# 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…

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## References

SHOWING 1-10 OF 10 REFERENCES

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

- Geology, 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

- Geology
- 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

- Geology
- 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

- Geology
- 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…

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

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