Application of a mathematical method in geophysics: Separating anomalies of horizontal gradients of the spontaneous potential field based on first-order difference

Abstract

To highlight weak local anomalies of surveys using the spontaneous potential field method, the local and regional background horizontal gradients of the field need to be separated. Based on the genesis of the spontaneous potential field, this work establishes a mathematical model for calculating the background field of horizontal gradients. Subsequently, using the first-order forward and central differences, the approximate calculation formula for the first-order derivative of potential horizontal gradients is deduced. Accordingly, the corresponding relationship between the minimum of the difference filtering function and characteristic points of the linear regional background field is established. Using the derived profiles, we separate local anomalies and the regional background field of horizontal gradients of the spontaneous potential field, which allows smoothing and low-pass filtering for measuring errors and geologic noise of these gradient values. We apply this difference filtering function to water search using the self-potential method in the Longrui Depression of southwestern Guangxi, China. Results show that the interference of the regional background field on local anomalies of the horizontal gradient of the spontaneous potential field can be reduced using this approach, improving the acquisition of geologic information about the channels of karst underground water. The feasibility and effectiveness of this method are verified through drilling observations.