3D gravity inversion by planting anomalous densities

Geophysics, 2012

We have developed a new gravity gradient inversion method for estimating a 3D density-contrast distribution defined on a grid of rectangular prisms. Our method consists of an iterative algorithm that does not require the solution of an equation system. Instead, the solution grows systematically around user-specified prismatic elements, called “seeds,” with given density contrasts. Each seed can be assigned a different density-contrast value, allowing the interpretation of multiple sources with different density contrasts and that ...

Geophysics, 2009

We have developed a gravity inversion method to estimate a 3D density-contrast distribution producing strongly interfering gravity anomalies. The interpretation model consists of a grid of 3D vertical, juxtaposed prisms in the horizontal and vertical directions. Iteratively, our approach estimates the 3D density-contrast distribution that fits the observed anomaly within the measurement errors and favors compact gravity sources closest to prespecified geometric elements such as axes and points. This method retrieves the geometry of multiple gravity sources whose density contrasts ͑positive and negative values͒ are prescribed by the interpreter through the geometric element. At the first iteration, we set an initial interpretation model and specify the first-guess geometric elements and their target density contrasts. Each geometric element operates as the first-guess skeletal outline of the entire homogeneous gravity source or any of its homogeneous parts to be reconstructed. From the second iteration on, our method automatically redefines a new set of geometric elements, the associated target density contrasts, and a new interpretation model whose number of prisms increases with the iteration. The iteration stops when the geometries of the estimated sources are invariant along successive iterations. Tests on synthetic data from geometrically complex bodies and on field data collected over a mafic-ultramafic body and a volcanogenic sedimentary sequence located in the Tocantins Province, Brazil, confirmed the potential of our method in producing a sharp image of multiple and adjacent bodies.

Geophysical Journal International, 2011

We present a gravity-inversion method for estimating the geometry of an isolated 3-D source, assuming prior knowledge about its top and density contrast. The subsurface region containing the geological sources is discretized into an ensemble of 3-D vertical prisms juxtaposed in the vertical direction of a right-handed coordinate system. The prisms' thicknesses and density contrasts are known, but their horizontal cross-sections are described by unknown polygons. The horizontal coordinates of the polygon vertices approximately represent the edges of horizontal depth slices of the 3-D geological source. The polygon vertices of each prism are described by polar coordinates with an unknown origin within the prism. Our method estimates the horizontal Cartesian coordinates of the unknown origin and the radii associated with the vertices of each polygon for a fixed number of equally spaced central angles from 0 o to 360 o . By estimating these parameters from gravity data, we retrieve a set of vertically stacked prisms with polygonal horizontal sections that represents a set of juxtaposed horizontal depth slices of the estimated source. This set, therefore, approximates the 3-D source's geometry. To obtain stable estimates we impose constraints on the source shape. The judicious use of first-order Tikhonov regularization on either all or a few parameters allows estimating both vertical and inclined sources whose shapes can be isometric or anisometric. The estimated solution, despite being stable and fitting the data, will depend on the maximum depth assumed for the set of juxtaposed 3-D prisms. To reduce the class of possible solutions compatible with the gravity anomaly and the constraints, we use a criterion based on the relationship between the datamisfit measure and the estimated total-anomalous mass computed along successive inversions, using different tentative maximum depths for the set of assumed juxtaposed 3-D prisms. In applying this criterion, we plotted the curve of the estimated total-anomalous mass m t versus data-misfit measure s for the range of different tentative maximum depths. The tentative value for the maximum depth producing the smallest value of data-misfit measure in the m t ×s curve is the best estimate of the true (or minimum) depth to the bottom of the source, depending on whether the true source produces a gravity anomaly that is able (or not) to resolve the depth to the source bottom. This criterion was theoretically deduced from Gauss' theorem. Tests with synthetic data shows that the correct depth-to-bottom estimate of the source is obtained if the minimum of s on the m t × s curve is well defined; otherwise this criterion provides just a lower bound estimate of the source's depth to the bottom. These synthetic results show that the method efficiently recovers source geometries dipping at different angles. Test on real data from the Matsitama intrusive complex (Botswana) retrieved a dipping intrusion with variable dips and strikes and with bottom depth of 8.0 ± 0.5 km.

GEOPHYSICS, 1998

We present two methods for inverting surface gravity data to recover a 3-D distribution of density contrast. In the first method, we transform the gravity data into pseudomagnetic data via Poisson’s relation and carry out the inversion using a 3-D magnetic inversion algorithm. In the second, we invert the gravity data directly to recover a minimum structure model. In both approaches, the earth is modeled by using a large number of rectangular cells of constant density, and the final density distribution is obtained by minimizing a model objective function subject to fitting the observed data. The model objective function has the flexibility to incorporate prior information and thus the constructed model not only fits the data but also agrees with additional geophysical and geological constraints. We apply a depth weighting in the objective function to counteract the natural decay of the kernels so that the inversion yields depth information. Applications of the algorithms to synthet...

2014

Applying 2D algorithms for inverting the potential field data is more useful and efficient than their 3D counterparts, whenever the geologic situation permits. This is because the computation time is less and modeling the subsurface is easier. In this paper we present a 2D inversion algorithm for interpreting gravity data by employing a set of constraints including minimum distance, smoothness, and compactness. Using different combination of these constraints provide either smooth images of the underground geological structures or models with sharp geological boundaries. We model the study area by a large number of infinitely long horizontal prisms with square cross-sections and unknown densities. The final density distribution is obtained by minimizing an objective function that is composed of the model objective function and equality constraints, which are combined using a Lagrangian multipliers. Each block's weight depends on depth, a priori information on density and the all...