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.

极值点深度 (DEXP) 方法可用于估算震源深度并提供粗略图像作为反演的起始模型。然而，DEXP 方法的应用受到缺乏有关结构索引的先验信息的限制。在此，我们描述了一种从欧拉齐性方程导出的自动 DEXP 方法，我们将其称为 Euler–DEXP 方法。我们证明其标度场与结构指数无关，并且标度指数对于任何势场或其导数都是常数。因此，我们可以在一张 DEXP 图像中同时估计具有不同几何形状的源深度。Euler–DEXP 方法的实施是全自动的。随后可以利用估计的深度来确定结构指数。此方法已使用具有单一和多个来源的合成案例进行了测试。所有估计的解决方案都符合理论源参数。我们用黑斯廷斯盐丘的重力场数据证明了 Euler-DEXP 方法的实用性。结果最终代表了对盐丘的几何形状和深度的更好理解。