Automatic DEXP method derived from Euler’s Homogeneity equation

The depth from extreme points (DEXP) method can be used for estimating source depths and providing a rough image as a starting model for inversion. However, the application of the DEXP method is limited by the lack of prior information regarding the structural index. Herein, we describe an automatic DEXP method derived from Euler’s Homogeneity equation, and we call it the Euler–DEXP method. We prove that its scaling field is independent of structural indices, and the scaling exponent is a constant for any potential field or its derivative. Therefore, we can simultaneously estimate source depths with different geometries in one DEXP image. The implementation of the Euler–DEXP method is fully automatic. The structural index can be subsequently determined by utilizing the estimated depth. This method has been tested using synthetic cases with single and multiple sources. All estimated solutions are in accordance with theoretical source parameters. We demonstrate the practicability of the Euler–DEXP method with the gravity field data of the Hastings Salt Dome. The results ultimately represent a better understanding of the geometry and depth of the salt dome.