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 ◽  
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.

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 ◽  
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.

REDUCTION OF UNEVENLY SPACED POTENTIAL FIELD DATA TO A HORIZONTAL PLANE BY MEANS OF FINITE HARMONIC SERIES

Geophysics ◽  
1971 ◽  
Vol 36 (5) ◽  
pp. 856-866 ◽  
Author(s):  
Roland G. Henderson ◽  
Lindrith Cordell
Keyword(s):  
Horizontal Plane ◽  
Field Data ◽  
Vertical Displacement ◽  
Harmonic Series ◽  
Reference Plane ◽  
Magnetic Data ◽  
Residual Variance ◽  
Potential Field Data ◽  
Variance Estimates ◽  
Gravity And Magnetic Data

Conventional reductions of gravity and magnetic data do not lead to values that are effectively on the same horizontal plane, although it is common practice to regard them so. In regions of high topographic relief, failure to take into account local differences in vertical gradients can result in appreciable error. In this study a method is developed for reducing to a common level gravity or magnetic anomaly data observed at unevenly spaced stations at various elevations above a reference plane. The reduction is effected by means of finite harmonic series approximations in which the coefficients are determined by matrix methods and least squares. Traditional Fourier methods are not applicable because uneven station spacing and relative vertical displacement of stations preclude the use of the orthogonality properties of the trigonometric functions. The number of terms required to represent the data adequately is discussed in terms of “cutoff” wavenumbers empirically determined from residual variance estimates. The method is illustrated by application to theoretical and field data.

Reduction of potential field data to a horizontal plane

Geophysics ◽  
1990 ◽  
Vol 55 (5) ◽  
pp. 549-555 ◽  
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.

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

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. J43-J52 ◽  
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.

An improved approach for detecting the locations of the maxima in interpreting potential field data

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Luan Thanh Pham ◽  
Ozkan Kafadar ◽  
Erdinc Oksum ◽  
Ahmed M. Eldosouky
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Potential Field Data

Adaptive sampling of potential-field data: A direct approach to compressive inversion

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. IM1-IM9 ◽  
Author(s):  
Nathan Leon Foks ◽  
Richard Krahenbuhl ◽  
Yaoguo Li
Keyword(s):  
Potential Field ◽  
Adaptive Sampling ◽  
Field Data ◽  
Computational Cost ◽  
Large Field ◽  
Magnetic Data ◽  
Data Sampling ◽  
Data Types ◽  
Data Set ◽  
Potential Field Data

Compressive inversion uses computational algorithms that decrease the time and storage needs of a traditional inverse problem. Most compression approaches focus on the model domain, and very few, other than traditional downsampling focus on the data domain for potential-field applications. To further the compression in the data domain, a direct and practical approach to the adaptive downsampling of potential-field data for large inversion problems has been developed. The approach is formulated to significantly reduce the quantity of data in relatively smooth or quiet regions of the data set, while preserving the signal anomalies that contain the relevant target information. Two major benefits arise from this form of compressive inversion. First, because the approach compresses the problem in the data domain, it can be applied immediately without the addition of, or modification to, existing inversion software. Second, as most industry software use some form of model or sensitivity compression, the addition of this adaptive data sampling creates a complete compressive inversion methodology whereby the reduction of computational cost is achieved simultaneously in the model and data domains. We applied the method to a synthetic magnetic data set and two large field magnetic data sets; however, the method is also applicable to other data types. Our results showed that the relevant model information is maintained after inversion despite using 1%–5% of the data.

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