The inversion of gravity data into three‐dimensional polyhedral models

Abstract

A nonlinear inversion scheme is described for the inversion of gravity data into a three‐dimensional polyhedral model. As presented, the inversion scheme is quite general and could have application to a wide range of nonlinear problems. Constraints, in the form of independent geologic information, play an essential role in the analysis. The parameterization of the problem allows inclusion of exact linear constraints to limit possible model shapes and to construct multiple body models. It also significantly reduces the degrees of freedom in a problem and can help the stability of the iterative process. Plausibility constraints are used to limit the total departure of the solution from a starting model known to a specified level of confidence. The optimal trade‐off between fitting noisy data and remaining close to a plausible starting model is determined empirically for each problem. The utility of the inversion scheme is illustrated with an example of estimating depth to bedrock from gravity data in Avra Valley, Arizona. The basin is modeled using three‐dimensional polyhedra. The analysis indicates two deep portions in the elongate basin separated by a 0.8‐km‐deep saddle point. Uncertainties in the solution are estimated, and the three controlling factors are independent control of depth to bedrock, data density, and basin depth.

Fast gravity inversion of basement relief

“…As a result, the final solution was constrained to be close to the initial guess. Richardson and MacInnes (1989) use the Tikhonov stabilizing functional of order zero that biases the solution to be close to zero.…”

Reconstruction of geologic bodies in depth associated with a sedimentary basin using gravity and magnetic data

“…To increase the chances that the estimated solution is close to the true one, the minimum of the regularizing function must occur in a region of the parameter space close to the true solution (Silva, Medeiros and Barbosa 2001c, 2002). Examples of successful inversion of gravity (or magnetic) data to estimate topography by using nonspectral information are given in Fedi (1997), Richardson and MacInnes (1989), Barbosa, Silva and Medeiros (1997, 1999b), Gallardo‐Delgado, Pérez‐Flores and Gómez‐Treviño (2003), Nunes, Barbosa and Silva (2008), Martins, Barbosa and Silva (2010) and Silva, Oliveira and Barbosa (2010). Because the regularizing function imposes, on the solution, certain geological attributes, these methods differ from each other in the particular regularizing function used and therefore, in the bias imposed by the geologic information introduced through the regularizing function.…”

Gravimetry and Gravity Field Models

“…This solution was assessed with a covariance error analysis of the corresponding linear problem indicating good resolution of the basement depths. An inversion technique was described by Richardson and MacInnes [1989] to solve, from gravity data, for the geologic structure modeled as a collection of polyhedra. Uniqueness was ensured by including independent geologic data in the form of constraints.…”