Chapter 4

AMPLIFIED PROFILES

Chapter 4 Chapter 4

Chapter ⁴

Vertical ^{rnagnetic gradient analysis}

of two-dimension t ^{rnagnetic sources}

4.L Introduction

Quantitative analysis of magnetic anomalies involves the determination of the parameters (depth, thickness,

dip,

depth extent, strike extent, magnetic susceptibility contrast and magnetization)

of the

magnetic

source. The

magnetic signature

of the main study

area

is

characterized by numerous anomalies caused

by

magnetic bands

within

dipping metasediments.

A

preliminary

interpretation

revealed

that the majority of

magnetic sources were

linear to

curvilinear, and

that

depths appeared

to

be near-surface. Though many techniques

for interpreting

anomalies caused

by

two-dimensional sources exist, the parameter usually determined is the

depth.

Since

the majority of

magnetic sources appeared

to be

near-surface, knowledge

of the

dips

of

the metasediments would be of great use

in

structural interpretation.

Graphical methods were used on

total

magnetic

fleld

and

vertical

gradient anomalies and selected profiles were modelled on computer using

GAMMA1.

The techniques presented

in

this chapter were used

to

provide quick depth and dip estimates

for

two-dimensional sources.

4.L.L Modelling algorithms

The two most common models which have been successfully applied

in

magnetic interpretation are

the prism

and dyke

models.

Numerous techniques have been devised

to

solve

for the

pa- rameters of the

total

magnetic fie1d anomalies due

to

these sources (for a review re"

Åm,

^1972).

These methods can be grouped

into

graphical and computer methods. Despite the simplicity of

the

dyke model, no one technique can be applied

to all

cases

with

a reasonable degree of accu-

racy (Åm,

op.

cit.). Part of the

problem

is

due

to

imperfect resolution caused

by

interference from neighbouring magnetic sources and

part

is due

to

the errors involved

in

assigning a simple geometrical model

to

a complex geological structure.

The parameter estimates obtained from the use of standard techniques on the

total

magnetic

field

anomaly can

be

improved

by interpreting the gradient

anomaly as

well. As

has been demonstrated

in the

previous chapter,

the vertical

gradient _has a number

of

advantages over

lThe _{forward modelling algorithm} GAMMA was w¡itten by Dr. J. W. Paine of the Unive¡sity of Adelaide.

6- ó:

dip(0'<ó<180')

strike of the sheet

with

^respect

^to

^{magnetic north}

(0"<d<180")

intensity of the Earth's magnetic field

inclination of the Earth's magnetic field

(-90" < ¿ <

_90")

tan

L

arctan

--;-7

$rrl

I

vertical gradient of the

total

field

strength of the remanent magnetization

(if

any) Koenigsberger

ratio = + _nT

inclination of the remanent

lield (-90" _< N ^<

90") strike of the rernanent magnetic field

with

respect

to

magnetic

north (0" < C <

^180')

arctan

tanN

stn14,:6';

inclination of the resultant field

(-90' ^< M ^<

90") strike of the resultant magnetic field

with

respect

to

magnetic

north (0" < B <

^180')

tan

II

arctan

rt"(d - ^B)

| ₊

_Q2

t

^{2QþlLr-,[ sin,l{}

*

^{cos -L cos}

^N

^cos

^C)

T=

L=

À-

V=

R

a:

¡Í:

C:

u:

M=

B=

O=

0- I=

p

^+p-ó-90"

^sin -t ^sin

M

^

2nT.:.SL

sln

^ sln _/-¿

Figure 4.1: Nomenclature

for

symbols used

in

Chapter ^4.

centre P(t) ^centte

) )

õ

P(y)

w h h

ô

Figure 4.2: Geometry of the

thick

dyke and edge models.

CHAPTER 4. VERTICAL MAGNETIC GRADIEN? ANAIYSIS

⁴⁵

the total field:

resolution is improved, neat-surface anomalies are enhanced, and much

of

the regional field is removed.

In

contrast

to the

abundance

of total field interpretation

methods, there are few methods directed

at the interpretation of

^gradient

data.

Those which are available, (Rao and Prakasa Rao, 1970; Nabighian, 1972; Rao et a\.,1972;

Atchuta

Rao et a\.,1981), generally require both horizontal and

vertical

gradient

data.

Nelson (1988) outlines some techniques which may be applied

to total

gradient anomalies.

As part of the interpretation

^procedure used

in this

thesis, stacked proflles

of the

one- dimensional vertical gradient were ^used

in

visual interpretation (Section 3.2). The aeromagnetic survey data interpreted

in

this thesis did not include vertical gradient measulements. Therefore the one-dimensional vertical gradient was computed from

total

magnetic fleld profile data using a quadrature

filter

(differencing interval: 4, sampling

interval:

1) developed by Paine (1986). For two-dimensional ^sources, Paine (op.

cit.)

has shown

that

the approximated gradient (computed

by

convolution

or

Fourier analysis) compares favourably

with the

theoretical

gradient.

Since profiles of the computed vertical gradient were available and had proved very useful in qualitative

interpretation, the next

obvious stage was

to

see whether

they

could be used

for

quantitative

interpretation

as well.

4.L.2 Geometricalmodels

The

geometrical models which have been used

in this

thesis are

the

dipping dyke, horizontal edge, prismatic polygon and isolated pole. Vertical cross sections through the dipping dyke and horizontal edge model are shown

in

Figure 4'2'

The prismatic polygon model is similar to the dipping dyke model

in

that

it

has inflnite strike

extent.

However the vertical cross section is polygonal. Such a model allows for a non-horizontal top and non-parallel sides. The prismatic polygon model was only used during forward modelling on

the

computer.

The isolated pole model

is

used

to

model chimney

or

pipe-like

structures. It

represents a steeply dipping dipole whose cross section is small compared to its length, so

that

the lower pole has negligible effect on

the

measured magnetic

field. This

model was used

in

modelling ^deep basement features.

The models

for

which techniques are presented here are

the dipping

dyke

(thin

and thick) and

the

edge models. The

thin

sheet

or thin

dyke

is

a special case

of

a dyke whose

width (

depth.

The

principal

profile is taken

to

be perpendicular

to the

strike of the magnetic source.

Note

that the

eastern end of the profile (or the northern end

for d =

0") is considered positive, and

that the dip is to

be measured

from this end.

The parameters

of all

three models include

the depth h, full width u,

dyke centre yo,

dip

ó, strike

/

and susceptibility contrast

rc.

The strike extent and depth extent are assumed

to

be inflnite.

The strike angle,

þ

^can be easily determined from contour maps or rnaps of stacked profiles.

The dyke centre ys of

thin

^dykes can be located using Werner's (1953)

midpoint

method. The nomenclature used

in

this chapter is given

in

Figure 4.1.