Estimating automatically multiple regression lines and their wave number ranges from the power spectrum of a gravity or magnetic field

Abstract

　We propose a method to automatically estimate regression lines indicating the average depths of the causative layers and their wavenumber ranges from the power spectrum of potential fields, such as gravity anomalies or magnetic anomalies, by setting the adjusted coefficient of determination (R²_adj) as the indicator. In the proposed method, the data in all wavenumber zones are set as the initial data, and the regression line indicating the depth of the deepest layer is then estimated. The regression lines are estimated by sequentially reducing the data from the higher- wavenumber side, and R²_adj is calculated each time the regression line is estimated. When R²_adj of one line assumes the highest value, this line is considered the optimum regression line. The same process is then applied to the residual data (high- wavenumber side), resulting in a regression line indicating the second deepest layer. By repeating these processes, the number of causative layers is automatically determined, and the regression lines are obtained, indicating the layer depths and wavenumber ranges. In numerical tests, we confirmed that our method could estimate the model parameters correctly using L₁ and L₂ norm minimisation. We applied our method to the spectrum analysis of the Bouguer anomaly in central Kyushu, Japan, and obtained the following results as the average depth of causative layers: 8.9 km, 2.2 km, 0.6 km by L₁ norm minimizations and 9.2 km, 2.2 km, 0.6 km by L₂ norm minimizations. There were no significant differences among the results estimated by L₁ and L₂ norm minimisation and no differences in the wavenumber range for each regression line estimated by each minimisation.