EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Field surveying and corrections: Survey procedures Noise and corrections Anomalous total field strength δF

Analyses of magnetic anomalies General concepts Mathematical derivation of horizontal and vertical dipole components Depth estimates (symmetric asymmetric profiles)

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-01

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic As with any geophysical survey, correct station determination is crucial. Similar to gravity surveys, magnetic surveys require a base station. A dedicated magnetometer could be deployed for continuous readings of the natural variations in the Earth’s magnetic field, or a regular return with the profiling magnetometer to a base station can be performed. In case of airborne magnetic surveys returning to a base station is often not possible. This problem is overcome by flying in a regular pattern with tie-lines, where the crossing points are used to correct for natural variations in the field. It is important to check data immediately in the field, especially to avoid spatial aliasing. If a station spacing appears not to produce meaningful results, a finer spacing may be tried. In case of airborne or ship-based surveys these parameters are not easily adjustable and are often pre-arranged in a contract. However, Reid (1980) developed a set of guidelines of how to measure aliasing as function of flying-height (h) and line spacing (δx). EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-02

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Spatial aliasing in airborne surveys for the total field Ft and the vertical gradient Fg: h / δx

Ft

Fg

0.25

21

79

0.5

4.3

39

1

0.19

5

2

0.0003

0.03

4

0

0

Recommended line spacing (δx) as function of height: What is measured

Purpose

δx

Total field

Regional contour map

2h

Total field

Computation of gradients

h

Vertical gradient

Vertical gradient map

h

Total field

Single anomalies

h/2

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-03

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Noise: Basically anything metallic (e.g. watch, knife, key-chain) near the magnetometer creates distortion of the measurements and is generating noise. It is important to have no such objects on you when doing a magnetic survey and if surveyors are switched throughout a survey, it is important to maintain a consistent style of measurement as well as avoiding metallic objects. Passing trucks or unknown underground pipes or buried objects can (if they are not the target) create noise in the survey (if e.g. a regional map of the geology is to be created). The most significant variation to catch are those of the diurnal variations of the Earth magnetic field. Typically the base-station magnetometer will record these variations, which will have to be subtracted later from the measured profile.

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-04

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic 95

Datum of survey 90

Magnetic file dstrength (nT)

85

diurnal drift correction 80

75

70

65

60 0

2

4

6

8

10

12

14

Time during the day (hrs)

Demonstration of correction for diurnal variation in magnetic field. EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-05

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Correction for latitude/longitude The Earth’s magnetic field varies from 25,000 nT at the equator to almost 69,000 nT at the poles. This change in field strength needs to be taken into account if regional surveys are conducted over larger areas. Survey data at a given location can be corrected by subtracting the theoretical value (Fth) obtained form the International Geomagnetic Reference Field (IGRF) from the observed data value (Fobs). This works well if you are near such a reference station, but often the IGRF is too crude. Instead it may be easier to determine the gradients of the magnetic field strength with latitude (φ) and longitude (θ) directly from the measured data (δF/δφ, δF/δθ). These gradients are typically expressed in nT/km. For example in Great Britain gradients of 2.13 nT/km north and 0.26 nT/km west are used.

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-06

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Anomalous total field strength: δF = Fobs – Fdrift - (F0 + δF/δφ + δF/δθ)

[nT]

(EQ 2.7)

Where Fobs is the measured data value, F0 is the value of the base station, and the gradients for latitude and longitude. Fdrift is the term accounting for the natural diurnal variation/drift in the Earth’s magnetic field. Example: F0 = 49,000 nT; δF/δφ = 2.13 nT/km, δF/δθ = 0.26 nT/km, Fobs = 50248 nT If the station is located 15 km north and 18 km west of the base station and the diurnal correction is 100 nT, the magnetic anomaly δF is equal to: δF = 50248 - 100 - (49500 + 2.13·15 + 0.26·18) nT = 611 nT EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-07

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Similar to gravity survey, a regional trend may be removed from the data to isolate magnetic anomalies:

From Reynolds, 1997 EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-08

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic

How is a measured magnetic profile related to a dipole in the subsurface?

From Reynolds, 1997

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-09

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic This similarity between gravitational and magnetic field suggests that the magnetic potential must be inversely proportional to the distance between the two poles: ⎛μ ⎞M V =⎜ 0 ⎟ a ⎝ 4π ⎠ d (EQ 2.8) The bar magnet produces a magnetic field around itself that exerts force to any magnetic pole that is placed in its neighborhood. The potential of the north pole is by definition positive, and that of the south pole is negative. In the figure below a bar magnet of length d and magnetic pole strength m is shown. The point A is located at a distance r from the centre of the bar magnet , having distances r1 and r2 to the poles. The magnetic potential at A can then be defined as:

⎛μ ⎞ ⎛ 1 1⎞ V = ⎜ 0 ⎟m⎜⎜ − ⎟⎟ ⎝ 4π ⎠ ⎝ r2 r1 ⎠

(EQ 2.9)

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-10

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Using the last diagram, we can express the distances r1 and r2 in terms of r and the angle θ:

⎛μ ⎞ d V = ⎜ 0 ⎟m 2 cos θ ⎝ 4π ⎠ r

(EQ 2.10)

Using the definition of the magnetic dipole moment (p): we get:

v ⎛ μ 0 ⎞ p cos θ V =⎜ ⎟ 2 ⎝ 4π ⎠ r

v p = m⋅d

(EQ 2.11)

We want to calculate the horizontal and vertical component of the field that we can measure in the field with a magnetometer.

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-11

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic From the diagram we see that: y cos θ = r Substituting this into the equation for the magnetic potential yields:

⎛μ V = −⎜ 0 ⎝ 4π

y ⎞ v ⋅ p ⎟ ⎠ x2 + y2

(

(EQ 2.12)

)

3/ 2

To calculate the vertical component of the magnetic field we take the derivative with respect to y: Horizontal and vertical components of a vertical dipole EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

dV Fy = − dy EPS435-Potential-05-12

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Applying this yields:

y ⎛ μ 0 ⎞ v d ⎛⎜ Fy = ⎜ ⎟p ⎝ 4π ⎠ dy ⎜⎝ x 2 + y 2

(

⎛μ ⇔⎜ 0 ⎝ 4π

1 ⎞ v ⎡⎛⎜ ⎟ p⎢ ⎠ ⎢⎣⎜⎝ x 2 + y 2

(

(

)

3/ 2

)

2 ⎞ ⎛ 3 y ⎟−⎜ ⎟ ⎜ x2 + y2 ⎠ ⎝

⎛ μ 0 ⎞ v ⎛⎜ x 2 + y 2 − 3 y 2 ⇔⎜ ⎟p 5/ 2 π 4 ⎝ ⎠ ⎜⎝ x 2 + y 2

(

)

3/ 2

⎞ ⎟ ⎟ ⎠

(

) ⎞⎟ ⇔ ⎛⎜ μ

)

5/ 2

⎞⎤ ⎟⎥ ⎟⎥ ⎠⎦

⎞ v x2 − 2y2 ⎟p 5/ 2 π 4 ⎝ ⎠ x2 + y2

⎟ ⎠

0

(

)

Lets define the depth of the dipole as d:

⎛ μ 0 ⎞ v x 2 − 2d 2 Fy = ⎜ ⎟p 5/ 2 ⎝ 4π ⎠ x 2 + d 2

(

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

)

(EQ 2.13) EPS435-Potential-05-13

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Similarly we can derive the horizontal component Fx of the magnetic field:

Fx = −

dV dx

y ⎞ v d ⎛⎜ p ⎟ 3/ 2 ⎠ dx ⎜⎝ x 2 + y 2 ⎤ 3 xy ⎛ μ0 ⎞ v ⎡ ⇔ −⎜ ⎟ p⎢ 5/ 2 ⎥ 2 2 ⎝ 4π ⎠ ⎢⎣ x + y ⎥⎦

⎛μ ⇔ −⎜ 0 ⎝ 4π

(

⎞ ⎟ ⎟ ⎠

)

(

)

Defining the depth of the dipole as d yields:

⎛μ Fx = −⎜ 0 ⎝ 4π

3xd ⎞ v⎡ p ⎟ ⎢ ⎠ ⎢⎣ x 2 + d 2

(

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

⎤ 5/ 2 ⎥ ⎥⎦

)

(EQ 2.14)

EPS435-Potential-05-14

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic In the case of a horizontal dipole: cos θ = x

r

Thus we get:

⎛μ V = −⎜ 0 ⎝ 4π

x ⎞ v ⋅ p ⎟ ⎠ x2 + y2

(

)

3/ 2

Without detailed derivation, we can show that the horizontal and vertical component of the magnetic field of a horizontal dipole are given by:

⎛μ Fx = −⎜ 0 ⎝ 4π Horizontal and vertical components of a horizontal dipole EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

⎞ v d 2 − 2x 2 ⎟p 5/ 2 ⎠ x2 + d 2

(

)

3 xd ⎛μ ⎞ v Fy = ⎜ 0 ⎟ p ⎝ 4π ⎠ x 2 + d 2

(

(EQ 2.15)

)

5/ 2

EPS435-Potential-05-15

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic In geomagnetic anomaly analyses, the shape of the magnetic profile is regularly exploited to determine the depth of a magnetizes body, similarly to the gravity method. Two simple rules were developed to estimate the depth: (a) Peter’s half-slope method (Peters, 1949) (b) Parasnis’ method (Parasnis, 1986) A more complex approach is forward modeling using a computer and a function describing a dipole at the subsurface (similar to those derived earlier).

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-16

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Peter half-slope method A tangent is drawn (line 1) to the point of maximum slope, and a second line (line 2) is constructed with half that slope of that of the first line. Two additional lines (line 3, 4) are drawn with the half-slope value where they fit the observed profile. The horizontal distance (d) between the intersection point of the two additional tangents is a measure for the depth (z) to the magnetized body: z = (d cos α) / n

(EQ 2.16)

Where 1.2 ≤ n ≤ 2.0 (typically n = 1.6), and α is the angle subtended by the normal of the strike of the magnetic anomaly and true north.

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-17

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic

From Reynolds, 1997 EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-18

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic Parasnis’ method A different technique was proposed by Parasnis (1986). This method aims a asymmetric profiles, but simplifies tremendously for a symmetric profile. For an asymmetric profile as shown on the next page, the depth to the anomaly is: z = (- x1· x2) ½

(EQ 2.17)

In case of a symmetric anomaly, the depth simply becomes half of the width of the anomaly at half the maximum value: z=w/2

(EQ 2.18)

For use of symbols, see figure on next page.

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-19

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic (1) Asymmetric profile

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-20

EPS – 435

Geophysical Applications

Potential field methods - Geomagnetic (1) Symmetric profile

EPS435 – Fall 2008 Dr. Michael Riedel [email protected]

EPS435-Potential-05-21