Kernel Density Derivative Estimation of Euler Solutions

Abstract

Conventional Euler deconvolution is widely used for interpreting profile, grid, and ungridded potential field data. The Tensor Euler deconvolution applies additional constraints to the Euler solution using all gravity vectors and the full gravity gradient tensor. These algorithms use a series of different-sized moving windows to yield many solutions that can be employed to estimate the source location from the entire survey area. However, traditional discrimination techniques ignore the interrelation among the Euler solutions, so they cannot be employed to separate adjacent targets. To overcome this difficulty, we introduced multivariate Kernel Density Derivative Estimation (KDDE) as an extension of Kernel Density Estimation, which is a mathematical process to estimate the probability density function of a random variable. The multivariate KDDE was tested on a single cube model, a single cylinder model, and three composite models consisting of two cubes with various separations using gridded data. The probability value calculated by the multivariate KDDE was used to discriminate spurious solutions from the Euler solution dataset and isolate adjacent geological sources. The method was then applied to airborne gravity data from British Columbia, Canada. Then, the results of synthetic models and field data show that the proposed method can successfully locate meaningful geological targets.