LE.50)fiDDF=5IF( IYRANGE.LE. 100 )NEDF=10IF(IYRANGE.GT.100) NfODF=50YS =NTRACEOXSC

CC PLOTF Y(ThM) AXESC-- - - - - - - - - -


COMMON/14 FILTDT /IDD(1o),IFILTYP(Io),NWHASE,FF1(1O)DIMENSION XX(I024),YY(1024)LOGICAL MPHASEINKON=2INKOFF=3R= 0.0YOu9.0XO=0.75IF(IOBT.EQ.1)CALL SYN3OL(XO,6.5,.1,

+"PRESSURE "I,90.,24)IF(IOBT.EQ.2)CALL SYMBOL(XO,6.5,.1,+"VERTICAL DISPLACEMENT ",90.,24)IF(IOBT.NE.I.AND.IOBT.NE.2)CALL SYMBOL(XO,6.5,

* +.1,"1REFLECTIO4 OEFFICIENT 11,90.,22)IF(LOBS.NE.0)GO TO 1000 TO 15

*10 CALL SYMBOL(XO+.26,6.5,.1,+"AT 085 IN LAYER AT M DEPTH ",90.,39)CALL NUMDER(XO+.26,8.1,.1,FLOAT(LOBS),90. ,-1)CALL SYMBOL(XO..52,6.5,.l,"FREQ(NW)=",90. .9)CALL NUMBER(XO..52,7.4,.l,NW,90.,-l)CALL SYMBOL(XO+.52,9.5, .1,"T(MEECS)=",90. 19)

CALL NUNUER(XO..52,9.3, .1,TSEC,90.,-1)K=LOBS-1IF(K.LT.2) G0 TO 11DO 20 1=2,K

R=R+T( I)- *20 ONtTINUE

11 CALL NUMBER(XO..26,8.7,.1,R,90.,1)15 CALL SYN9OL(XO+.8,6.4,.l," MIN =HZ ",90.,17)

CALL NUMBER(XO+.8,7.2,.1,(1/TSEC)01O00. ,90.,2)*CALL SYMBOL(X0+.8,8.1,.1,"MAX= HZ",90.,14)

CALL NUMBER(XO+.8,8.55,.l,(NW/TSEC)'1000. ,90. .2)IF(NMULT.LT.0)CALL SYMBOL(XO+1. 1,6.5, .1,

+"FULL RESP014SE (ALL MULTIPLES) ",90.,29)IF(NMULT.EQ.0)CALL SYMBOL(XO*1.1,6.5,.1,"PRIMAkRIES ONLY,

* +90. ,14)IF(NMULT.GT.0)GO TO 250O TO 28

25 CALL SYMBOL(XO+1.1,6.5,.1,"NUMBER OF MULTIP.LES 11,90.,21)CALL NUMBER(XO+1.1,S.7,0.1,FLOAT(NMULT),90. ,-1)

28 IF(NFILT.GT.0)GO TO 27CALL SYMBOL(2.5,6.5,.1,"NO FILTERS",90.,10)GO TO 31

27 IF(.NOT.MPHASE)GO TO 33CALL SYMBOLCXO+1.8,8.5,.1,"---FILTERS =MINIMUM PHASE---",90.,29)GOTO34

or

*APPENDIX 8 as

*989 FORMAkT(5X,F1O.0,SX,P1O.5,6X,F1O.O,SXF1O.5)IF(NFILT.EQ.0)0O TO 985DO 15 I1I,NFILTREAD( 1, 966 )IFILTYP( I) ,IDB(I) ,FF1(I)

986 FORMAT(12X,12,1OX,I3,19X,F5.1)15 CONTINUE

*985 READ(1,987)IOBT,LOBS,NMULT,CRUST,IAGC,WINDOW987 FORMAT(6XI1,6X,13,7X, 15,7X,F1O.5,6X,l3,7X,F7.2)

NT=2*NWDO 5 I=1,NL

READ(1 ,102 )CL(I) ,QL(I) ,RHO(I) ,T( I)102 FORMAT(4X,F5.2 ,4X,F6.0,5X,F5.2,3X,F6.1)5 CONTINUE

DO 10 I=1,NTREAD( 1, 101 )REFT( I)

101 FORMAT(5X,20.14)10 CONT INUE

RETURNEND

C -----------------------------------------------------------------------C

*C SUBROUTINE INITPLT* C

c C---------------------------------------------------------------------SUBROUTINE INITPLTCOMMON/ CHAR /TITLE($)COMMON/ PLTPAR /NTRACE,YSIDE,TSEC,TSC,TLAG,ASC,REFT(1024),NW

+, IOBT,LOBS,NMULT,NL,CL(200) ,QL(200) ,RHO(200) ,T(200) ,TLNTH,XO+ ,CfUST, IAGC,WINDOW,NFILT

* COMMO.N/ FILTDYT /IDB(I0),IFILTYP(10),WMHASE,FF1(10)CALL SYMBOL(.S,.5,0.15,"VISP; ",90. .6)CALL SYMBOL(.5,.8,.15," PLOTS OF PARAMETERS

+90.0,34)CALL SYPUOL(1.5, .5,.1,TlTLE,90. .80)CALL SYMB~OL(.5,6.5,.12,TITLE,90.,80)XO =1 5RETURNEND

C ---------------------------------------------------------------------CC SUBROUTINE RSPMDLCC ---------------------------------------------------------------------

SUB ROTIINE RSPNI)LCOMMON/ PLTPAR /NTRACE,YSIDE,TSEC,TSC,TLAG,ASC,REFT(1024),NW*, IOBT,LOBS,NMULT,NL,CL(200) ,QL(200) ,RHO(200) ,T(200) ,TLNTH,XO*,CRtUST, IAOC,WINIXOV,NFILT


CCC PROGRAM PLTV ISPCC (PLOTTING ROUTINE FOR PROGRAM VISP)CC ,MODIFIED FOR CDC 855 USE AT INDIANA UNIVERSITYC FROM PLOTTING CODE DEVELOPED BY FRAZER,BATESC AND RUDMAN AT THE HAWAII INSTITUTE OF GEOPHYSICSC

" C INPUT FOR THIS PROGRAM IS GENERATED AS A FILEC ON TAPE 4 (AND DESIGN4ATED "PLTIN") BY PROGRAMC VISP (SEE SUBROUTINE WRTPLT).CC-------------------------------------------------------------------------CC MAIN PROGRAMCC-------------------------------------------------------------------------

PROGRAM TSTPLT(TAPE1 ,OUTPUT,TAPE4=OUTPUT,PLOT,TAPE7=PLOT)COMMON/ CHAR /TITLE(S)COMMON/ PLTPAR /NTRACE,YSIDE,TSEC,TSC,TLAG,ASC,REFT(1024),NW+,IOBT,LOBS,NMULT,NL,CL(200),QL(200),RHO(200),T(200),TLNTH,XO,CRUST,IAGC,WINDOW,NFILTCOMMON/ FILTDT /IDB(10),IFILTYP(10),MPHASE,FF1(10)CALL IDENT(7)CALL READINPCALL INITPLTCALL PARMPLTCALL RSPMDLCALL PLOT(0.,0. 999)STOPEND

C---------------------------------------------------------------------CC SUBROUTINE READINPC

SUBROUTINE READINP

COMMON/ CHAR /TITLE(S)COMMON/ PLTPAR /NTRACE,YSIDE,TSEC,TSC,TLAG,ASC,REFT(1024),NW+,IOBT,LOBS,NMULT,NL,CL(200),QL(200),RHO(200),T(200),TLNTH,XO+ ,CRUSTIAGC,WINDOW,NFILTCOMVN/ FILTDT /IDB(10),IFILTYP(IO),MPHASE,FF1(10)READ( 1,1001)TITLE

1001 FORMAT(8A10)READ(1 ,999)NTRACE,YSIDE,NW,TLNTH,NL,NFILT,MPHASE

999 FORMAT(7X, 14,7X,F5.2,4X, 15,7X,F5.2,4X, 13,7X, 13,BX,L2)READ(1,989)TSEC,TSC,TLAG,ASC

. % 31APPENDIX 3+ "DECLARATION LINES")')

ELSEIF (NERR .EQ. 23) THENWRITE(6,'(/" *** ERROR - NFREQ ",14M" MUST BE A POWER OF 2"

"+ 16-512")') LNR

ELSEIF (NERR .EQ. 2S) THENWRITE(6,'(/" *s* ERROR - TIME ",14," TOO SHORT (MINI I SEC)"

+ )') LNR

ELSEIF (NERR .EQ. 27) THENWRITE(6,'(/" se ERROR - NTRACE 1 10")')

ELSEIF (NERR EQ. 29) THENWRITE(E,'(/" *** ERROR - ASC 1 1 OR 1 100")')

ELSEIF (ERR .EQ. 30) THENWRITE(6,'(/" S** ERROR - 1 10 FILTERS REQUESTED: ",14)')

+ LNRELSEIF (HERR .EQ. 31) THEN

WRITE(6,'(/" s* LAYER FOR OBS PLACEMENT 1 2 OR I NUIER",

" OF LAYERS")')

ELSEWRITE(6,'(" UNKNOWN ERROR, NUMBER: ",14)') HERR

ENDIF. STOP

END

Vii

I

p

APPENDIX 4 45

TEST 3 - OcL. FULL RESPONSE (ASC = 100). TEST 3 - OW2L. ONE-MULTIPLE OPTION.

REFLECTION COEFFICIENT REFLECTION COEFFICIENT

AT 055 IN LAYER I AT* .0 M DEPTH AT 055 IN LAYER I AT .0 M DEPTH

FREOINW)= 512 T(M5ECS= 1000 FREQCNW)= 512 TIM5ECSI= 1000

MIN = .OO-Z MAX =512.00 HZ MIN = .O0IZ MAX =512.00 HZ

FULL RESPONSE (ALL MULTIPLES] NUMBER OF MULTIPLES I

NO AGC. ASC = 100. NO AGC. ASC = 100.


.. 0 1 ff%0 M I i R 1

15 R2 R2

-- M 4

Zeno

Z sc Z 5'

400-- -c Zm

) -.-- O-M,F7 M

550 C-)S

65.

750 in5

sa0 400

.. oo

Flgure 5. (Test 3) Reflections from a two-layer model (fig. 3B) for A, full-response option and B, one-multipleoption. Reflections R and multiples M are Identified in table 4.

The following records (table 4) were used test of one multiple only, has the same inputa input to Program VISP to generate all records except MLTPL is changed from -1 tomultiples shown in figure 5A. Figure 5B, a 1.

. w3 '' " ." " .. ' ',,"/" .. "w'_ "" ."=-',"",' ' ".'' ,'.', ..- " > .- "-- _V-"- ------ ,- *-" '- "- ' -


TEST 4 - OIL. BAND PASS (10-50 HZI TEST 4 - OWIL. BAIN-PASS (10-500 NZI. TEST 4 - OWIL. HIGH CU- (ZERO PmIA3EI.

--- FILTERS .MINIMUM PHASE..- --- PILTERS - MINIRUM. I14 --- --- FILTERS - ZERO PHASE~

• :IGu UT AT 50. -Z*.96 0 SLOPE HIGH CUT AT .00. nZI 00 SIL/OELOWl .UT AT 10. iZ:96 C0 SLOPE LOW CUT AT 10. KuISS 01 SLO E NIGH CUT ATS. lZ:U 0

an m

a. -. B

_4 -4 w7

17 " -i

Lo

TES OPE

TEST 4 - OW L I H U (M N IMUM PASIE ) . TE T 4 O I O U M N IMU M' "HS J --- FILT E'RS -MIN MUM P HA SIE---

--- FILTERS' - MIIMU PHSE- ---K

FITR, IIMMPAE- [GM CUT AT 50. 4Z;6 08 SLOP{E

" Gl4 CUT AT 75. mz 9 6 S O ELON CU A . Z* 19S OPE LONl CUT AT 10. '-1.6 010 SLOPE

mm

m •

-.4 A -B- C

a.. a= z=

ab. -:

LJ

%no.

a. a. a,

TES A 2.FLERSOE1 8

m.

am m,

za.,mZ. a

APPENDIX 4 47

Test 4. FiltersTEST 4 - DOlL. LOW CUT (ZERO PNASE)

S--- FILTUM • ZERO M-- A single layer 250 m thick is overlain by aLow CUT A S. MD96 W S E half space with the sam e velocity (1.5 km /sec)

and underlain by a half space with a velocityV. of 3.0 km/sec (fig. 3A). This one-layer model

was used to test all filter options. Layer andhalf spaces have identical Q (200) and densityMi (1.1). The single reflector permits a study ofthe waveform as a variety of filter parametersare changed (figs. 6A-6G).

Band Pass. Comparison of a minimum-phase band pass of 10-50 hz (fig. 6A) versus

._10-500 hz (fig. 6B) shows high frequencies inthe wider band pass (in the form of a spike).

Z- The dominant period on the 10-50 hz record74 is 30 msec (or 33 hz), about the center of the

band pass. Band-pass slope was unchanged infigures 6A and 6B.

Table 5 is a copy of the input records usedto generate a 10-50 hz band-pass filter (fig.

D 6A). To generate a 10-500 hz band-pass filter.-.. I(fig. 6B), one needs only to change the cutoff

'1 frequency from 50 to 500.:1 i"Notch Filter. If a notch filter is desired, the

input is similar to the band-pass option exceptthat the "filter-type" is designated as 3 forboth input lines. (See table 5.)

High and Low Cut (zero phase). A high-cutfilter (low pass) set at 75 hz with 96-db slope

REFLECTION COEFFICIENT and zero phase shows the reflection with aA OB. IN LAYER I AT .0 M DEPTH dominant period of 15 msec or 66 hz (fig.

FREQ(NWj= 512 TIMSECS)= 1000 6C).

MIN 1.0O1Z MAX =51Z.00 HZ A low-cut filter set at 5 hz with 96-db slopeNand zero phase shows the reflection character-

PRIMARIES ONLY ized by a sharp spike (fig. 6D). Because theNO ,'r . low-cut filter essentially passes all frequencies,

~.AC-we expect to see a spike. A zero-phase filtei is -

noncausal; arrivals occur before the expected~arrival times of 333 msec (two-way distanceof 500 m at 1500 m/sec). Note that the

Figure 6. (Test 4) Reflections from a one-layer model dominant arrival (maximum amplitude) oc-(fig. 3A) used to display filter options. A, band pass curs at 333 msec.of 10-50 hz; B, band pas of 10-500 hz; C, D, E, F, Table 6 is a copy of the input records usedhigh and low cut with minimum and zero phase; to generate a high-cut filter (fig. 6C). ToG, band pass with 6-db slope versus 96-db slope generate a low-cut filter (fig. 6D), changeused In A. "filter-type" from 1 to 2 and change cutoff

frequency from 75 to 5.

"% 'i' ~

'V = : :. - ,.:.= = : - - . -, .' , , . =I . . - .. 1_" -48 GENERATION OF VERTICALLY INCIDENT SEISMOGRAMS

Table 5. Input data used to test a 10-50 hz band-pass filter (fig. 6A)

TEST 4 - DIL. BAND-PASS (10-50 HZ).EPS SIGMt YSIDE XSIDE0.001 0.1 40. 6.CL QL RHO THICKNESS1.5 200. 1.1 0.1.5 200. 1.1 250.

- 3.0 200. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(MSEC) IN/MSEC AMP-SCALE MLTPL AGC WINDOW

5 512 1000. .006 1.0 0 0 0DETECTOR TYPE DETECTOR LOCATIONREFLECTION LAYER 1FILTER PHASE1 (MINIMUM PHASE)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY1 96 502 96 10

Table 6. Input data used to test a high-cult filter with zero phase (fig. 6C)

TEST 4 - DIL. HIGH CUT (ZERO PHASE).EPS SIGMA YSIDE XSIDE0.001 0.1 40. 6.CL QL RHO THICKNESS1.5 200. 1.1 0.1.5 200. 1.1 250.3.0 200. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(MSEC) IN/MSEC AMP-SCALE MLTPL AGC WINDOW5 512 1000. .006 1.0 0 0 0

DETECTOR TYPE DETECTOR LOCATIONREFLECTION LAYER 1FILTER PHASE0 (ZERO PHASE)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY1 ..196 75

High and Low Cut (minimum phase). The msec. This is consistent with the minimum-model used to study the zero-phase filter phase characteristics of high frequencies

"- (above) was rerun with minimum-phase occurring at the front of the waveform. Note

option. A high-cut filter set at 75 hz with that the minimum-phase filter passes a tail of96-db slope and minimum phase (fig. 6E) lower frequencies (fig. 6F), although the samedisplays a slightly different waveform than zero-phase filter does not.the zero-phase filter. Now instead of the Table 6, used to generate the high-cut filteramplitude maximum at 333 msec, the first with zero phase, may also be used to generateb motion occurs at that time. the minimum-phase filter. The user only

A low-cut filter set at 5 hz with minimum needs to change "filter-phase" from 1 to 0 tophase (fig. 6F) also shows a sharp peak at 333 obtain figure 6E. To obtain the low-cut

,...

w.°

*% .. . . . . . ..

APPENDIX 4 49

minimum-phase seismogram of figure 6F, theuser needs to also change the filter type from TEST 5 - 02L. FULL RESPONSE (ASC = 1).

1 to 2 and the cutoff frequency from 75 to 5. REFLECTION COEFFICIENT

Filter Attenuation. The user may select the AT 055 IN LAYER 1 AT .0 M OEPTHfilter-attenuation factor (slope in decibel per FREO(NWJ= 51Z T(MSEC5= 1000octave) for high- and low-cut filters Note the MIN = 1.00Z MAX =512.00 HZslope in decibels in a Butterworth filter isrelated to the number of poles (- DB/6 + 1). FULL RESPONSE (ALL MULTIPLESi

Variations in slope were tested on a NO AGC. ASC = 1.

miniraum-phase 10-50 hz band-pass filter (fig. NO FILTER6A). With a slope of 96 DB/octave, the10-50 hr. band pass is a boxcar-type filteryielding a reflection signal ringing at 33 hz,about the center frequency of the band pass.But the same filter with a slope of 6DB/octave yields a reflection with a narrowspike (fig. 6G). The low slope passes a largerange of frequencies to generate the spike.Figure 6G is generated with the input records asshown in table 5 except for a change of slopefrom 96 to 6 db.

MSTest 5. Amplitude Scale -,

The user has available a simple amplitude -4"

multiplier (ASC). A two-layer model (fig. 3B), Z75 m and 100 m thick, was used to test this -u,option. For this model, reflections andmultiples repeat at a 67-msec interval. For afull-response option, an ASC - 100 displays -six events (fig. 5A); for an ASC - 1, only 'U

three events are readily visible (fig. 7). Notethat amplitudes greater than 0.5 inch areclipped. Table 4 with amplitude scale changedfrom 100 to 1 will generate figure 7.

FIgure 7. (Test 5) Reflections from s two-layer model(fig. SB) with amplitude scale (ASC) - 1. Comparewith amplitude scale of 100 in figure 5A.

1


TEST 6 - 02L. TEST OF AGC. TEST 6 - 02L. TEST OF AGC.

REFLECTION COEFF IC IENT REFLECTION COEFFICIENT

AT 05 IN LAYER I AT .0 M DEPTH AT OB5 IN LAYER 1 AT .0 M OEPTI

cE(NWI= 512 TIMSECSI= 1000 FREOINW)= 512 TIMSECS= 100C

MIN = 1. OC-Z MAX =512.00 HZ MIN = 1. OCZ MAX =512.00 HZ

FULL RESPONSE (ALL MULTIPLES) FULL RESPONSE (ALL MULTIPLES)

NO AGC. ASC = 1. AGC WINDOW = 10. MSECS

---FILTERS = MINIMUM PHASE--- --- FILTERS = MINIMUM PHASE---

i:SH CUT AT 100. HZ;96 C3 SLOPE HIGH CUT AT 100. HZ;96 38 SLOPE

-R2

_ _1

"++0 Au

4 - Ml

0 O "" 00'

3 0 35

, *0,

-50

Soo 00

S50 nds

3000

950 too

Figure 8. (Test 6) Full response from a two-layer model (fig. 3B) for A, no AGC; B, AGC with window - 10 msec;ZC, AGC with window - 60 minec; D, AGC with window -500 msec. Reflections R1 and R2 and multiple M1 are

identified in table 4.

.'%I,

APPENDIX 4 51

TEST 6 - 02L. TEST OF AGC. TEST 6 - 02L. TEST OF AGC.REFLECTION COEFFICIENT REFLECTION COEFFICIENT

AT 055 IN LAYER I AT .0 M DEPTH AT 005 IN LAYER I AT .0 M DEPTH

FREG[NW)= 512 T(MSECSJ= 1000 FREO{NW)= 512 T(MSECS= 1000

MIN = 1.001Z MAX =512.00 HZ MIN = 1.Oi1Z MAX =512.00 HZ

FULL RESPONSE (ALL MULTIPLES) FULL RESPONSE (ALL MULTIPLES)

AGC WINDOW = 60. MSECS AGC WINDOW = 500.MSECS

---FILTERS = MINIMUM PHASE--- ---FILTERS = MINIMUM PHASE---

HIGH CUT AT 100. HZ;96 08 SLOPE HIGH CUT AT 100. HZ:96 D8 SLOPE

IS 1 - 7 14 so R2i

no f f f CF

m mnZ50 MI,450 4m

NOC weO

"°~N C ""

m no

Not

U0ue8 Cotne


Test 6. Automatic Gain Control

Theory. Normally we perform automatic suitable window of fixed length. Therefore ifgain control (AGC) by dividing our time series f(t) is the input signal, fc(t) is the AGC signal,by its own RMS value computed by using a and fr(t) is the RMS signal, we have

fr(t) = (ff2 (T) W(t-T)dT) 1 /2 (10)

and

fe ( t ) = flt)/fr(t) (1

where

W(t) = (l+COS(2w t] /TW) / 2TW(12)

is a window of length TW designated by the transform of f2 (t) and F(W) the Fourieruser. For convenience, Program VISP carries transform of W(t). F" is the inverse Fourierout part of this computation in the frequency transform. Thendomain. Let F(f 2 ) denote the Fourier

f(t) = f(t) / IF-I F(f 2 )F(W)JJ 1/2C (13)

is the algorithm used.Window Size. A two-layer model (fig. 3B), noise (fig. 8C). If the window (520 msec) is

75 and 100 m thick, was used to test the one-half or more of the time span of theaction of the AGC window size. Without AGC entire record (1000 msec), a seismogram isand ASC 1, two reflectors (R1 and R2) and obtained similar to the original recordone multiple (Ml) were observable (fig. 8A). without AGC (fig. 8D). The ENCODE/DE-The time interval between events is 67 msec. CODE statements in subroutine AGCFREQA small window (10 msec) yields a noisy were included to circumvent difficulties with(ringing) record that does not allow easy significant figures. Users may have to adjustidentification of the early events (fig. 8B). A this part of the code for their computers.window comparable to the expected time Table 7 is a copy of the input records usedintervals (60 msec) still has some (ringing) to create figure 8C.

1 1j,

APPENDIX 4 53

Table 7. Input data used to test automatic gain control (fig. 8C)

TEST 6 - D2L. TEST OF AG.EPS SIGMA YSIDE XSIDE0.001 0.1 40. 6.0CL QL RHO THICKNESS1.50 200. 1.1 0.1.50 200. 1.1 75.3.00 200. 1.1 100.1.50 200. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(IMEC) IN/ISEC AMP-SCALE MLTPL AGC WINDOW5 512 1000. .006 1.0 -1 1 60.

DETECTOR TYPE DETECTOR LOCATIONREFLECTION LAYER 1FILTER PHASE1 (MINIMUM PHASE)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY1 96 100

Test 7. Computational Frequency (NW)

A model with a single layer (fig. 3A) was as: not acceptable, poor, and excellent.used to test the importance of the user's Although not shown here, record quality forchoice of computational frequencies (NW) for NW - 128 was good. For NW - 512 thea fixed record length of T - 1000 msec. record was identical to 256. On a CDC CyberFigures 9A, 9B, and 9C show signal quality 170/855 the times, excluding compilation andfor computational frequencies of 16, 64, and plotting, varied from 0.088 sec for 16 hz,256 hz. A 10-50 hz minimum-phase band-pass 0.196 sec for 64 hz, and 0.621 sec for 256 hz.filter was applied to the output. Comparison Table 8 is a copy of the input records usedof NW - 16, 64, and 256 yielded seismograms to create figure 9.that were subjectively evaluated, respectively,

Table 8. Input data used to test computational frequencies (fig. 9C)

TEST 7 - DIL. ROLE OF FREQUENCIES (NW).EPS SIGMA YSIDE XSIDE

0.001 0.1 40. 6.0CL QL RHO THICKNESS1.5 2'0. 1.1 0.1.5 200. 1.1 250.3.0 200. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(IMEC) IN/MUEC AMP-SCALE MLTPL AGC WINDOW5 256 1000. .006 1.0 0 0 0

DETECTOR TYPE DETECTOR LOCAT IONREFLECTION LAYER 1FILTER PHASE1 (MINIMUM PHASE)FILTER-TYPE DO SLOPE CUT-OFF FREQUENCY1 48 502 48 10


7EST? - OIL. ROLE OF FREQJENC:ES INWI TEST 7 OIL. ROLE OF FREQUENCIES (NWI TEST 7 - OIL. ROLE OF FREQUENCIES (NW).?E LECTION COEFFICIENT REFLECTION COEFFICIENT REFLECTION COEFFICIENT

AT M 1N LAYER I AT .0 M0ET"T AT O IN LAYER I AT .0 M OEPTH AT 00 IN LAYER I AT .0 MI I PTH

p: . = 1 TIMSECSI- 1000 FEOIFNWI 84 T(MECS 1000 FEO(P - 2S6 T( SECS)- 1000

1.0041 MAX 1 8.00 MIZ MIN * .00"1 9AX .64.00 KZ MIN I 1.001Z MAX .- 25.0041

ZQ:"AR:E5 ONLY PI[ARIES ONLY PRIMlIES ONLY

SC AGC. ASC . 1. NO AGC. ASC * .NO AGC. AC - 1

--- FILTERS5 . Y!NIPIJI PHASE --- --- FILTERS - MINIMUM PHASE~- --- FILTERS - MINIMUM* PHASE---

* CUyT AT 50. "Z;48 DO SLOPE HIGH CUT AT 50. mZ;40 00 SLOPE 4109 CUT AT SO. HZ;4a 00 SLOPEI. :UT AT 10. "Z:48 08 SLOPE LOW CUT AT 10. 1Z:48 08 SLOPE LOW CUT AT 10. 1Z:48 06 SLOPE

-- ,LM (n1mf,)m

I - B-C

"! I - ,.

iJ,

Figure 9. (Test 7) Variations of computational frequency (IN) for a single reflectr modi (fig. 3A) for A, NW - 16;.. B, N - 64; C, N - 256.

Test 8. Record Length (TSEC)

The interrelationship between the time 10A). Therefore all the arrivals on figure 10Aspan of the seismogram (TSEC) and computa- other than 110, 1l, and Rt2 are wraparoundtional frequency (NW) is examined with a events.six-layer model (fig. 3C). The record length A record length of 2000 msec (fig. 10B) is(TSEC) was varied from 500 to 4000 msec in sufficiently long that all events (1R0 to R6) arethe presence of a fixed computational observable at their proper arrival times.frequency NW - 512 hz. The minimum Excessive time length, however, reduces thefrequency is given by 1/TSEC, and the frequency of content of the signal and maymaximum (Nyquist) frequency is given by not be desirable. Note that a record length ofNW/TSEC. The results shown in figure 10 TSEC - 2000 msec (fig. 10B) gives an fmax ofdemonstrate that the user's selection of time only 256 hz versus 1024 hz for the(TSEC) must influence the appearance of the seismogram with TSEC - 500 msec. Oneseismogram. For example, reflector R3 of the should first choose TSEC to avoid wrap-six-layer model (fig. 3C) is at a depth of 300 around and then choose frequency (NW) tom and has a predicted arrival time of 550 obtain the desired (maximum) frequencymsec. (See table 10.) The choice of record content.length TSEC - 500 msec is too short, and R13 Table 9 is a copy of the input records usedarrives as a wraparound event at 50 msec (fig. to generate figure 10B.

W, 21 .6 %

APPENDIX 4 55

TEST 8 - 06L. TEST OF TSEC (= 500) TEST 8 - 06L. TEST OF TSEC (= 2000)

REFLECTION COEFFICIENT REFLECTION COEFFICIENT

AT OBS IN LAYER 1 AT .0 M DEPTH AT. OBS IN LAYER 1 AT .0 M DEPTH

FREQINW]= 512 TI MSECSJ=500 FREO(NW)= 512 T(M5ECS)=2000

MIN 2.0OIZ MAX = 1024.001Z MIN = .50 HZ MAX =256.00 HZ

PRIMARIES ONLY PRIMARIES ONLY

NO AGC. ASC = 1. NO AGC. ASC = 1.


- -RO - 80

ISO

-R1 M0 -R2'Z° R3 -

150350

400

00

50 R3

000

" -R4

DO ~ r'ltoo

Mo- -- -R2 900

Z Z 10'-: N: o o-

U') | U)11,,mm .-

1301351401145i

1-.551ISO

110

Ito

Is

Flgure 1.(ft8) Variation of record length (TSEC) for a six-layer model (fig. 3C). A, TSEC -500 and B, TSEC -2000. Reflections RO through R6 are Identified In table 10.

A&. . .. . . .

au* .05 *


Table 9. Input data used to test record length (fig. 10A)

TEST 8 - D6L. TEST OF TSEC (= 2000)EPS SIGbMA YSIDE XSIDE0.001 0.1 40. 6.0CL QL RHO THICKNESS1.5 10000. 1.1 0.2.0 10000. 1.1 50.3.0 10000. 1.1 250.1.5 10000. 1.1 250.1.6 10000. 1.1 100.3.0 10000. 1.1 250.2.8 10000. 1.1 300.

-. 1.5 10000. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(NBEC) IN/NSEC AMP-SCALE MLTPL AGC WINDOW5 512 2000. .003 1.0 0 0 0

DETECTOR TYPE DETECTOR LOCATIONREFLECTION LAYER I

FILTER PHASE2 (NO FILTERS)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY

Test 9. Arrival Times and Amplitudes

A six-layer model with constant Q thicknesses of the layers; RO is from the top10,000 and p - 1.1 (fig. 3C) was used to of layer 1, and R6 is from the top of the halfexamine arrival times and amplitudes for the space. Theoretical (predicted) amplitudesreflection-coefficient seismogram (fig. 11A). were also hand calculated for the model byTo generate a noise-free record, no multiples using the usual relationships for reflectionwere included. A record length of T - 1200 coefficients and two-way transmission coeffi-msec avoided wraparound problems. To avoid cients. Study of the results (table 10) showsamplitude distortion, the seismograms were that the reflections arrived with correctnot filtered. amplitudes, polarities, and times.

Arrival times for the seven reflectors (RO to Table 11 is a copy of the input recordsR6) were computed from the velocities and used to generate figure 11A.

Table 10. Observed and predicted times and amplitudes of reflectioncoefficients for a six-layer model (fig. 11A)

Predicted Observed Predicted ObservedReflector times times amplitudes amplitudes

index (rsec) (msec) (cm) (cm)(See fig. 11A) (normalized)

RO 0 0 +.14 .14

Ri 50 50 +.20 .22

R2 217 215 -.31 -.32

R3 550 550 +.03 +.03

R4 675 675 +.25 +.27

R5 842 840 -.03 -.03R6 1056 1050 -.22 -.25

' " "'" . " ".,-:- ' "," ".,;,_- "w" . . o . , ,. , - - .- .' ,' , .', .' "'- '.. " " " "" ".." " '- - " ,' "."- " "- "- - ", ' . ,,-, . -.-.-.-'---lt

APPENDIX 4 5

TEST 9 - 06L. ARIVAL TIME TEST. TEST 10 - 64. ARRIVAL TIME TEST. TEST 10 - 06L. ARIVAL TIME TEST.

R[FLECTION COEFrICIENT VERTICAL OISPLACEMENT PRESSIXAT O IN LAYER I AT .0 M DEPTH AT O IN LAYER Z AT o M OEPTM AT DIP IN LAVER 2 AT .0 M O6PTMFREOIPNI, 51? T I MSECSI. 1200 FAO(NMI SIZ T I SECS) I 120 FRgE(N I- Si TIMSCaS). 1o0"IN . .83 NZ lAX .425.67 Z "IN - .83HZ lAX 425. .?F u MIN . .03HZ MAX 426.SOF ZPRIARES ONLY PRIMARIES ONLY PRIMAIES ONLY

N- AGC. ASC • 1. NO AG. ASC - IN O AGC. ASC - 1.

NO FILTERS NO FILTERS NO FILTERS

* RO• t R1.

- -R3

s 1s :9 :

R. R2 " -

-- S-4 -,e

-a.

T-. , • R4:Z-4 a

- - -R5

R6I . : ' " R - --.- i i - ,-

A . BC

FIgure 11. (Tests 9 and 10) Arrival times and amplitudes for a six-layer model (fig. 3C) for A, reflection coefficient;B, vertical displacement; C, pressure.

Table 11. Input data used to test times, amplitudes, and polarities of reflections

(fig. 11A)

TEST 9 - D6L. ARRIVAL TIME TEST.EPS SIGMA YSIDE XSIDE

. 0.001 0.1 40. 6.0CL QL RHO THICKNESS1.5 10000. 1.1 0.2.0 10000. 1.1 50.3.0 10000. 1.1 250.1.5 10000. 1.1 250.1.6 10000. 1.1 100.3.0 10000. 1.1 250.2.8 10000. 1.1 300.1.5 10000. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(MSEC) IN/MSEC AMP-SCALE MLTPL AGC WINDOW5 512 1200. .003 1.0 0 0 0

DETECTOR TYPE DETECTOR LOCATIONREFLECTION LAYER 1FILTER PHASE2 (NO FILTERS)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY

.4' ,. , - .-. " ."" : - -,i , - "" -.:i -:. ... ,. : .',. --:- .,. -:: , . - -.. . ' .. ,"-,,, " ., - -- " :- . ".:

I - w ~ - 4. . -


Test 10. Pressure and Vertical Displacement

The same six-layer model (fig. 3C) used to top of layer 2 (in effect at the same depth astest arrival times and amplitudes for the the reflection-coefficient output but acrossreflection-coefficient seismogram (fig. 11A) the interface).was also used to test the waveforms and Comparison of the three outputs showspolarity of the options to plot vertical-dis- that vertical-displacement (fig. 11B) andplacement and pressure seismograms (figs. pressure seismograms (fig. 11C) have the sameliB and I1C). The algorithm for Program polarity for reflectors R1-R6 but differVISP is so designed that the vertical-displace- slightly in amplitude. Reflections R1-R6 onment and pressure output may be activated the reflection-coefficient seismogram (fig.only if the receiver is specified to be within 10A) have the opposite polarity. Because ofone of the layers, not within the half space. the receiver location, noted above, the firstThe reflection-coefficient plot is obtained arrival (RO) on the reflection-coefficientonly when the receiver is at the bottom of the seismogram is a reflection, but the first arrivalupper half space. Therefore, for computation- on the other two seismograms is a transmittedal purposes, the receivers for the three wave of opposite polarity.seismograms in figure 11 are located as Table 11 is a copy of the input recordsfollows: the reflection-coefficient output (fig. used to generate figure 11A. To generate11A) is from the receiver at the bottom of the figures 11B and 11C one needs only to changehalf space (layer 1), and vertical displacement REFLECTION to either VERTICAL or(fig. 11B) and pressure (fig. 11C) are from the PRESSURE and LAYER 1 to LAYER 2.

Test 11. Receiver Depth

The user may place the receiver within anyof the layers. The source is always within thehalf space, and zero time begins when the Table 12. Arrival times for a buried receiverpulse encounters the top of layer 1. The (fig. 12)six-layer model (fig. 3C), without multiples,was used to test this option. The receiver was Computed Observedplaced at the top of layer 3 (fig. 12A), and Reflections times timesvertical displacement was plotted. The reflec- (msec) (msec)tion-coefficient option is not available withinthe layers but only at the bottom of the Direct 108 110upper half space. Table 12 shows the R3 442 440computed and observed times for the primary R4 567 560reflections for vertical displacement (fig. R5 733 73012B).

The seismogram (fig. 12B) shows the major R6 947 950reflectors arriving at the computed times with

4" the appropriate polarities. Table 13 is a copyof the input records used to generate figure12.

%"

4APPENDIX 4 59

V P OF PARAMETERS TEST 11 -06L. RECEIVER DEPTH.VISP PLT5 F PAAMEER5VERTICAL DISPLACEMENT

AT OBS IN LAYER 4 AT 300.0 M DEPTHFREO(NW)= 512 T(MSECS]= 1200

TEST II - 06L. RECEIVER DEPTH. MIN = .83 HZ MAX =426.67 HZ

RHO [PRIMARIES ONLYZL IKM/SEC) OL* .001 RHO [GM/CC]

NO AGC. ASC = 1.

01 2 3 1 1 21 . I 3 I NO FILTERS

*Source

RsoR1 -- Direct

4, 4 0 0

•ReceiverNo

00

400

' 450 "- R3-- R3

. .+ - - R4 -o .. R4

Soo70 R4 01

LOR5 C7 750R

- R6 Io .R6

AB

its

1 2 3 10 1 21t

FIgure 12. (Test 11) Primary reflections for a six-layer model (fig. 3C) for a receiver at the top of layer 4 (where theupper half space is termed layer 1).

" h-.

/1. "

'I•

1.- w¢°*w-


Table 13. Input data used to test receiver depth (fig. 12)

TEST 11 - D6L. RECEIVER DEPTH.EPS SIGMA YSIDE XSIDE0.001 0.1 40. 6.0CL QL RHO THICKNESS1.5 10000. 1.1 0.2.0 10000. 1.1 50.3.0 10000. 1.1 250.1.5 10000. 1.1 250.1.6 10000. 1.1 100.3.0 10000. 1.1 250.2.8 10000. 1.1 300.1.5 10000. 1.1 0.

9999 9999 9999 9999#TRC #FREQ T(MSEC) IN/MEC AMP-SCALE MLTPL AGC WINDOW5 512 1200. .005 1.0 0 0 0

DETECTOR TYPE DETECTOR LOCATIONVERTICAL LAYER 4

FILTER PHASE2 (NO FILTERS)FILTER-TYPE DB SLOPE CUr-OFF FREQUENCY

Test 12. Interpolated Layers

It is possible to have layer velocities specified layers: 0, N, T where 0 is the flag,uniformly increase (or decrease) within N is the number of layers to be inserted, andspecified depth intervals without hand calcu- T is the total thickness of the layers. Table 14lating the values (fig. 13). The user enters a is a copy of the data used to generate figuresequence of values within a sequence of 13.

Table 14. Input data used to interpolate layers (fig. 13)

TEST 12 - INTERPOLATED LAYERS.EPS SIGMA YSIDE XSIDE

0.001 0.1 40. 6.0CL QL RHO THICKNESS1.5 200. 1.1 0.1.5 200. 1.1 75.0.0 5 500 13.0 200. 1.1 100.1.5 200. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(MSEC) IN/MSEC AMP-SCALE MLTPL AGC WINDOW5 512 1000. .006 1.0 0 0 0

DETECTOR TYPE DETECTOR LOCATIONREFLECTION LAYER 1FILTER PHASE

1 (MINIMUM PHASE)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY1 96 100

4.%

172

APPENDIX 4 61

VISP; PLOTS OF PARAMETERS

TEST 12 - OIL. INTERPOLATED LAYERS.

CL CKt/SEC) QL* .100 RHO 1GM/C)

I 2 3 2O 1 2

rnrn

'4J

I'' [ " ... ..... I . . . . . . . .

1 2 3 20 1 2

Figure 13. (Test 12) Generation of interpolated layerswith uniformly increasing velocities.

Test 13. Absolute Depth

The user may specify the absolute depth negative values. Table 15 is a copy of thebelow the bottom of the upper half space input that in effect generates the six-layerinstead of specifying the interval thickness of model (fig. 3C) used throughout this paper.each layer. The absolute depths are entered as

£4


Table 15. Input data used to generate a six-layer model using absolute depths (fig. 3C)

TEST 13 - 1 ABSOLUTE DEPTH INPUT.EPS SIGMA YSIDE XSIDE0.001 0.1 40. 6.0CL QL RHO THICKNESS1.5 10000. 1.1 0.2.0 10000. 1.1 -50.3.0 10000. 1.1 -300.1.5 10000. 1.1 -550.1.6 10000. 1.1 -650.3.0 10000. 1.1 -900.2.8 10000. 1.1 -12001.5 10000. 1.1 0.9999 9999 9999 9999#TRC #FREQ T(MSEC) IN/MSEC AMP-SCALE MLTPL AGC WINDOW5 512 1200. .005 1.0 0 0 0

DETECTOR TYPE DETECTOR LOCATIONVERTICAL LAYER 4FILTER PHASE2 (NO FILTERS)FILTER-TYPE DB SLOPE CUT-OFF FREQUENCY

4. ' 'o " i" " ' ,. .. ' : , ' 'r I , . . . . . -

DIDIANA GEOLOGICAL SURVEY GEOPHYSICAL COMPUTER PROGRAMSERRATA

Geophysical Computer Program 1 (Occasional Paper 10)

Page 9, 19 lines from the bottom of the pop:

Second line of R(MN,4) now Mds 1+lI+1,,41I+1,J-1''(I-l,,41 -,J-1))/S.O

Second line of R(M,N,4) should read 1+P(I+1,J+2)+P(I+1,J-2)+P(I-1,I2).P(I-1,J-2))/8.0

Pae 9, 4 lines from the bottom of the page:

Second line of R(M,N,11) now reads 1P(I.20,J-15)+P(I-15,J-15)+P(I+20,J+15)+P(I+15,J+20)

Second line of R(MN,11) should read 1P(I-20,J-15)+P(I-15,J-20)+P(I+20J+15)+P(I+5,J+20)

Page 14, line 6, which reads C(6,12)-.0.04007, may be deleted.


Page 11, line 18:

Now reads: (1,170)ITYPE,Z(I),Xl(I)

Should read: (2,230)ITYPEZ(I),X(I)

Page 12, after line 18:

Insert: 230 FORMAT (I1,F4.0,F4.1)


Page 12, line 11:

Now reads: 10 A(I+MN)-A(1)

Should read: 10 A(M+K-I)-A(N+K.I)

Geophysical Computer Propgas 4 and 5 (Occasional Papers 22 and 23)

Geophysical Computer Programs 4 and 5 require many significant figures. Double precision may beneeded on some computers Indiana University computers use 60-bit words.

Geophysical Computer Progpam 7 (Occasional Paper 29)

Subroutine MYLINE2 has been removed from the program. Delete all references to this subroutineand read all references to "11 subroutines" as "10 subroutines."

Page 38:

Now reads: 30 X 27 km region

Should read: 31 X 27 km region

Page 39:

Now reads: 6 X 40 n mreOon

Should read: 10 X 40 km reion

Page 44:Now reeds: distance 200 km

Should read: distance 20 kon

Pae 52:

Now reads: as a function time

Should read: as a function of time


Pe 13, line 16:Now reeds: 110 THETA-PI/2.0

mould read: 110 THETA1-PI/2.0

- ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ) Z2 - 2- Z%)7\p .~;~4. -~i~~7~J

FILMED

1-85

DTIC

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