Linear inversion of gravity data for 3-D density distributions

Abstract

We have developed an improved Levenburg‐Marquart technique to rapidly invert Bouguer gravity data for a 3-D density distribution as a source of the observed field. This technique is designed to replace tedious forward modeling with an automatic solver that determines density models constrained by geologic information supplied by the user. Where such information is not available, objective models are generated. The technique estimates the density distribution within the source volume using a least‐squares inverse solution that is obtained iteratively by singular value decomposition using orthogonal decomposition of matrices with sequential Householder transformations. The source volume is subdivided into a series of right rectangular prisms of specified size but of unknown density. This discretization allows the construction of a system of linear equations relating the observed gravity field to the unknown density distribution. Convergence of the solution to the system is tightly controlled by a damping parameter which may be varied at each iteration. The associated algorithm generates statistical measures of solution quality not available with most forward methods. Along with the ability to handle large data sets within reasonable time constraints, the advantages of this approach are: (1) the ease with which pre‐existing geological information can be included to constrain the solution, (2) its minimization of subjective user input, (3) the avoidance of difficulties encountered during wavenumber domain transformations, and (4) the objective nature of the solution. Application to a gravity data set from Hamilton County, Indiana, has yielded a geologically reasonable result that agrees with published models derived from interpretation of gravity, magnetic, seismic, and drilling data.

A three‐dimensional gravity inversion applied to São Miguel Island (Azores)

“…Such an interpretation must be considered as nonunique for two reasons: First, there is a fundamental nonuniqueness in potential field inversion, and second, gravity data are generally measured only on discrete points and are subject to experimental errors. For the first problem, the challenge is to develop spectral approach [Xia and Sprowl, 1992 [Bear et al, 1995;Burkhard and Jackson, 1976]. There are other approaches which account for concepts of information theory and which are able to determine geometric and density parameters simultaneously [Tarantola, 1987;Strykowski, 1995].…”

3D density inversion of gravity gradient data using the extrapolated Tikhonov regularization

“…Liu (2013) and Wang et al (2014) extrapolated the Tikhonov regularization to the density-constrained 3D inversion of gravity data. Bear et al (1995) used an improved Levenburg-Marquart algorithm in order to invert Bouguer gravity data to obtain the 3D density distribution. Li andOldenburg et al (1996, 1998) applied the depth weighting function to surface magnetic or gravity data inversion and recovered the 3D distribution of the density contrast.…”

Constrained Two-Dimensional Inversion of Gravity Data

“…An inversion technique is usually employed to obtain a plausible subsurface model whose theoretical response (or calculated data) fits the observed data. Therefore, the inversion of gravity data constitutes an important step in the quantitative interpretation of gravity anomalies [6,7].…”