A New Scheme for Gravity Data Interpretation by a Faulted 2-D Horizontal Thin Block: Theory, Numerical Examples, and Real Data Investigation

A nonlinear optimization algorithm has been described for the inversion of gravity data profile by a faulted 2-D horizontal thin block. The algorithm simultaneously optimizes for the depth to the center (
$z$
) of the faulted block, the amount and direction of dip (
$\theta $
) of the fault plane, and the amplitude coefficient (
$A$
), which is dependent on the amount of throw
$t$
and the density contrast
$\Delta \rho $
of the block. The objective functional of this algorithm coupled with both the space of logarithmed absolute values of the observed and predicted gravity data and the space of logarithmed [
$\log (z)$
,
$\log (|A|)$
, and
$\log (\theta $
)] model parameters is the basis of the new inversion scheme introduced here. It has been found essential that the objective functional of this scheme be formulated in this particular combination so that the iterative solver/minimizer (the Gauss–Newton (GN) method) can converge. The developed scheme has been successfully verified on numerical models without noise and achieved superior convergence. It is found stable and can determine the inverse parameters of the faulted block with acceptable accuracy when applied to data contaminated with insignificant noise levels and/or geologic interference. In order to investigate the usefulness of the developed scheme, a published gravity profile has been inverted and analyzed, suggesting new results that are of some geologic significance. The computational efficiency, thorough analysis of the investigated numerical examples, and comparisons of the real data inverted in this paper have demonstrated that the scheme developed here is advantageous to the existing gravity data inversion schemes that solve for the characteristic inverse parameters of a faulted thin block.