Airborne Gravity 2010 - Geoscience Australia

Airborne Gravity 2010
� � 2
o p
� � W ( d � d ) , (5)
d
d
2
p
where d � o
and d � are respectively predicted and input data (which are often a processed version of
the original observations), and W d is a data weighting matrix. Assuming independent errors, the
elements of W d are the inverse of the data standard deviations. The model objective function is
defined by
2
2 2 ��w(
z)
� �
�� ( �)
� � �w( z)
��
dv � lx
� � dv
x � �
V
V � � �
(6)
2
2
2 ��w(
z)
� � 2 ��w(
z)
� �
ly
� � dv � lz
dv
y
� � � z �
V � � �
V � � �
where l x , l y , and l z are the scale lengths in the three axis directions that dictate the smoothness of
the recovered model, and w (z)
is the depth weighting function.
The bounds on density contrast are usually derived from specific knowledge of the geology for the
area over which the data were acquired. For flexibility, we implement the algorithm to allow different
bounds for each individual cell. The ability to incorporate variable density bounds is important because
the density contrast varies with region in complex geologic settings. In addition, this also allows one to
"freeze" the density contrast values in certain regions by imposing a tight pair of bounds. This
flexibility, therefore, provides an alternative means to incorporate information that might be available
independently from other sources.
We use an interior-point method to perform the minimization, in which the bound constraints are
implemented by including a logarithmic barrier function (Nocedal and Wright, 1999). The solution is
obtained by a sequence of linearized sub-solutions with decreasing weights on the barrier term. We
utilize a conjugate gradient solver at each iteration for its numerical efficiency.
Field Example
We now examine the 3D inversion of a set of airborne gravity gradiometry data from an iron ore
exploration project. The data were acquired in the western part of the Quadrilátero Ferrífero in Brazil.
The iron formations within the region are localized along the Gandarela Syncline trending northeastsouthwest
(Dorr, 1965). The survey area has rugged terrain with canyons, plateaus, and valleys.
The iron ore bodies are generally shallow and can range from 25 to 150 m below the surface. The ore
deposits follow the structure of the host formation and are generally tabular and dipping southeast with
an approximate dip of 25�. The contact between the ore and host itabirite (i.e., laminated,
metamorphosed, oxide-facies iron formation) is usually abrupt. The average grade of the high-grade
ore deposits is 66% Fe, with the intermediate grade ore containing an average of 63% Fe (Dorr,
1965). The high-grade deposits are easily differentiated from the dolomitic and quartz-rich country rock
by the high density contrast. The host rocks have an average density close to 2.67 g/cm 3 , while the
density of the hematite ranges from 3 g/cm 3 to 5 g/cm 3 . The density contrast between the ore deposits
and the surrounding host rock make gravity gradiometry an ideal exploration tool.
Gravity gradient data were collected along lines spaced 100 m apart. In this study, we focus on a subarea
of 4 km by 5 km (Figure 7). The semi-draped survey had terrain clearance values from 60 to
500 m. Magnetic and LiDAR data were acquired in addition to the gravity gradient data. We have used
both the LiDAR DEM and a coarser version of this DEM to carry out separate terrain corrections.
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