# Estimating the Extreme Values in Gridding Data using Gauss Elimination Method: A New Approach in Potential Field Processing

• Nguyen Kim Dung Institute of Marine Geology and Geophysics, Vietnam Academy of Science and Technology
• David Gómez-Ortiz Department of Biology and Geology, Physics and Inorganic Chemistry, ESCET, Universidad Rey Juan Carlos, Móstoles, Madrid, Spain
• Zaidoon Taha Abdulrazzaq Directorate of Space and Communications, Ministry of Science and Technology, Baghdad, Iraq
• Saada Ahmed Saada Geology Department, Faculty of Science, Suez University, Suez, Egypt
• Tran Tuan Dung Institute of Marine Geology and Geophysics, Vietnam Academy of Science and Technology
Keywords: Maxima detection, Potential field data, Gauss elimination, Vietnam continental shelf

### Abstract

The position of a maximum point of a function depends on its coefficients and order. The maximum horizontal gradient method is a popular method that greatly contributes to the detection of maximum points and approximation of geological structures edges. By adopting a mathematical logic, Blakely and Simpson established a quadratic function based on the characteristic of three points of a straight line in the fundamental directions. However, for potential field data like gravity and magnetic data, the coefficients of a quadratic function in each direction are not only dependent on the values of three points on a straight line, but also, they depend on the values of the surrounding points. This article proposes an algorithm which can detect maximum points more effectively in order to delineate geological structures boundaries from potential field data. The proposed algorithm uses a 3×3 neighborhood data grid to establish a two-variables function and to determine its coefficients by applying the Gaussian elimination method. After the two-variables function has been established, the algorithm estimates any extreme points and their positions from a set of four single-variable functions which correspond to the horizontal, vertical and the two diagonal directions by the cases x = 0, y = 0, y = -x and y = x of the main function. Finally, the conditions to detect the maximum point from the extreme points are defined. The validity of the algorithm was demonstrated on synthetic datasets generated by two different model structures. A real data application of the method has also been realized by estimating the geological boundaries by gravity data in the Vietnam’s continental shelf. The results obtained from the synthetic applications of the algorithm proved that it can determine more maximum points as compared to Blakely and Simpson method, and as a result, in all the test cases, it has drawn the real boundaries of the model structures more accurately. The application results of the method on real data revealed new boundary delineations in the research area, interpreted to be faults or fractures which lies between deep trench in the East Vietnam Sea.

Published
2021-11-26
Section
Articles