Interactive gravity inversion

Geophysics, 2011

We applied the mathematical basis of the total variation ͑TV͒ regularization to analyze the physicogeologic meaning of the TV method and compared it with previous gravity inversion methods ͑weighted smoothness and entropic Regu-larization͒ to estimate discontinuous basements. In the second part, we analyze the physicogeologic meaning of the TV method and compare it with previous gravity inversion methods ͑weighted smoothness and entropic regularization͒ to estimate discontinuous basements. Presenting a mathematical review of these methods, we show that minimizing the TV stabilizing function favors discontinuous solutions because a smooth solution, to honor the data, must oscillate, and the presence of these oscillations increases the value of the TV stabilizing function. These three methods are applied to synthetic data produced by a simulated 2D graben bordered by step faults. TV regularization and weighted smoothness are also applied to the real anomaly of Steptoe Valley, Nevada, U.S.A. In all applications, the three methods perform similarly. TV regularization, however, has the advantage, compared with weighted smoothness, of requiring no a priori information about the maximum depth of the basin. As compared with entropic regularization, TV regularization is much simpler to use because it requires, in general, the tuning of just one regularization parameter.

Geophysics, 2006

We present a method for inverting magnetic data with interfering anomalies produced by multiple complex 2D magnetic sources having arbitrary shapes and known magnetization vectors. Our method is stable and can recover a complex 2D magnetization distribution, leading to a reliable delineation of sectionally homogeneous sources with complex shapes. Our method, although similar to interactive forward modeling, is unique in that it automatically fits the observations and only requires that the interpreter know the outlines of the sources expressed by simple geometric elements such as points and line segments. Each geometric element operates as a skeletal outline of a particular homogeneous section of the magnetic source to be reconstructed. Also, the interpreter can define the geometric elements interactively without worrying about data fitting because data are fit automatically. The examples with synthetic data illustrate the good performance of the method in mapping the complex geometry of magnetic sources. The solution sensitivity to uncertainties in the a priori information shows that to produce good results, the uncertainty on the magnetization intensity of each homogeneous extent of the source should be smaller than 40%.Awrong magnetization vector direction can be detected easily because it often leads to poor data fitting and to estimated sources with abrupt borders. The method is also applied to two sets of real data from the Northwest Ore Body at Iron Mountain Mine, Missouri, and the Hatton-Rockall Basin in the northeast Atlantic Ocean. The estimated magnetization distribution in all tests demonstrates a good correlation of estimated magnetic sources with corresponding known geologic features.

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 Prospecting, 2012

Nonparametric inverse methods provide a general framework for solving potentialfield problems. The use of weighted norms leads to a general regularization problem of Tikhonov form. We present an alternative procedure to estimate the source susceptibility distribution from potential field measurements exploiting inversion methods by means of a flexible depth-weighting function in the Tikhonov formulation. Our approach improves the formulation proposed by Li and Oldenburg (1996, 1998), differing significantly in the definition of the depth-weighting function. In our formalism the depth weighting function is associated not to the field decay of a single block (which can be representative of just a part of the source) but to the field decay of the whole source, thus implying that the data inversion is independent on the cell shape. So, in our procedure, the depth-weighting function is not given with a fixed exponent but with the structural index N of the source as the exponent. Differently than previous methods, our choice gives a substantial objectivity to the form of the depth-weighting function and to the consequent solutions. The allowed values for the exponent of the depth-weighting function depend on the range of N for sources: 0 ≤ N ≤ 3 (magnetic case). The analysis regarding the cases of simple sources such as dipoles, dipole lines, dykes or contacts, validate our hypothesis. The study of a complex synthetic case also proves that the depth-weighting decay cannot be necessarily assumed as equal to 3. Moreover it should not be kept constant for multi-source models but should instead depend on the structural indices of the different sources. In this way we are able to successfully invert the magnetic data of the Vulture area, Southern Italy. An original aspect of the proposed inversion scheme is that it brings an explicit link between two widely used types of interpretation methods, namely those assuming homogeneous fields, such as Euler deconvolution or depth from extreme points transformation and the inversion under the Tikhonovform including a depth-weighting function. The availability of further constraints, from drillings or known geology, will definitely improve the quality of the solution.

Brazilian Journal of Geology

The Santos Basin, with an area of about 350.000 km 2 , is the largest salt basin of the South Atlantic, and due to its high economic hydrocarbon potential, it is a recurrent theme in scientific studies. The salt structures over the region present great importance for hydrocarbon accumulation and the geological/geophysical studies are performed from seismic reflection data, which requires time and efforts for acquisition and data processing. We identify salt structures using a new workflow based on inversion of residual gravity anomalies, where we use the Moho and basement depths obtained from gravity inversion, followed by the calculation of the gravity residual anomaly, assumed to be representative of the salt structures. This workflow is tested for a geological profile in the Santos Basin, and the results are evaluated along a 2D seismic section tied to well markers. The geometry of the stratified salt obtained from gravity inversion correlates with the seismic interpretation, with the advantage of estimating the entire salt package, including halite and stratified salt. With only seismic data, sometimes the stratified salt can be misinterpreted as sediments. The procedure can be applied to identify salt in sedimentary basins where seismic data is unavailable or of low quality.