Euler deconvolution of the analytic signal and its application to magnetic interpretation

Abstract

A B S T R A C TEuler deconvolution and the analytic signal are both used for semi-automatic interpretation of magnetic data. They are used mostly to delineate contacts and obtain rapid source depth estimates. For Euler deconvolution, the quality of the depth estimation depends mainly on the choice of the proper structural index, which is a function of the geometry of the causative bodies. Euler deconvolution applies only to functions that are homogeneous. This is the case for the magnetic field due to contacts, thin dikes and poles. Fortunately, many complex geological structures can be approximated by these simple geometries. In practice, the Euler equation is also solved for a background regional field. For the analytic signal, the model used is generally a contact, although other models, such as a thin dike, can be considered. It can be shown that if a function is homogeneous, its analytic signal is also homogeneous. Deconvolution of the analytic signal is then equivalent to Euler deconvolution of the magnetic field with a background field. However, computation of the analytic signal effectively removes the background field from the data. Consequently, it is possible to solve for both the source location and structural index. Once these parameters are determined, the local dip and the susceptibility contrast can be determined from relationships between the analytic signal and the orthogonal gradients of the magnetic field. The major advantage of this technique is that it allows the automatic identification of the type of source. Implementation of this approach is demonstrated for recent high-resolution survey data from an Archean granite-greenstone terrane in northern Ontario, Canada.

An appraisal of the Serra da Cangalha impact structure using the Euler deconvolution method

“…The Euler deconvolution method is a quasi-automated interpretation method often used for estimating depths and delineating boundaries of anomalous bodies (Keating and Pilkington 2004;Cooper 2002). Application of the method to the derivatives of potential field data to estimate depths has been shown to be effective and useful (Ravat et al 2002b;Hsu 2002).…”

“…Therefore, by estimating η, we can provide information on the geometry and depth of the magnetic sources. A poor choice of the structural index has been shown to cause a diffuse solution of source locations and serious biases in depth estimation (Hsu 2002;Keating and Pilkington 2004). Both Thompson (1982) and Reid et al (1990) suggested that a correct η gives the tightest clustering of the Euler solutions around the geologic structure of interest.…”

Three-dimensional interpretation of magnetic and gravity anomalies using the finite-difference similarity transform

“…The degree of homogeneity, a parameter indicative of the source geometry, is prescribed ͑Thompson, 1982; Reid et al, 1990͒ or estimated ͑Stavrev, 1997Hsu, 2002;Gerovska and Araúzo-Bravo, 2003;FitzGerald et al, 2004;Keating and Pilkington, 2004;Gerovska et al, 2005͒. As an alternative to inversion for source parameters using equation 1, the definition equation for a homogeneous function ͑Courant and John, 1965͒ f͑tv 1 ,tv 2 ,...,tv i ,...,tv j ͒ ‫ס‬ t n f͑v 1 ,v 2 ,...,v i ,...,v j ͒, ͑2͒…”

Integrated gradient interpretation techniques for 2D and 3D gravity data interpretation

“…In the early 1970's, a variety of automatic and semiautomatic methods, based on the use of gradients of the potential field, were developed as efficient tools for the determination of geometric parameters, such as locations of boundaries and depth of the causative sources (e.g. O'Brien, 1972;Nabighian, 1972Nabighian, , 1974Cordell, 1979;Murthy, 1985;Barongo, 1985;Blakely and Simpson, 1986;Hansen et al, 1987;Hansen and Simmonds, 1993;Reid et al, 1990;Keating and Pilkington, 1990;Ofoegbu and Mohan, 1990;Roest et al, 1992;Marcotte et al, 1992;Marson and Klingele, 1993;Hsu et al, 1996Hsu et al, , 1998Salem and Ravat, 2003;Keating and Pilkington, 2004;Aboud et al, 2005). The success of these methods results from the fact that quantitative or semi-quantitative solutions are found with no or few assumptions.…”