CHAPTER 4. VERIIICAL MAGNETIC GRADIENT ANAIYS/S 49

CHAPTER 4, VERTICAL MAGNETIC GRADIENT ANALYSIS 46

CHAPTER 4. CHAPTER 4. VERIIICAL MAGNETIC GRADIENT ANAIYS/S 49

Computed gradient anomaly

Part of a

total

field profile and

its

computed gradient is reproduced

in

Figure 4.7. The magnetic anomaly

Z

^car-

be

correlated

with a pyrite

bearing

quartzite (strike

_Ó

= ^5")

^{which has been}

folded

into the Monarto

Syncline (Mancktelow,

1979).

Using stacked proflles

of the

vertical gradient,

this

magnetic

unit

can be followed

for

over

30km,

and easily traced around the fold of

the

syncline.

A drill

hole, located 3.5

km north of

Z, intersected bedded layers

of

sulphides (containing

both

magnetite and

pyrrhotite) within

the quartzite,

at

a depth of 30 metres.

The

anomaly

Z

was interpreted

to be

due

to a thin

sheet

at a

depth

of

116m below the sensor,

with

an index parameter d

=

^{319o and}

I :

15360. Taking the average sensor height

to

be

80m

^gives

the

depth below ground surface

to

be

36m.

Assuming rlo remanent component,

the dip

was estimated

to be 44"W and 0.16m to be the product of the

susceptibility and thickness. The depth estimate

is

reasonably accurate, considering the undetermined extent of weathering and the shallow depth involved, and while the dip estimate could

not

be verified,

it

was consistent

with

the general dips in the area. Measured susceptibilities vary from 100 x 10-5 SI

to

1000

x

10-5 SI. The corresponding thicknesses would then vary

from

¹⁶⁰

to

16 metres.

4.2.2 Error ^analysis

Vertical gradient profiles computed from the measured one-dimensional

total

magnetic field over two-dimensional structures are reasonably accurate when the depth to the top of the source lies between

A

and 10z\,

A

being

the

product

of the

differencing

interval

and

the

sample spacing (Paine, 1986). When computed gradient anomalies ^are interpreted, errors

in

the gradient values result

in

inaccurate parameter estimates.

To study the

effect

of filtering

errors

on

parameter estimates,

a FORTRAN

^{program was}

written to carry out the error

analysis

for a

wide tange

of

^parameter

^(depth

^and

d)

^va,lues.

The theoretical

total

field anomaly over a

thin

sheet was computed

for

different values of d and depth, using a sample spacing of 25 metres and

with

the origin of the model as a sample point.

The profiles were taken perpendicular

to strike.

The vertical gradient was computed from the

total

field as described

in

Section 4.1.1.

The errors

in

the estimates were defined ^as follows:

eIIOIh eIrOId

100

x (true

depth

-

^{estimated depth)}

/ ^true

^depth

true0-estimatedd.

Depths were varied from 60m

to

1500m while á was varied from 0o

to

180o. For ^each depth value

the

vertical gradient anomaly was interpreted, parameter estimates recorded, and errors computed. The errors varied both

with

depth as well as d and

for

a given depth, varied widely

with 0.

For each depth value,

the

minimum and maximum errors

in the

parameter estimates were used

in

drawing Figures 4.8 and ^4.9.

Where depth

to the top of the

sheet

is ( _A,

_there

_is

_a

_{lot of} "ringing" in the

computed gradient and

the

accuracy

in the

estimated depth varies

with

^d and

the error

can be as much as

80%.

For depth

: A, the

error

in

depth estimates can go as

high

as 30%,

but

is generally

within

10%

error.

For depths between

1.64

and

84,

depth estimates are well

within

10% error and estimates of d

within

^6o

error.

For depths

> 94,

^{the peaks} tend to flatten

out

and accuracy decreases. Where

the origin is not a

sampling

point, the

nearest sampling

point

can

be

at

llrrr

16

l2

WIDTH/DEPTH RATIO

-.2000 0 300 600 900

1 200

.3

a p

ì

o Þ

5 p

ÌtÈ dl (ú

.FÉ

tho Þ.E

of

Þ

8

É.ll

oçÍ

É.

LrJ 6

-9 -9

-12 -12

-15

Figure 4.10: Error

in

using

A,

as a

width

estimator of a dy.l,-e

too-.ly.

't50.0

100.0

50.0

0.0

.4000

.æ00

.0000

f-_E

'tÕ

õ

iT

€'

l- c

o

o-o

o

Figure 4.11: Total magnetic fieid intensity and

its

vertical gradient over a

thick

dyke: (Dyke1)

CHAPTER 4. VERTICAL MAGNETIC

GRADIENT

ANAIYSIS

⁵⁰

the

most 12.5 metres away. There

is

no significant change

in

the parameter estimates and for

1.64 <

depth

( _84,

_{accuracy is}

still within

acceptable limits.

The

accuracy

in

parameter estimation

in

using

the

nomogram

on the

computed gradient

is

dependent on

the

accuracy of the gradient values. These values are reasonably accurate for two-dimensional structures when

the

depth

to the top

lies between

À and 104, A

being the

product of the

differencing

interval

and

the

sample spacing. Depth estimates are

well within

10% error provided

that

the

true

depth lies between

1.64

and

84.

Estimates of 0 are accurate

to

^a few degrees over a wider range of

true

depth values.

4.3 Interpretation of thick dyke anomalies

The equations

for

the

total

magnetic

field

and

its

vertical gradient over a

thick

dyke are given

in

equations 4.6 and 4.7. As the

width to

depth

ratio

of a dyke incteases, the number of ^peaks

on its vertical

gradient anomaly increases

from two to flve. The original

aim

in

solving for characteristic points on the gradient anomaly was to

find

relationships between the peak values and locations which would yield all the parameters of the model. Since peak values could not ^be described by analytical expressions, they were calculated by forward modelling. The theoretical gradient was computed

for

model dykes: the

width to

depth

ratio

was varied

from

.5

to

10 in steps of .5, and d ^was varied from 0o

to

360o

in

steps of 5o.

A

computer program was

written

to search the gradient anomalies

for

the peak values and positions. As before, the main minimum is Vrrri. and the main maximum Vrrr.*. The distance between the peak positions of Vr,¡. and

V-r*

along the profile is defined

to

be

Ar.

The

initial

ratios which ^were investigated were vertical ratios (ratios of different combinations of the peak values) and horizontal ratios (ratios of the profile distance between different peaks

to Ar.

No satisfactory

width to

depth estimator ^was

found.

However, the analysis showed

that for

the dykes investigated:

1. A,

is a good

width

estimator

for all

values of d provided

that

^the

width to

depth ratio is greater

than or

equal

to 2.

The error bars

in

Figure 4.10 indicate the maximum possible elrors,

2. Lalh

and V..¿;o

=

lVrninlVror*l are complicated functions

of the

dyke parameters.

If

the

width to

depth

ratio

can be determined

by

some other method,

then

I/.'¿¡o

is

unique for a given value

of d.

Once d

is

known,

the

depth

to

the

top

can be determined using the appropriate value

of Lolh.The

two main sources of error

in

estimating depth and d arise from the inaccuracies

in the

approximation of the vertical gradient and

in

the estimation of the

width to

depth

ratio.

Note

that if

the anomaly is symmetric, then V,,,¡,, is taken to be the most westerly (or southerly) minimum and Vrrr"* is the most easterly (or northerly) maximum.

This method ^was tested on two dykes. Figures 4.11 and 4.12 show the

total

field and vertical gradient anomaly caused

by

two different dykes. The intensity of the Earth's magnetic field is

taken

to

be

60000nT

and

its inclination to

_{be -65o.}

The

width to

depth ratios

for

each dyke were determined using Barongo's (1985) "straight slope" method. Tables

for

the V¡¿¿¡6 and

A,

as functions of the

width to

depth

ratio

(these are included

in

Appendix G) were used to compute the

width,

depth and á and the results are given

in

Table

4.2.

The correct determination of the

width to

depth

ratio

is

critical to

the success of

tr

_c

o

õ iI

Ê

È

g

(5

o_o

o

100.0

50.0

0.0

.4000

,2000

.0000

0 300 600 900

Figure 4,12: Total rnagnetic field intensity and

its

vertical gradient over a

thick

dyke: (Dyke2).

Parameter

Dykel

Dyke2

True ue timated Value

00

200m 700 m

400 500 B

225m

675 m 45"

450 E

True value Estimated Value Strike

Depth

width

0

Dip

00

200m 300 m

300 600

w

178m 266 m

300

600w

Table 4.2: Results of interpreting the models shown

in

Figures 4.11 and

4.I2