To: “Magnetic interpretation in three dimensions using Euler deconvolution,” by A. B. Reid, J. M. Allsop, H. Granser, A. J. Millett, and I. W. Somerton (GEOPHYSICS, p. 80–91, January 1990)

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 502-502
Keyword(s):  
Three Dimensions ◽  
Euler Deconvolution ◽  
Magnetic Interpretation

Please note that Figures 3 (p. 85) and 5 (p. 87) are not identified. The misplaced captions appear at the bottom of pages 86 and 88, respectively.

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

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1805-1810 ◽  
Author(s):  
Misac N. Nabighian ◽  
R. O. Hansen
Keyword(s):  
Magnetic Dipole ◽  
Hilbert Transform ◽  
Natural Generalization ◽  
Three Dimensions ◽  
Explicit Calculation ◽  
Euler Deconvolution ◽  
Hilbert Transforms ◽  
Vertical Magnetic Dipole ◽  
Generalized Hilbert Transform ◽  
Practical Level

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 practical level, the new algorithm helps stabilize the Euler algorithm by providing at each point three equations rather than one. We illustrate the algorithm by explicit calculation for the potential of a vertical magnetic dipole.

Magnetic interpretation in 3‐D using Euler deconvolution

1988 ◽  
Author(s):  
Alan B. Reid ◽  
Jennifer M. Allsop ◽  
Harold Granser ◽  
Anthony J. Millet ◽  
Ian W. Somerton
Keyword(s):  
Euler Deconvolution ◽  
Magnetic Interpretation

Reply by the authors to N. L. Mohan

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1215-1216 ◽  
Author(s):  
W. R. Roest ◽  
J. Verhoef ◽  
M. Pilkington
Keyword(s):  
Analytic Signal ◽  
Three Dimensions ◽  
Magnetic Interpretation

The purpose of our paper (Roest et al., 1992) was to present the generalization of the analytic signal (Nabighian, 1972) from two to three dimensions and illustrate its use in magnetic interpretation. The comments by Dr. Mohan can be separated into three categories.

Magnetic interpretation in three dimensions using Euler deconvolution

Geophysics ◽  
1990 ◽  
Vol 55 (1) ◽  
pp. 80-91 ◽  
Author(s):  
A. B. Reid ◽  
J. M. Allsop ◽  
H. Granser ◽  
A. J. Millett ◽  
I. W. Somerton
Keyword(s):  
Calculated Data ◽  
Real Data ◽  
Three Dimensions ◽  
Magnetic Survey ◽  
Good Precision ◽  
Structural Index ◽  
Magnetic Interpretation ◽  
Model Studies ◽  
Index Model ◽  
Using Data

Magnetic‐survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using Euler’s homogeneity relation. The method employs gradients, either measured or calculated. Data need not be pole‐reduced, so that remanence is not an interfering factor. Geologic constraints are imposed by use of a structural index. Model studies show that the method can locate or outline confined sources, vertical pipes, dikes, and contacts with remarkable accuracy. A field example using data from an intensively studied area of onshore Britain shows that the method works well on real data from structurally complex areas and provides a series of depth‐labeled Euler trends which mark magnetic edges, notably faults, with good precision.

Magnetic interpretation using the 3-D analytic signal

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 116-125 ◽  
Author(s):  
Walter R. Roest ◽  
Jacob Verhoef ◽  
Mark Pilkington
Keyword(s):  
Magnetic Field ◽  
Impact Crater ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Eastern Canada ◽  
Magnetic Interpretation ◽  
Absolute Value ◽  
Cape Breton ◽  
Derivatives Of ◽  
The Magnetic Field

A new method for magnetic interpretation has been developed based on the generalization of the analytic signal concept to three dimensions. The absolute value of the analytic signal is defined as the square root of the squared sum of the vertical and the two horizontal derivatives of the magnetic field. This signal exhibits maxima over magnetization contrasts, independent of the ambient magnetic field and source magnetization directions. Locations of these maxima thus determine the outlines of magnetic sources. Under the assumption that the anomalies are caused by vertical contacts, the analytic signal is used to estimate depth using a simple amplitude half‐width rule. Two examples are shown of the application of the method. In the first example, the analytic signal highlights a circular feature beneath Lake Huron that has been identified as a possible impact crater. The second example illustrates the continuation of terranes across the Cabot Strait between Cape Breton and Newfoundland in eastern Canada.

Advantages of using the vertical gradient of gravity for 3-D interpretation

Geophysics ◽  
1993 ◽  
Vol 58 (11) ◽  
pp. 1588-1595 ◽  
Author(s):  
I. Marson ◽  
E. E. Klingele
Keyword(s):  
Gravity Data ◽  
Vertical Gradient ◽  
Three Dimensions ◽  
Gravity Gradient ◽  
Horizontal Gradient ◽  
Euler Deconvolution ◽  
Model Studies ◽  
Combined Use ◽  
Deconvolution Techniques ◽  
Vertical Gradient Of Gravity

Gravity gradiometric data or gravity data transformed into vertical gradient can be efficiently processed in three dimensions for delineating density discontinuities. Model studies, performed with the combined use of maxima of analytic signal and of horizontal gradient and the Euler deconvolution techniques on the gravity field and its vertical gradient, demonstrate the superiority of the latter in locating density contrasts. Particularly in the case of interfering anomalies, where the use of gravity alone fails, the gravity gradient is able to provide useful information with satisfactory accuracy.

Reply by the authors to Craig Ferris

Geophysics ◽  
1994 ◽  
Vol 59 (11) ◽  
pp. 1786-1786
Author(s):  
I. Marson ◽  
E. E. Klingele
Keyword(s):  
Vertical Gradient ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Quantitative Interpretation ◽  
Euler Deconvolution ◽  
Vertical Gradient Of Gravity

Our paper is a discussion aimed to show how the vertical gradient of gravity can be successfully used for quantitative interpretation in three dimensions (i.e., solving for the three coordinates [Formula: see text], [Formula: see text], and [Formula: see text] of the source body) with methods like analytic signal and Euler deconvolution.

High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

1988 ◽  
Vol 46 ◽  
pp. 14-15
Author(s):  
P.J. Lea ◽  
M.J. Hollenberg
Keyword(s):  
Electron Microscopy ◽  
Pigment Epithelium ◽  
Retinal Pigment ◽  
Rat Hepatocytes ◽  
Three Dimensions ◽  
Objective Lens ◽  
Rat Tissues ◽  
Thin Sections ◽  
Reconstruction Methods ◽  
Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

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