3-D probability density imaging of Euler solutions using gravity data: a case study of Mount Milligan, Canada

Abstract

Euler deconvolution is a widely used automatic or semi-automatic method for potential field data. However, it yields many spurious solutions that complicate interpretation and must be reduced, eliminated, recognized, or ignored during interpretation. This study proposes a post-processing algorithm that converts Euler solutions produced by tensor Euler deconvolution of gravity data with an unprescribed structural index into probability values (p values) using the B-spline series density estimation (BSS) method. The p values of the Euler solution set form a probability density distribution on the estimation grid. The BSS method relies on the fact that while spurious solutions are sparse and ubiquitous, Euler deconvolution yields many similar or duplicate solutions, which may tightly cluster near real sources. The p values of the Euler solution clusters form multi-layered isosurfaces that can be used to discriminate neighboring target sources because the p values of spurious solutions are vanishingly small, making it simple to remove their interference from the probability density distribution. In all synthetic cases, the geometric outlines of anomaly sources are estimated from probability density isosurfaces approximating synthetic model parameters. The BSS method was then applied to airborne gravity data from Mount Milligan, British Columbia, Canada. Subsequently, results from synthetic models and field data show that the proposed method can successfully localize meaningful geological targets.

FFT-Based Probability Density Imaging of Euler Solutions

“…Therefore, the BSS algorithm, which is based on normalized B-splines, is adopted to separate each cluster based on the similarity and clustering degree of the Euler solutions in order to identify various sources of anomalies [ 7 ]. To introduce the BSS algorithm [ 21 ], let be an independent and identically distributed random sample of a d -dimensional probability density function (pdf) f . The sample i th can be represented as .…”

“…A homogeneous cube has analytical solutions and its theoretical structural index is 2 [ 21 , 57 ]. Therefore, a single cube model with a center , a size of 2000 m × 2000 m × 2000 m, and a residual density of 0.36 g/cm 3 is constructed to further test the adaptability of the B-spline density estimation to Euler solutions and the reliability of the algorithm.…”

“…Therefore, the BSS algorithm, which is based on normalized B-splines, is adopted to separate each cluster based on the similarity and clustering degree of the Euler solutions in order to identify various sources of anomalies [7]. To introduce the BSS algorithm [21], let X 1 , . .…”

“…FitzGerald et al [ 7 ] pointed out that the Euler deconvolution yields many similar or duplicate solutions, which may be tightly clustered in the vicinity of real sources, i.e., the 14th strategy in the paper [ 7 ]. Based on this strategy, Cao et al [ 21 ] proposed a non-parametric estimation method based on the normalized B-spline probability density (BSS), aiming to separate the Euler solution clusters to mark different anomaly sources according to the similarity and density characteristics of the Euler solutions [ 22 , 23 ]. B-spline curves are linear combinations of B-spline basis functions connected by node vectors [ 24 ].…”