A New Approach to Compact Gravity Inversion Algorithm
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Date
2021-06-28
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Addis Ababa University
Abstract
The gravity method is one of the geophysical methods that has been used in a
wider range of geophysical prospecting and investigations. One of the indispensable
steps in this method is the inverse modelling of the measured data to estimate the
subsurface density distribution and geometrical properties (e.g. shape and depth) of the
causative bodies. Particularly, delineating localized and blocky geologic features,
through the inversion of gravity data is an important goal in a range of geophysica l
investigations and it is still a subject of interest and concern in the scientific communit y.
Most conventional inversion algorithms generally yield smooth models with poor edge
definition. These methods have difficulties in recovering non-smooth distributions that
have sharp boundaries. The main objective of this thesis was then to develop and
implement a gravity inversion algorithm that can produce compact and sharp images,
aiming at recovering localized and blocky geologic features with varying geometric
representations. In the course of the thesis work, this goal has been achieved by
presenting a gravimetric inverse modelling method that has been tested to be effective.
At the heart of the developed inversion method lies the usage of the 𝐿0-norm
minimization of the objective function, which consists of data misfit and L0-norm
stabilizing function, by an efficient iteratively reweighted least-squares (IRLS)
algorithm. As a major contribution, the presented method incorporates three novel
technical advancements. At first, the method incorporates an auto-adaptive
regularization technique, which automatically determines a suitable regulariza t ion
parameter, and a modified error weighting function that helps to improve both the
stability and convergence of the method. The other advantage of the auto-adaptive
regularization technique and error weighting matrix is that they are not wholly
dependent on the known noise level. Because of that, the method can yield reasonable
results even when the noise level of the data is not properly known.
The other major contribution is the use of a new depth weighting function. The
advantages of the newly proposed depth-weighting function can be summarized as
follows: (I) It properly counteracts the gravity kernel decay, so that the inversion results
can provide realistic depth information. (II) It avoids the selection of the depth
weighting function parameters through trial and error, which was common in the
traditional methods, through the usage of automated parameters selection techniques.
Especially, this has a significant advantage when there is no prior depth informa t ion
that helps to choose the optimum parameter in using the traditional depth weighting
function.
Furthermore, to achieve geologically plausible results and also reduce solution
ambiguity, a physical parameter inequality constraint algorithm has been developed and
employed to constrain the obtained density contrast values.
Finally, the implementation of an effectively combined stopping criterion has
been used to terminate the iterative inversion procedure, when geologically viable
solutions are obtained. The proposed combined termination criteria are shown to
outperform traditional termination criteria, used in most iterative geophysical invers ion
algorithms, through the modeling of synthetic and published measured data
To test the new method, forward and inverse modeling codes were written using
Python programming in a Linux environment. The validity of the overall Python codes,
and the practicality and efficiency of the presented inversion method were tested by
inverting a number of synthetic data sets from geometrically complex bodies and field
data sets from different geological settings. The results of the inversion confirmed the
capability of the developed inversion method in producing geologically acceptable
compact and sharp models that define the shape, location, and density distribution of
the causative subsurface bodies. This proves, the reliability and effectiveness of the
developed inversion method in practical applications to delineate sharp discontinuit ies
and blocky features such as distinct layering or formation of localized bodies in the
subsurface.
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Keywords
Gravity Data, Inverse Modeling, Regularization, Compact and Sharp Image