Airborne Gravity 2010 - Geoscience Australia

Airborne Gravity 2010
where is an observation point, and integration is conducted over the variable . The derivatives of
the gravity field form a gravity gradient tensor:
where:
, (14)
for . Expressions for the gravity gradient tensor components can be calculated based on
equations (13) and (15):
where the kernels are equal to:
for . To evaluate numerical expressions for the gravity field and tensors, the 3D earth
model is discretized into a regular rectangular grid of cells where we assume that the density is
constant within each cell, resulting in a discrete form of equations (13) and (16); for example:
The integration of the Green’s function may be evaluated either analytically (e.g., Li and Chouteau,
1997) or numerically. The latter presents opportunity for choosing a desired accuracy at the expense
of speed. For airborne surveys, the errors of using a single point Gaussian integration are insignificant
compared to the analytic equivalent (Zhdanov et al., 2004). For borehole surveys, higher order
Gaussian integration can be used. Equation (18) then reduces to:
where the gravity field kernel is:
The same approach can be used to compute the gravity tensor components. Thus, the discrete
forward modeling operators for the gravity field and its gradients can be expressed in matrix notation:
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(15)
(16)
(17)
(18)
(19)
(20)
(21)