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

@article{Nabighian2001UnificationOE, title={Unification of Euler and Werner deconvolution in three dimensions via the generalized Hilbert transform}, author={Misac N. Nabighian and Richard O. Hansen}, journal={Geophysics}, year={2001}, volume={66}, pages={1805-1810} }

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…

## 152 Citations

An improved Tilt-Euler deconvolution and its application on a Fe-polymetallic deposit

- GeologyOre Geology Reviews
- 2019

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

- Mathematics
- 2004

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¿

- Mathematics
- 2003

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

- 2005

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

- Mathematics
- 2012

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

- Physics, Mathematics
- 2005

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

- Mathematics
- 2004

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

- Physics
- 2010

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

- Geology
- 2003

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

- Geology
- 2014

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…

## References

SHOWING 1-10 OF 10 REFERENCES

Toward a three‐dimensional automatic interpretation of potential field data via generalized Hilbert transforms: Fundamental relations

- Mathematics
- 1984

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

- Mathematics
- 1993

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

- Geology
- 2002

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

- Physics
- 1999

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

- Mathematics
- 1972

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

- Geology
- 1974

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