AD-A123.986 A ONE-PARAMETER S OLUTON FOR SEAMOUNT SLOPE(U) NAVAL ISURFACE WEAPONS CENTER DAHLGREN VA W J GROEGER APR 82NSWC /T8 R291

UNCLASIFID F/ 7/9NL

EhhhhhhmmmhIMlEEMmmhhhhmmlnEOEOE

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11 1.8

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ICl-V 7

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UIN( LASS! Fl Fl)S;ECU.'ITY CLASSIFICATION OF THIS PAGE rWltn Data Entered)

REPOT DCUMNTATON AGEREAD INSTRUCTIONSI REORT OCUENTAION AGEBEFORE COMPLETING FORM

RPRNUMB ER IOVT ACCESSION No. 3 RECIPIENT'S CATALOG NUMBER

NSW( R8-9

A TiLE'lndS~ittl) 5 TYPE OF REPORT & PERIOD COVERED

A ONE-PARAMEFTER SOLUTION FOR Filial

SEAMtOUNT SLOPE 6 PERFORMING ORG. REPORT NUMBER

7 AUTHOR,'&, S. CONTRACT OR GRANT NUMBER(s)

Walter J. G roeeer

9 PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASKAREA G WORK UNIT NUMBERS

Naval Surface Weapons C'enter (K 1 2) 63701 BDaigren. Virginia 22448

11 CONTROLLI1NG OFFICE NAME AND ADDRESS 12, REPORT DATE

Headquarters, Defense Mapping Agency Ap~ril 1982

Washington. DC 20360 13. NUMBER OF PAGES

6814 MONITORING AGENCY NAME & AODRESS(ft different from ControlingI Office) IS. SECURITY CLASS. (of this report)

UNC LASI FlED15.. DECLASSIFICATION DOWNGRADING

SCHEDULE

16 DISTRIBUTION STATEMENT 'of thi. Report,

Approved for puLblic release distribution unlimnited.

1? DISTRIBUTION STATEMENT (of the abstra entered in Block 20, it different from Report)

III SUPPLEMENTARY NOTES

I9. KEY WORDS (Continue on reverse side If necessary and Identify by block number)

Seamnount surveySeamiount model parameter estimiationSatel-lite radar altinietrvOcean geodesy

20. ABSTRACT (Continue on rev.erse side if necessary and Identify by block number)

-This report docume'nts a com1pu~ter program that augments anl already operational,automnatic seamlount detector. Featured again are a digital filter, a miodified roughnessindicator, a physical model accounting for the effect of seamnount gravitation on the seasurface, as well as thle algorithmn perfornmg thle actual miodel paramieter estimation. kliilethle existing seamiount detector calculates the seamnount peak submergence depth in the

(see back)

DD JAN 3 1473 EDITION OF I NOV 65 IS OBSOLETE UNCLASSII I IS'N 0102.LF .014-6601

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

UNC'LASSIFIE-'DSECURITY~ CLASSIFICATION OF THIS PAGE Mi~en Date Ent.ed)

process of' solving for the seamouint base widith, it is now, assumed that the latter quantity

may be readily deduiced f'rom the altimetry pattern. It becomes then possible to simnul-

taneously' com1pute the seamount peak depth and the slope angle. InClUded once more are anerror analysis program segment and an appendix listing the nuimerical chieckout data.,

Iceso eNTIS GRA&IDTIC TAB [UnannouncedJust if icat I crn

Distribut ion/

Ava2ability CodesAvail and/or

Dist Special

ale

UNCLASSIFIII,)SECURITY CLASSIFICATION OF-THIS PAGE(Whn~r Deem Entered)

NSMW I? 8~2-91

All tucirertf itnilatic Neaiii&)tint snr evBC 1CCll) ilL tie -iSAelt- id.11ilncI scl

dCVI.~v 'C(&. dind Cv,,! nit e d uineUh tI Ii.'pa INNO \CdIS. It %a biSd M!c~l I .0l1 cllji pil 1 I il1 Ill

terring thle NC IIIIOtinlt Sl0pC FronIIi thre i ax ii ve rtical delIction values tm thec ,,,I IIri a&C

.*djUStillent 0u' thle rnArilil 'ceord elevaitoii Calculated from an idealitcd. theore tical xvai1(lntll 10l'i

to tile ixr\ rinal 'eo id Ce vati- r~obSe~ Ovil o tile altimeitry track permitted thle Seanrloirrt p1CaJe I'i

to be es1111uted. SalhSCeqentlv. a nevv% seamn1OUnt iiodel hecalii available. Bein) Irtieli lie

tailed thadn die orre! ist Mentioned.l it MAde )ossible a compuIter 1td-\J',iiin1teesa

*details of, tHe scallIolIlt slope angl estimation. H'ie new insichlts intlo tleic nture of eiuoil

para meter estimation t lien led to 'tile deveIlment of' a Second detctor- algori thinl doenrncn ted Ill

the p reseniit report. It is anticipated that thle new algorithm will augment rat her thain rep lae fhtc

* first.

D r. BI. /o ndc of' the Space and Surface Systems Division contributed thle mlat elieaI hI'ltCl r s

well as the potenmtial theory involved inl the interaction Of thle seamloun 1t and1 It" ri iot ith the

Sea surlace. Johin Lllis of' the P~hysical Sciences Software Branch performed thle comtl)1er cod inc'

anmd eomnputeri program cheickout. Ihei anuthor is responsible for thle co11in pt er prouraml lo i i-

latioii. -I- veril thle niumerical compu)Lter programi chieckout. the ant hor also0 prot-rairlii e te

alooritli for use oi ii a electronic calCLator- and made a large nuimiber of checkout cae ic iiis.

File work documente11d here v\ as done in the Space aiid Surface Systems I )iision and \Nv is

funded aIs part of' the development of computer programis connected with thle cvalu;itiori of seal-

ilh)Uiit survey techniq ues.

keleasecd i)

I) . BR{ I ON. I fcadk',tratcerc S \ i It c~ l)cp1rr ti ir

iiOL I

NSWC(R S2-91

C ONTENTS

IN T R O I) IO N .......................... ........ ....................

SPECIFI(.A lION 01:I 11i ONI -IARAM I I- k SOI FlION10R S 0M O U NT SLOI I ...................................... . ............

S\ H: I-LI I RA,,I)AR AL I-,INl. I I)A A 1.. FORMA I ............................

M A UI ('11F I) 1: 11 , l R ... .... ............................ .... ...... .. ....

RO lUG IIN ISS )1 IC O R .......................................

SI-A NIO LINT L )( ATO R ........................................

('.ALCULAION O1 INITIAl. S1AMOINI PIARANII lRS .................... 3

0( 1 A N !)1.I' I A IG O R ITIit .............................................. 14

ISlIM A IIO N 01: PEAK D II ............................................ 14

ANALYSIS OF DAI'A DISPERSION ......................................... 10AUI ONI\TI( ANALYSIS OF SATELLITE ALTIMETRY ...........................

R I FI R i. N C I:S ................................................................ . o(

API:tNIIXI-S

A TRIAL DAI'A FOR ISOSTATI" C(('OM ENSATION ........................... 31

B TRIAL DATA FOR A TYPICAL CAS I0: GFNIRAL (ONIP-NSATION ......... 43

C TRIAL I)ATA FOR AISI:N(' OF ROOT ................................... 55

DI STRIBIBIION

k .. ...V

~--... ~3I

BLh~ ~~AiiLI

NSWC 1R 82-91

INTROD)UCTION

Aln e\pcVriiiintal c011lipter program for SeatnIount1 mnodel paramcltel Cstiliatiojil

becamie av ailable last V car. It is an ati oa tic rot inck deSigne1ld for appl1)icationI to SI ,S.- I -A-

satellite radar altimetr\ and is capable of' pcrforming scamnount surveyNCs %kithl 3 ruinilomLll ot

h un internion10 . 1111S computerC prograil is based onl an cempirical tornmula that intl rs the

SCamoont111 ,lop;: fioni tile iia\iiual verti'cal dLct"ion1 VALtiCe oil tile Sea Sufface. Ohuo c the e~i-

moun,11t. It estitilatc, thle SeaMnOunt1 peak depth in tlic process of' adin1sting, tile 11naXInMal eo

Ce2ation ca.Lclated from an idealmed. theoretical scan)ioijnt modelV to tile 1IMNaxitual gCOid . LA ajom0

0bsers cd abOs e tie Seaiiioun1t On thle satellite track. ScamOunt11 peak geographical coord ilhtcs ale,

byprod oLct. U pon succsl u.C l1 coimip let iOn 01' tile nu1merical clieckoti t. tile new% conmpoutcer progra iii1 %k a'

subjected to a prelin inarx test and evalu~ationl involving, several SILASAT-A altinmet r\ t ra cks I')

each Of a n oinbe1'r Of gICOp)l1ysicahll diverse occan arcas. Hlut studyI was sevcrclv liited M\ 1tie

ast gaps in fihe coveranc of' the globe L\ thc SI-.ASAV*I-A tracks. Nevcrt heless. thle resullts of tis'

first attcempt at generating quan31titative data mneasurng the performance of' thc ex perimental sca-

1111,1i detector 2 indicated that thi~s comnputer program can be expected to0 beco nme a usefL-1

device tor satellite :it imet ry data analysis.

I'lie principal wecak ness of lie juLst-nienlt ionied experimental seamnIoont1 detector is not 111Csimpicity of' thle seamlount moe %:11INL thishl capadble of' calcolat inc thle gcOid detiCct ion

resulting, from the preVSeCe) of- tIme SOamiioui il ic hesamiotin ts sv nmirN ax is 00 Is) PO rat her

he e mpirical fOrmul.1a that relates tilie slope Of' tlie seanm1ounit to that of' thle sea sourface a hose

I'lhis fo riiiii a had been) devised by sc Rotinli/ing1 a num her)Cl of GL [0-3 radar altimmd rx data tracks

passing over scanliounts ill thle New hileanld Seamlounlt province. The study hiad been confined.'L

to that part of the world bcause a rathter dense iiet of' altinietry itracks and reliable hat li niet r\were hoth Ii aailable there. As part of' the work preparatory to the design of' an improved de-

ccto r algori I i ii. thle iitvof' tle slope angle fo0rmula w\as reinvestigated-3 under more genural

~oitdit ions thani h1ose prev'ailinge in the Yi estern North Atlantic. Although Ln equally useful conmihi-

nat ion of reliable 1h atli\ inc tir\ a id Skfic iei otly- denlse groun d tracks still could no0t he foun1d

clsecre III the oca ts. ,m renew:%ed slopeC aile1 study became feasible becauIse of thle corn-

plc111 t 1 J i i msssa ilii f itMiodel. Hie nessk modecl permit ted simulation of' thle geoid shape Ihos o.file seimmioi ut sciliouilt root ,slcsei as the combined effect ot' a collectionl of gravitating disks,

tie'CI Ie't] ouniile1S. LlMICiiensmos. anid denC~sities Of' Which could he individuall\, Specified. \lo,1

iiiporta it l\ thIiis ic ss computer rout ine was able to reproduce geoid iteimpht and vertical deflect ion

ahos \e tieC ,Caimomuit .mlg spicified straight1 surface tracks intersectinig tlie seaiioit symmet rsw \s or offset troni it. lo obtain a detailed relationlship between seamount slope and i11mamal

sert meal i,,i lctioii. t our drasicalls d iITer inI,- values ot' oceaii depth, fivec seamni tm peatk \un(

incruc ice: depths, aid .rioris t\ pical slope angles ssCrC 1nw assuni1ed. For echC1 Of alt0Othe OU

dfi ffere!ntI iiodcl cmnotils. each coinsisting of' 2(1 disks pAlus a 1orrespimdiii Ouibr~f kiliks

iprcscntiiig 11 t I loots. the L 1) i 111iiia signIature slopeCs Wee calculated anld Ceonipaied w\ith t1me

assumed~k slope andes.' Addit ioimllk, the postulated widths of' the seaniount11s at theirt ba1se were

NSWC rR 82-91

Compared to tilhe associated Sienlatl ore widthis. [lie result w as C hat hie origo ial1 ciprcltonl-

ship between sealnount slope anld sig-nature slope proved to he illaCeLiratle under thkie arict\ ot

C0itditiiiits1 ciosidcred. On the other hanld, it %was re',al.ii that1 tile raiO o i S,ttiie \Nidtli to

scamount11' w idthl at thle base is talirl\ inisensitive to chian'es inl the seamnounlt paieterscii- and oceanl

depthI. Hie signa tutre \k mdt h being kinow n fronm thle alt inet r data t raeck, it now bcame pos,,ible

to calculate thle seanioun.11t Width A thle base. prior to the actuial sealtionot1 parameiter c.,timiatioll.

Se r\ sinipl\ aaid rat her aCCUrate l\.

!t (hln appeared advijsable that a second seamoont dete ctor Sho old be deC\elopeCd.s rii

w i 1h thle new relationship connellcting- thle Sh-icatore Width and thle seamoon(lit i)asc wiitth anld

Snbseq Lien t lv proceed inc to tile SeanlIOo mit ModelI paranieter estiniation iii thle coUrse ot* wIi cl the

predicted geoid elevaJtionl would be mlatchedk to tile obser-ved geoid height abo\ c tile seaLioumi.t. Ilispite Of' thle sefulless Of' tilie seanioun t disk Model for thle purp-jose Of the, 110% loeanl

studV, no part iCl. advanltage could bie realized by incorporating it in to tilie new estimator algo-

rith m. The original seamoun i m nodel was thbus retained. Inl its iaor out lines, the niew sea m1ount

detector is sinijar to the experimental computer aluorithn described inl Reflerence 11. S peciticall\.

it features thle digital filter necessar), to recognize anld enhance thle seamounlt signa1tures concealed

among, thle radar altimetry data. the basic model' containing- tile SeaMoun.1t related p)otential

theory. and a mathematical estimator for thle physical Sealiou t paranieters. ['lie latr est imat or

adjulsts thle characteristic properties of' the radar altinietry signature pred~jicd Iront11 thle theoretica

model to thle corresponlding'- (huantities aniong- the empirical data. ile present and thle experi-

mental seamount detectors differ mainly inl this latter compouter p rograii segmen t Wli ile tile

previous algorithmn performs ait this point a one-paraiieter solution for thle seamoont base wkidth.

the present version of the seamiount detector first calculates the Seamuoo111 it ase Wid thI fromi the

Sil-InatUre wvidth and then iteratively varies the remaining, seaimtOn11t d ileliSions (ill priua.slope

anll"e anld peak submergence dlepth) unltil tile oMi)ited maX inli -Coid elevationl above the Sea-

m1oon t ftma tehCS tile alt inetry Sica Cure lieight within a specified margin. sobSek)l ien t\ atitribut ingc

thle reslting, peak depIthl and slope angle to thle actual Seamount Acain because ol' tile imuper-

fections inherent inl our present knlledge Of Seamoon01t comp1enlsation,. thiS estimlation is done1

twice per de~tectionl. separately for the cases of perfect iSOStaS\ anld absence of' root. with anl

option to prescribe arbitrary compensation if desired. Thie actulJ depth vale is once MOre as-

sunmed to b e b rac keted by thle depth values resulting from the isost at ically coimpenisa ted and

uncompensated cases.

It should be noted thiat a change was specified for the ex perimcn tat seamiountt detector

a fter it was d ocumuen 1ted. hi rgely as a resolt of' thle work laigto thele VC italcori thi in li s

change concerns thle conmputer program segimentt Rouhnes eteto' t pagIs N an1d 0) of' Ref-

e renlc I ), inl pa-rticular. thle de finiit ion of' the V'nxiiumi- hw tdw.' bis. se-mentt of thle

algorithim has been deleted. It wa~s replaced by a new version that is ideitiah to thie "Roighmness

D etector- specified below as part of' the presentt -Omie-Paranteter Solution for Seamu1on it Slope."'

NSWC TR S2-91

SPECIFICATION OF THEI ONE-PARAMETER SOLUTIONFOR SEAMOUNT SLOPE

SATE-LLITE RADIAR ALTIMETRY DATA FORMAT

Ihei Sa tellbte altimetry Ldata to ble processed oy tile scamotlnt detector call he recalledi I r. wpermnanent sto rage in thle format indicated ill TaL)IeS I and 2 (G. B. WestI. utphisAd i d.

10 7, S . 1 -\ Itr 'ct troml thle data file header the timne interval. A~t. inl seconds anld K,1 sobUidt11 illveo~t\~.in kml sec. Frum each segnment of the altimectry data record, obtain toy- e"acn 6. ItL,

Ipoint tme11 inst4anlti. in seconds) thle filtered geoid ficight. N, t y inl meLters. t11iC del ICernol' thle ertical. 5, = 6(y1. in arc Seconds, thle latitude. 'j ;( ti) in raaians, and thein:tlast. =1 My,1 in radians. Convert p and Aj to decimal fractions of' de!crees. \otc tlidt 1:R-

atmtydata Serving as inpuLt to this seamlou~nt detector are not the rawv altitnetr\ datJi tlLKbult reSUlt themselves from a fitrnprocess explaied inl References 22 and 23 o1 'NsW( IPs Il-200.t I Here and inl the following, we shiall refer to N, and 6i as "'filtered"' \\;)enl s i1I!,

emiphtasize thecir origin, ow Kahman smoothing, from the raw, satellite radar altinietr\ -0il

rete- rence to the present seamlount1 detector, N, and 8j will usually be considered "unfiltered ainanied SO because thley' serve as input data to the maitched filter.

TABILE 1. SUASAT-A FILTERED U,.EOlD HEIGHT OATA FILE (TYPE FD)HEADER RECORD (COSMMON HEADER)

App~roximate RangeVVo rd Type -- of Significance D~escription

II XXXX Number of points in file2 I XXXXX Rev number3 1 XX Starting year of seenient4 1 XXX Starting- day of seg-ment

-SR XXXXX.xxx Starting seconds of segment (see)6 R ,XXXXXX Time interval (sec)7 A YYDDD Year and Julian da (right adjutsted)

8 1XXX Altimeter moue9 K XXXX Autocorrelation distance (kil)

10 R XX.XX Standard deviation of data (mn)I I R XX.XX Standard deviation of geoid heights (in)1 2 R XX.XX Standard deviation of vertical defleetions (ajrc ie13 R XXX RMS of filtered-raw differences (l14 K< ±XXX Maximum) vertical (oeflection (arc see)1I R X.XXX Average velocity (km/see)10 R XXX Antenna distance f'rom~ satellite center of era\ ii in1 7 R XX, X Radar instrumnlt delay distance equivalent (cm)18 ±.xxx Timie correction (sec)1 1< Spare

3

.. ~, 7

NSVV(T1Z 82-91

TUILL 2. SLAS AU- A FILITRI) GdLOMl H 1 11 I lA : I YPML Eti)DATA RECORD ('ONINION DI)A i

Approximate~ Range.~

S o rd TN pe of' si'lificaince Dcription

I R A.AxANAx Li ti i Ldc, ad 'i

- '.NX.X NAX I (fli"IthIc i (d)

1<R :NN.NN ('Cud (acIch Ia

4 R ±NNNAN \.rlicaldc.llccunal (aic sc..

R ± NA. AN Rav 1wiadhith (111n

0R NAN. ( 'Old iil : h c011ii) I ICC i01tilid (111

7 R N A.x N . C rIicijI L1ItICCI ii) Clfid ti c C ['hMII (Jd arC sc..

NAN (4)vbi nnlcvtaintx if) -'Oid~i hlts (11110R . AN ( rhu iaiiccrtaint iv incrtical cfklctions arcsec)

I2 R \X. x uSWkI 1 1113 R~ Au.\tomiatic lcainl control tUB1)14 R \N a -AG *.(d B13

I5 R ' x FNilt SWt f correction (fitI

IR l.xX illt trald

ill R X\. A onosphcric correction (cmii

I I R \\N A tnio~phicric pivssurc nih)

IL0 R A. -v uop ic correctioni (cmi)20 R .. A Wi tioposplicric orcif c

21 R ±NX..N. hiCk (in1)

22- R A. AN lBaro ro pic :oriction Ii)

13 Rx A VXiid scdk n)

24 R X.Nx Wind dircction ( rid)

25R V A. A SCI atalc ts\\ It cor-CCitiufl (Ilm

26) R< AN. N .\ tmc \\ac, lCIIroposphcric corrcctcoi (c... )

217 R NN.A Rain raic ) inn iii -

25R NN. N SlCI ac orrcci con ) cii)

2QR Spr

30 R spar.:

4

NSW( [R S2-91

MA1CHLI) ULrLR

I lie IhatC. *l filter is anl optiiiied. digital. inhpastilter plelii.llk tl\soed ''11 Ih: *

Olliputer s t t Itsaplcto to tile Kalmian tiltered SI:ASA[ -A ,iltimctrs\ daIt' n).i'.e ) Ii

purpo-es ot the scaniount dector t, conitrolled 6 tin SI ASA I - \A oii ili

set ltiiobei assNOCetatd \w I tile pArtILtL1i1 1-001Ut101n 11iliibhl .. lld W, Ck flit,;! u~od,

L,11tter sN F 111CIr tO t Ie C11ito Il \ i\ ck 1, ll N\ kh i it I1C IIIt c ,ill' LW t l e h I 'I Ir I,' .! ]I

N ioI 'ilk Spciied ill tlttm of! kml. \ t\I-1 peALI 101u Sr AIS. I -A kdata is 1

eIl % \.il LIe pairs for N. duLld P Ir

N 5(1 kill ..... 0.212100Io killp ..... 47N.~~~ 1= kin 1 J4U~

Adopt tile tollo\ing terutinoloun. N Iare thle "LUn flitered iz'eoid hejetItl 11uc ii C2

t ile2 LilIil Iered ertICal Lieflc tio I I- vale>, Appl 1Iiton I I th ie matchedk filter toI 11, 1 1AAresullt Inl the N and o' data traeks,. N are tiite "filtered _,coid ltiets im and' :I

titeedvrtiejl de1tltios .. n ar11 11 eeCC. Ihle indel\ *i' is related ito tile time '. %alieI i

N t ithahcs the ihiture of tile ilter algorntinL no filtered data vitaes \ ill

(see heiok for definition) onl a Ldta track shall start itlt the first available tittered -. ok i'

dat vaUes. hurt her. thet description oi' tile control eard dck and data1 Cards on a1 e 0 1l1d

o' K [e ere nce I are iio\ obsolete anld muLst he repIlaced Mr tile Card1s listed inl F1IaicS

T.ABLE 3. CONTROL CA\RDS FOR NIATCHLD FILTER

\('(*()[\'I CARD)

BI' ,IN, lWIPISA. Y (10 Vl=.\\S = .;,dl \

XI X our-digit rewolttion numbher i l\diples, 0747. i 94 ct;. i

NI' ~...........I. Device set turn Kr associated \%. it I St ASA I tile i( I)o\ \ \\ I

Y)Y.............Fractional part of, thle input paraleter "rhto"

NS N C I R~ S2-9 I

tie II lcciticd 0o1 the. loi c ki II*I 11ien i ktciwii 1 I i iii I: ini :L .~i im, hll , II'11, 1

eittrchd I)\ teI All I *( ( intetInrh cit4 ici~tltri ittd I

ROL§IH'NLSS D)ILI.((R

InpIut D.11.1

D I ) Ia K ii . .JiL SC.

Dnat~~i l'.knSC'

JenIliranh~l \ li IIIiciifl

A - l o r i t h i l i nl t l \ I I

A AA

Consider the Ciltered data trac~s N and c i .ssieii tic %aluc tero to dI1 that ov n icgative.

Speccit\v data track -'wirdo% s. The numiber of the data points Wit In cacti 'A ndo\ I."

I L NT+

I himin Ite all data track portions that, Ater application of the matched hilte. ha c a numnber of

points that is, less than 1.5 to 2.0 timesC, the niTIhCr- 1n of data1 p)oints \Jthin thle s\ indc\. Stairt

thle first windowk at thle first data point not omiit ted byv tile filter. t K. and calen late

S~k ~ K(3021D~o the samie for thle next wkind ow. N k+ I 12 kt Obtaining

SN 4P Nki (303)

i=

:1 NS%( 'IR S2-9 1

mand for each following window. obtami g

S = - 4(;I,4S \ N1 +1 I~

Until the data track N is exhauStCd.

I-rom no , Oi, consider onl, thoe data % ldo,, folr wi h SN d ln. N ic ht ti 0 1 .

requirement di idels the new% d a t.a track I ons11isrile o the SN 1a11c' O nt,1*isl .. I ' .

iat. island. calculate the center ot eraLiit\

SN = S.N (t) . ,S\ S.\ SN

t (); v SN

where the sum ma tioln extends over the island under consideration. Note that t(-o wll % nIrI:i,

not exactly coincide with a t data V'alue. Once t(o(; has been found sulbstit ute for it the t

value directly preceding it or. if more convenient, the t, value nearest to t0oo(; . t( (, t

From all data windowks associated with the data island, select then that wkindow that ik chirwL<.

ized by t*o(- (the first data point of which has the time value t~o c

Extend finall the thus-chosen data windows (one for each data island) to the left b\ 'i

data points and to the right by in data points ii.e., by data points taken from nne ,just-calculated SN values). TIhe number in is

I1 = INT (1t -

Output Data

I-or each of the latter, extended windows, store and print out

t t + . . . . . . t + n 1

N N, AN 4 A .... .. N p + n -I

SN,

N N ...... Nm+-I

A IA+1 .. .. +n -

7

NSW(T 1kS2-91!

SLXMOUN"I XUA OR

Subroutine "'LX Uk'

IKnuxvn ale three cita points. 1. = . 3L u n a datai track \1 k (\1.\\U)cta h

p1)ils bracket a 1.i,\1I11LiI1I Or Iiilln.1hli 1 Ike 1 \a1tlC'. Ilile ahfl I"' \ afue. \P .aNsochateJ m JI

t11w C\tCmliH Ut k I then

\ \ -~(4011

i 2 XI

hd (402)

y3 1 XI 3 - II

cd - -403)

1 Y3 1

Subroutine 'INI'LRPOL-1"

Known arc three data Points. i 1. 2, 3. on a data track v, NI H .Fnd, fOr a specifiedabscisa value, x .the ordinate value Ny y( X

y= a + b (x -x) + C(x~ - (404)

f Y - Yi(X~2 - , )2

d -- (406)

- - (407)Li

3- Xl- y I

(X ( 2 - X I) (X3 X I ) (X3 - x 2 (408)

8

NSWC TR 82-91

11- 1 i ac in data points. i 1, ', 3, 4. oil a data tracky y x . (o fluae,pc!cihlcki ah,,civ~as ltic .vx thle ordinatCe value V. = y( Xp

-~X - X1~~ )3

y3 1 (-\3 1 )2 (X 3 - X 3(4111

x(X4 (X4 - x1 P 1

X, - 1 X , x )3

X3X3- Y1 (X3 f412

-, X, 4 - Y 1 I yX i 1)

- ~ ~ ~ X ~'i (~- )2 ( 2 - Y 1 )\3 1 (x 3 Y 3 (414

Note Concerning the Subroutines

optionlally, tile comlputer programmner may implement the above subroutines by anl\ of the

classical interpolation schemes. If' desired, tile polynomial coefficients canl be evaluated by a Icast-squares fit method. Irrespective of the method chosen, it must however be kept in] inld thatrather frekqnen tly along thle altimectry track. the argument values (time or distance - depeiidimn onlthe interpretation of x. ) will be large compared to thle timel required for a seamiount overflightlor to the seaniount width. implying x. (x - x )To avoid loss of si.-nificant dhiIt d116i1LSk

hie evaluation of the determinants, it is advisable to first transform the x. values to corresponldilpaILues SO that thle origin of' the x' systemn coincides with x1 X, = (x1 x1 ) implying j=0

[hie particular interpolation method chosen may then be executed. Subseq uently, the results miusthe transformed hack into thle x/y coordinate system. Note that this precautio isuncsayI

hie SUbroutines are ap~plied in thle form specified above.

9

NSWCT R 82-9)1

Ii(M LJe) data1 wdo.liC aJNihhlc

N~ Li titlcrcd 'iCOid hI~2l~ l M I

6 it L lbi'ivtlcrcd vcrt ical dc ticiion 11rk eC

Iillic arcti lil I si

I 11rIitndC IList fromin lt imctr\ tilc LIc2

LatitudeC k-oi11 JltiniCtr tile d C2.

Seainount Locator .Xkorithm

For eachI Of the sjeC~jiid da1ta \Nilhd LMS. n)ow con1sider t he until t red !eoid iji t ' N anid

hie unfiltered deflections of the \erticat. ( Also keel, iljl mind thiat iL iN possible to jssoli c

with the discrete nuinbcr Sets 1 and .theC1011U i.C 10w1 c'nin(u Iucin Ni ind 6l Li rcprc cilig

L hle '-Co0i d h1CiilL t n- d VCr-t iCa de thctiont in (lit. "'real %orHo or .siillp) being JsNIJicd to hesulilabl flnCtionS ZIkLpJted to NI, iti nd 6 it I hk lcaSt-LarcS IL or- otherl I11CM16121tll IliLetOdS.

F or the p resent purpose, it is suttici nt till pos ISLIlkLtC that NM Li 1L and ) 6 111,1Z\ be r-caliieul inat lie-

IlatiCAllv it* n1ccded. Perform thc 1tOIIOv~ing1 calclatiionls.

1.When Itraversing the 11ww idOw froml thw lef tLo t 1w right Liproceed ing from ikme r \atucs olI, to higher ones) e x pect to crncouier negaL i~e 61 valueS and. ain0o11 t hcil. Lin a bSOlLit c

minlimulm value. Consider the dlata point 51(Yt~ associated \ ithl Ihis illiimilu value plus

tile data point to the left and the data point to tILL right of it. AppI\ to thesc three

data points the subLroutine -l \ I R- to Cud Ill, albscissa aluce I Abcelow-,ing, to the

lliillnuii Ot the Clim\e 6t tiassOciaJICd \kitii thle ilit sp)ccitied tht[cc data1 pollits.

Ini the saine mianner. flid the1l1CictC tine aSSOCiated witt t11L' absolute 11W\1111111

value ol 611i Ithat skill ocui iLurtlicr doswn [li data track [lut Still s\ ithinl the data

3. \k ithlthe 11w iidosM. thc datad (rack N iti ma\ oc cxpccted to hliavill ablsolute Inammni.

I iid N1w dta %liie represeiliiwo Ilds niaxitil. Also finld the ncLhoin dt points

to the left and to10 thetit'l 0I this lildiiaxiiuii .Appl\ "uhroiitilnc I WR' to finld tlictimei Iau 1 \1 (tI ic mia\ iiI ilI ot N(I) i ated to thle j List-detiiwed t1itre dalta pointsI.

SMo

NSW TR 82-91

4. N ox appl\ subroutine "NiNIIRPOL- I'to t d the three data points olit \1

track rom i hich was deteriind in step 3, obtaining N(t S - "

Ne.(, determine tile four data points on tile N track tht are ncarcst to the fi/,

alLute 1A Appl to theii subroutine INTL RPOL-2'' to evaluate the N valie ,i atoiatcd

\%. t e s Nit A ) = NA)

0. I'Lirtller. proceed as in step 5 to find MtH = NB

7.Proc.eed as ff1 step 5 to find Wt A 6A

S. Proceed as in step 0 to find bSt ) = B,.

9. Consider now the data tracks N. and 6. in the neighborhood of tS in particular. Ohw

time value t. = tM just to the left of tprior to) tSM and the lime value t, = 1 to

the right of ( following) tSM Note that t- < tS1 and t' > t,. In the radar files,SM SMts and ts are associated with the values of longitude East and latitude on thesuLbsatellite track.

is M S %I and 'PM

+; X+1 "" and p+

Evaluate tile longitude East and the latitude of the "signature peak."

X+ - X-s M SMxS\ = X'SM 4 +tSM - ts, M415§

tS tSM

sM - SM

'PSM = SM I ttSM - tSM (41 o!it+M - tSM

10. Note that above the data were postulated to conform to the typical seanlount altiielry

pattern illustrated in Figure 1. If the data fail, altogether or in any cssentia detailto match this pattern, reject the data window.

Seamount LocatorOutput

For each data window successfully processed, store and list the following.

II

NSWii R N2-91

3-

A B

x,..S' M

N N

010 20 XA 30 40 0 XB 6 ' x

km

6

o XA

-jIU- 0X

LU10 20 30 40 50 ' 6 0 703I XsmI km

A

FIGUJRE 1. I'YPICAL GLOII) OLIT PATIAN AND VERICA.L DI)LI 1] ION

AIIOVL A SLANIOUNI

NSW(" 1R N2-91

t k A A

14N B IIB NB

S M 'I s \1 M S M

SeaIount Iongitude and LaitiudC arc to thc specified in deciimal dgrees aN kcll a . ' tercc hU,

- secoind formuat.

CALCULATION OF INITIAL SEAMIOUNT PARAMETERS

Input Data

t S C

N A

NH in

A arc sec

16 arc sec

k3 User-defined constant

Dlefault value: k3 = 1.74

k5 User-defined constant

lDefault value: k5 = 2.00

vs ki!!/sec

I) n ( for definition, see algorit fun Soglncni ()(I A\1) FPTI I ALGORFI'"

Algo}rithm

Nc 1.7 NSN- ANA + N]) 15t11

13

NSVVCTRS2-9l

hI) = k, + 0 ii) -3000 (50 2

B " = 51)1 x S it - t iK 1 03 1

7r + s= 1.51 + 05) ___ __ __ _

SI'iW1 x 3000 2

Output Data

N Lcoid c atii "observed' at the

Se.alIoll it center to he matched ('y t he

calculated I-eoid elCvatiol dluring~

paranie icr adjustmnt Mi i

Bs I[St inate of sealmon ntl half, Width at

0; o flit jal eStimateC Ot seaouIIILt Slol)eane1le d eu

OCEAN D)EPTH- ALGORITH.M

[or each data wvind w successtullv proccssed. the ocean depth. 1). at the seainount perinmeter

is required. Suitable ocean depth da'ta RKefcrence 25 in NSWC TR S l-20fl are available asaverages over one-by-one de-ree surface area elements, as a permanent data file onl the localcompu)Lter system. It' necessary, convert D) to meters.

ES1 1\t [ION OF PEAK U)LPTH-

Suibrotiine 'I)N" - Input Data

1) W)ean depth at seamnont p~erimeter IIn

dor Ll omjtl 01seamounL~t pekIII

S Seamlount slope ang10e de-

V C rustal thickness InI

14

NSWC TR 82-91

R Iilt' Nidth Of SCallonL it root s base

H1R I)CpthI, bClow, CrLt U, 01 NVii1)LMIit root III

Ps ScaIMouint density I II-

kiater dcnsil. ir ii

PR Root tLcnSitV ii III

Maintle density gr il -

( Ratio of Newton's constant to surtace Lravity n 2 r

It not otherwise specified. assume

Ps= 2.0 1-+-0 g.ri 3

= 1.03 L+00 °in3

PR 2.95 F+06 r1i3

9 M = 3.40 L+0 gr, I 3

Cig = 0.68024 L-14 m er

Subroutine )N'" - Algorithm

Reflrence is made to Filure 2. Perform the following calculations.

Ca s = tan rs -0]

O3S = di [is I'-()'

R = IiR iBR 703)

OR = (1) + F + i1R )'l R :0)4H

evaluate I:Ut s , s ) (Subroutine "IFT.") 705

evaluate F! (oR , R ) (Subroutine "1'") "()0

15

NSV. I]R 82-91

AXIS OF ROTATIONALSYMMETRY

t I SEA SURFACE-

ds OCEAN

HsSEAMOUNT

EARTH'S CRUSTT

SEAMOUNTROOT IEARTH'S

MANTLE

HR

P

FIGURE 2. GLONIETRY OF SIAMOUN'T MOD)EL

NSWC 1k 82-91

D)NS I - ) 112 0 ~Q. ~

I)NR (p- -R 112 - ihtIR R.

D\N D\LS - INR

Subroutine '*)N" - Output

D)NS in ill

DNR inl in

Subroutine I-U'

21T~~ ~ + a, I +i+ ~

+ a2__27_______T,

2l1+Q~ a,'3, -I -x + 2 (l+ 3)2 - C,2 +

Subroutine 1F'"

_I + C, + (V + "2

UN / Ll3(/ +a2 +1) \ +\±- -+A \-l--(-5 -j2 i

17

NSWC IR 82-91

Lsiiti (ai of' Pea~k D~epthI for ISOszitiC.1k C01111IpeS.ted SC1amoun11t 1111)u1 LDa t

Ni (

I I2 I ColIi ondCae

Rviecrie is mad to -iiaire 2. -\cC~tc (lie folmk I-- est Ths ts nv3 jis th t te Sa

pirmi 1Illul e k t e lia, slt c .. d 0 11. t is, p o u ig h rc

pI1not ot lie\ dept siati sunes ertand crthe mr easurt arte tn iias valusclised nuder\\

tall I -C 14) (Jld ae

Re[rcue ~nietoIju e .I cut tlefolwiie et.Ii stetasnme ha hesa

I RIS

11iIVKCL \k ith 1 It EU l tip.: Cstilllute~t CIm I 1 1Iur1,llt ICtl' .

Es! iilat ionl of Peak Deh fo1 r Isttit.c1gIN (opctissicd

1) -

el,,. tColtti LIC I I* no. -,o to 2 3 I

AII

B h"~

It 0

j) \ 1 R

I )V N IC I , 1

NSMA(iR h2-91

"I 1) [is3 tall

[is 1 30

SI

R I S

RNI D I1 SI SI I BR I

Retcrcncc is maIdC tOI 1ig-Urc U.singI the itbo~c Ipaaiictcr', wit indies -0U anld as

11211aJ) VWIJCS. ela M IIOh le 101l]O\\ i112 itCratix C 1001):

NC 1> (-34)

d" 1) - 3, tail -3 ,, I

It- \C,,. C01TlILIC. It' 110. LO tO(

22

;S./ 2 tall-'

uifl 2 tall ;

BR = B -0

PS P\.

I+- IS+ RiSi+ * ' - II 1 ("141

DN.= Ih 1). d , "S 0'ls+,'-.BR Ri 274

10(

NS , C R S2-91

NC -- - IJN- -- 4-

tI'N 2 NC

ON

'S

" S 1 S"S .- i " S 2

FIGURE 3. ILLUSTRATION OF ITLRATION

I1 xe. st,01p the iteration . (all the parameters associated with the index i + . the estimatcd

",l,,ammmti pmr mirr cers. In particular,

d S dSt. 2

It no. reenter (he iterative loop with the "'i + 1I" and i + 2'" parameters Is the in li al uam .

Es imlation of Pea k I)epth for Isostatically Compensated

Sealmount Oulput )ata

ds = d S1+ 2 Estimated peak depth in In

S- Estimated slope angle in deg

2l

NS"CTrR 82-91I

BsI A~ ~ltdSJ~OU~ dtid l

II if 11", ,ih ILIO I~ IC i.i ll I

I ~ I tlll~dI 1\k i'it i t Ioot ill Ink 2

i In casc dtc patiit'r e\1ima1tionL I,, tvrni ati ,C d I I I qLuttiml AS ). 1-2I) JIJC 10 t11W C'tjti L 1

,camob untt paramc(Ilt-r .01 S CCItI M 01,1 1ha IttCF L(111,111011

* ELstimation of' Peak Depth IoM the GencraIN Coipens~itcd

S amnount Input O).Lt

II ol ~r

PS £r I3

grs ML

or, In

sk

I' Ill

NSW(- TR 82-9 1

It' no0t otherwise Speied, assunie for G p. and thle four densities thle nomin11al vaILueS liStedI Under"SLubroutine *)N' Inpu)Lt D)ata."

Estimation of' Peak Diepth tor Generaly Comipensated

Seamtount Remioval of 11-Conditioned Cases

Reference is made to 1-jeure .2. Lxeeute thle following test. I hlis test assumles 111,i the sva-mount is as large as thle estimated seanlount half width at thle base anid the loc:al ocean depthi

permit I seallint peak to he ne~ar SU rtae . .. . .. d* = 10 m1) t 1Ii u produnji t heclicsmaXimlal i2eoid eCe atiOnl )N * consistent with the particlar Bs and D VALues. If' )N * is smallerthan the obserx ed maximal geoid elevation N .thle next program segtment will be unlable to

perform the depth estimation unless certain corrective measures are taken as presc:rioed b~elow.

13* =1B (74oS s

*10 i'47t

4 - tan- ( D- dJ)t

If* D - 10 i '49)

l3* = sk x 13~ 7 sot

If It R

DN l)NII). ,1*. ~. I 1 1* It*) 5ssS R~ R

l)N* N * ( 3

if Yes. l)rOed With thle nlext eOmpu)Lter programl segment. Otherwise, print out "(.\LIIONILL-CONDlITION H) CASE,- pertonni thle assignment N (. =I)N*. and conlsider thle juIst ca~lultdparameters marked with a ""' to be the estimated seamlount parameters.

23

NSWC TR 82-91

Estimation of Peak l)epth for the Generally CompensatedSea mount - Algorithm

Perforui the following calculations.

dt =)- a

It yes, continue. If no, ,go to (757).

do = 10 In (750)

Os o =t a n - I B- -7 5 7 )I~ni

tIs = D-Jd 78HSO D 0 d

BR sk x B 75)

)NO = DN(D, do ,,s o, Hso0 T, BR, ttR 7o0)

'SI =0.8X 5 0o (701)

dI =D- Bs tan s1 (702)

Its = 1)- di (763)

BR =skxB s (704)

DN t = DN(D,d1,iPS1, Hsi, T, BR I1) (7o5)

Using the above parameters with indices "0" and "I" as initial values, enter now the following

iterative loop:

N - DN

PSi+2 =' Si + I - DNi 'Si+ - 'Psi) (700)

24

NSWC TR 82-91

d 12 ) - B. tan 'PSi2 0

di_ 0 ? (

If yes, continue. If no. go to (770).

d 2 = 10( 111 {( '6 ))

/ 1)

'Si+2 tan- - (770)

lli+ =3 B'1Si+2 S tanSi+2

BR = sk x Bs (772

I)N,+, = I)N(D. di+ 2, p'5s+2' ''Si+2' , B R' HR) (773)

C = 0.00001 in ('74

NC - DN i+2 (75

i+2 < '.1 76

If yes, stop the iteration. Call the parameters associated with the index i + 2 the estimatedseamou~nt parameters. In particular,

is =tdSi+2

'Ps : 's= +2

If no, reenter the iterative loop with the "i + I- and "i + 2"' parameters as the initial values.

Estimation of Peak )epth for the Generally Compensated

Seamount--Output )ata

ds d Si+ 2 Eastimated peak depth in In

25

NSVC TR 82-91

2 I stilia~tcd slope allgIc ill k1C

IIS = II I-tinidtCd SCainoUnlt lICIcIlt inl Ill

BR = k lsI tI A d it 0110 1il M

Specified height of' root ill ill

I n case t he paramiete r cstiniatiol ii s te rulillated at I- qlat ion 753. assign %ames to tile estimated

s.ca m1ounlt paramnet ers as SpCified inl that litter eq nlat ion.

ANALYSIS OF D)ATA t)ISPLRSION

* Input D~ata

Obtarnl the followinlu f rom the SI-\SA I'-A data track anld or' data tr ack header I-ah[les 3 anld

4 of' ]R-8l-20O).

0 (a Iculated average of' all o ("\ord 0. -labe 21N N

onl datai track under considera tioni. llis is tilie

ave rage gzeoid he~ich It conlIid~lC ene ou1d, ill

06 Calculated average of' Lill (j5 (Word 7. I'able 2)onl data track uinder consideration. [his is thleaverage vertical deflection contfideClIe b)Ound arc sec

vs Satellite subtrack velocity ill sec

At Ihue interval bet ween data points sec

Iltirflher, have available

Rl Iarthi's ''radiuis' (R R z 6378000 inl)

PSg 1 P~* - l Pm~ as specified above

I) Ocean depth ill

NSWC Tit 82-91

'..1) U ertainty i n ocean depth (User input).

Normally. USe the value of 10'' of 1)

I" ('rustal thickness (user input) M

AI Uncertaint% in crustal thJcKless (user input) ii

';s Initial estimate of slope angle dot

N 'Observed" geoid elevation above seaniount center n

B Scamount half witdth at base n

sk Geometry factor for generally compensated cases

It "leight" of root for generally compensated case,, M

Error Estimates

At S - At

A IIAt A -1 t| B A t !'t

A,"s 15'+ 05 ) - A00 ,.6 deg Oo 1

N(. - 0.3 N. CW1

vs At 180_- _ A,;deg s %I z

H1 IT

A1 s z 1.4 vs At 000 i (SIM1

27

NSWC TR 82-91

Data IDispersion fo~r lscistaically Compilensate-dSeaio(unts

Sv Ibloli/ e he computer routine that performis the peak depth and slope es( i Iilition for

iSOStatiCaill compenC1Sated seamounM Ch l

1.11I t l C011111. 13 N1.Y ,-S BS

Let

SV m1boli,.e all evain at iOll Of the above funct1:i011 ( COMIpu ter ron tine ui I. s" uf all argumnentCsnominal eweepz thle parameter indicated b\ -p.-' I-he latter shiall enter the routinle with a valuepertUrbed by its error increment.

Calculate now

'I(Lis. t t co lp )D . 1

disostat. c01lliv. i]

,biso ia. Cli . - 5

I s n t 1 . B + .

Iso St at. c otIn p. N + (

and

( A ) a I s o s t . c o i n p . D + a 1 ) - L I O s a I c n

(Ad)a (LIo t - disk)S Iat. Cki Ili p1 (813)

(sd) )s(ii. col) r +IpS - dLI.ott n1 (814)

Ad ) a B S ( isstId. c 0fip . )3S+aB -diso s t t. k: , i 11. 8 5

(LLIIa N C ( d is'st at c ft p . )N c + A N C - dLiostI. co 11p1. (816)

28

NSWC TR 82-91

D~ata D~ispersion AXnalysis for Genierally Compensated Secainounts

S\111i00lie 11hC COnIpuLter routine that performs thle peak depthl and slopc: ci imatitm 1(,

I-C1C3i\ al coinpcnsatcd seanliounits by

Indt -Acul,11N1

- S S)C4 dI)p- I + S e) 1 eC W 41 111 p.

.1d) (d-d 9

aL B n ) B- I! Ie1j

J Additional Djetails Conceniing the D~ata lDispersion .Xnali ss

Note that tile tWO alg'orit nms indicatedl J) Iquat ions, ? l ulad s17 dcpcnd on add ition ilu nlisted. parameters. Not specifically mnentijoned. for ex amplc. arc t hc densitie". Also. sk and HIRare ornitted from Lqu1.ationl 81 7. All these qIuantities were disregarded bCcaUSC til eccMrquantitative data concerning thle Structure Of thle Seam1OUnt root sx stem1 and thle -SeanlOU it coin p0-.st ion were not availaoie %kith the dcree Of aCCeUrac\ t hat w\ould Make inlclusion inlto thle datIa

dispersion Study mleamuilgful.

AUTOMATIC ANALYSIS 01: SATELLITE ALTINILTRY

l o perform ain automatic seamount survcy on S LASA I-A altimetry. first specify tile kcsiicd

data track per device set number and revolutionl nlumber. Be aware that a SLASAV-A allinietr\track is likely to consist of' several distinct track segmients. For each of these trac:k segiilts. thekpresent Seamoun.11t detector will automatically perform the Matched F~ilter. thle Rougehne Dl~ecctoii

thle Seamon n Locator, and thle Calculation of' Initial Sea mount Pa ramneters. F or each1 t rae1 ceni n, ]M3

indicate the cases rejected and those retained for further processing. For tile casecs .cjcceed N

well a,; for those retained, p~rint out the longitude N M and thle latitude rSN, resulting f I1Ii1

[quations 41 5 and 416.

t-or the valid detections, execute the [stimation of' Peak D~epth for Isostatically (omipeiisatcdSOJ110IM pl)us tl associated Analysis ofDaa iscio.Te exut h

29

NSWC IR 82-91

IN bea ,SC (Sk =2 1n1LI 11 = 0.00000 1 11) 01f thle stimlation of' Peak 1c)pth tbr ( jencrai\ ('()11 penj-.ated scamlounts ILs tile associatedf I)alfDaa 1)ispersion.

MIa ke p)ro~ jsion Ii tr thle User to execute, automat ically f'or the entire data track or. optio10 Ia

tor selected i idnlab dectect ionls. the [ st imation of' Peak I )pth f or ( ;enera11v (0jC o penAtcdSeatnOLi Its andk thle aSSOCiated A\naly sis of' Da~ta Dispecrsion 1"r a rbi trarily sp~eci lied valnes of' sk

Arrangb-e tilie operational conmiu ter in iton t of' thle iliPIt data and resuilts. as indicated tly theeen~e tall diata intontS reprod need inl AppendliiXes A throu.-h C. for which credlit is d ne to0J10111 n [is ot" lie IPi~sicail Sciences Soft ware B~ra nch.

REFER ENC ES

.%. J. Iroegr An Experimental C'omputer Algorithm for Seamount M~odel Paramneter

E'stintation Based on SF-ISATI'A Satellite Radar Altimetrv, NSWC TR 81-200 tIDalgbrcni.

a.. Setember I1)8 I1L

2.S. L. Smith Ill and WV. J . (;roeger. "Preliminary EVALuation of' anl Experimental SeamlounltDetector andi [irst Collection of' Trial CaseS." Unpu)Lblishied Working Notes (DIhgren. Va..Jun le 198 1.

-3. W. J. .;roe,_,r. Notes on Estimating the Seamnount Slope from Vertical Deflection. N SW(IR 81-20 _t(ahlgrenl. V'a., September 1981).

4. Ii ondek. Maximial Geoudl.' Aei'atiom due to .Simidual(d Seamnounts, NSWC, DL TR-39)15IDahlgren. Va., November 1978).

30

NSWC-TR S2-91I

APPELNDIX A

rRIAL I)AF[A FOR ISOSI'.VI( COMPIL[S.XION

Ir-A

"S\m, R I1S 2-9

S E A M 0 U N T JE T E C T 0VERSION EE

USER INPUT

TYPE OF C3MPENS4TICN ISOSTATIC

CRUST THiCKNESS 5000.00 m

L 70.00 KMCELN .200 m

u/G = .63O240000t-14 M**2/GRkHO.M z 3400000.0 GR/?'**3RHJ.R 29500C0.0 GR/P*'3RHO.S 2600060.0 GR/M*3RIJ.W = 1030000.0 GR/1*3

K, = 1.7 4

K5 = 2.000

COG ROUGHNESS OETECTOR WILL OE USEO WITHF ()ATA WINOOW WIDTH FACTOR) = 1.30

PEJECT UoITA SEGMENTS NOT INSIDE THE AREA BOUNDED BY:LATITUEF = 3C 60LiNGITUOE 285 330

* NOTE - ANY ]ATA SEGMENT WITH FEWER THAN8 6 DATA POINTS WILL BE REJECTE@.

PRCCESS NEW DATA SEGMENT ((<<<<

HEADE< RECORD

REV NUMBER = 1375RHO .21-10N =3DELTA TIME = .490024 SECSATELLITE VEL.: 6.7i4J KM/SECNO. OF C TA POINTS = 11

DATA SEGIENT NOT IN DEFINED AREA, SKID IT.

33

NSv( I R S2-91

>2.)>>>>>> PP)CESS NEW DATA SEGMENT <<<<<C(<<

E-.EE °,EC OP.2

L ,huM-E z 137';HE = .2120

=3.L"A TI-E = .490124 SEC

L TFLLTII VtL. 6.766) KM/SECNJ. CF ,TA POINTS = 156

*'*' TATA ISEGMENT NCT IN DEFINED AREA, SKIP TT.

>>))>>>>>> PROCESS NEW DATA SEGMENT <<<<<

HEA-EQ RECORD

Ptv NUle3r p 1375

p.HJ .2120N I 3

OELTA TIME = .490024 SEC

SATELLITE VEL.- 6.766J KM/SECNJ. Or- CATA POINTS = 8

NOT ENOUGH DATA POINTS IN SEGMENT, SKIP IT.

)>~>>>>>), PROCESS NEW OATA SEGMENT <

HEADER RECORD

f.LV NUMPER = 1375PHO = .2120N = 3

CELTA TIME .490024 SEC

SATLLLITE VEL.= b.7790 KM/SECNO. OF CATA POINTS = 1645

NuM8EP OF DATA POINTS IN EACH WINDOW 22

NUM3ER OF DATA POINTS IN EACH "COG" DEPIVEO WINOOW - 28

34

.I

NSAC TR 82-91

WIN)OW Ni. I

FIRSTt LATITU3E 49 20 2 CEG,MINSECLONGITUDE= 306 54 36 CEG,MINSEC

LAST : LATITUDE = 48 38 18 CEG,MIN,SECLONGITU)E= 306 17 32 CEGMINSEC

• REJECTED, 4IN. VERT. OEFL. IS LAST PT. OF WINOW *'"

-----------------------------------------------------------------------------------------------------

>>>>>>)> PROCESS NEk GATA SEGMENT <(<C((<(

HEADER RECORD

REV NUMPER 1375

RHO - .2120N 3DELTA TIME .4 00Z4 SECSATELLITE VEL.= 6.8743 KI/SECNO. OF OATA POINTS = 994

NUM9ER OF dATA POINTS IN EACH WIN30W 22

NUM3ER OF DATA POINTS IN EACH "COG" DERIVED WINDOW = 25

35

NSWC 'R 82-91

WINOOW N10. I

FIRST: LATITUDE = 46 49 38 CEGMIN,SECLONGITUDE= 304 45 49 DEGMIN,SEC

LAST : LATITUJE = 46 7 21 CEGMIN,SECLONGITUDE= 304 11 49 EGMINSEC

' Q-JECTEu, IN. VERT. DEFL. IS FIRST PT. 3F WINDOW '

WINDOW NC.. 2

FIRST: LATITUDE = 39 16 5? CEGMINSECLONGITUGE: 299 21 24 GEG,MINSEC

LAST z LATITUJE = 38 33 28 [EG,MINSECLONGITUCE= 298 54 0 CEG,MIN,SEC

ACCEPTE2 FOR FURTHER ANALYSIS

------------------------------------------------------------------------

FIPSTi LATITUOE 32 45 59 DEGMINSECLONGITUCE: 295 32 21 CEG,MINSEC

LAST I LATITUDE : 32 1 50 GEGMIN,SECLONGITUOE- 295 8 35 CEG,MIN,SEC

ACCETFTEC FOR FURTHER ANALYSIS

--- 'C

NSWC TR 82-91

RESULTS OF ANALYSIS ON WIINOCW NO. 2

GEOPHYSICAL CONSTANTSt

G/G = .680240OUE-14 MI2/GRRHO.S = 2600000.0 GR/nIW3RHO.W = 1030O00. GR/MN*3RHO.R = 2950000.0 GR/'M*3RHO.M = 3400000.0 GR/M**3

OCEAN DEPTH AND CRUST THICKNESS:

C = 4900.0000 MT = 5000.0000 M

PESULTS FROM SEAMOUNT LOCATCR:

T.A 145.74795 SECT.9 151.65393 SECT.SM 148,80395 SECN.A = -35.552558 14N.B = -35.832625 4N.SM = -34.796667 MOELTA.A = -11.436224 ARC SECOELTA.B = 15.777345 ARC SECLONG.SM = 299.14165 OEG

299 8 30 OEG,VIN,SECLAT.SM = 38.942604 DEG

38 56 33 OEGMIN,SEC

INITIAL ESTIMATESI

R.S = 41153.715 MN.C : 1.4977448 mPHI.SC = 9.895132s BEG

ESTIMATED SEAMOUNT PARAMETERStISOSTATIC COMPENSATION

O.S = 103.2883PHI.S = 5.2848116 DEGB.S : 41153.715 mHIS 38d6.7117BoR = 41153.715 .HR =13281.194 M

37

NSWC TR 82-91

DATA OISPERSION ANALYSIS ON WINCOW NO. Z

AVG. GEOID HT. = .41 4373iE-01 MAVG. Vr_'T. OEFL. .33135406 ARC SEC

SATELLITE VEL. 6.7840000 KM/SECTIME INTERVAL = .490024 SEC

EARTH RADIUS 6375000.0 M

UNPERTUR8EO INPUT PARAMETERS:

C = '900.0000 MT 5000.0000 MPHI.SO= 9.9951328 JEGB.S 41153.715N.C 1.4977448 hi

ERROR ESTIMATESt

DELTA 0 = 490.00000 MDELTA T = 500.00000 MLELTA PHI.S0= .60457773 DEGDELTA 3.S = 4654.0519 MDELTA N.C -.44932343 M

RESULTS

CHANGEPARAMETER NEW 0.S PHI.S H.S B.R H.R IN 0.SCHANGED VALUE (M) (OEG) (M) (m) (M) (m)

o 5390.000 1491. 5.412 3899. 41154. 1360o 397.50

T 5500.000 11. 5.177 3729. 41154. 13009. 78.154

PHI.36 10.500 1093. 5.285 3807. 41154. 1326t 0.

B.S 45807.767 1239. 4.569 3661. 45808. 12772, 146.09

N.C 1.048 1919. 4.143 2981. 4L154. 10400. 825.81

38

NSWC TR 82-91

RESULTS OF ANALYSIS ON WINDOCW NC. 3

' * ' WARNING - ILL-CONCITICNEO CASE *,o

GEOPHYSICAL CONSTANTS:

G/G = .68024000E-14 9*2/GRRHO.S = 2600000.0 GR/M'*3RHO.W = 1030000.0 GR/M**3RHO.R = 2950000.0 GR/ri'*3RHO.4 = 3400000.0 GR/I4"3

OCEAN DEPTH AND CRUST THICKNESS:

O 4000.0000 MT 5000.0000 M

RESULTS FROM SEAMOUNT LOCATCRI

T.A z 265.53176 SECT.B 270.7057? SECT.SM 268.05602 SECN.A = -42.206865 mN.8 = -42.330503 4N.S'4 = -40.359934 mDELTA.A = -33.073740 ARC SECDELTA.8 = 33.362061 ARC SECLONG.SM = 295.31911 DEG

295 19 5 DEGMINSECLAT.SM = 32.357063 OEG

32 21 25 OEGMINSEC

INITIAL ESTIMATES:

B.S 32818.998 MN.C 1.5232942 4PHI.SO 24.156746 DEG

ESTIMATED SEAMOUNT PARAMETERS8ISOSTATIC COMPENSATION

O.S = 10.000000 MPHI.S = 6.9317687 QEGB.S = 321118.993 4H.S = 3990.0000 14B.R = 32d18.998 4H.R = tj920.661 1

39

NSWC TR 82-91

DATA DISPERSION ANALYSIS ON WINDOW NO. 3

AVG. GEOID HT. = .4124373!E-01 MAVG. VERT. DEFL. .83135406 ARC SEC

SATELLITE VEL. = 6.7840000 KM/SECTIME INTERVAL = .490024 SEC

EARTH RADIUS = 6371000.0 M

UNPERTURBED INPUT PARAMETERS$

D 4000. 0000 4T 5000.0000 MPHI.SO= 24.156746 OEG8.S 32818.998 NN.C 3.2448749 m

ERROR ESTIMATESI

DELTA D = 400.00000 MDELTA T = 500.00000 1DELTA PHI.SO= .60457773 DEGDELTA 8.S = 4654.0519 "lDELTA N.C = -. 9734624E M

RESULTS

CHANGEPARAMETER NEW O.S PHI.S H.S B.R HoR IN Do.SCHANGED VALUE (M) (DEG) (m) (14) (P) (4)

0 4400.000 10. 7.619 4390. 32819. 15316o 0.*' WAPNING - ILL-CONOITIONEO CASE ,"'

T 5500.000 10. 6.932 3990. 32819. 13921. 0.**** WARNING - ILL-CONDITIONED CASE ""'

PHI.SO 24.761 10. 6.932 3990, 32819. 13921. 0.***** WARNING - ILL-CONOITIONEO CASE 0*,0,

8.S 37473.050 10. 6078 3990. 37473. 1392t. 0.""'o WARNING - ILL-CONOITICNED CASE ="'

N.C 2.271 10. 6.932 3990. 32819. 13921. 0.""',D WARNING - ILL-CONDITIONED CASE 's"'

40

NSWC TR 82-91

>>1,> > PROCESS NEW DATA SEGMENT <<<<c<

HEADER RECORD

REV NUMBER = 1375RHO = 2L20N =3

DELTA TIME = .490024 SECSATELLITE VEL. = 6.7800 K4/SECNO. OF OATA POINTS 226

OATA SEGMENT NOT IN DEFINED AREA, SKIP IT.

>>>>>>>>> PROCESS NE% DATA SEGMENT <<<'<<

HEACER RECORD

REV NUMBER : 1375RHO = .2120N -3

DELTA TIME .490024 SECSATELLITE VEL.= 6.7480 KM/SECNO. OF DATA POINTS = 3048

'~D ATA SEGMENT NOT IN DEFINED AREA, SKIP IT.

>>>>>>>>]> PROCESS NEN DATA SEGMENT <<<<<

HEADER RECORD

REV NUMBER = 1375RHO .2120N =3DELTA TIME .490024 SECSATELLITE VEL.= 6.7800 KM/SECNO. OF DATA POINTS = 2206

D DATA SEGI1ENT NOT IN DEFINED AREA, SKIP IT.

4 NBZSE5O /1/4 END OF LIST ilNBZSE5O Il/I END OF LIST /I/!

41

6L_

NSWC TR 82-91

APPENDIX B

TRIAL DATA FOR A TYPICAL CASE

OF GENERAL COMPENSATION

43

AULI

NSWC TR 82-91

S E A M O UN T 0 E T E C T 0 RVERSION EE

USER INPUT

TYPE OF COMPENSATION GENERAL

CRUST THICKNESS = 5000.00 M

SK = 2.C0HR = 3200.0000

L = 70.00 KMOELN .0200 "t

G/G .68024000E-14 M**2/GRRHO.M = 3400000.0 GR/P"4 3RHO.R 2950000.0 GR/P*43RHO.S 2600000.0 GR/M*3RHO.W = 1030000.0 GR/'**3

K3 = 1.740KS = 2.000

COG ROUGHNESS DETECTOR WILL BE USED WITHF (9ATA WINDOW WIDTH FACTOR) = 1.30

REJECT OATA SEG4ENTS NOT INSIDE THE AREA BOUNDED BYILATITUDE = 30 60LONGITUDE = 285 330

" NOTE - ANY DATA SEGMENT I4TH FEWER THAN80 DATA POINTS WILL BE REJECTEO.

PROCESS NEW DATA SEGMENT <<<<<<

HEADER RECORD

REV NUMBER = 1375RHO - .2120N -3DELTA TIME = .490024 SECSATELLITr VEL.= 6.1840 KM/SECNO. OF DATA POINTS = 141

*" 'e DATA SEGMENT NOT IN DEFINED AREA, SKIP IT,

45

NSV(C"'R h2-91

>>>> NPROCESS NEW DATA SEGMENT <<<<<'<

HEADER RECORD

REV NUMBER = 1375RHO - .2120N = 3DELTA TIME : .490 24 SECSATELLITE VEL. 6.7660 KM/SECNO. OF CATA POINTS - 156

*'' DATA SEGMENT NOT IN DEFINED AREA, SKID IT.

>>>>>>>>>> PROCESS NEW DATA SEGMENT (<(<<C(<<C

HEALIER RECORD

PEV NUMBER 1375

RHO .2120N =3LELTA 'I'mE = .490024 SECSATELLITE VEL.= 6.7660 KM/SECNo. OF JATA POINTS = 8

" NOT ENOUGH OArA POINTS IN SEGMENT, SKIP IT.

>>~,>>> PROCESS NEW OATA SEGMENT <<<<((<<<

HEAOER RECORD

PEV NUMBER 1375e =l .2120N =3DELTA TI4E = .490024 SECSATELLIT_ VEL.= 6.7790 KMISECNO. OF DATA POINTS = 1645

NUMER OF OATA POINTS IAI EACH WI40)OW 22

NU'iEP CF DATA POINTS IN EACH "COG- DERIVED WINOOW 28

4o

wID3Ow ri. I

FIRST' LATITUDE 493 20 2 0EGMINSECLONGITUDE= 306 54 36 DEG,MIN,SEC

LAST I LATITUDE = 46 38 18 OEG,MIN,SECLONGITUDE= 30Ob 17 32 OEGMINSEC

REJtCTEC, MIN. VERT. OEFL. IS LAST PT, OF WIN3OW '

>>P>>>>R>> FRCCESS NEW DATA SEGMENT ((<('((

HEADER RECORD

REV NUMBER = 1375RHO = .2120N =3DELTA TIME : .490024 SECSATELLITE VEL.= 6.7640 KM/SECNO. OF DATA POINTS 994

NUM3ER OF DATA POINTS IN EACH WINDOW = 22

NUM3EP OF DATA POINTS IN EACH "COG" DERIVED WINOOW 2 28

47

NS' C Jh 2-91

W:N30W NC. I

F1,. T: LATITUOE = ,r, I9 38 OEGMINSECLONGITUDE= 304 45 49 OEGMIN,SEC

LA2. LATITUDE = 46 7 21 DEG,MIN,SECLONGITU'E= 304 11 49 DEGMINSEC

I " LJECTEO, MIN. VEf<T. DEFI. IS FIRST PT. OF WINDOW "'

WINSOW NG. 2

' I ., LATITUDE = 3) E 57 OEGMIN,SECLONGITU.E= 299 21 24 OEG,MIN,SEC

LAT7 S LATITUDE = 38 33 28 OEGMINSECLONGITUDE= 298 54 0 OEGMIN,SEC

ACCEPTEC FOP FURTHER ANALYSIS

WINOW NO. 3

FI9ST: LATITUdE = 32 45 59 OEGMIN,SEC

LONGITUDE= 295 32 21 CEG,MIN,SEC

LaV:r LATITUO = 32 1 50 OEG,MIN,SECLONuITUCE= 295 5 35 CEG,.4INSEC

ACC!PTEO FOI FUQTHER ANALYSIS

48

i F SJL TS A AL YS1 S ON W1IN90W NC. 2

C atP014y-S CAC 7Qt '2TANTSI

G/, *oou?>4_'00E-14 NI*'2/GRRHO.S =2EU0500.9 GP/M14'3PtlO.w= 1U'sc %Ls . 0 R 4

RhO.' 34#i00UJ.0 JP/m*3

OCEAN J E VTH Alit- C4UST THICKNESSI

T -300.00UOQ

GENERAL CCMPENS;TIO~i OATt:

SK 2.0O.60O0GH.= 3200.0000 Nj

RESULTS FROm ISEANIOUNT LOCATOR:

T .A t45.74795 SECT 151.655393 SEC

T .S 148 .10 395 SECN.A -35.552558 P4

N.9-35.602828 P4N.SM -34.-'Th667 PCELTA.A z-11.436224 ARC SECCEL'A.~3 15.777345 ARC SECLONG.SNI 299.14165 DEG

299 8 30 OEG,#iI?,SECLAr.SM z35.942604. DEG

38 56 33 OEG,MINSEC

INITIAL FS TINIATESt

8.5 41153.715 mN.C 1.497744d NIPHI.SO 9.8951328 OEG

ESTIMATED SEANIOUNT PARAMETERS:GENERAL CCNIFENSATION

D.S 1932. Y 62 P4PHI. S 4. 1?43 482 DEGB.S =41153. 715 P4H.S 2967.513S P4B.R =82307.429 NI

H 3?fjo .3001 P4 49

NS( IN h2-91

. DISPERSION ANALYSIS ON WINCOW NO. 2

aVG. GECIO HT. .41'43731E-01 4VERT. UEFL. .3135406 ARC SEC

.AT LLITE iVEL. = 6.784(0000 KN/SECT IM INTERVAL = o490024 SEC

E' TH PAIUS = 6373000.0 M

- DTU'BED 0INPUT PARAMETERS:

, 49U0O.O00 mT 5000.0000 4SuHI.SO= 9.6395132(3 EG

41153. 715 M6 z 1.4977448 1

Et OR ESTIMATES:

'C.L T A 1 490.00000 m)EL T4 T 500.00000 mC-LTA PHI.SD= .60457773 DEGCEL1A R.3 = 4654.0519 M-tLTA N.C -. 44932343 M

RESULTS

CHANGEPAk4IETER NEW D.S FHIS H.S 8,R H.R IN O.SCHANGEO VALUE (M) (DEG) (M) (N) (M) (M)

5390.000 Z378 4,186 3012. 82307. 3200.0 445.70

T 5500.000 1948. 4.103 2952. 82307. 3200.0 15.330

Pd1.SC 10.500 1932. 4,124 2968o 82307. 3200.0 O.

H.S 45801.767 2063. 3.544 2837. 91616. 3200.0 130.09

1.048 2296. 3.620 2604. 82307. 3200.0 363.78

50

NSWC TR 82-91

RESULTS CF ANALYSIS ON WINDOW NO. 3

• o WARNING - ILL-CONOITICNED CASE '

GEOPHYSICAL CONSTANTS1

GIG .bO24000E-14 4**2/GRRHO.S = 2600000.0 GR/N 3RHO.W = 103000J.0 GR/P9 3RHO.R = 2950000.3 GR/MHS3RHO.M = 3400000.0 GR/M**3

OCEAN OEFTH AND CRUST THICKNESS:

o 40. 00.0000 H

T = 5000.0000 M

GENERAL COMPENSATION OATAS

SK = 2.0000000

HR = 3200.0000 M

RESULTS FROM SEAMOUNT LJCATORS

T.A 265.53176 SECT= 270.70577 SECT.SM = 268.05602 SECN.A = -42.206865 PN,8 = -42.330503 NN.SM = -40.359934 NDELTA.A = -33.073740 ARC SECDELTA.9 = 33.362081 ARC SECLONG.SM = 295.31811 DEG

295 19 5 JEG,MINSECLAT.SH = 32.357065 DEG

32 21 25 OEGMIN,SEC

INITIAL ESTIHATESI

B.S = 32816.998 MN.C = 2.3492570 mPHI.SO = 24.i5E746 DEG

ESTIMATES SEAMOUNT PARAMETERS:GENERAL CGMFENSATION

Dos = 10.000000 04PHI.S = 6.9317687 3EGB.S = 32t18.998 4HS = 3990.OCOU 1R.R = 65637.996 '4 51H = 3200o0000 '4

NSWC TR 82-91

DATA DISPERSION ANALYSIS ON WINCOW NO. 3

AVG. GECID HT. = *.1243731E-01 MAVG. VEkT. DEFL. = .83135406 ARC SEC

SATELLITE VEL. = 6.7840000 KM/SECTIME INTERVAL = .490024 SEC

EARTH RADIUS 6373000.0 M

UNPERTUR9ED INPUT PARAMETERS:

o = 4000.0000T = 5000. 0000 1PHI.SO= 24.156746 DEG

B.S 32818.998 1N.C 3.2448749 '4

E NROR ESTIMATES:

DELTA 0 4 4000O000 MDELTA T = 500.*0000 mDELTA PHI.SO= .60457773 CEGDELTA 8.S = 4654.0519 MDELTA N.C = -. 97346246 m

RESULTS

CHANGEPARAMETER NEW O.S PHI.S H.S BeR H.R IN D.SCHANGED VALUE (M) (DEG) (M) (iI) (H) (M)

O 4400.000 10. 7.619 4390. 65638. 3200.0 0.*' 'J WARNING - ILL-CONUITIONEO CASE *,",

T 5500.000 10. 6.932 3990. 65638. 3200.0 0."*''' WARNING - ILL-CONOITICNED CASE ".,

PHI.SO 24.761 10. 6.932 3990. 65638. 3200.0 0."' WAPNING - ILL-CONOITICNED CASE "~'

6.s 37473.050 10. 6.078 3990. 74946. 3200.0 0."*"** WAPNING - ILL-CONOITICNED CASE ""'6,

N.C 2o271 82. 6.809 3918. 65638. 3200.0 71.523

52

NSWC 'IR 82-91

'>>>>> > > PRJCESS NEW OATA SEGMENT <<(<<<<

HEA-:L PECLR_)

REV NUM6ER = 1315RHO : .2120N -3DELTA Ti"E : .490024 SEC

SAT.LLITE VEL.= 6.7800 KM/SECNO. OF OATA POI.NTS = 2?6

OATA SEGMENT NOT IN OEFINED AREA, SKIP IT.

>>>>>>>>>> PROCESS NE% DATA SEGMENT <<<<<<<<<

HEACER RECORD

REV N(IJMER 1375RHO = .2120N =3

DELTA TIME .490024 SECSATELLITE VELo= 6.7483 KM/SECNO. OF DATA PCINTS = 3G48

DA'A SEGMENT NOT IN DEFINEO AREA, SKIP IT.

>> , ,,, PROCESS NEW DATA SEGMENT <<<<<<<<

HEAOER RECORD

REV NUMBER = 1375RHO - .2120N -3DELTA TIME = .490024 SECSATELLITE VEL.= 6.7800 KM/SECNO. OF CATA POINTS = 2206

" ' DATA SEGMENT NOT IN DEFINED AREA, SKIP IT.

N8ZSE5N I/I END OF LIST IINBZSESN I//I END OF LIST //f

53

,i 7_ b

NSWC TR 82-9 1

APPENDIX C

TRIAL DATA FOR ABSENCE OF ROOT

55

NSWC TR 8i2-91

S E A MOU N T D E T E C TO0RVERS[ON EF

------------------------- ------------

USER INPUT

TYPE OF COM(PENSATION =GENERAL -UNCOMPENSATD

CRUST THICKNESS = 5000.00 M

SK = 2 .C 0HR = .10000000E-05 M

L 70.00 KMOELN .0200 M

G/G * 66024C00E-14 M**2/GRRHO.?I 3400000.0 GR/?443RHO.R = 2950000.0 GR/MN'3RHO.S = 2600000.0 R143RHO.W = 1030000.0 GR/104*3

K3 = 1.740KS = 2.000

COG ROUGHNESS DETECTOR WILL BE USED WITHF (DATA WINDOW WIDTH FACTOR) = 1.30

REJECT DATA SEGMENTS NOT INSIDE THE AREA BOUNDEO BY:LATITUDE = 30 60LGiNGITUOE =285 330

'~NOTE - ANY DATA SEGMENT NITH FEWER THAN80 DATA POINTS WILL 9E REJECTED.

F RCCESS NEW4 DATA SEGMENT ( "'

HEADER RECORD

REV NUMBER =1375

RHO * 2120N =3DELTA TIME o 490024 SECSATELLITE VEL.= 6.7840 K4/SECNO. OF DATA POINTS =141

SDATA SEGMENT NOT IN DEFINED AREA, SKIP IT.

57

NSWC TR 82-91

>>>>>>> PROCESS NEW DATA SEGMENT <<<<<<

HEAOER RECORO

REV NUMBER = 1375RHO = .2120N =3DELTA TIME - .490024 SECSATELLITE VEL.= 6.7660 K9/SECNO. OF DATA POINTS = 156

, ' JATA SEGMENT NOT IN DEFINEO AREA, SKIP IT.

PROCESS NEW DATA SEGMENT "("'<<c<<,

HEADER RECORD

REV NUM3ER = 1375RHO :2t20N =3

DELTA TIME 0 490024 SEC

SATELLITE VEL.= 6.7660 K.4/SECNO. OF DATA POINTS 8

NGT ENOUGH DATA POINTS IN SEGMENT, SKIP IT.

> PROCESS NEW DATA SEGMENT <""<<(<<<,

HEADER RECORD

REV NUMBER 1375RHO = .2120N =3DELTA TIME = .490024 SECSATELLITE VELt. E#7790 KM.ISECNO. OF QATA POINTS = 1645

NUNf~3ER OF DATA POINTS IN EACH WINDOW = 22

NUMBER OF DATA POINTS IN EACH "COG" DERIVED WINDOW = 28

58

NSWC TR 82-91

WINOOW NO. 1

FIRSTS LATITUDE = 49 20 2 DEGMINSECLONGITUOE= 306 54 36 DEGMIN,SEC

LAST : LATITUDE = 4d 38 18 OEGMINSECLONGITUDE= 306 17 32 DEGoINSEC

*" REJECTED, MIN. VERT. OEFL. IS LAST PT. OF WINDOW "

>)),,, PROCESS NEW DATA SEGMENT -c cc<-(4

HEACER RECORO

REV NUMBER = 1375RHO = .2120N =3

DELTA TIME .49002. SECSATELLITE VEL.= 6.r840 KM/SECNO. OF DATA POINTS = 994

NUMBER OF DATA POINTS IN EACH WINDOW = 2Z

NUMBER OF OATA POINTS IN EACH -COG- DERIVED WINDOW 28

59

NSWC TR 82-91

WIN3OW NO. 1

FIRST: LATITUDE 46 49 38 VEGMINSECLONGITUOE= 304 45 49 0EGMINSEC

LAST t LATITUDE = 46 7 21 IEGMINSECLONGITUDE= 304 1i 49 DEGMIN,SEC

REJECTED, MIN. VERT. DEFL. IS FIRST PT. OF WINOOW "

WINO3W NO. 2

FIRSTt LATITUDE = 39 IE 57 DEG,MINSECLONGITUDE= 299 21 24 CEGtMIN,SEC

LAST t LATITUDE = 38 33 28 OEGMINSECLONGITUDE= 298 54 0 DEGMIN,SEC

ACCtEPTEO FOR FURTHER ANALYSIS

-------------------------------------------------------------------------------WINDOW NO. 3

FIRST$ LATITUDE = 32 45 59 DEG,MINSECLONGITUDE= 295 32 21 DEG,MIN,SEC

LAST : LATITUDE = 32 1 50 DEGMINSEC

LONGITUDE= 295 8 35 OEG.MIN,SEC

ACCEPTED FOR FURTHER ANALYSIS

60

NSWC TR 82-91

RESULTS OF ANALYSIS ON WIOCW NC. 2

GEOPHYSICAL CONSTANTS:

G/G = .680240OOE-14 M4"2/GRRHO.S = 2600000.0 GR/443RHO.W = 1030000.0 GR/M 93RHO.R = 2950003.0 GR/Mr4*3RHO.4 = 3400000.0 GR/M'*3

OCEAN DEPTH AND CRUST THICKNESSS

O 0 = 4900.0000 Mr = io a.ooo

GENERAL COMPENSATION DATA:

SK = 2.0000000H.R = .10000000E-05 M

RESULTS FROM SEAMOUNT LOCATOR:

T,A 145.74795 SECT.3 151.85393 SECT.S* 4 148.80395 SECN.A -35.552558 FNi -35.662828 mN.SM -34-.796667 FlOELTA.A = -11.436224 ARC SECDELTA.8 = 15. 777345 ARC SECLJNG.SM z 299.14165 DEG

299 8 30 OEG,MINt SECLAT.SM 38.942604 OEG

33 56 33 OEGMINSEC

INITIAL ESTIMATES1

SOS 41i53.7t5 MN.C 1.4977448 MPHI.SO 9.3951321 DEG

ESTIMATED SEAMOUNT PARAMETERS I

GENERAL COMPENSATION - NO RCOT

O.S = 3568.2760 MPHI.S 1.6256144 IEGS.S = 41153.?15 *4H.S 1311.7240 4S-R 82307.429 m 61H*R .10000000E-05 'M

NSWC TR 82-91

DATA DISPERSION ANALYSIS ON WINCOW NO* 2

AVG. GEOID HT. = .41243731E-01 MAVG. VERT. DEFL. = .83135406 ARC SEC

SATELLITE VEL. = 6.7840000 KM/SECTIME INTERVAL = .490024 SEC

EARTH RADIUS 6378000.0 M

UNPERTURBED INPUT PARAMETERS:

o 4900.0000 4T = 5000.0000 4PHI.SO= 9.8951328 DEG6.S 41153.715 4N.C : 1.4977448 4

ERROR ESTIMATES:

DELTA 0 =490.00000 MDELTA T = 500.00000 MDELTA PH1.SQ= .60457773 CEGDELTA B.S 4 4654.0519 MDELTA N.C = -.44932343 4

RESULTS

CHANGEPARA4ETER NEW O.S PHISS H.S B.R H.R IN D.SCHA!4GEO VALUE (M) (DEG) (M) (I) (m) (PI

o 5390.000 4052. 1.862 1338. 82307. .iOOoE-05 464.07

T 5r;00.000 3588. 1.826 1312. 82307. ,1O000E-05 .54133E-08

PHI.SO 10.500 3588. 1.826 1312. 82307,. *OO9OE-05 0.

8.s 45807.767 3740. .450 1160. 91616. .1O00E-05 151.81

N.C 1.048 3976. 1.28? 924. 82307. .LOOOOE-05 387.39

62

NS C TR 82-91

RESULT% OF ANALYSIS ON WIINOCW NO. 3---- ------------------------------

GEOPrYSICAL CONSTANTS:

G/G .6o02400OE-l4 1*4?/GRRHO.S = 2600000.0 GR/M**3RHO.W = 1030G00. 0 GR/tl* 3RHO.0 = 295000.0 GR/M*i*3

RH I=3400003.0 GR/ 444 3

OCEAN DEPTH AND CRUST THICKNESS:

Z = 4000.OOO MT 5000.0000 4

GENERAL ZOMPENSATION OATAI

SK = 2.00G0000H.R = .1OOOOOOOE-05 M

RESULTS FROM SEAMOUNT LOCATOR:

T.A 265.53176 SECT.B = 270.70577 SECT.S = 268.05602 SECN.A = -42.206665 NN.8 = -42.330503 mN.SM = -40.359934 NOELTA.A = -33.073740 ARC SECOELTA.B = 33.362081 ARC SECLONG.SM = 295.31811 OEG

295 19 5 OEGiMNtSECLAT.SM = 32.357068 DEG

32 21 25 9EGMINSEC

INITIAL ESTIMATESI

B.S 32818.998 MN.C : 3.2446749 MPHI.SO : 24.156746 DEG

ESTIMATEC SEAMOUNT PARAMETERS$GENERAL COMPENSATION - NO ROOT

O.S = 613.88354 MPHI.S 5. 90677i DEGB.S 32818.998 '4H.S = 33o6.1165 MB.R 65637.996 'IH.R .:iOOOt00E-05 M 63

NSWC TR 82-91

DATA DISPERSION ANALYSIS JN WINCOW NO. 3

AVG. GEOIO HT, = .41243731E-01 MAVG. VERT. OEFL. = .83135406 ARC SEC

SATz.LLITE VEL- 6.784000 KM/SECTIME INTERVAL .490024 SEC

EARTH RADIUS 63730O0.0 M

UNPERTURBED INPUT PARAMETERS$

0 4000.0000 mT = 5000.0000 4PHI.SG= 24.156746 DEGB.S = 32oi8.998 '1N.C = 3.2448749 m

ERROR ESTIMATES:

DELTA 9 400.0000a M

DELTA T = 500.00000 M

DELTA PHI.SO- .60457773 CEGCELTA B.S = 4654. 0519 MDELTA N.C = -.97346246 m

RESULTS--------------------------------------------------

CHANGE

PARAMETER NEW O.S PHI.S H.S SeR Hq IN O.S

CHANGED VALUE (M) (OEGI (MI (oil (') I

o 4400.O0C 943. 6.013 3457. 65638. ,IOO00E-05 329.17

T 5500.000 614. 5.891 3386. 65638. .1003GE-95 .58208E-08

PHI.SO 24*761 614. 5.891 3366o 65638. 10090E-05 I.

B.S 37473,050 1055. 4.494 2945. 74946. •iOOOE-05 440.70

N.C 2.271 1571. 4.232 2429. 65638. .10000E-05 957.46

64

NSWC TR 82-91

>>>>>>> PROCESS NEW DATA SEGMENT <<<<<<<<<<

HEADER RECORD

REV NUMBER 1375RHO - .2120N =3DELTA TIME .490024 SECSATELLITE VEL.= 6.7803 KM/SECNO. OF ,ATA POINTS = 226

DATA SEGMENT NOT IN DEFINED AREA, SKIP IT.

>>>>>>>>>> FROCESS NEt, DATA SEGMENT '<<<""

HEAOE,? RECORDO

REV NUIBER = 1375RHO 0 .2120N 3DELTA TIME .490024 SECSATELLITE VEL.= 6.7483 KM/SECNO. OF DATA POINTS = 3048

" DATA SEGMENT NOT IN DEFINED AREA, SKIP IT.

>~>>>>>>>> PROCESS NEW DATA SEGMENT <<<(<

HEACER RECORD

REV NU43EP 1375RHO ..2120N =3DELTA TIME .490024 SECSATcLLIf'T VEL.= 6.7300 KM/SECNO. OF DATA POINTS = 2206

' O OATA SEGMENT NOT IN DEFINED AREA, SKIP IT.

N3ZSESL I//I EtNC OF LIST /1NgZSESL f//i END OF LIST //I

65

I ka

NSC TR 82-91

)ISTRIBUTION

Deftense \t .pping Age-ncy NASA - WAlops [light CenterNaval ObscNatory Building 5( Al I'N: J. Mc(Gooean

A FIN: 0. W\ Williams \allops Island, VA 23337U. MartinP). M. Sci\m immer NASA - (Goddard Space Flight Center

A. senu Al IN: J. (I. MarshR. berkowitz R. kolenkiewicz

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Jet Propulsion Liboratory

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AFFN: L. B. Decker 1'. RvghM. Schultz A. Loomis

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)efense Mapping \geaev

Hlydrographic Topographic Center NOAA - National Ocean Survey/National Geodetic Survey

6500 Brooks lane 6001 ExecuLtive Blvd.

ATTN: It. ticuerman ATTN: B. it. Choviti,

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efense technieal Information (enter NOAA - Pacific Marine Environmental Laboratory

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S. ( )dn thal A FTN: John McArthurC. Kilgis

Blay St. Louis. MS 39)522 Silver Sprin,,. M) 20910

NSWC TR 82-91

D)ISTRIBUTION (Continued)

Oceanographer of the Navy University of lexasNaval Ooservatorv Building I Dept. of Aerospace EngineeringWashingtoil. DC 20360 AT TN: B. 1). Tapley

B. SchultzNaval Oceanography Division Austin. TX 787 12Naval Observatory Building I

AIFN: C ode NOP-95 2 (11. Nicholson) Scripps InIstituitionl of Oceanography-Washinuton. DC 20360 ATTN: R. Stewart

R. L.. BernsteinD~eputy Chief of Naval Operations LaJolla. CA 9)209)3ATTN: NOP-21 11)

Washngtn, C 2350WoodsIS l~oll Oceanographic InstituteATTN: J. A. Whjitehead

Strategic Systems Project 3ffice WoodIs 11ole, MA 02543ATTN: SP20123 (P. Fisher)Washington. D)C 20376 Institute of i ne and Atmospheric Science

City U~niversity of New, YorkOffice ot'Naval Research ATTN: W. J. Pierson800 N. Quincy St. New York, NY 1003 1A FTN: 11. C. badglceyArlington. VA 22217 D~epartment of Geodetic ScieceIC

Ohio State UniversityNaval Research Lathoratorv ATTN: R. RappAT-IN: V. Noble Columu. 11)L01-I 43210

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(ur mlia nder F4 1

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