An empirical law for wavelet maxima interpretation of potential fields: Application to the Uinta Mountains range

Abstract

Wavelet methods have been used in potential fields study to estimate source properties such as depth or structural index, through the analysis of Wavelet Transform Modulus Maxima Lines (WTMML) intersections and slopes at high scales. Little has been done on the study of maximum points of the wavelet diagram, that we call here Maximum Wavelet Coefficient Scales (MWCS). Previous works have shown interesting correlations between MWCS and source depths, depending on the wavelet used in regards to the source nature and the data derivative order. In this paper, we introduce an empirical law involving spectral parameters that have not been studied so far, which allows analytical calculation of the MWCS, knowing the source characteristics and using certain wavelets. In return, the study of MWCS allows recovering source characteristics from the use of a single wavelet, without prior knowledge on the source.We demonstrate through synthetic models that the new capability of predicting the source type and depth according to the wavelet coefficient behaviour allows new ways of potential fields' sources characterization and identification. We show an application of the formula on a real case example in the Uinta Mountains (Utah, USA).