APPLICATION OF HILBERT TRANSFORMS TO MAGNETIC PROFILES

Geophysics ◽  
1972 ◽  
Vol 37 (6) ◽  
pp. 1043-1045 ◽  
Author(s):  
Ralph T. Shuey
Keyword(s):  
Linear Combination ◽  
Hilbert Transform ◽  
Magnetic Data ◽  
Two Dimensional ◽  
Total Field ◽  
Hilbert Transforms ◽  
Vertical Field ◽  
Reduction To The Pole

Three related operations commonly performed on total‐field magnetic data are 1) conversion to vertical‐field anomaly, 2) reduction to the pole, and 3) computation of pseudogravimetric anomalies. This note shows that for profile or flight line data for which the source can be assumed to be two‐dimensional, all these operations amount to linear combination of the profile with its Hilbert transform.

On: “Interpretation of two dimensional magnetic bodies using Hilbert transforms,” by N. L. Mohan, N. Sundararajan, and S. V. Seshagiri Rao (March 1982 GEOPHYSICS, 52, p. 376–387)

Geophysics ◽  
1997 ◽  
Vol 62 (2) ◽  
pp. 690-691
Author(s):  
B. N. P. Agarwal
Keyword(s):  
Magnetic Field ◽  
Hilbert Transform ◽  
Two Dimensional ◽  
Hilbert Transforms ◽  
The Hilbert Transform

While going through some of the publications (Mohan and Babu, 1995), I became interested in the work of Mohan et al. (1982) which proposed a technique for interpretation of magnetic field anomalies over different geometrical sources using the Hilbert transform (HT). Before I put forward my observations, it would be appropriate to look into some important properties of HT (Whalen, 1971, pages 63 and 69.)

scholarly journals Enhancing the quality of interpretation magnetic data at low latitudes

2017 ◽  
Vol 1 (T4) ◽  
pp. 105-114
Author(s):  
Hai Hong Nguyen ◽  
Nhan Thanh Nhan ◽  
Liet Van Dang ◽  
Thu Ngoc Nguyen
Keyword(s):  
Magnetic Anomaly ◽  
Hilbert Transform ◽  
Amplitude Spectrum ◽  
Data Interpretation ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Low Latitudes ◽  
Reduction To The Pole ◽  
Signal Method

Magnetic anomalies are antisymmetrical and often skewed to the location of the sources, because both of the magnetization and ambient field are not directed vertically, so it’s difficult to interpret. For reducing the magnetic anomaly to a symmetrical one – this located on the source of the anomaly – people often use the reduction to the pole (RTP) where the magnetization and ambient field are both directed vertically. However, at low latitudes (an absolute inclination less than 16o30’), the amplitude spectrum of the RTP’s operator was amplified at higher frequencies (short wavelengths) can form a narrow pie-shaped; so it produces artifacts elongated along the direction of the magnetic declination. Therefore, many methods of RTP at low latitudes are given to solve this problem, but most of them are not efficiency. In this paper, we performed enhancing the quality of interpretation of magnetic data at low latitudes by some RTP methods for magnetic data at low latitudes and the analytic signal method using gradient operator and Hilbert transform. This method is applied to a model and to a real magnetic anomaly to find out the best method. Then this method was applied to enhance the quality of magnetic data interpretation in the Southern Vietnam. The result showed that the analytic signal method using Hilbert transform allowed enhancing the quality of interpretatio of magnetic data n at low latitudes is the best.

On: Interpretation of some two‐dimensional magnetic bodies using Hilbert transforms (GEOPHYSICS, v. 47, p. 376–387).

Geophysics ◽  
1983 ◽  
Vol 48 (2) ◽  
pp. 248-248
Author(s):  
J. Roth
Keyword(s):  
Hilbert Transform ◽  
Potential Field ◽  
Two Dimensional ◽  
Hilbert Transforms ◽  
The Hilbert Transform

The above‐cited paper usefully examines and extends the application of the Hilbert transform to potential field interpretation. However, the authors’ terse mention of Nabighian’s paper (Geophysics, 1972) fails to characterize adequately and acknowledge his original insights and contributions to the Hilbert transform presented in that paper. It is surprising as well that none of the reviewers and/or editors saw fit to rectify this undeserved omission.

Two-dimensional empirical mode decomposition by finite elements

2006 ◽  
Vol 462 (2074) ◽  
pp. 3081-3096 ◽  
Author(s):  
Y Xu ◽  
B Liu ◽  
J Liu ◽  
S Riemenschneider
Keyword(s):  
Finite Element ◽  
Linear Combination ◽  
Empirical Mode Decomposition ◽  
Spline Interpolation ◽  
Basis Functions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Mode Decomposition

Empirical mode decomposition (EMD) is a powerful tool for analysis of non-stationary and nonlinear signals, and has drawn significant attention in various engineering application areas. This paper presents a finite element-based EMD method for two-dimensional data analysis. Specifically, we represent the local mean surface of the data, a key step in EMD, as a linear combination of a set of two-dimensional linear basis functions smoothed with bi-cubic spline interpolation. The coefficients of the basis functions in the linear combination are obtained from the local extrema of the data using a generalized low-pass filter. By taking advantage of the principle of finite-element analysis, we develop a fast algorithm for implementation of the EMD. The proposed method provides an effective approach to overcome several challenging difficulties in extending the original one-dimensional EMD to the two-dimensional EMD. Numerical experiments using both simulated and practical texture images show that the proposed method works well.

Constrained 3D inversion of magnetic data with structural orientation and borehole lithology: A case study in the Macheng iron deposit, Hebei, China

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. B121-B133 ◽  
Author(s):  
Shida Sun ◽  
Chao Chen ◽  
Yiming Liu
Keyword(s):  
Remanent Magnetization ◽  
Magnetic Data ◽  
Iron Deposit ◽  
Reference Field ◽  
Total Field ◽  
Equivalent Source ◽  
Structural Orientation ◽  
Amplitude Data ◽  
Ore Bodies

We have developed a case study on the use of constrained inversion of magnetic data for recovering ore bodies quantitatively in the Macheng iron deposit, China. The inversion is constrained by the structural orientation and the borehole lithology in the presence of high magnetic susceptibility and strong remanent magnetization. Either the self-demagnetization effect caused by high susceptibility or strong remanent magnetization would lead to an unknown total magnetization direction. Here, we chose inversion of amplitude data that indicate low sensitivity to the direction of magnetization of the sources when constructing the underground model of effective susceptibility. To reduce the errors that arise when treating the total-field anomaly as the projection of an anomalous field vector in the direction of the geomagnetic reference field, we develop an equivalent source technique to calculate the amplitude data from the total-field anomaly. This equivalent source technique is based on the acquisition of the total-field anomaly, which uses the total-field intensity minus the magnitude of the reference field. We first design a synthetic model from a simplified real case to test the new approach, involving the amplitude data calculation and the constrained amplitude inversion. Then, we apply this approach to the real data. The results indicate that the structural orientation and borehole susceptibility bounds are compatible with each other and are able to improve the quality of the recovered model to obtain the distribution of ore bodies quantitatively and effectively.

scholarly journals On the p-norm of the truncated n-dimensional Hilbert transform

1991 ◽  
Vol 43 (2) ◽  
pp. 241-250 ◽  
Author(s):  
J.N. Pandey ◽  
O.P. Singh
Keyword(s):  
Linear Operator ◽  
Linear Combination ◽  
Hilbert Transform ◽  
Bounded Linear Operator ◽  
Measurable Subset ◽  
Bounded Linear ◽  
Finite Linear Combination ◽  
The Hilbert Transform ◽  
Finite Linear ◽  
Hilbert Type

It is shown that a bounded linear operator T from Lρ(Rn) to itself which commutes both with translations and dilatations is a finite linear combination of Hilbert-type transforms. Using this we show that the ρ-norm of the Hilbert transform is the same as the ρ-norm of its truncation to any Lebesgue measurable subset of Rn with non-zero measure.

Using airborne vector magnetic data to calculate the projection of magnetic anomaly vector onto normal geomagnetic field

Geophysics ◽  
2021 ◽  
pp. 1-47
Author(s):  
Rukuan Xie ◽  
Shengqing Xiong ◽  
Shuling Duan ◽  
Jinlong Wang ◽  
Ping Wang ◽  
...  
Keyword(s):  
Magnetic Anomaly ◽  
Geomagnetic Field ◽  
Approximation Error ◽  
Magnetic Data ◽  
Total Field ◽  
Projection Formula ◽  
Total Magnetization ◽  
Vector Formula ◽  
Relationship Of ◽  
Anomaly Formula

The total-field magnetic anomaly [Formula: see text] is an approximation of the projection [Formula: see text] of the magnetic anomaly vector [Formula: see text] onto the normal geomagnetic field [Formula: see text]. However, for highly magnetic sources, the approximation error of [Formula: see text] cannot be ignored. To reduce the error, we have developed a method for calculating [Formula: see text] by using airborne vector magnetic data based on the vector relationship of geomagnetic field [Formula: see text]. The calculation uses the magnitude of the vectors [Formula: see text], [Formula: see text], and [Formula: see text] through a simple approach. To ensure that each magnitude has the same level, we normalize the magnitude of [Formula: see text] using the total-field magnetic data measured by the scalar magnetic sensor. The method is applied to the measured airborne vector magnetic data at the Qixin area of the East Tianshan Mountains in China. The results indicate that the calculated [Formula: see text] has high precision and can distinguish the approximation error less than 3.5 nT. We also analyze the characteristics of the approximation error that are caused by the effects of different total magnetization inclinations. These error characteristics are used to predict the total magnetization inclination of a 2D magnetic source based on the measured airborne vector magnetic data.

scholarly journals Norm variation of ergodic averages with respect to two commuting transformations

2017 ◽  
Vol 39 (3) ◽  
pp. 658-688 ◽  
Author(s):  
POLONA DURCIK ◽  
VJEKOSLAV KOVAČ ◽  
KRISTINA ANA ŠKREB ◽  
CHRISTOPH THIELE
Keyword(s):  
Harmonic Analysis ◽  
Hilbert Transform ◽  
Singular Integrals ◽  
Quantitative Result ◽  
Square Function ◽  
Two Dimensional ◽  
Ergodic Averages ◽  
Multilinear Singular Integrals

We study double ergodic averages with respect to two general commuting transformations and establish a sharp quantitative result on their convergence in the norm. We approach the problem via real harmonic analysis, using recently developed methods for bounding multilinear singular integrals with certain entangled structure. A byproduct of our proof is a bound for a two-dimensional bilinear square function related to the so-called triangular Hilbert transform.

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