Regularized two‐dimensional Fourier gravity inversion method with application to the Silent Canyon caldera, Nevada

Abstract

A modification of the 2‐D Fourier gravity inversion method includes regularization and a linear density variation with depth. Explicit downward continuation in the Fourier inversion of gravity observations from mass distributions at depth produces instability in the presence of noise and shallow mass distributions. A data‐adaptive regularization filter tapers growth of the exponential continuation function. An empirical relationship between the regularization filter parameter and a parametric model of potential field spectra results in automatic selection of the filter parameter for a given continuation depth. Inversion of synthetic data from a random noise‐contaminated basin type model produces a depth model that agrees with the synthetic structure with an rms error commensurate with the data noise. A model of the Silent Canyon caldera, buried beneath Pahute Mesa at the Nevada Test Site, results in a gravity field that agrees with the observations to within a 4 percent rms error. The caldera gravity model supports the hypothesis of a high‐density half‐space (precaldera lithology) beneath a lower density caldera infill (postcaldera volcanic activity).

Fast gravity inversion of basement relief

“…In the class of wavenumber-domain gravity inversion methods, Oldenburg (1974) uses Parker's (1973) forward formula and applies a suitable low-pass filter to the data. Using the same formula, Reamer and Ferguson (1989) use Tikhonov et al's (1968) filter to regularize the downward continuation through Parker's (1973) formula. In the class of spacedomain gravity inversion methods, Pedersen (1977) regularizes the parameter correction vector in the iterative nonlinear inversion to prevent large parameter modifications at each iteration.…”

Three‐dimensional Fourier gravity inversion with arbitrary density contrast

“…Linear, quadratic, and exponential variations, either in the space or in the frequency domain, are the basis of several methods. See, among others, the papers by Granser (1987), Chai and Hinze (1988), Reamer and Ferguson (1989), and Rao et aI. (1990).…”

“…The well-known result given by Parker (1973) corresponds to a zero degree polynomial, and a polynomial of first degree with constant coefficients leads to Reamer and Ferguson's (1989) formula.…”

Three-Dimensional Gravity Inverse Modeling for Basement Depth Estimation Integrating Maximum Difference Reduction (MDR), Trend Surface Analysis (TSA) and Total Variation Regularization

“…Other approaches of gravity forward modeling and inverse modeling in the spatial frequency domain have been proposed by Parker [3] and Oldenburg [4]. However, the resulting solutions were not stable, so that the concept of Tikhonov regularization was introduced to stabilize the computation process [5,6]. In its applications, the Tikhonov regularization has several variants, such as smoothness, total variation, minimum support, gradient minimum support, minimum entropy, etc.…”