Unification of Euler and Werner deconvolution in three dimensions via the generalized Hilbert transform

  title={Unification of Euler and Werner deconvolution in three dimensions via the generalized Hilbert transform},
  author={Misac N. Nabighian and Richard O. Hansen},
The extended Euler deconvolution algorithm is shown to be a generalization and unification of 2-D Euler deconvolution and Werner deconvolution. After recasting the extended Euler algorithm in a way that suggests a natural generalization to three dimensions, we show that the 3-D extension can be realized using generalized Hilbert transforms. The resulting algorithm is both a generalization of extended Euler deconvolution to three dimensions and a 3-D extension of Werner deconvolution. At a… 
An improved Tilt-Euler deconvolution and its application on a Fe-polymetallic deposit
Abstract The Tilt-Euler deconvolution based on the first derivatives of the tilt angle is advanced from the routine Euler deconvolution and it is widely used. It estimates both the horizontal
A multilevel generalization of euler deconvolution and its comparison with the continuous wavelet transform
Recent implementations of Euler deconvolution allow to solve simultaneously for the source position and the structural index. This opens the way to a comparison between this technique and the
Grid Based Euler Deconvolution: Completing the Circle With ¿2D Constrained Euler¿
Mushayandebvu et al. (2001) introduced a second equation, described as a rotational constraint. The profile based method is known as profile ‘extended Euler’ where is assumed zero in the above
3D multiple-source Werner deconvolution for magnetic data
Werner deconvolution has been widely used for at least 30 years for rapid interpretation of magnetic data. Since 1993, a multiple-source generalization of the method has been known, and at least two
Generalized Hilbert transforms of the effect of single magnetic sources
ABSTRACTThe generalized Hilbert transforms of potential fields, particularly magnetic fields, provide a useful resource for improving interpretation. Even though x- and y-Hilbert transforms of a
On the application of Euler deconvolution to the analytic signal
Standard Euler deconvolution is applied to potential-field functions that are homogeneous and harmonic. Homogeneity is necessary to satisfy the Euler deconvolution equation itself, whereas
Grid Euler deconvolution with constraints for 2D structures
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
Analytic signals of the gravity gradient tensor and their application to Euler deconvolution
The analytic signal concept can be applied to the gravity gradient tensor data in three dimensions. For the gravity gradient tensor, the horizontal and vertical derivatives of gravity vector
Euler Deconvolution of Gravity Data
Euler deconvolution of both profile and gridded magnetic data (Thompson, 1982; Reid et al, 1990) has found wide application. It has been implemented by many organisations and individuals and is
Multiridge Euler deconvolution
Potential field interpretation can be carried out using multiscale methods. This class of methods analyses a multiscale data set, which is built by upward continuation of the original data to a


Toward a three‐dimensional automatic interpretation of potential field data via generalized Hilbert transforms: Fundamental relations
The paper extends to three dimensions (3-D) the two‐dimensional (2-D) Hilbert transform relations between potential field components. For the 3-D case, it is shown that the Hilbert transform is
Multiple-source Werner deconvolution
A reformulation of the Werner deconvolution algorithm using the analytic signal is extended to multiple source bodies. The extended algorithm involves solving a linear least‐squares problem; the
Multiple-source Euler deconvolution
Rapid three-dimensional (3-D) source location methods can be extremely useful in framing a subsurface structural model from gravity or magnetic data. However, existing implementations of Euler
Magnetic Imaging using Extended Euler Deconvolution
The Euler homogeneity relation expresses how a homogeneous function transforms under scaling. When implemented it helps to determine source location for particular potential field anomalies. In this
The analytic signal of two-dimensional magnetic bodies with polygonal cross-section; its properties and use for automated anomaly interpretation
This paper presents a procedure to resoive magnetic anomalies due to two-dimensional structures. The method assumes that all causative bodies have uniform magnetization and a crosssection which can
Additional comments on the analytic signal of two-dimensional magnetic bodies with polygonal cross-section
In a previous paper (Nabighian, 1972), the concept of analytic signal of bodies of polygonal cross‐section was introduced and its applications to the interpretation of potential field data were
Multiple-source Euler deconvolution: Geophysics, in press
  • Multiple-source Euler deconvolution: Geophysics, in press
  • 2002
Multiple-source Euler deconvolution: submitted to Geophysics
  • 2000
Multiple-source Werner deconvolution: Geophysics
  • Multiple-source Werner deconvolution: Geophysics
  • 1993
The analytic signal of two-dimensional magnetic bodies with polygonal cross-section: Its properties and use for automated interpretation: Geophysics
  • The analytic signal of two-dimensional magnetic bodies with polygonal cross-section: Its properties and use for automated interpretation: Geophysics
  • 1972