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.

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.

Automatic 3-D interpretation of potential field data using analytic signal derivatives

Geophysics ◽  
1997 ◽  
Vol 62 (1) ◽  
pp. 87-96 ◽  
Author(s):  
Nicole Debeglia ◽  
Jacques Corpel
Keyword(s):  
Signal Amplitude ◽  
Vertical Gradient ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Practical Implementation ◽  
Potential Field Data ◽  
Gravity And Magnetic ◽  
Second Derivatives ◽  
Gravity And Magnetic Data ◽  
Derivatives Of

A new method has been developed for the automatic and general interpretation of gravity and magnetic data. This technique, based on the analysis of 3-D analytic signal derivatives, involves as few assumptions as possible on the magnetization or density properties and on the geometry of the structures. It is therefore particularly well suited to preliminary interpretation and model initialization. Processing the derivatives of the analytic signal amplitude, instead of the original analytic signal amplitude, gives a more efficient separation of anomalies caused by close structures. Moreover, gravity and magnetic data can be taken into account by the same procedure merely through using the gravity vertical gradient. The main advantage of derivatives, however, is that any source geometry can be considered as the sum of only two types of model: contact and thin‐dike models. In a first step, depths are estimated using a double interpretation of the analytic signal amplitude function for these two basic models. Second, the most suitable solution is defined at each estimation location through analysis of the vertical and horizontal gradients. Practical implementation of the method involves accurate frequency‐domain algorithms for computing derivatives with an automatic control of noise effects by appropriate filtering and upward continuation operations. Tests on theoretical magnetic fields give good depth evaluations for derivative orders ranging from 0 to 3. For actual magnetic data with borehole controls, the first and second derivatives seem to provide the most satisfactory depth estimations.

VERTICAL GRADIENT OF GRAVITY ON AXIS FOR HOLLOW AND SOLID CYLINDERS

Geophysics ◽  
1966 ◽  
Vol 31 (4) ◽  
pp. 816-820 ◽  
Author(s):  
Thomas A. Elkins
Keyword(s):  
Hollow Cylinder ◽  
Sudden Change ◽  
Vertical Gradient ◽  
Outer Radius ◽  
Gravity Gradient ◽  
Gradient Effect ◽  
Vertical Gravity Gradient ◽  
Vertical Gravity ◽  
Special Case ◽  
Vertical Gradient Of Gravity

The recent interest in borehole gravimeters and vertical gravity gradient meters makes it worthwhile to analyze the simple case of the vertical gravity gradient on the axis of a hollow cylinder, simulating a borehole. From the viewpoint of potential theory the results are interesting because of the discontinuities which may occur when a vertical gradient profile crosses a sudden change in density. Formulas for the vertical gradient effect are given for observations above, inside, and below a hollow cylinder and a solid cylinder. The special case of an infinitely large outer radius for the cylinders is also considered, leading to formulas for the vertical gradient effect inside a borehole on its axis and inside a horizontal slab. Some remarks are made on the influence of the shape of a buried vertical gradient meter on the correction factor for changing the meter reading to density.

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.

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

Geophysics ◽  
1984 ◽  
Vol 49 (6) ◽  
pp. 780-786 ◽  
Author(s):  
Misac N. Nabighian
Keyword(s):  
Hilbert Transform ◽  
Potential Field ◽  
Field Data ◽  
Three Dimensional ◽  
Analytic Signal ◽  
Three Dimensions ◽  
Hilbert Transforms ◽  
Potential Field Data ◽  
Automatic Interpretation ◽  
The Hilbert Transform

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 composed of two parts, with one part acting on the X component and one part on the Y component. As for the previously developed 2-D case, it is shown that in 3-D the vertical and horizontal derivatives are the Hilbert transforms of each other. The 2-D Cauchy‐Riemann relations between a potential function and its Hilbert transform are generalized for the 3-D case. Finally, the previously developed concept of analytic signal in 2-D can be extended to 3-D as a first step toward the development of an automatic interpretation technique for potential field data.

Relative precision of vertical and horizontal gravity gradients measured by gravimeter

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 99-101 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Survey Data ◽  
Hilbert Transform ◽  
Gravity Data ◽  
Gradient Methods ◽  
Vertical Gradient ◽  
Gravity Gradients ◽  
Relative Precision ◽  
The Hilbert Transform ◽  
Vertical Gradients ◽  
Vertical Gradient Of Gravity

Several recent publications advocate the use of the vertical gradient of gravity from gravimeter measurements at two elevations in a portable tower (Thyssen‐Bornemisza, 1976; Fajklewicz, 1976; Mortimer, 1977). Contrary opinions have also been expressed (Hammer and Anzoleaga, 1975; Stanley and Green, 1976; Thysen‐Bornemisza, 1977; Arzi, 1977). The disagreement revolves around the question of practically attainable precision of the vertical gradient tower method. Although it is possible to calculate both horizontal and vertical gradients from conventional gravity survey data by use of the Hilbert transform (Stanley and Green, 1976), it should be noted that highly precise gravity data are required. Also the need for connected elevation and location surveys, the major cost in gravity surveying, is not avoided. This is a significant advantage of the gradient methods. The purpose here is to present a brief consideration of the relative precision of the horizontal and vertical gradients, as measured in the field by special gravimeter observations.

Magnitude of anomalies in the vertical gradient of gravity

Geophysics ◽  
1981 ◽  
Vol 46 (11) ◽  
pp. 1609-1610 ◽  
Author(s):  
Sigmund Hammer
Keyword(s):  
Vertical Gradient ◽  
Spherical Body ◽  
Density Contrast ◽  
Maximum Gradient ◽  
Maximum Value ◽  
Simple Mass ◽  
Spherical Mass ◽  
Vertical Gradient Of Gravity

The maximum gradient which can be caused by a simple mass is that of a spherical body. The equation for the vertical gradient at the point P above the center of a spherical mass of density contrast σ (see insert on Figure 1) can be written in the form [Formula: see text] where G is the universal gravity constant [Formula: see text] Expressing the gradient in the Eötvös units, we have [Formula: see text] In terms of percentage of the earth’s normal vertical gradient, the anomaly is [Formula: see text] of 3086 E°. At the surface of the sphere (h = 0), we have the maximum value [Formula: see text] of 3086 E° which is independent of the radius R.

On: “The normal vertical gradient of gravity” by J. H. Karl (GEOPHYSICS, 48, 1011–1013, July 1983).

Geophysics ◽  
1986 ◽  
Vol 51 (7) ◽  
pp. 1505-1508 ◽  
Author(s):  
T. R. LaFehr ◽  
Kwok C. Chan
Keyword(s):  
Data Reduction ◽  
Normal Gravity ◽  
Traditional Approach ◽  
Vertical Gradient ◽  
Gravity Gradient ◽  
Average Value ◽  
Terrain Model ◽  
Vertical Gradient Of Gravity

In his reply to C. J. Swain’s (1984) discussion Karl states that no one has disagreed with his proposed (0.265 mGal/m) “average value” for the normal gravity gradient and that his global terrain model can be used to challenge the validity of the traditional approach to data reduction. Our investigations show that Karl is in error on both counts, and we hope that the following analyses will help toward a clearer understanding of this question.

Author’s Reply to discussion by Thyssen‐Bornemisza

Geophysics ◽  
1971 ◽  
Vol 36 (1) ◽  
pp. 216-216
Author(s):  
Sigmund Hammer
Keyword(s):  
Theoretical Analysis ◽  
Vertical Profile ◽  
Vertical Gradient ◽  
Specific Topic ◽  
Foregoing Discussion ◽  
The Subject ◽  
Vertical Gradient Of Gravity

The foregoing discussion by Dr. Thyssen‐Bornemisza calls attention to interesting extensions of the rather simplified theoretical analysis in my paper. Dr. Thyssen‐Bornemisza has published extensively on the subject of the vertical gradient of gravity and its applications in exploration. My paper was limited to a very specific topic, namely the variability of the vertical gradient along a vertical profile above an anomalous mass.

Sign in / Sign up

Export Citation Format

Share Document