resin, a fortran iv program for determining the area of ... - Science Direct

Computers & Geosciences, Vol. 2, pp 249-260. PergamonPress, 1976. Printed in Great Britain

RESIN, A FORTRAN IV PROGRAM FOR DETERMINING THE AREA OF INFLUENCE OF SAMPLES OR DRILL HOLES IN RESOURCE TARGET SEARCH DONALD A. SINGER U.S. Geological Survey, Reston, VA 22092, U.S.A. (Received 12 March 1976)

Abstraet--A FORTRAN IV program that calculates the area of influence of drill holes or samples with respect to the size and shape of elliptical or circular resource targets is presented. Program options include determination of the degree to which areas within a region have been explored and estimation of probabilities that points are centers of undiscovered deposits. Errors of recognition can be utilized in the program input. Key Words: Area of Influence, Exploration, Mineral Resources, Occurrence Models, Search.

AREA OF INFLUENCE PROCEDURES

INTRODUCTION

Prior to decisions on the level of investment in exploration, information should be obtained not only about the characteristics of the exploration process, but also about the probability of undiscovered resources existing in the region. Exploration decisions, therefore, should focus on two fundamental considerations: (1) estimates must be made of the probabilities that deposits having various characteristics occur in the region; and (2) given these probabilities of occurrence, the probabilities that deposits will be discovered at various levels of exploratory effort must be estimated. The program RESIN (Resource Area of Influence) provides a procedure by which the array of drill holes or samples from previous exploration in a region can be used to aid in the estimation of the first category of probabilities--the occurrence probabilities. In this paper the program and an explanation of its use are presented; a more complete development of the concepts and possible uses of the method is provided by Singer and Drew (1976). As holes are drilled or samples taken in a region, two phenomena occur: (1) each hole drilled or sample taken has some area around it where a resource target might have been found if it had been there, thus each sample or hole sweeps out or explores part of the total region available: and (2) successful exploratory holes or samples reduce the quantity of undiscovered resources in the region. The part of the region that has been explored is determined by the area of influence and spatial arrangement of those holes or samples. The area of influence of a single sample or hole is determined by the size and shape of the target sought. The area of influence can be calculated for circular and elliptical targets by a method presented here. The method then is expanded to the situations of multiple holes or samples and errors of detection. An option of the program whereby each sample locality is assigned a probability of having been taken from the population of interest is next presented. Possible extensions to the program followed by examples of the card input, output, the references, and the program listing then are presented.

Procedures used in the RESIN program rely upon the geometry of targets and the positions of drill holes or samples. Shapes of natural resource targets in many situations can be approximated by ellipses or a circle. Although the program is designed for these shapes, the general method can be adapted to any target shape (Singer and Drew, 1976). An assumption is made initially that a drill hole penetrating a target would be recognized; later in the paper this restriction will be relaxed. Also assumed is equally likely chance of occurrence of target centers in the region of interest and penetration of the horizon of interest by the drill holes or samples. The geometry of targets and the assumptions are used to explain how the program RESIN calculates the area of influence. Determination of how well a particular point is explored is made with respect to a given target and the distance between the point of interest and the drill hole or sample. For example, if a single drill hole and a given circular target are considered, any point within the distance of the radius of the circle about the drill hole could not have had a target centered there without the target having been detected. Thus, the probability of complete search is equal to 1.00 for all points of increasing distance away from the drill hole until the radius of the target is reached, beyond which the probability drops directly to zero. The same logic is used for etliptically shaped targets: for points less than the distance from the hole or sample of the semiminor axis of the ellipse, the probability of complete search is equal to 1.0. Points at a distance greater than the length of the semimajor axis away from the drill hole could be centers of targets at any orientation without being detected; therefore, the probability of complete search is 0.0 for these points. For points of distance between the semiminor and semimajor axis lengths away from the hole, the effects of orientation must be considered. It is assumed in RESIN that all orientations are equally likely to occur. Given this assumption, the probability of the ellipse being hit by the drill hole is equal to the arc length of the possible hit orientations, that is those in angle ~ divided by all 249

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TE~T FxA4PLE

Table I. Example of areas explored option of RESIN

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RESIN. a FORTRAN IV possible orientations, that is 180°. The angle ¢b is calculated as follows: & =2tan ' b , l~/( a\rj_b~} 2-rJ~

for

a>re>b,

where a is the length of the semimajor axis of the target ellipse, b is the length of the semiminor axis of the target, and re is the distance between the drill hole or sample and the point being considered. The probability of complete search at the point being considered is .then &/180°. In the program RESIN, the number 1.0 is placed in the appropriate one degree step positions of an array called DI for each possible hit orientation. Use of this procedure allows the program to account for multiple drill holes or samples. For multiple samples, the angle within which a target centered at a point of interest could be hit is equal to the sum of all possible hit angles minus the angles of multiple hits. The degree to which the point is explored is this new summary angle divided by 180°. Placing numbers in positions representing possible hit orientations in the DI array also allows the program to be used in situations in which errors of detection occur. This allows the assumption of certainty of recognition to be relaxed: thus, holes penetrating a target or samples from a target are only recognized as such in some portion of the trials. For example, if it is known from past experience that only 30 percent of the samples from a target are recognized as being from the target, then 70 percent of the samples represent errors of target detection and in the possible orientations where a target could be hit twice, the probability that the target would be detected is 1.0(0.7). (0.7) or 0.51. In RESIN, the probability of not recognizing the target (0.7 in the given example) is read into the program and used in the calculation of the values placed in the DI array. The values in the DI array then are summed in the same manner as when there are no errors of recognition. Consideration of errors of recognition is important for some types of resource drilling, however, it is a necessity when samples such as those from geochemical exploration are being evaluated. RESIN provides a means by which samples with errors of recognition can be combined with the spatial distribution of the samples to evaluate the degree to which a region has been explored: in these situations the target does not necessarily represent the actual mineral deposit sought. Another option of the program allows each sample or drill hole to have an estimate of the probability that the sample did not come from the population of interest. The resultant map produced shows the probability that any given point is the center of the target sought. This option requires estimation of the probability that a particular value obtained from sampling could have come from a target having a specific size and shape: although this task is not simple, rough estimates might prove useful in identifying areas where additional sampling would be beneficial.

procedure would be to determine the function that describes the angles of possible hits at various distances away from the center of the target divided by all possible hit angles. For regular geometric shapes this is a relatively simple task: for irregularly shapes bodies, values determined graphically and placed in a look-up table would be a feasible procedure. The printed map could be changed in three forms. The program could be run on a computer with a print train having a square character set. This would eliminate the distortion of the map caused by rectangular characters used on most printers. The second change would be to place the output on tape or disk for processing with a contour plotting package. A third method would be to change card RESIN 091 to PSCALE = 0.6. This produces a change in scale in the Y direction by dropping some intermediate rows from the calculations and map. In certain situations it may be desirable to allow for a preferred orientation of resource targets. If firm evidence exists that the targets are oriented within some restricted range then the program can be altered to account for this by defining the array DI only for the orientations of interest and changing the divisor in card RESIN 274 to reflect the restricted range of orientations. DESCRIPTION OF RESIN INPUT

For each run of the program four types of input cards are needed. The program lists the values on the input cards, therefore an example of the input is provided in the following section.

CARD 1 TITLE

CARD 2 NWELLS

IX

IY

CARD 3 A

B

PROBF

CARD(S)4

EXTENSIONS TO THE PROGRAM

One possible extension to the RESIN program is the use of target shapes other than circles and ellipses. The

253

XI(II

Format (20A4) Punch any title desired to identify the run. Format (315) The number of drill holes or samples are punched here. This is used to determine how many type 4 cards are to be read. The number of points to be plotted in the X direction (abscissa) are punched here. As many as 128 points can be used. This is restricted by printer. Punch the number of points to be plotted in the Y direction (ordinate). Any number of points is allowed. Format (3F10.0) Punch the length of the semimajor axis of the target of interest in units commensurate with the map scale. The length of the semiminor axis of the target should be punched here. The probability that the target would not be recognized if sampled is punched here. Whenever the target would be recognized with certainty or the option of possible target centers are used, PROBF should be set equal to zero. Format (3F10.0). One card for each drill hole or sample is needed. Up to 1,000 locations can be used. Punch the X coordinate of the drill hole or sample location.

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IIIIIII-IIIII122233~5S555~3332~II IIII1--1111112223##56666675~#332221

II~e?~%~SYS~;IIIIII] ......... 7 ..................... I11112223479999988777655#433 I L l ! l ; ~ 3 ~ 3 ~ l l l l l l. l. . . . . . . . . . . . . . . . . . . . . . . . . . . . l l. l l.l 1. 2 2 3 ~ 5 9 9 9 9 9 8 7 7 7 6 S S 5 ~ a 3 3

] l l ] ~ T 7 7 7 ~ 3 ~ l t l l l l l l - l l l l .I. .]. . .! . . . . . . . . . . . . . . . . l~I~?3~tT~?~.~?llllllll--ll111 .......................

IIIIIII---IIIII1222223333322222111-IIII11111-IIIII1222~33333333322221111 II]IIII-IIIII1222~333~4~3~221111

I0 .................. II .................

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

l [ l ~ 3 ~ T l ~ V l ~ 3 ; ~ l l l t l l l l l l ? ~ l . .l . .l . . . . . . . . . . .

b ................. ..............

[ I I I ~ 7 ~ 3 ~ ? P I I I I I I I I 1 2 ~ .I. . .I. . . . . . . . lll?~d~Tt~3P?lllllllll~22~2~ll .............

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

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

.................. 5 ..................

IIIIII~>~Ii111]I[III-III~2111

I I I I ? ~ ? ~ I I I I I I I I I I I I ~ P ~ I I I l l ~ t ~ J ~ ? ~ l l l l l l l l l l 2 ? ~ ? ~ l l

P ................... ..................

1...................

~l2.~567q.~d3~q~L~9~h~1~l23~7~9~l~3~Sb7Hq~34567@~l23~56?@9~3456789~234~6789~|234567B9~23¢56789~|23~56789

Table 2. Example of target centers option of RESIN

>

u

o z

~ i - = v ~).',~=';

lO,=(

u. ''= ,j ,~:~=:

2.=Y ,+r.cy

d" ~ = "

P'=Y

91.=x

~H.=X %~.=>:

i-]

/.=,

.~r.=~ !".=~

~v.=~

Table 2.

(Contd)

I] ] i ? 2 _ 2 ~ 5 ~ 5 ? R ~ q c ) ' ~ , ) ~ ) q g q s q s / ~ 3 3 3 1 3 3 3 3 3 3 3 3 ~ 3 3 3 ~ ? . ? . I l l l l

,,.=v

~.=Y J~.=Y

~,vL=u

;). [ i = ° f.~*~=P

';.~.=Y ~!.i?=P

~ ) .~1~'~

OF

~').=~

~2.=X ~.=X

¢I.=X :).V]=~ ~ O.Pq:l~

2~,=Y O.V~=~;

4~.=Y ;.=Y

2 h , = Y O,[O=P

TI~T/~L ROOM

~b,=X

76.=X 3bo=X

~b,=X

~I,=Y

3q.=Y 35.=Y

O,~R=P

O.|7=P 0.2q=P

4 5 , = Y O,21=P

[ I ] ] ,~22"~.~4 %6,~I~4;~L)QgQ~)Qg~].q~4 [ / 5 ; 3 ~ ? d 3 3 3 3 3 3 3 3 ~ 3 3 3 P . ~ ! 1222 ~.~/+A'~£*;~QgUWQO~q ~ 10~. 1 3 ? 2 2 d ~ 3 " ~ # 4 q 4 3 3 3 3 ~ P _ P . ] I [ ~?,)_ 3 q / 4 w ' ~ 6 ~ w c } ' 4 Q ' ) Q ~ ) q [ 4 7 1 5 % 3 3 2 _ ~ _ p 2 ~ 3 ~ . u , 5 % % D J 3 3 2 7 ~ ] i ................. ~ I )~2:~ ~ b ~ 7W'.),.)wWHq7&(94 : ~ : ~ 3 2 , ) ? p . ~ 3 ~ 5 5 q q D ~ 3 2 2 ? 2 1 1 1 [ ! 12~)~,45q6 ~,~''~/7:~q%aa3332p2E~555%5563~.P_~l 1| ] 1 .................. 1 ! I ~'~ ~ ~ %~z~gS55'&u~%%~a ~3 ~ 3 P ? P ~ , ~ . ? ~ 5 5 5 5 b # 3 P 7 . I 1 ] I ] ................... I ~ [,Y_P2 4 { ~ 4 ~ 4 ~ , , ~ 4 ;.~39~t;-'?p_@~2.95~%Sbj?~lll] ..................... ' I ] I :~;P2 ~3 ~ 3 ' ~ , 4 ~ 99~3142~'P~p~,Z~pp3~%A3,~p_I 1 ] .......................

lO,=X

86.=X ~6.=X

~3,=X

I 1 I 1111 l .......... I l | 11 . . . . . . . . . . l 1 | l-I ........... .............. P2d I ] I ] ................ ?I I ] I 1 ............. "--111 I l 1 ................

l t ! ;~-,2-~ ~~-~.~q,~.~HR,~H~R~.~t ~33-~P_~_2?2;?3333Lt34~4*~.33PP. r ~ I ~ PC'~,-'_~.},,~'~.H~9'-~-~,~,~ ~ (lb~;I ~9"~3333333..t$33,~33~111 11 ~ P;~ ? ~.'I.~,V-:,'~.T-' ~.~ 9 ~ 9 ~ q ~ R q ~ 7 5 4 3 3 3 3 3 3 3 ]3333ZP. 333332~?~1

• ~," 'I ~!qt,)=

~,4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

~ ~ ...................................

'~'~). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 .................................. %1 .................................. 5? ..................................

~+~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

/+7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. a~ ..............................

~' ~ . . . . . . . . . . . . . . . . . . . . . . . . . . ~'~" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ ..............................

O,&O=P

18.=Y

52o=Y O,gR=P

0.76=P O.I]=P 0.37=P

24.=Y 9.=y 44,=Y

Z

"n O -]

Z

rn

~lLIhl~4l ,)

I)t

I (',

T '

X

I

TP

I