Airborne Gravity 2010 - Geoscience Australia

Airborne Gravity 2010
Abstract
The advantages of the full tensor over Gz
Wayne Stasinowsky 1
1 Pitney Bowes Business Insight (formerly Encom Technology)
(wayne.stasinowsky@encom.com.au)
Use of the full gravity tensor provides advantages over the vertical component (Gz) in a number of
situations. Small discrete bodies such as kimberlite pipes can be directly interpreted in their correct
location even if they occur between survey lines. Interpretation of these and other bodies do not
require prior gridding and can be inverted without first levelling the data, thereby providing significant
advantages in areas with rugged terrain. Inversions are also more robust in the presence of noise and
need fewer points over the anomaly to obtain a solution.
While the tensor can be obtained from filtering a grid of any single component, the advantages are
greatest when using a directly measured tensor rather than one derived from a grid of Gz. Derived
tensors reflect the information content of the source component, and can induce artefacts in the
interpretation such as errors in position and depth of the source.
Examples of the advantages of the tensor over Gz are demonstrated through forward models and joint
inversion of synthetic multi-channel tensor data.
What is a Tensor?
Potential fields such as Gravity are vector fields. In a Cartesian coordinate system, each vector can be
represented in terms of its components in X, Y and Z-axis directions. If we consider small increments
in each of the component directions, we can visualize a tensor as the changes in each component
vector.
In Figure 1, the reference vector and tensor measuring point is at the origin (red vectors). The Xcomponent
is reduced by half as it moves in the X direction (red to yellow vectors) so Gxx equals 0.5.
The Y-component doubles when moving in the X-direction (red to yellow vectors) so Gxy equals 2.0.
However, the Z-component does not change in the X-direction, so Gxz equals 0. In the Y direction (red
to green vectors), the Y-component halves, so Gyy equals 0.5, etc.
The rate of change or gradient of each component can occur in 3 directions for each of the 3
components giving 9 elements to the tensor which can be represented as a 3 by 3 matrix as follows:
Gxx Gxy Gxz
Gyx Gyy Gyz
Gzx Gzy Gzz
In the case of potential fields, the matrix is symmetrical with Gyx equal to Gxy etc., so the lower left 3
elements are redundant. Given that potential fields satisfy the Laplace Equation, one of the 3 diagonal
elements (Gxx, Gyy or Gzz) is also redundant, leaving only 5 independent elements.
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