Inversion of potential‐field data by iterative forward modeling in the wavenumber domain

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 126-130 ◽  
Author(s):  
Jianghai Xia ◽  
Donald R. Sprowl
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Single Layer ◽  
Large Data ◽  
Uniform Density ◽  
Data Sets ◽  
Potential Field Data ◽  
Wavenumber Domain ◽  
Solution Convergence ◽  
Forward Calculation

Direct inversion of potential‐field data is hindered by the nonuniqueness of the general solution. Convergence to a single solution can only be obtained when external constraints are placed on the subsurface geometry. Two such constrained geometries are dealt with here: a single, nonplanar interface between two layers, each of uniform density or magnetization, and the distribution of the density or magnetization contrast within a single layer. Both of these simple geometries have geologic application. Inversion is accomplished by iterative improvement in an initial subsurface model in the wavenumber domain. The inversion process is stable and is efficient for usage on large data sets. Forward calculation of anomalies is by Parker’s (1973) algorithm (Blakely, 1981).

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

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 104-108 ◽  
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.

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.

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

Geophysics ◽  
1993 ◽  
Vol 58 (4) ◽  
pp. 515-523 ◽  
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.

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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