- Journal: Geophysical Journal International
- PDF: paper-radial3d-gradients-2013.pdf
- doi: 10.1093/gji/ggt307

Oliveira Jr, V. C., and V. C. F. Barbosa (2013), 3-D radial gravity gradient inversion, Geophysical Journal International, 195(2), 883-902, doi:10.1093/gji/ggt307.

We have presented a joint inversion of all gravity-gradient tensor components
to estimate the shape of an isolated 3-D geological body located in subsurface.
The method assumes the knowledge about the depth to the top and density
contrast of the source. The geological body is approximated by an
interpretation model formed by an ensemble of vertically juxtaposed 3-D right
prisms, each one with known thickness and density contrast. All prisms forming
the interpretation model have a polygonal horizontal cross-section that
approximates a depth slice of the body. Each polygon defining a horizontal
cross-section has the same fixed number of vertices, which are equally spaced
from 0° to 360° and have their horizontal locations described in polar
coordinates referred to an arbitrary origin inside the polygon. Although the
number of vertices forming each polygon is known, the horizontal coordinates of
these vertices are unknown. To retrieve a set of juxtaposed depth slices of the
body, and consequently, its shape, our method estimates the radii of all
vertices and the horizontal Cartesian coordinates of all arbitrary origins
defining the geometry of all polygons describing the horizontal cross-sections
of the prisms forming the interpretation model. To obtain a stable estimate
that fits the observed data, we impose constraints on the shape of the
estimated body. These constraints are imposed through the well-known zeroth-
and first-order Tikhonov regularizations allowing, for example, the estimate of
vertical or dipping bodies. If the data do not have enough in-depth resolution,
the proposed inverse method can obtain a set of stable estimates fitting the
observed data with different maximum depths. To analyse the data resolution and
deal with this possible ambiguity, we plot the ℓ_{2}-norm of the
residuals (*s*) against the estimated volume (*v _{p}*)
produced by a set of estimated sources having different maximum depths. If this

*Perspective views of the simulated salt-dome cap rock (red wire-frame body) with depth
to the bottom at 460 m and volume 0.366 km³. Perspective views in blue prisms of the (a)
initial approximation, (b) and (c) estimated body. The estimated body in (b) and (c) is
obtained by inverting noise-corrupted synthetic data.*

@article{oliveirajr.2013a, title = {3-D radial gravity gradient inversion}, volume = {195}, issn = {0956-540X, 1365-246X}, doi = {10.1093/gji/ggt307}, number = {2}, journal = {Geophysical Journal International}, author = {Oliveira Jr, V. C. and {Barbosa}, V. C. F.}, month = sep, year = {2013}, pages = {883--902}, }