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| Titel |
An improvement approach to the interpretation of magnetic data |
| VerfasserIn |
H. L. Zhang, X. Y. Hu, T. Y. Liu |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250059971
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| Zusammenfassung |
| There are numerous existing semi-automated data processing approaches being implemented
which specialize in edge and depth of potential field source. The mathematical expression of
tilt-angle has recently been developed into a depth-estimation routine, known as
“tilt-depth”.
The tilt-depth was first introduced by Salem et al (2007) based on the tilt-angle which use
first-order derivative to detect edge. In this paper, we propose the improvement on the
tilt-depth method, which is based on the second-order derivatives of the reduced to pole
(RTP) magnetic field, called edge detection and depth estimation based on vertical
second-order derivatives (V2D-depth).
Under certain assumptions such as when the contacts are nearly vertical and infinite depth
extent and the magnetic field is vertical or RTP, the general expression published by
Nabighian (1972) for the magnetic field over contacts located at a horizontal location of x=0
and at a depth of z0 is
( )
–x–-
ΔT (x,z) = 2kFc-
arctan z0 - z
(1)
Where kis the susceptibility contrast at the contact, F the magnitude of the magnetic field,
c = 1 - cos2i -
sin2A, A the angle between the positive h-axis and magnetic north, i the
inclination of earth’s field.
The expressions for the vertical and horizontal derivatives of the magnetic field can be
written as
-ΔT–= 2kF c-
–-z0–-z–-
-h x2 +(z0 - z)2
(2)
-ΔT–= 2kF c-
––– x––
-z x2 +(z0 - z)2
(3)
Based on Equations 2 and 3, we have
2
Tzz = --ΔT-= 2kF c-
–-2x(z0–-z)–
-z2 [x2 + (z0 - z)2]2
(4)
2 2 2
Tzh = --ΔT-= 2kF c-
-(z0 –z)–-x-2
-z-h [x2 + (z0 - z)2]
(5)
° –––– x2 + (z - z)2
TzG = Tz2h +T 2zz = 2kFc -
–––-0––2-
[x2 + (z0 - z)2]
(6)
Using Equations 4, 5 and 6, when z=0, we can get
Tzz x
T–-+-T–= z-
zG zh 0
(7)
The V2D-depth is defined as
( T ) ( x )
θ = tan- 1 ––zz–- = tan-1 –
TzG + Tzh z0
(8)
The V2D-depth amplitudes are restricted to values between –45Ë and +45Ë . It has the same
interesting properties like the tilt-depth. Its responses vary from negative to positive. Its value
is negative when outside the source region, passes through zero when over, or near, the edge,
and is positive when over the source. This can not only outline edge but also indicate the
relative magnetization contrast. As we know that tilt-depth which use the zero amplitude of
first-order vertical derivative for edge detection is not the best. The tilt-depth calculates
the depth to top by measuring the physical distance between tilt-angle pairs, with
particular emphasis on the locus of the complementary 0Ë and ±45Ë pairs. As
Ahmed Salem et al pointed out in 2007, because of the anomaly interference and the
breakdown of the two dimensionality assumption, the distance between the two ±45Ë
contours and the 0Ë contours is not everywhere identical around the perimeter of each
body.
Comparison with the tilt-depth approach, this V2D-depth method can obtain a clearer
field source edge and inverse a more realistic depth, while it also overcomes the interference
by superimposed anomaly which tilt-depth approach does. The numerical experiment shows
the method is effective. |
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