基于欧拉齐次方程的自动DEXP法

Automatic DEXP method derived from Euler’s Homogeneity equation

DEXP(Depth from Extreme Point)法具有快速估计场源深度的优点,并能够提供场源的粗略成像。但缺乏构造指数(或缩放指数)的先验信息将会限制该方法的应用。本文描述了一种由欧拉齐次方程推导出来的自动DEXP方法,称之为Euler-DEXP法。我们证明了该方法的尺度场与构造指数无关,且任意位场或者其导数的缩放指数均为常数。因此,我们能够在一张成像图中估算出不同地质体的深度信息,且该方法能够自动进行。而构造指数也可以利用所求深度计算出来。通过单一场源和多场源模型数据对该方法进行了验证,所求结果与实际源参数完全一致。最后我们把该方法应用到黑斯廷斯盐丘的重力场数据中,验证了Euler-DEXP法的实用性,并对盐丘的几何形态、深度有了一个更好的理解。

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 diff erent 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.