A TI-59 pocket calculator magnetic modeling program

Compufer$ & Oeosciences Vol. 8, No. 3-4, pp. M9-3M, 19~2 Printed in Great

009$-~04]ti2/030349-.~$03.00/0 Igt2Perlgamom P i c a Ltd.

Brian.

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A TI-59 POCKET CALCULATOR MAGNETIC MODELING PROGRAM KAREN A. VORCEand WILLIAMC. PEARSON Three-D Gravity, Inc., Denver, CO 80204, U.S.A. (Received 13 January 1982)

INTRODUCTION

The use of modeling to match observed and calculated anomaly curves often is required for the quantitative interpretation of magnetic data. Simplified two-dimensional models assume that the profile along which the anomaly curve is measured runs perpendicular to strike. Geologic bodies are defined by a cross-sectional, polygonal prism with an infinite axis along strike. DEVEIJ)PMEN'r Taiwani and Heirtzler (1964) developed formulas for computing the total magnetic field from a two-dimensional, semi-infinite prism. Figure 1 shows an example of a simple two-dimensional body defined by a 4-sided polygon. The prism extends infinitely along the Y axis. Total magnetic intensity, T, for anomalies which are small with respect to the earth's total field, may be determined by dotting the anomaly vector with the earth's field vector: T - V sin/+ H cos/cos (C - D), where V and H are the vertical and horizontal comportents of the anomaly, I is the earth's field inclination, C is the azimuth of the positive X axis, and D is the declination, or azimuth, of the earth's field vector. According to equations (5) and (6) of Talwani and Heirtzler (1964) and Figure I, V and H are defined by: V = 2(JxQ - JzP) H = 2(JxP - JzP),

The previous expressions are for a single facet; the total V and H, therefore, are the summation of all facets of the polygon• I~SCIWrlON Parameters needed to compute a magnetic model are: (1) susceptibility in ~tcgs, (2) earth's field strength in gammas, (3) earth's field inclination in degrees, (4) earth's field declination in degrees, (5) strike or azimuth of the prism axis perpendicular to the paper, (6) (X, Z) polygon comer pairs in feet, with X positive to the right and Z positive downward; comers are in clockwise order and the first corner is repeated following the last corner, (7) first observation point's horizontal position in feet; vertical position is assumed zero, (8) observation line's horizontal increment in feet, and (9) number of polygon comers plus one (for repeated comer). Although the distance units are requested in feet, a different distance unit may be used, if applied consistently. The calculator determines the total magnetic anomaly at sucessive observation points, be t,innln~ with X0, and • incrementing by DELX until the user pushes the R/S key to terminate calculations. Output units are gammas. Operation of the calculator is simple and straightforward. The calculator is placed in the print cradle and both the calculator and cradle are turned on. The pro/

where Jx, Jz are the components of the magnetization vector (susceptibility times F) along the X and Z axes, respectively, and P and Q are given by:

f d

//

P=~

Z~,

,r

/

F/d

Z,,X,: log r2r, ( O,- 02)+ ~

X~Z~

Xz,zz

O-:~ ( o , - o=)-~, ,og~ L,21 -T- ~X 12

x4,z,

and X~:

__

X, - X2,

Z2, = Z 2 - Z,,

2 r, = N/(XI2 + Z,), r2 = ~/(X~ + Z~).

x3,z~

Figure 1. Polygon representation of two-dimensional body. 349

350

Short Notes

gram is keyed into the calculator using the learn mode. Appendix 1 contains a complete program listing. After the program has been stored correctly, it should he written onto magnetic cards so that successive runs can be started by merely reloading cards. Now, a model can be calculated by following these user instructions:

Figure 9 of their ~,'ticle is used to test the calculator program, because the body can be represented by a two-dimensional polygon prism. The study presents a calculated curve for comparison of results. Figure 2 shows a 9-sided polygon approximation of the quartz monzonite intrusion, with the observed and cal-

ENTER

PRESS

Turn calculator and cradle on. Enter the 4 sides of the two program cards as follows: Key in the side number of the card; press INV 2nd WRT; feed the card into the right side of the calculator with the side number desired nearest the calculatorand the printedside up.

1 2 3 4

Key the X coordinates of the clockwise polygon corners into storage locations 1-11, and the Z coordinates into storage locations 12-22.

XI X2 i : ZI Z2 i

STO 01 STO 02

XO DELX I D NV + I K S F

STO 23 STO 24 STO 25 STO 26 STO 27 STO 29 STO 32 STO 56

0.0174533

STO 30 1 INV 2nd LIST

Key in the parameters: first observation point in feet observation line increment in feet inclination in degrees declination in degrees number of corners l~lus 1 ' susceptibility in p, cgs strike in degrees earth's field strength in gammas Key in the constant: radian conversion factor Verify values.

2nd 2nd 2nd 2nd

WRT WRT WRT WRT

i STO 12 STO 13

RST R/S

Start calculations. Stop calculations.

ItI~ULTS A geophysical study of the Paradox Basin (Case and Joesting, 1972) investigated the magnetic and gravity anomalies of geologic bodies in order to help understand regional geologic structures and periods of tectonism. Magnetic anomalies along the southwestern edge of the Uncompahgre Uplift gave evidence of magnetic quartz monzonite intrusions. These Precambrian intrusions occurred along a regional zone of weakness, suggesting that the Uncompahgre Front may have existed as a structural and lithologic discontinuity since Precambrian time. In order to study quantitatively the location, susceptibility, and structure of one of the quartz monzoulte intrusions, Case and Joesting (1972) calculated a twodimensional magnetic model of the body. Profile MM' in

INV INV INV INV

R/S

culated magnetic anomalies. The solid curve is the observed field. Case and Joesting's (1972) detailed, computed model is shown by circles. The calculator model is shown by dots. Both computed curves were DC adjusted to allow for regional trend in the observed data. In order to run the model for profile MM', the following parameters are keyed into the calculator by the method discussed above: XO DELX I D NV + 1 K S

0 5000 66 15 10 0.0035 290

Short Notes 4¢

(m

Calculator

_,

~

Anomoiy,

351

~

,.,

,_,-Computer Anomaly ObWrved MagneticIntensi~,'o

m

22OO

8500 5000 SE:A LEVE 500C

A

~

A K=,0035

•

AKsO

I0000

O 20000 40000FEET I I t I I Figure 2. Interpretation of malp~tic profile MM' comparing calculator and computer models (after Case and Joesting, 1972). F XI, ZI X2, Z2 X3, Z3 X4, Z4 XS, Z5 X6, Z6 X7, Z7 X8, 7,8 X9, Z9 X10, ZI0

55O00 33OOO 37200 43300 489O0 54.f~

47500 3000 16700 23500 33000

rather to provide quick modeling capability to geophysicists, geologists, and technicians involved in magnetic interpretation.

2000 1200 1900 1300 1900 18000 18000 14000 7500 2000

CONCLUSIONS The convenience of calculator modeling of simple bodies is not meant to replace computer modeling, but

Rm~&F2W..ES Case, J. E., and Joesting, H. R., 1972, Regional geophysical investilpttions in the Central Colorado Plateau: U.S. Geol. Survey Prof. Paper 736, 31 p. Talwani, M., and Heirtzler, J. R., 1964,Computation of magnetic anomalies caused by two.dimensional structure of arbitrary shape, in Parks, 6., ed., Computers in the Mineral Industries: Stanford University Press, California, p. 464-,180.

Program listing n i-i3

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001 002 A 03 004 1305 006 007 0.0:3 nO9 010 !711 012

.2,- X : T 70 R A B 4 7 RCL 2 ':;: 2 9 65 x 4 _7 R C L ~:= 56 9 .=- = ,=$~ STO Z :-; 28 4 :. R C L ,-' ,_ ~" :7 A_

0

i-! l :'=',

" ~

::'::

014 015 016 017 018 019 020 021 022 02 .:, 024 025 026 027

4:7 R C L :-':.'5 25 95 = 43 S T D 4:3', 43 :3? C rlS 42 S T B 4E, 46 4-; " R C L 4...:i 4 :B :3;~ S I N 42 S T n 47 47 4:-: RCL

028 029 030 031 032 033 034 035 036 037 038 039 040 041

:30 30 65 x 5:-; ( 09 9 0~7! 0 :=:5 + 4 7 RCL 32 32 75 4:7 RCL 26 26 54 ) 95 = 39 C B S

352

S~ 042 04:3 044 046 047 I. 4 .,:,. . . 049 050 0 !51 05:;_'

42 58 4:'i 24 22 44 ,:: :'.., 76 " '~ : i :. :~ i

1_-15:::

..:; ;

045

054 12t5 5

056 057 i.'l 5:3 059 060 061 062 On:~_ _ AA4

0 E,5 066

4:.: :3 ::t 4] :2,4. 44 2 :-~ 4:.--: LI ~ 75 -~.~:' 2 ]: . 9 .42

STD 48. RCL 25 IN',,,'

SIJM 23 LBL

FI 0 STD . .:,

STD :-I 4 RCL 24 SUM 2:3 RCL 01 RCL =' '"

= :.--;TO

0 6 E:

47:

RCL

1"16 '9

" 2

1 2

i-i70 071 072 07:3 07 4 075 076 077 078 079

4: STn -: ' . .~. . . C, v" :2,1~ .....z 85 + 4 _:: R C L -:5 :35 7: ::: X z g5 = r . T rl 42 .:,. :39 ::: 9

01=I0

47:

0:3 t _ ,:, .." I-I ' "~ _ ',.~.:, 0:34 i3',=35 086 087 088 13,'R . . ':)." 090 . . .~. I'I'~. 092 09:-: 0'94 095 096 0'97

::!',5 67 i 2

-

09:3

099 1 0 fl.. I !-I I i3~ 10:2, I i3,1 . . . .

I 06 10;' 1 0 E:

I0 9 I If:? l I ~

I12

r',

RCL

:35 El) 8 22 II'lV 1'? GE : :.~ C. 4> RCL :3 "2 37 ~"= ,1. + 47: RCL ,"= j._ :35 '95 = 22 INV .-h:. T A N 42 :-;TO 4 i 41 1'6 LBL 24 D il E "-~ -.'* :- 'STO ; 57 < LBL = E 7 .! R C-~ ~

~ f

i":~- R C L ::-: :' --' 92= 4STEI ..""":,: :-'-:E, ,~: RCL

11:3 114 11 =_, it6 t 17 I 1 :-', I 19 12 Fi I ~: " 1

122 12:3 124 125 126 ~. , I A. : " "' - ~ . , 1 2 ,a •_~0 1:-]- i 1._.-i :-::3 134 I "> =, ., .. 136 137 1:38 1:3'? 141-t_ 141 142 14:3 144

145

14 E, 147 148 149

151-I 1 ...... ' -'~:.:' ...,

-.,

154

155 156 157 l R- i:: _ 159 160 161 162 I,,~ "-' 1 _,.:, 164 165 166 167 16:-:

169 I 70 I ,'1 I -':", " i72 174 17.5 176 1 7 ,.-'

Notes :'!i : 57 :ii: '+ J : 1 (i: I ,:4 = :# ] '.:';TO .:~"::: :=x_:', 7 } R i-: ::7 :..... ~ ':' ,~, ~- Ni-IP 4.- S T I ] 3 .~ -' '-' 3 . : ::.::z 9 % + ~: R i:: L " -:'2 :3 E, :::i7- ...... '-4-:- = " ~+:: STO ~,L 40 ' : F.:CL ~... :2,~ :36 t,' EQ ~" =2 'y'::*C ;22 [NY 77 I': E : ;, A ' -,-"': RCL :': '-" ~, ':J5 = :-', e~" 1 ..",:-:: ~: = ::':." "~: 'C' .5 3 :" ,D " 95 = 2:-: I N ' , : :3 C T FIN 4:-- :_-';TO 42 7~:. L B L i i

E:{ i

4. ]

RC:L :2,- . : 3 7 75 4:? R C L :3:- ._, -:, ,_, o 95 = 67 EQ 2L: CLR 4 ? RCL . 4: 41 7~ .~i: R C L 42 42 9F_. = 42 :.-.',TO .j ,: F, 1.4 ~ ' " 22 I N';,' 77 r;E 1 :--; C 75 :-: -~ l] 95 =

6,7 2:-,

EQ LDG

179

77

I 8 I-I

~;', ~:~:

L I1171

~

.~-,

182 1 ,:, .:,

94 4 -:

LBL +...RCL

i,.

r~E

184 i ',:5i

5:-: 7?

58 I]E

I'86

l,- B'

4 'D, '°'

i 'o 0

E''.

1:39 19N".

02 2 ',-:=._, + 4 :.-z R C L

191 19".:193 194 195 196 197 I. o I-'?-9 "200 201 2ri2 1"1"" -.:, 2• r i 4 205 206 208 209 210 211 21 o 2 1 °._, 214 2 15 .-,

>(

5 :'?5

58 =

42

STrl

4 l.-~ 7-, 2---: 4i~ 5~ <~" 4 3 "i -i ?' -

4:_--:, E" LBL

LDG RCL 58

:_-',TO

42 E ' LBL i~ D ' 4 .~ R C L

,-:' -_F: 9 6Fi :' ::~ :, 4Z ~r_, ' :' 7-: ::3
4 >:: -' = STFi 4 :-', LBL E' RCL

-."18 ."~19

:35

:35

.?. _.o FI -.'-- 1

4 "; RCL :2:- . . . . . .

.- .- .:, 224 225 •5 .", -" .-" ." b - 3 0 ~. -,-," .-, .-, ,~ ..... 2 2 '3 230

@'.:, -:', '* :::-: 42 ~ ...= 4": :-', L= 7-,

.16

217

.o, .~ .~ -" -" C.

~, .--,

..'oi <. 233 2:34 235 " 3 E, -'." ~--:, ," ..-.~ ,:,

-. --: ~ --. . .

= . : , ..

~ ::

240 241 •. - 4 ~ •- ' 4 o 244

•"-" 2, i

245 246 257 248 249 250 251 252 25:3 254

=

':-;TO '-~ ._,I >..:i STFI 5:." RC.L 3 ::: 4-: RCL 7: ? 3 ," 95 = 4 2 '.-;TO =J 7 59 3 3 ::,.:z '+= S T O .~ .:~ .~, -~

65 4:-:

RCL

"> 1 .-, ::.::

RCL

5 ? 59 95 = 42 STn 54 54 4 * : RCL 4 Ci 40 ._ :5 + 43 RCL :---',--" :39 95 = 2 '; L N :::: =': +

Short N o t e s

255 2~;,

0 2:

262 263, -' f: "~ 265 266

~."r

5 :_ 55 4 -; R F:L 5~ 52 "'= + ~ :: R C L 5 -' 53: qE ,; -.'-: '.-;TO 4.'49 31 .-."X e, 5 ::.:: 4 - R CL ' l " }' ., 5 :}: '2,

4. -~ R C L 4 3: 4:3 ?5 + 4- 3: R C L "•-,-~ 54

277

~: : , . , ~

•" , ::', 279 .

4:-RC:L "'=j

55

2;R~7 2:71 2:72 2 ::: ::-: 2:34 .':'. .'=' . . .F,. 2:::6 2 ::; 7 ,..,,:,

== 4 3 49

RCL

290 291

65

3

El ::1_

~" tZl 4 305 306 3.,.~.0 7,-, •=,LI,:, 3:0 '3. 3 t 0 3:1 i 312 3i:7 14 •.,°15 3:1 6 317 •,D i

.

3 ;d l:J •-, ,: i

....~3:2:3:

,.:,- ~ - .....

':'.,_=

~ 21 45 76 ~~: 4 .-4. 4 44 :3 4_: 45

44 :;4 4 3 "• , :

=

:~;T 13

45 LBL EE F.:C L 44 S LI M ~--' RCL 45 L=;I.IM :34 RC L 36

. :-

4 : I ~: C: L :i:; -: :S :-: ~ '.---;T D ,.:-, ::: - ' "(" 4RCL 4 3 42

~-'

3 29 330

353

ST[3

41 RCL

--".-',.:,

40 40 4:-STO ""-' :::9 Ili 1 1 4 4 SUM

•. . . ' , 4

5 ,....v~,

":" "'-"~ :336,

:;. 7.

47

f

PCL 5,.."

('=

-

:338

01

1

:~:E: '~

7 =l.

1

l:, 4,.I

4 -, F.:IZ:L 2: c,"

•: , 4 c 343 344 345 :.-.,3 4 6 o 4 ,. 348 .:, " 4.~ •"~ :,~5 L7 :751

95 = 22 INV " ['~" j] E 15 E L-!2 2 6, 5 ::. 4::-' R C L ] 2 ~£i 2 8

:35:3 .:,~ 4:355 "F, " 357 :758

6

>:'.

5 _

,::

:359

46 46 6 .. >:: '~:-: RC:L 4- :'. 65 ::-:: 43. R C L :7:"~; ~ .':' . , -El

3 6, i-i _

',.,: ' ~°,

+

361 •R F "-' ....-" :363

4:]' 47

RCL 47 ::..

9 _

::-92 ";-~93 294 .5 295 4 31 RLTL 296, "= 55 .=-9 7 65 ::.:: 298 4-RCL •:,¢~,a .., 7 53 300 I 55 + :~.I-i_I 4:'~- R C:L 3:172 4 ": 49

'-' ~-':'

341

49

=,= + 4 -: RCL 4'~ 49

42 4- ~ ~

•_ ~

::-::

= 4---STO 4 44 ~ - RC:L ~ 4 3: F,5 ::':: 4-=: R C L 54 54

•- , - . ,

." '.".- '. .~•

"=' :'~ ~

::.::

.,

~:

.:,o l

-

267 2 6 ',3 ::' 6 9 271-1 _ 2 71 a , :-' [" ":' 274 2,"5 2,-"6,

;26:'-a-

•"=, ?

':'~ -

258 .:r5 9 260 261

--'

~- ~ 47 -D '" -~'

397' -~. °, Q ~ .o .,

401

6 -,

4:2~ R C L 4 :' 48

.

-

._,..

"='q I

,:4=. . .

:79 -" :79:3 394

65 ::-:: 47-: R C L 4- 7 47

•Rq~, --

-"

"-

:'-',96

,.-,= Z,

J

=

%

4:-', RF:L

x

404

95

405 406 407 40L='40'?

':)5 P R T 6 ! F;Trl i I £ 7,-LBL 2.5 C L R

=

410

:~,3

411 412 413 414 4,o

42 STB 44 44 4~ STD ,~.5 45 61 GTB

416 417 • ~ t,D 4 • ,_, 419

=,:: .... 7:~. : :3 4 7

0

EE

LE:L C R t7.:L

4--C

5:7

421 • .-, .-, 4 a.4-" • " .=, "-'

':= . 4 .=; R F: L

424 4,'._ 426, 427 42 $ 4.--9

430 4:31 . .-~--~ 4...."

4o.:, 4:'-:4 4 .o., 436 4._ ,. 4:38 4.39 440 441 442 44:3

462

o

>(

402 40:7

4 6 FI 46,1

:~ ~:,~ :366 367

49

3,~.Q -. R C L . . . . ., -', 400 46 46,

RCL 34 ) ~.j .-~ 95 = 36:3 42 STB 369 4F 49 37 0 0:2 2 371 65 :."-: .... ,4 : RCL -:' ," .:, 2 '--" - _, •"=,," 4 >.'." (, 5 3 ,."5 57; ,:: ~'~# 4- -': R C L o--, 46 46 •_ 7 ,R _ .. 5 ~, ~:, >:: '-" -', CI * ..... 4"-; R C:L :380 ~::: 48 .-, ¢% •:, o 1 65 ::-:: ".', C', . - , ..... c 4.-:, R C L " "~'- . . . . "~ 34 :384 75 385 4-!: F'CL 386, 47 47 :=:8 7 65 x :38:3 4- i: RCL :38 9 :3. 3:3 ., ) 390 = -,~ 364

4 ? 65

444 445 446

447 448 449

450 451 4 .., -."

453 454

455 456

457 45,:, 4 ~_,. , ~

'"= 95 22 .2,

465

46,6 46,7

35

-

:3--: ':'=

=

INV TRN. +

',.:',i~' 'U 95 = 42 STO 4

41

1;.4 II 7~.. L B L i 2 B :79 11 55 + F~2 2 95 = ,;2 '.-;TO 4 i 4 ! 14 B 76 LBL 45 'f x '-'~ C,., 11" + 2 =

~=" 02

'3,5

:-:;TO 42 _,' -, B ' 76 LBL 16 R' 4:-: R C L ::~ : -':'" 55 + 4_:: R C L :'-i6 36, 95 = 22 l N' :=::-" T R N :[-'-'_~ , + :.--'~ ; o" 42

4Z

/

..,

464

" ~f" .:1

=

~ ::' :-;TD 42 42 ' B ' 7 LE:L

3s4