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Finite-difference Euler Deconvolution Algorithm Applied to the Interpretation of Magnetic Data from Northern Bulgaria

机译：有限差分欧拉反卷积算法在保加利亚北部磁数据解释中的应用

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摘要

Here, we propose a new, finite-difference algorithm for Euler deconvolution, based on the Euler’s homogeneity equation accounting for a constant background field which allows simultaneous depth and shape estimation. The algorithm uses as input data the measured anomalous field and its first-order derivatives, in contrast to methods based on the input of higher order field derivatives. The test of the algorithm on a model of interfering fields of elementary sources with different field fall-off rates, resulting in background close to a linear one, shows that it can give a good estimation of both the depth to the sources singular points and their respective structural indices. A set of tests was carried out on column-like models with shapes ranging from the elementary model of a dipole to that of a point pole, and of models of arbitrary shape with two singular points in between. It showed that when the ratio of the distance between the observation plane and the source’s top and the length of the body allows classification of it as a dipole or a point pole, the value of the estimated structural index is close to the integer value, typical for the respective elementary source. In such cases the estimated depth value refers to that of the special internal point of the respective type of source. This can facilitate in certain situations the interpretation of non-integer structural indices and their associated depth estimates obtained with the new Euler deconvolution algorithm. Inversion of a set of magnetic data from northern Bulgaria, caused by basaltic bodies of different shape, with the proposed method confirmed that the most intense anomalies are caused by column-like bodies outcropping on the surface and with considerable depth extent.
机译：在此，我们基于Euler的均匀性方程，考虑了恒定的背景场，提出了一种用于Euler反卷积的新的有限差分算法，该背景场允许同时进行深度和形状估计。与基于高阶场导数输入的方法相比，该算法将测得的异常场及其一阶导数用作输入数据。在具有不同场衰减率的基本源的干扰场模型上对该算法进行测试，导致背景接近线性场，表明该算法可以很好地估计源奇异点及其深度的深度各自的结构指标。对柱状模型进行了一组测试，这些模型的形状范围从偶极子的基本模型到点极子的模型，以及任意形状的模型，中间有两个奇异点。结果表明，当观察平面到源极顶部的距离与物体长度的比值允许将其分类为偶极子或点极时，估计的结构指数值接近于整数值，通常用于相应的基本来源。在这种情况下，估计的深度值是指相应类型的源的特殊内部点的深度值。在某些情况下，这可以帮助解释使用新的Euler反卷积算法获得的非整数结构索引及其关联的深度估计。所提出的方法对保加利亚北部一组形状各异的玄武岩引起的磁数据进行了反演，证实了最强烈的异常是由表面上露露的柱状体引起的，而且深度范围很大。

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