Geomagnetic Methods
3.8 Quantitative interpretation
3.8.2 Simple depth determinations
It is possible to obtain a very approximate estimate of depth to a magnetic body using the shape of the anomaly. By referring to either
60°
45°
30°
0°
0 100 200 300
–100 –50 0 50 100 150
Survey line position (m)
Anomaly (nT)
(A)
0 100 200 300
–100
Survey line position (m)
Anomaly (nT)
–60 –20 20
-60°
-45°
-30°
0°
(B)
Figure 3.42 Total field anomalies over a 5-m-thick dyke dipping at 45◦to the north with an east–west strike direction but with different magnetic inclinations along the 0◦Greenwich Meridian, with (A) the northern hemisphere, and (B) the southern
hemisphere, taking account changes in magnetic field strength with latitude. (C) The total field anomaly for a vertical dyke but at two different magnetic latitudes and directions, to illustrate how the magnetic anomaly over a magnetised body can become insignificant by only changing the magnetic latitude (inclination) and strike direction.
0 100 200 300
–100 –50 0 50 100 150
Survey line position (m)
Anomaly (nT)
(C)
N-S strike
I= 60°, F= 50 000 nT 45° strike
I= 30°, F= 30 000 nT
Figure 3.42 (Continued)
a simple sphere or horizontal cylinder, the width of the main peak at half its maximum value (δFmax/2) is very crudely equal to the depth to the centre of the magnetic body (Figure 3.44). In the case of a dipping sheet or prism, it is better to use a gradient method where the depth to the top of the body can be estimated. The simplest rule of thumb to determine depth is to measure the horizontal extent, d, of the approximately linear segment of the main peak (Figure 3.44). This distance is approximately equal to the depth (to within
±20%).
A more theoretically based graphical method was devised by Peters (1949) and is known as Peters’ Half-Slope method (Figure 3.45). A tangent (Line 1) is drawn to the point of maximum slope and, using a right-angled triangle construction, Line 2 with half the slope of the original tangent is constructed. Two further lines with the same slope as Line 2 are then drawn where they form tangents to the anomaly (lines 3 and 4). The horizontal distance, d, between these two tangents is a measure of the depth to the magnetic body (see Box 3.8).
Parasnis (1986) derived alternative methods of depth determina- tion for a magnetised sheet of various thicknesses and dips using the anomaly shape as well as amplitude. Given an asymmetric anomaly (Figure 3.46) over a dipping dyke of known latitude, dip and strike directions, the position of, and the depth to, the top of the dyke can be determined from the anomaly shape. If the maximum and minimum numerical values are denotedδFmax andδFmin respec- tively (i.e. irrespective of sign), the position of the centre of the top edge of the dyke is located at the position of the station where the anomaly amplitude equals the sum of the maximum and minimum values (taking note of their respective signs, positive or negative) and which lies between the maximum and minimum values. For example, ifδFmax =771 nT andδFmin = −230 nT, the position
-60° -30°
60°
A
B
C
N
F F'c
F'b F'a 150°
0 100 200 300
Survey line position (m)
Anomaly (nT)
–200 –100 100 200 300
No NRM I = -60°, D = 180°r r I = -30°, D = 0°r r I = 150°, D = 0°r r
F = 50 000 nT I = 60°
D = 0°
A B C
I
I I I I I I I I I
I
I I I I I I I I I
I
I I I I I I I I I
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I
0
Figure 3.43 Total field anomalies over a vertical dyke striking east–west with either no remanent magnetisation (∗), or remanent magnetisation of 150 nT in three directions as indicated by the schematic vector diagram.
of the centre of the dyke would be located whereδF =771−230 nT=541 nT. Expressions from which the depth to the top of the dipping sheet can be derived (see Box 3.9) relate the amplitudes of the minimum and maximum values and their respective sepa- rations. Expressions for thick dipping sheets and other models are much more complicated to calculate and are not discussed further here. Derivations of mathematical expressions and full descriptions of methods to determine shape parameters for a variety of dip- ping sheet-like bodies have been given by Gay (1963), ˚Am (1972),
d
x δF
δFmax
ω≈ z and d ≈ z ω
δFmax/2
Figure 3.44 Simple graphical methods to estimate the depth to the top of a magnetised body.
Parasnis (1986) and Telford et al. (1990), for example. Manual cal- culation of parameters has been largely superseded by the ease with which computer methods can be employed.
For the analysis of aeromagnetic data and where source structures have vertical contacts, there is no remanent magnetisation and the magnetisation is either vertical or has been reduced to the pole (see the next section), the magnetic tilt-depth method can be used to derive estimates of the depth to the magnetised structure (Salem et al., 2007). The magnetic tilt angle is a normalised derivative based upon the ratio of the vertical and horizontal derivatives of the Re- duced to the Pole field (RTP), as described originally by Miller and Singh (1994); the expressions for these two derivatives have been de- scribed by Nabighian (1972). In short, the tilt angle (θ) is restrained between±90◦and is equal to the arc tangent of the ratio of the horizontal distance (h) and depth to the magnetised structure (z), i.e. tanθ=h/z. The location at which the tilt angle becomes zero lies over the vertical contact (Figure 3.47). The depth to the magnetised structure is equivalent to half the horizontal distance between the
±45◦contours of the tilt angle profile. The method can be applied to aeromagnetic data to produce maps of the tilt angle from which the locations at whichθ=0◦can be determined (the 0◦contour on a tilt angle map), and the corresponding distances between the +45◦and−45◦contours computed, from which values of z can be derived (see also the paper by Salem et al., 2008). This method is most suited to the analysis of aeromagnetic data for hydrocarbon exploration or large-scale regional geological studies, and is less useful for mineral exploration unless the qualifying criteria apply and the scale of the targets is large enough.
0 10 20 30 40 50 3
2 1
4
d
Magnetic anomaly
Field intensity (nT)
60
Distance (m)
70 80 90 100 110 120 130
Figure 3.45 Peters’ Half-Slope method of determining the depth to the top of a magnetised dyke (see text for further details).
Box 3.8 Peters’ Half-Slope method of depth determination (see Figure 3.45)
The depth (z) to the top of the magnetised body is:
z=(d cosα)/n
where d is the horizontal distance between half-slope tangents;
1.2≤n≤2, but usually n=1.6;αis the angle subtended by the normal to the strike of the magnetic anomaly and true north.
Example: If d=24 m, n=1.6 andα=10◦, then z≈15 m.