Potential field continuation between arbitrary surfaces — Comparing methods

The continuation of potential field data from one irregular surface to another, not always horizontal, is often a necessary component within the data processing and interpretation stream. The most common requirement is to reduce field values (or some related component or derivative) to a horizontal plane, to facilitate further quantitative processing. Methods available to continue data comprise two main approaches. The first (source-based) involves calculating a source distribution that produces a fit to the data and can be used to calculate the field at any other point above. The second (field-based) requires no source determinations and deals with only fields but may involve calculating the field on some intermediate surface. Nine different continuation methods were compared (four source based and five field based) through synthetic tests and on real data from a helicopter-borne survey in Yukon, Canada. The preferred methods of Guspi and Hansen are those that do not involve any theoretical or geometric approximations and involve intermediate calculations on a plane or surface close to the observation surface. The Guspi approach is faster, based on using frequency-domain processing, but the Hansen method uses equivalent sources close enough to and consistently below the observation surface so that no low-pass filtering needs to be used.

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Reduction of potential field data to a horizontal plane

Geophysics ◽

10.1190/1.1442866 ◽

1990 ◽

Vol 55 (5) ◽

pp. 549-555 ◽

Cited By ~ 25

Author(s):

Mark Pilkington ◽

W. E. S. Urquhart

Keyword(s):

Potential Field ◽

Horizontal Plane ◽

Field Data ◽

Synthetic Data ◽

Mirror Image ◽

Source Distribution ◽

Aeromagnetic Survey ◽

Potential Field Data ◽

Equivalent Sources ◽

Topographic Gradients

Most existing techniques for potential field data enhancement and interpretation require data on a horizontal plane. Hence, when observations are made on an irregular surface, reduction to a horizontal plane is necessary. To effect this reduction, an equivalent source distribution that models the observed field is computed on a mirror image of the observation surface. This irregular mirror image surface is then replaced by a horizontal plane and the effect of the equivalent sources is computed on the required horizontal level. This calculated field approximates the field reduced to a horizontal plane. The good quality of this approximation is demonstrated by two‐dimensional synthetic data examples in which the maximum errors occur in areas of steep topographic gradients and increased magnetic field intensity. The approach is also applied to a portion of a helicopter‐borne aeromagnetic survey from the Gaspé region in Quebec, Canada, where the results are a horizontal shifting of anomaly maxima of up to 150 m and changes in anomaly amplitudes of up to 100 nT.

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Discrete linear transformations of potential field data

Geophysics ◽

10.1190/1.1442676 ◽

1989 ◽

Vol 54 (4) ◽

pp. 497-507 ◽

Cited By ~ 29

Author(s):

Jorge W. D. Leão ◽

João B. C. Silva

Keyword(s):

Potential Field ◽

Field Data ◽

Amazon Basin ◽

Real Data ◽

Damping Factor ◽

Linear Transformations ◽

Potential Field Data ◽

Data Window ◽

Green’S Matrix ◽

Equivalent Layer

We present a new approach to perform any linear transformation of gridded potential field data using the equivalent‐layer principle. It is particularly efficient for processing areas with a large amount of data. An N × N data window is inverted using an M × M equivalent layer, with M greater than N so that the equivalent sources extend beyond the data window. Only the transformed field at the center of the data window is computed by premultiplying the equivalent source matrix by the row of the Green’s matrix (associated with the desired transformation) corresponding to the center of the data window. Since the inversion and the multiplication by the Green’s matrix are independent of the data, they are performed beforehand and just once for given values of N, M, and the depth of the equivalent layer. As a result, a grid operator for the desired transformation is obtained which is applied to the data by a procedure similar to discrete convolution. The application of this procedure in reducing synthetic anomalies to the pole and computing magnetization intensity maps shows that grid operators with N = 7 and M = 15 are sufficient to process large areas containing several interfering sources. The use of a damping factor allows the computation of meaningful maps even for unstable transformations in the presence of noise. Also, an equivalent layer larger than the data window takes into account part of the interfering sources so that a smaller damping factor is employed as compared with other damped inversion methods. Transformations of real data from Xingú River Basin and Amazon Basin, Brazil, demonstrate the contribution of this procedure for improvement of a preliminary geologic interpretation with minimum a priori information.

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On: “Reduction of Unevenly Spaced Potential Field Data to a Horizontal Plane by Means of Finite Harmonic Series,” by R. G. Henderson and L. Cordell (GEOPHYSICS, October 1971, p. 856–866)

Geophysics ◽

10.1190/1.1440315 ◽

1972 ◽

Vol 37 (6) ◽

pp. 1046-1046

Author(s):

K. N. Khattri ◽

A. N. Datta

Keyword(s):

Fourier Series ◽

Potential Field ◽

Horizontal Plane ◽

Field Data ◽

Harmonic Series ◽

Potential Field Data ◽

Interesting Article

We have read the interesting article by Henderson and Cordell (197l). The authors transform the observed data using the finite Fourier series and compensate for the distortion introduced in the observed potential field due to observations taken on uneven topography.

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A method for inversion of 1D vertical soundings of gravity anomalies

Geophysics ◽

10.1190/geo2017-0186.1 ◽

2018 ◽

Vol 83 (2) ◽

pp. G15-G23

Author(s):

Andrea Vitale ◽

Domenico Di Massa ◽

Maurizio Fedi ◽

Giovanni Florio

Keyword(s):

Potential Field ◽

Field Data ◽

Gravity Data ◽

Finite Size ◽

Gravity Anomalies ◽

Real Data ◽

Gravity Inversion ◽

Chain Process ◽

Potential Field Data ◽

Gamma Density

We have developed a method to interpret potential fields, which obtains 1D models by inverting vertical soundings of potential field data. The vertical soundings are built through upward continuation of potential field data, measured on either a profile or a surface. The method assumes a forward problem consisting of a volume partitioned in layers, each of them homogeneous and horizontally finite, but with the density changing versus depth. The continuation errors, increasing with the altitude, are automatically handled by determining the coefficients of a third-order polynomial function of the altitude. Due to the finite size of the source volume, we need a priori information about the total horizontal extent of the volume, which is estimated by boundary analysis and optimized by a Markov chain process. For each sounding, a 1D inverse problem is independently solved by a nonnegative least-squares algorithm. Merging of the several inverted models finally yields approximate 2D or 3D models that are, however, shown to generate a good fit to the measured data. The method is applied to synthetic models, producing good results for either perfect or continued data. Even for real data, i.e., the gravity data of a sedimentary basin in Nevada, the results are interesting, and they are consistent with previous interpretation, based on 3D gravity inversion constrained by two gamma-gamma density logs.

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Potential‐field continuation between irregular surfaces—Remarks on the method by Xia et al.

Geophysics ◽

10.1190/1.1444301 ◽

1998 ◽

Vol 63 (1) ◽

pp. 104-108 ◽

Cited By ~ 4

Author(s):

Bruno Meurers ◽

Roland Pail

Keyword(s):

Magnetic Fields ◽

Potential Field ◽

Field Data ◽

Potential Field Data ◽

Irregular Surfaces ◽

Equivalent Source ◽

Wavenumber Domain ◽

Excellent Method ◽

Reducing Potential ◽

Field Continuation

Xia et al. (1993) offer an excellent method for potential‐field continuation between irregular surfaces by applying the equivalent source technique. This method has proven to be the fastest and most stable procedure for solving the problem of reducing potential‐field data to a constant datum (e.g., Pail, 1995) as long as no sources exist between observation surface and the equivalent stratum. The authors suggest using special equations for the continuation of magnetic fields. Theoretically this is correct, but neither necessary nor well suited, because of the characteristics of the operator for magnetic fields applied in the wavenumber domain.

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On: “Reduction of Unevenly Spaced Potential Field Data to a Horizontal Plane by Means of Finite Harmonic Series” by Roland G. Henderson and Lindrith Cordell (GEOPHYSICS, October 1971, p. 856–866)

Geophysics ◽

10.1190/1.1440295 ◽

1972 ◽

Vol 37 (4) ◽

pp. 703-703

Author(s):

Alan T. Herring

Keyword(s):

Gravity Field ◽

Potential Field ◽

Horizontal Plane ◽

Field Data ◽

Bouguer Anomaly ◽

Harmonic Series ◽

Potential Field Data ◽

Topographic Relief ◽

Vertical Gradients

The authors recommend on page 864, that their technique for correcting for anomalous vertical gradients in the gravity field be applied only in “cases where high topographic relief produces large corrections to the station Bouguer anomaly.” The correction applied by the authors amounts to the continuation of the observed gravity field onto a single‐elevation plane from the varying elevations of the observation points. The authors should therefore caution the reader against choosing the datum plane such that the gravity field is continued through sources of interest lying above the datum plane—an easily made mistake in areas of high topographic relief.

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Inversion of potential field data in Fourier transform domain

Geophysics ◽

10.1190/1.1441943 ◽

1985 ◽

Vol 50 (4) ◽

pp. 685-691 ◽

Cited By ~ 17

Author(s):

J. C. Mareschal

Keyword(s):

Fourier Transform ◽

Laplace Transform ◽

Potential Field ◽

Homogeneous Problem ◽

Source Distribution ◽

Flow Profile ◽

Surface Source ◽

Potential Field Data ◽

The Laplace Transform ◽

The Fourier Transform

A relationship is derived between the Fourier transform of a potential field at the Earth’s surface and the transform of the inducing source distribution. The Fourier transform of the field is the Laplace transform of the source distribution spectrum when the Laplace transform variable p is equal to the wavenumber. This relationship can be used to determine all possible source distributions compatible with the data. The solution is the superposition of a particular solution to an inhomogeneous problem and of the general solution to the homogeneous problem (i.e., for which the field vanishes at the surface). Source distribution can be expanded into a set of known functions; coefficients of the expansion are determined by solving a system of linear equations. Physical constraints can be introduced to restrict the variation range of the coefficients of expansion. Two examples are presented to illustrate the method: a synthetic gravity profile and a heat flow profile are inverted to determine density or heat source distributions compatible with the data.

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An adaptive iterative method for downward continuation of potential-field data from a horizontal plane

Geophysics ◽

10.1190/geo2012-0404.1 ◽

2013 ◽

Vol 78 (4) ◽

pp. J43-J52 ◽

Cited By ~ 23

Author(s):

Xiaoniu Zeng ◽

Xihai Li ◽

Juan Su ◽

Daizhi Liu ◽

Hongxing Zou

Keyword(s):

Iterative Method ◽

Tikhonov Regularization ◽

Potential Field ◽

Horizontal Plane ◽

Field Data ◽

Regularization Parameter ◽

Downward Continuation ◽

Tikhonov Regularization Method ◽

Potential Field Data ◽

Wavenumber Domain

We have developed an improved adaptive iterative method based on the nonstationary iterative Tikhonov regularization method for performing a downward continuation of the potential-field data from a horizontal plane. Our method uses the Tikhonov regularization result as initial value and has an incremental geometric choice of the regularization parameter. We compared our method with previous methods (Tikhonov regularization, Landweber iteration, and integral-iteration method). The downward-continuation performance of these methods in spatial and wavenumber domains were compared with the aspects of their iterative schemes, filter functions, and downward-continuation operators. Applications to synthetic gravity and real aeromagnetic data showed that our iterative method yields a better downward continuation of the data than other methods. Our method shows fast computation times and a stable convergence. In addition, the [Formula: see text]-curve criterion for choosing the regularization parameter is expressed here in the wavenumber domain and used to speed up computations and to adapt the wavenumber-domain iterative method.

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An edge-assisted smooth method for potential field data

Journal of Geophysics and Engineering ◽

10.1093/jge/gxaa072 ◽

2021 ◽

Vol 18 (1) ◽

pp. 113-123

Author(s):

Shijing Zheng ◽

Xiaohong Meng ◽

Jun Wang

Keyword(s):

Edge Detection ◽

Potential Field ◽

Field Data ◽

Real Data ◽

Linear Functions ◽

Detection Methods ◽

Edge Preserving ◽

Potential Field Data ◽

Tectonic Boundaries ◽

Derivatives Of

Abstract Edge detection is one of the most commonly used methods for the interpretation of potential field data, because it can highlight the horizontal inhomogeneous of underground geological bodies (faults, tectonic boundaries, etc.). A variety of edge detection methods have been reported in the literature, most of which are based on the combined transformation results of horizontal and vertical derivatives of the observations. Consequently, these edge detection methods are sensitive to noise. Therefore, noise reduction is desirable ahead of applying edge detection methods. However, the application of conventional filters smears discontinuities in the data to a certain extent, which would inevitably induce unfavourable influence on subsequent edge detection. To solve this problem, a novel edge-preserving smooth method for potential field data is proposed, which is based on the concept of guided filter developed for image processing. The new method substitutes each data point by a combination of a series of coefficients of linear functions. It was tested on synthetic model and real data, and the results showed that it can effectively smooth potential field data while preserving major structural and stratigraphic discontinuities. The obtained data from the new filter contain more obvious features of existing faults, which brings advantageous to further geological interpretations.

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Correction of topographic distortions in potential‐field data: A fast and accurate approach

Geophysics ◽

10.1190/1.1443434 ◽

1993 ◽

Vol 58 (4) ◽

pp. 515-523 ◽

Cited By ~ 28

Author(s):

Jianghai Xia ◽

Donald R. Sprowl ◽

Dana Adkins‐Heljeson

Keyword(s):

Potential Field ◽

Field Data ◽

Gravity Data ◽

Source Distribution ◽

Potential Field Data ◽

Equivalent Source ◽

Horizontal Shift ◽

Maximum Elevation ◽

Rms Error ◽

Forward Calculation

The equivalent source concept is used in the wavenumber domain to correct distortions in potential‐field data caused by topographic relief. The equivalent source distribution on a horizontal surface is determined iteratively through forward calculation of the anomaly on the topographic surface. Convergence of the solution is stable and rapid. The accuracy of the Fourier‐based approach is demonstrated by two synthetic examples. For the gravity example, the rms error between the corrected anomaly and the desired anomaly is 0.01 mGal, which is less than 0.5 percent of the maximum synthetic anomaly. For the magnetic example, the rms error is 0.7 nT, which is less than 1 percent of the maximum synthetic anomaly. The efficiency of the approach is shown by application to the gravity and aeromagnetic grids for Kansas. For gravity data, with a maximum elevation change of 500 m reducing to a horizontal datum results in a maximum correction in gravity anomaly amplitude of up to 2.6 mGal. For aeromagnetic data, the method results in a maximum horizontal shift of anomalies of 470 m with a maximum correction in aeromagnetic anomaly amplitudes up to 270 nT.

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