The use of curvature in potentialfield interpretation

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The use of curvature in potential-field
interpretation Exploration Geophysics, 2007, 38,
111119 Phillips, Hansen, Blakely Abstract.
Potential-field anomalies can be transformed into
special functions that form peaks and ridges over
isolated sources. All special functions have a
common mathematical form over an isolated source,
which leads to a common equation for estimating
the source depth from the peak value and the
curvature at the peak. Model-specific special
functions, usually calculated from a transformed
version of a potential field, are used to
estimate the locations of very specific source
types. Model-independent special functions
calculated from an observed or transformed
potential field can be used to estimate the
locations of a variety of source types. Vertical
integration is a particularly useful
transformation for reducing the effects of noise
and increasing the coherency of solutions from
model-independent special functions. For gridded
data, the eigenvalues and eigenvectors of the
curvature matrix associated with a quadratic
surface that is fitted to a special function
within 33 windows can be used to locate the
sources and estimate their depths and strikes.
Discrete source locations estimated in this
manner can be connected into lines that follow
contacts, faults, and other mappable features
based on distance and azimuth criteria. These
concepts are demonstrated on aeromagnetic data
from the Albuquerque basin of New Mexico, USA.
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The use of curvature in potential-field
interpretation, Exploration Geophysics, 2007, 38,
111119. Phillips, Hansen, Blakely.
4
The use of curvature in potential-field
interpretation, Exploration Geophysics, 2007, 38,
111119. Phillips, Hansen, Blakely.
5
The use of curvature in potential-field
interpretation, Exploration Geophysics, 2007, 38,
111119. Phillips, Hansen, Blakely.
6
The use of curvature in potential-field
interpretation, Exploration Geophysics, 2007, 38,
111119. Phillips, Hansen, Blakely.
7
The use of curvature in potential-field
interpretation, Exploration Geophysics, 2007, 38,
111119. Phillips, Hansen, Blakely.
8
The use of curvature in potential-field
interpretation, Exploration Geophysics, 2007, 38,
111119. Phillips, Hansen, Blakely.
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The use of curvature in potential-field
interpretation, Exploration Geophysics, 2007, 38,
111119. Phillips, Hansen, Blakely.
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From The use of curvature in potential-field
interpretation Exploration Geophysics, 2007, 38,
111119. Phillips, Hansen Blakely.
Comparison of results A composite view of the
estimated contact and fault locations (Figure 4d)
shows how the total gradient solutions from the
half vertical integral of the TMI (in green) and
the local wavenumber solutions from the first
vertical integral of the TMI (in blue) typically
plot close together. The horizontal gradient
solutions from the reduced-to-pole field (in red)
tend to be the most coherent and most easily
interpreted. They are typically offset from the
blue and green solutions, most likely due to
non-vertical dips on the faults and contacts.
Model studies (Phillips, 2000) indicate that, for
magnetisations collinear with the inducing
field, the offset of the HGM solutions should be
in the down-dip direction.
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From Phillips USGS_SFDEPTH GX as implemented
in Oasis Montaj The following model-specific
special functions are supported
Assumed_Source_Type SI Transform
Model-Specific_Special_Function Vertical_Magnetic
_Contact 0 RTP HGM of RTP
magnetic field Vertical Magnetic Sheet 1
RTP ABS of RTP magnetic
field Horizontal Magnetic Sheet 1 RTPVI
HGM of VI of RTP magnetic field Horizontal
Magnetic Line 2 RTPVI ABS of VI of
RTP magnetic field Vertical Magnetic Line
2 RTPVI ABS of VI of RTP magnetic
field Magnetic Dipole 3
RTPVI ABS of VI of RTP magnetic
field Vertical Density Contact -1 VD
HGM of VD of gravity field Vertical
Density Sheet 0 VD ABS
of VD of gravity field Horizontal Density Sheet
0 None HGM of gravity
field Horizontal Density Line 1 None
ABS of gravity field Vertical Density Line
1 None ABS of gravity
field Point Mass 2
None ABS of gravity field Model-independe
nt special functions include the Total Gradient
(TG) and the Local Wavenumber (LW). These are
calculated directly from the potential field or
from a vertical integral (VI) of the potential
field. The total gradient requires that a
structural index (SI) be assumed for the source.