Grid Euler deconvolution with constraints for 2D structures

Abstract

The conventional formulation of 3D Euler deconvolution assumes that the observed field in each Euler window varies in all directions. Where the source is 2D, this assumption leads to the production of poorly constrained solutions. If the source is 2D, the problem leads to a rank deficient normal equations matrix having an eigenvector associated with a zero eigenvalue. This vector lies in the horizontal plane and is pointing along the strike direction, thus allowing for the identification of a 2D structure and its strike. Finding a pseudoinverse via eigenvector expansion allows accurate source location, and the strike information allows the automatic implementation of profile-based techniques like extended Euler deconvolution to gridded data, thus allowing for the first time the estimation of strikes, dips, and susceptibilities from grids using an automatic process. We present a gridbased version of Euler deconvolution that has the ability to define within an Euler operating window whether the source is 2D or 3D in character so that the solutions can be treated differently. We illustrate the new approaches on model and real data.

A crustal thickness map of Africa derived from a global gravity field model using Euler deconvolution

“…3 For a detailed explanation of 3-D Euler deconvolution, the reader is referred to Reid et al (1990), Mushayandebvu et al (2004) and Florio et al (2006). A least-squares inversion algorithm is used to solve the Euler equation for an optimum source location.…”

Application of 3D Euler deconvolution and improved tilt angle to the aeromagnetic data of In Ouzzal terrane, western Hoggar, Algeria

“…Solutions of the equation system in the sense of least square are derived by resolving the inverse problem (Menke 1989). Detailed numerical development may be found in (Mushayandebvu et al 2004;Reid et al 1990). Let ∂M/∂x, ∂M/∂y, and ∂M/∂z be the partial derivatives of the magnetic field M. Following Miller and Singh (1994) and Verduzco et al (2004), briefly recall that this TAD transformation is given by:…”

Subsurface faults detection based on magnetic anomalies investigation: A field example at Taba protectorate, South Sinai

“…This equation is usually solved for the depth "z 0 ", surface location (x 0 , y 0 ) and the shape factor "N". Nevertheless, the reliability of the resulting values is uncertain due to imperfect representation of the geological model, insufficient data sampling, unknown magnetization values, and nonuniqueness of the inverse problem (Grauch et al, 2004;Beiki et al, 2010). In the study area, the software Oasis Montaj (Geosoft, 2015) was used to calculate the 3D Euler deconvolution from the total magnetic intensity grid.…”