Magnetic investigation of the Hett Dyke CHARLIE KENZIE

Department of Earth Sciences, University of Durham 2012

1. INTRODUCTION

1.1 Purpose of study

The Hett dyke is a vertical intrusion of

thoelitic dolerite, associated with the Whin

Sill complex, emplaced during the late

Carboniferous (Johnson & Dunham 2001).

Whinstone rock is particularly useful for

roadstone, and it is proposed that the Hett

Dyke is a potentially good source for

quarrying. Using a computer model, we focus

on the possible depths and widths of the dyke

in order to review its viability as a roadstone

resource.

1.2 Geological Setting

The Hett dyke is one of 4 major ENE-WSW

trending dykes associated with the Whin sill

complex (fig.1), a large basaltic intrusion in

northern England, which stretches on land

around 120km in a north-south direction and

80km in an east-west direction. It has been

proposed that the Hett dyke, along with its 3

large counterparts, represent feeders into the

sill complex (Anderson 1951 & Goulty et al

2000), with the Hett-Dyke feeding the

Hadrian’s Wall-Penine Sill (Liss et al 2004).

2. MAGNETIC SURVEY

2.1 Acquiring the data

The survey was conducted along a profile

perpendicular to the strike of the dyke, in

approximately a north-south direction (fig,2).

Due to the sensitivity of the instrument (0.5

nT)[1]

, the line of profile was chosen away

from the wire fences that surrounded the

survey area. Measurements were made at 10m

intervals, and then every 5m when differences

in 10m readings increased to the order of

20nT. This was done to measure the anomaly

gradient more accurately, and to avoid

missing shorter wavelengths. Repeat readings

were made at the base station to correct for

any possible drift.

To maintain a high level of accuracy, whilst

carrying out a survey that was quick and

logistically easy, a proton precession

magnetometer was used[1]

. A higher

sensitivity instrument was not required as the

gradient of the anomaly was not justifiably

large enough. Additionally, an instrument that

measured continuously was not needed for

this land survey.

2.2 Results and magnetic reductions

Total field readings ranged between

49296 ± 0.5 nT and 50214 ± 0.5 nT, equating

to a maximum anomaly of 918 ± 0.5 nT.

Since the error caused by the magnetometer

(0.5 nT) is only a minute fraction of the

anomaly, it has been justifiably disregarded.

The raw data is summarized in the appendix,

table 3.0. A sketch of the observed anomaly

profile is shown in fig.3, note the regional

field has been taken away to emphasize the

anomaly.

Although there was a difference of 2 nT

between the repeated readings at the base

station, a correction for drift is unnecessary

considering the small change relative to the

magnitude of the overall anomaly (> 800 nT).

A correction for latitude is also unnecessary

since the latitude variation is only in the order

of 0.01 nT / m (Telford et al 1990).

Corrections for terrain were also neglected as

the gradient of the profile was only of the

order of 10°, which is not likely to be

significant (Telford et al 1990).

3. MAGNETIC MODELLING

3.1 Ambiguities and the inverse problem

The intensity of magnetization in a dyke is a

vector component, and the orientation of that

component strongly affects the shape of the

magnetic anomaly. Consequently, two model

dykes of identical shapes can give rise to two

[1] Magnetometer used was the Geometrics G-856 with an accuracy of 0.5nT. For further information the reader is referred to

the Operation Manual (Geometrics Inc. 2007)

different anomalies. Similarly, and more

importantly, dykes of different geometries can

cause identical anomalies. For example a

dipping dyke may produce the same anomaly

to that of a vertical dyke, if its angle of

induced magnetization is so that the total field

component is identical (fig.4). This ambiguity

is known as the inverse problem, which

generally states that although the anomaly of

a given body may be calculated uniquely,

there are an infinite number of bodies that

could give rise to any specific anomaly

(Kearey 1984). To try to avoid the inverse

problem in our model, we constrain our

model geometry to that of a flat-topped

vertical dyke and consider a number of

models, with different parameters, to give a

range of possible geometries.

3.2 Computer model and parameters

The sedimentary rocks that surround the Hett

Dyke contain relatively negligible quantities

of ferromagnetic minerals (Goulty et al 2000)

and for the purpose of modelling our

magnetic anomaly, the surrounding

sedimentary strata can be assumed to have no

magnetization. Thus, the only parameters to

be changed are the geometry and

magnetization of the dyke.

Modelling in two dimensions is satisfactory

for bodies such as dykes that are elongated in

the strike direction (Goulty et al 2000). 2D

modelling of a profile perpendicular to the

strike allows us to disregard the component of

magnetization along the strike direction, as

this has no effect on the calculated anomaly,

and we can therefore only model the intensity

and direction of magnetization in the vertical

plane perpendicular to the strike.

Consequently, in our model we have fixed the

remanent declination to 357°. Other fixed

parameters are shown in table 1.0 below. Note

we have fixed the susceptibility to 0 even

though in reality the susceptibility of dolerite

is usually between 1×103 and 35×10

3 (Telford

qt al 1990). This is because we can only

model the total magnetization of the dyke,

which is the vector sum of the remanant and

induced magnetizations, so to model the

anomaly we applied the values of total

magnetization to the remanent magnetization

parameters and then set the induced

magnetization and the susceptibility to 0.

Additionally, it was found that changing the

limiting depth of the dyke had little effect on

the expected anomaly; therefore the limiting

depth of the dyke has been fixed to 1km.

In the 2D model we proceed with the above

fixed parameters and change the remanent

magnetization Mr, the inclination of the

remanant magnetization Ir and the geometry

of the model dyke, to find the best fit to the

observed anomaly. To limit the number of

possible dyke geometries, values are chosen

between 1.0 and 6.0 for the remanent

magnetization Mr and between 68° and 150°

for the inclination of the remanant

magnetization Ir. In our model Ir was found to

give an optimum fit between 80° and 100°

and its value was changed to fine tune the

anomaly, not to significantly change the half

width or amplitude of the calculated anomaly.

3.3 Depth to the top of the dyke

Maximum Depth

If the model dyke increases in depth from the

surface, the amplitude of the anomaly

decreases. Therefore, as we continue to model

Parameter

Fixed Value

Profile orientation

342°

Earth’s magnetic field

39 Am-1

Declination of earth’s field

357°

Inclination of earth’s field

68°

Susceptibility

0

Declination of remnant

magnetization

357°

Limiting depth

1km

Table 1.0 Fixed parameters for computer

modelling of the Hett Dyke

the dyke at greater depths, the amplitude of

the anomaly can be maintained by increasing

the remanant magnetization to its maximum

value of 6.0 and by continuing to increase the

width of the dyke. However, since increasing

width of the dyke also increases the half

width of the anomaly, continuing to thicken

the dyke in this way eventually causes an

undesirable fit to the observed anomaly.

Fig.5a shows the maximum depth that can be

achieved by a model dyke, before any more

increase in depth would require a further

increase in width and result in an even larger

half-width. The model parameters were

Mr = 6.0, Ir = 88°, width w = 10m, and

depth d = 3.8m.

Minimum Depth

Decreasing the depth to the top of the model

dyke is easier because you don’t get “stuck”

with only one parameter (width) to vary as

you change the depth. It is therefore possible

to decrease the depth to the top of dyke to 0m

and still achieve an almost perfect fit. This is

shown in fig.5b, where Mr = 4.4, Ir = 90°,

w = 6.0m and d = 0m.

3.4 Width of the dyke

Maximum Width

To find the maximum possible width, we

move the model dyke close to surface, as

greater depths will cause a larger half-width

and therefore an undesired fit. Since we are

modelling a thick dyke near to the surface, Mr

is decreased to lower the amplitude of the

calculated anomaly. The maximum possible

width of a model dyke is shown in fig.5c,

where Mr = 2.3, Ir = 85°, w = 13.6m and d =

0.1m. Any more thickening of the model dyke

would cause an increase in half-width,

resulting in an inadequate fit to the observed

anomaly.

Minimum Width

Decreasing the thickness of the model dyke

lowers the amplitude of the calculated

anomaly so that the remanant magnetization is

required to be increased to its maximum value

of 6.0 and, additionally, the dyke model is

moved closer to the surface. Fig.5d shows the

minimum width of a model dyke, before any

more thinning of the model would cause the

calculated anomaly to decrease in both

amplitude and half-width, causing and

unsatisfactory fit. The parameters for this model

were Mr = 6.0, Ir = 85°, w = 3.0m, and d = 0.2m.

Additionally, a summary of the maximum and

minimum widths and depths are displayed in table

2.0 below.

Maximum

Depth

Minimum

Depth

Maximum

Width

Minimum

Width

3.8m

0m

13.6m

3.0m

3.5 Preferred dyke model

We concentrated on applying values for width

and depth that were roughly in the middle of

the maximum and minimum geometries

investigated above. However, it was found

impossible to achieve a satisfactory fit if we

modelled a dyke with median values of the

ranges above. Problems arose due to the large

half-width created using these specific

geometries, and changing the remanant

magnetization parameters were not enough to

significantly reduce the calculated anomaly to

a satisfactory fit. In order to acquire a suitable

fit parameters were then changed freely from

the median values until an almost perfect fit

was achieved (fig.6). The parameters of the

model were Mr = 5.1, Ir = 90°, w = 5.0 and d

= 1.0m.

4. DISCUSSION

4.1 The model dyke

Although a very good fit was achieved with

the parameters chosen for our preferred model,

in truth, a satisfactory fit could also be

achieved by a number of other geometries

within the ranges shown in table 2.0. It is

therefore difficult to conclude that a specific

Table 2.0 Maximum and minimum possible

geometries of a computer-modelled dyke.

set of geometry values is the most ideal.

However, we can conclude that the dyke is

between 3 and 14m thick, with a depth to its

top between 0 and 4m. Any proposed

geometry of the dyke would show a relatively

small error in the depth to the top and a

relatively large error in its width.

4.2 Viability of locality for quarrying

roadstone

Computer modelling shows that the depth to

the top of the dyke is of no more than 3m. As

an overburden of this size could be easily

removed, for the purpose of quarrying, the

depth to the dyke is of less importance.

Additionally, in this case, the depth does not

limit the amount of material available for

quarrying and since the width of the dyke is

the only control on the amount of potential

resource it is of much greater importance.

However, we cannot be certain of the exact

width of the dyke, and there is a much larger

error associated in this dimension.

If we consider commencing quarrying along

the strike direction of the dyke for 500m and

to a depth of 100m, we can calculate the

theoretical mass of dolerite that could be

gained from a mine of this size. In these

simple calculations we used a known density

of dolerite from Lindisfarne (fig.1), which is

2800 ± 100 kgm-3

(Tasmania Department of

Resources and Energy 1992) and we assume

the dyke is at a 0m depth from the surface.

Firstly, a dyke of 3m in width would produce

a total mass of dolerite

4.2 ± 0.2×108 kg, or 420,000 ± 20,000 tons.

Secondly, a dyke of 14m in width would

produce a total mass of dolerite

2.0 ± 0.008×109 kg or 2,000,000 ± 78,400 tons

If we use the median width value (8.5m), and

assign the maximum and minimum masses

calculated above as an overall uncertainty

1,200,000 ± 800,000 tons.

Although these calculations are very crude,

they show the large uncertainty associated

with the width of the dyke.

The calculations above show vast

overestimates for the amount of material that

you would be able to mine. The Hett Dyke is

unsuitable for quarrying because:

1) The dyke is a thin structure, meaning you

would have to quarry to large depths in

order to extract a significant amount of

rock.

2) Additionally, you would have to quarry

along the strike of the dyke for a large

distance in order to extract a substantial

amount of rock.

3) Although quarries can stretch to depths of

100m, the area (or width) of the target

resource is usually much larger than that

of a few meters. To quarry to a depth of

100m would require a huge removal of

surrounding sediments.

A case study of a running quarry that mines

whinstone is the Force Garth Quarry (North

Pennines AONB Partnership, 2004) in

Teesdale, 24km SE of Alston (fig.1). The

bedrock quarried here is from the sill rather

than from an associated dyke. Although the

sill is unlikely to extend to the same depth as

a dyke, the target area here is in the order of

100,000 square meters (fig.7) and therefore

much easier to quarry.

4.3 Assumptions and limitations of the

model - need for further study

The interpretation of magnetic fields is

inherently ambiguous due to the inverse

problem. To avoid modelling an infinite

number of possible dykes, we set the

computer model to assume certain parameters,

which if changed could result in a very

different geometry. For example, we have

assumed that the dyke is vertical and flat-

topped, that no tectonic activity has caused

any deformation of the dyke, and that its body

is uniform and unbroken. All of these

parameters require the need of external

constraints, such as geological and borehole

data, to further investigate the likely geometry.

In addition, we also assume that the induced

magnetic field is homogenous throughout the

dyke. In reality the magnetization of a rock is

largely dependant on the amount, size, shape

and distribution of its contained ferrimagnetic

minerals (Kearey 1984) and these may only

represent a small proportion of the constituent

rock. A concentration of ferromagnetic

minerals, say near to the surface, would cause

a different observed anomaly to that of a

uniformly magnetized dyke, such a scenario

was not considered in our computer model.

4.4 Conclusion

In order to proceed with any certainty about

the exact geometry of the Hett Dyke external

constraints must be known. However, it is

clear from computer modelling that a vertical

dyke would be unsuitable for quarrying. This

is primarily because of its small width, and in

order to gain a substantial amount of rock,

quarrying would have to proceed to large

depths and a significant distance along the

strike of the dyke.

5. REFERENCES

ANDERSON, E. M. (1951). The Dynamics of Dyke

Formation. In E. M. Anderson, The dynamics of

faulting and dyke formation with applications to

Britain (pp. 40-44). Edinburgh: Oliver and Boyd.

GOULTY, N. R., Peirce, C., Flatman, T. D., Home, M.,

& Richardson, J. H. (2000). Magnetic survey of the

Holy Island Dyke on Holy Island, Northumberland.

Proceedings of the Yorkshire Geological Society ,

53 (2), 111-118.

JOHNSON, G. A., & Dunham, K. C. (2001).

Emplacement of the Great Whin Dolerite Complex

and the Little Whin Sill in relation to the structure

of northern England . Proceedings of the Yorkshire

Geological Society , 53 (3), 177-186.

KEAREY, P., & Brooks, M. (1984). Gravity Surveying.

In P. KEAREY, & M. Brooks, An Introduction to

Geophysical Exploration (2nd Edition ed., pp. 125-

135). Cardiff: Blackwell Science.

LISS, D., Owens, W. H., & Hutton, D. H. (2004). New

palaeomagnetic results from the Whin Sill complex:

evidence for a multiple intrusion event and revised

virtual geomagnetic poles for the late Carboniferous

for the British Isles . Journal of the Geological

Society , 161, 927-938.

North Pennines AONB Partnership. (2004). North

Pennines. Retrieved December 8, 2012, from

northpennines.org.uk:

http://www.northpennines.org.uk/Lists/DocumentLi

brary/Attachments/97//Whin_sill_lft.pdf

SLOANE, D. J. (1991). Some physical properties of

dolerite. Tasmania Departmen of Resources and

Energy, Division of Mines and Mineral Resources.

Tasmania Department of Resources and Energy.

Distance (m) F (nT) FR- (nT)

0 49355 55

10 49357 57

20 49358 58

30 49360 60

40 49364 64

50 49364 64

60 49373 73

70 49379 79

80 49376 76

90 49383 83

100 49390 90

110 49402 102

120 49419 119

125 49443 143

130 49456 156

135 49498 198

140 49552 252

145 49655 355

150 49992 692

155 50214 914

160 49688 388

165 49354 54

170 49297 -3

175 49296 -4

180 49297 -3

190 49308 8

200 49314 14

210 49320 20

220 49328 28

230 49329 29

240 49333 33

0 49353 53

Fig.1 Overview map of the Whin Sill complex and

it’s associated dykes. The Hett Dyke can be seen in

the southeast corner of the map trending in an

ENE-WSW direction. Taken from Liss et al (2004).

Fig.2 Map of survey area around Black Hill Top Farm.

Profile is shown as black dotted line labelled P. Map data

is © Crown Copyright Ordnance Survey, An EDINA

Digimap/JISC supplied service

Survey area

2km

150m

P

Base station

(0 meters)

Table 3.0 Shows the raw magnetic data. The last

column has the regional field of 49300 nT extracted.

Fig.5 Maximum and minimum possible depths and thicknesses of theoretical dykes shown by computer modelling.

The observed anomaly is the solid line and the calculated anomaly is dashed. Fixed parameters are shown in table 1.0.

(a) Maximum depth to the top of a model dyke; d = 3.8m, w = 10m, Mr = 6.0, Ir = 88°. (b) Minimum depth to the top

of a model dyke; d = 0m, w = 6.0m, Mr = 4.4, Ir = 90°. (c) Maximum width of a model dyke; d = 0.1m, w = 13.6m, Mr

= 2.3, Ir = 85°.(d) Minimum width of a model dyke; d = 0.2m, w = 3.0m, Mr = 6.0, Ir = 85°.

a b

c d

Fig.3 Anomaly profile of the magnetic data measured along

profile P (fig.2) above. The raw data is shown in Table 3.0 above.

Fig.4 Sketch showing a how a dipping dyke can

produce an identical total field anomaly if it’s the

angle of induced magnetization is rotated with

the dip.

Fig.6 Preferred dyke model with parameters: Mr = 5.1, Ir = 90°, w = 5.0 and d = 1.0m. A number of

other satisfactory models can be produced within the maximum and minimum geometries shown in fig.5

above.

Fig.7 Map showing the Force Garth Quary. Whin Sill sequence is shown in dark shading. Map data is ©

Crown Copyright Ordnance Survey, Geological Data is © British Geological Survey, Digital geology

data, An EDINA Digimap/JISC supplied service