Continuation Of Potential Field Data Research Articles

Gravity and Magnetic Joint Imaging Based on Gramian Constraints

Gravity and magnetic imaging produce numerical images proportional to the density and magnetization source distribution through the upward continuation of potential field data. However, the inherent ambiguity and non-uniqueness in gravity or magnetic imaging restrict the reliability of the imaging model. We develop a joint iterative imaging framework for gravity and magnetic data based on Gramian constraints. The imaging fields of gravity and magnetic field are initially calculated by the depth from extreme points method. With the recovered magnetization and density distribution, the gradient directions of the Gramian function for these model parameters are calculated and utilized to regularize the joint imaging directions for gravity and magnetic fields. The introduction of Gramian constraints achieves mutual complementarity of the gravity and magnetic data and generates density and magnetization models with more distinct boundaries and improved structural coherence. The proposed approach is tested by two synthetic examples and applied to field data from the Galinge iron deposit in Qinghai, China. The real case results are verified by information from drillholes and physical properties measurements of ore and rock samples. Joint imaging provides an alternative to joint inversion with improved resolution and reliability of imaging models compared to separate imaging through the complementarity of gravity and magnetic data.

Stable iterative downward continuation of potential field based on Runge-Kutta method

Downward continuation is a useful transformation in the processing and interpretation of potential field data. However, this transformation is known for its inherent instability. In this paper, we proposed a stable iterative Runge-Kutta method for downward continuation that uses an average slope over the interval of continuation. Because of the truncation error, we combine the ideas of Runge-Kutta with the iterative downward continuation methods in a single method to improve the accuracy and the precision of the method. The presented method needs only the computation of the first order vertical derivatives (slope) over the whole interval of continuation using the Tikhonov regularization. To validate the efficiency of the proposed method, various tests were conducted on synthetic magnetic data as well as real aeromagnetic data. The obtained results clearly show the stability of our method for the downward continuation of potential field data.

A Stable Downward Continuation of Potential Field Data: A Case of Study of the Kalatag Polymetallic District, NW China

A Stable Downward Continuation of Potential Field Data: A Case of Study of the Kalatag Polymetallic District, NW China

Geophysical imaging of multiple volcanic structures at the Huichapan Caldera Complex, Mexico

Detailed processing and analyses of aeromagnetic data supported by geological constraints shed new light on the structural framework and plumbing system of Huichapan Caldera and Nopala volcano in the northern sector of the Mexican Volcanic Belt. The interpretation of magnetic anomalies is complex due to the bipolar nature of the magnetic field so we applied reduction to the pole using a double fast Fourier transform to convert the magnetic anomalies into simplified patterns. Short optimal continuous analytical field filters enhanced subsurface and surface structures. The reduction to pole analysis filtered for the upward/downward continuation of potential field data improved both regional and detailed imaging since it was applied to different depths. Shallow subsurface structures as well as at depths of 1.25 km and 0.65 km, were correlated with the surface and regional features.The Huichapan Caldera has at least two contrasting ignimbrites. Results show that there are two large magnetic anomalies associated with different volcanic structures. The first one, a circular positive anomaly corresponds to the caldera rim and the other to the structure of the younger Nopala volcano to the west. Strong magnetic sources indicate the feeder dikes. This study provides geophysical evidence for the location of the head wall of the Huichapan caldera as well as a second rim on the south but E-W and NE-SW regional faulting has destroyed this older caldera on the north. Results show that the structures are tectonically controlled and that the caldera is open on the east and southwest. The trap door structure was associated with this regional fault.

A Constrained Scheme for High Precision Downward Continuation of Potential Field Data

To further improve the accuracy of the downward continuation of potential field data, we present a novel constrained scheme in this paper combining the ideas of the truncated Taylor series expansion, the principal component analysis, the iterative continuation and the prior constraint. In the scheme, the initial downward continued field on the target plane is obtained from the original measured field using the truncated Taylor series expansion method. If the original field was with particularly low signal-to-noise ratio, the principal component analysis is utilized to suppress the noise influence. Then, the downward continued field is upward continued to the plane of the prior information. If the prior information was on the target plane, it should be upward continued over a short distance to get the updated prior information. Next, the difference between the calculated field and the updated prior information is calculated. The cosine attenuation function is adopted to get the scope of constraint and the corresponding modification item. Afterward, a correction is performed on the downward continued field on the target plane by adding the modification item. The correction process is iteratively repeated until the difference meets the convergence condition. The accuracy of the proposed constrained scheme is tested on synthetic data with and without noise. Numerous model tests demonstrate that downward continuation using the constrained strategy can yield more precise results compared to other downward continuation methods without constraints and is relatively insensitive to noise even for downward continuation over a large distance. Finally, the proposed scheme is applied to real magnetic data collected within the Dapai polymetallic deposit from the Fujian province in South China. This practical application also indicates the superiority of the presented scheme.

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

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.

Downward Continuation of Potential Field Data Based on Chebyshev–Padé Approximation Function

To further improve the stability and accuracy of the downward continuation, we presented a new strategy based on the Chebyshev-Pad, approximation in the frequency domain. First, we compared the errors between the function exp(x) and its different approximation functions, including Taylor series, Chebyshev approximation, Pad, approximation, and Chebyshev-Pad, approximation. Meanwhile, the filter characteristic curves of the different functions in the frequency domain are calculated. It turned out that the Chebyshev-Pad, approximation is the most precise function. Similar to the Taylor series expansion, different downward continuation methods were established based on these approximation functions in the frequency domain. We compared the accuracy of these downward continuation methods using model tests with and without noise. The results showed that the downward continuation based on Chebyshev-Pad, approximation was insensitive to the noise and can obtain a more precise result. To further compare these methods and prove the superiority of Chebyshev-Pad, approximation, the iteration methods of downward continuation were proposed. We can obtain an accurate result within less iterations using Chebyshev-Pad, approximation. To further suppress the noise effect, we improved the iteration methods using upward continuation. Once again, the model tests showed that the Chebyshev-Pad, approximation is a preferred method to implement downward continuation. Finally, the method was applied on a field gravity data and showed its superiority. It demonstrated that we can use the Chebyshev-Pad, approximation to replace the classical Taylor series expansion to implement more precise and stable downward continuation.

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.

BTTB–RRCG method for downward continuation of potential field data

This paper presents a conjugate gradient (CG) method for accurate and robust downward continuation of potential field data. Utilizing the Block-Toeplitz Toeplitz-Block (BTTB) structure, the storage requirement and the computational complexity can be significantly reduced. Unlike the wavenumber domain regularization methods based on fast Fourier transform, the BTTB-based conjugate gradient method induces little artifacts near the boundary. The application of a re-weighted regularization in a space domain significantly improves the stability of the CG scheme for noisy data. The synthetic data with different levels of added noise and real field data are used to validate the effectiveness of the proposed scheme, and the computed results are compared with those based on recently proposed wavenumber domain methods and the Taylor series method. The simulation results verify that the proposed scheme is superior to the existing methods considered in this study in terms of accuracy and robustness. The proposed scheme is a powerful computational tool capable of applications for large scale data with modest computational cost.

An improved regularized downward continuation of potential field data

Abstract Downward continuation of potential field data plays an important role in interpretation of gravity and magnetic data. For its inherent instability, many methods have been presented to downward continue stably and precisely. In this manuscript, we propose an improved regularization operator for downward continuation of potential field data. First, we simply define a special wavenumber named the cutoff wavenumber to divide the potential field spectrum into the signal part and the noise part based on the radially averaged power spectrum of potential field data. Next, we use the conventional downward continuation operator to downward continue the signal and the Tikhonov regularization operator to suppress the noise. Moreover, the parameters of the improved operator are defined by the cutoff wavenumber which has an obvious physical significance. The improved operator can not only eliminate the influence of the high-wavenumber noise but also avoid the attenuation of the signal. Experiments through synthetic gravity and real aeromagnetic data show that the downward continuation precision of the proposed operator is higher than the Tikhonov regularization operator.

A stable iterative downward continuation of potential field data

Abstract Downward continuation is a useful tool in the processing of potential field data, which can effectively enhance weak anomalies and identify overlap anomalies, but we all know that the computation of downward continuation is unstable, and easily distorts the true feature of potential field data. Because the computation of upward continuation and horizontal derivatives is stable, we proposed using the combination of upward continuation and horizontal derivative to accomplish the downward continuation of potential field data. The proposed method is demonstrated on synthetic potential field data, and the results show that the proposed method can finish the downward continuation of the data stably and precisely, and the precision of the proposed method is higher than the traditional method. We also apply it to real potential field data, and the results show that the proposed method accomplishes the downward continuation of the real data stably.

An improved and stable downward continuation of potential field data: The truncated Taylor series iterative downward continuation method

We present a stable downward continuation strategy based on combining the ideas of the Taylor series expansion and the iterative downward continuation methods in a single method with better downward continuation and/or computer time/memory performance for potential field data containing noise. In the new truncated Taylor series iterative downward continuation (TTSIDC) method, a correction is made on the continuing plane by downward continuing the difference between the observed and the calculated field. The process is iteratively repeated until the difference meets the convergence conditions. It is tested on synthetic and field data and compared to other downward continuation methods. The proposed method yields sharper images and estimates more accurate amplitudes than most of the existing methods, especially for downward continuation over larger distances. The TTSIDC method also gives comparable results to the method of downward continuation using the least-squares inversion (DCLSI); however, the DCLSI method’s requirements of computer memory and time are substantially greater than our TTSIDC method, rendering the DCLSI method impractical for data sets of routine size on desktop computers commonly available today.

The Stable Downward Continuation of Potential Field Data

Filtering methods based on the Fourier transform are routinely used in the processing of geophysical data. Because of the nature of the Fourier transform, the data must be prepared before the transform is calculated. This preparation usually takes the form of the removal of any trend from the data, combined with the padding of the data to 2N points between the data edges. However, no data preparation procedure is perfect, and the result is that problems (in the form of edge effects) appear in the filtered data. When high-pass filters (such as derivatives or downward continuation) are subsequently used, then these edge effects become particularly apparent.This paper suggests three methods for the stable downward continuation of geophysical data (two of which may be combined). The first method is applied to an integrated horizontal derivative of the data rather than to the data itself. Since the horizontal derivative can be calculated in the space domain where fast Fourier transform (FFT) edge effects are not present, this reduces the enhancement of the data at frequencies near the Nyquist, resulting in smaller edge effect problems. The second method measures the FFT-induced noise by comparing data that has been downward continued using both the space- and frequency-domain methods. The data is then compensated accordingly, and the compensated data may be downward continued to arbitrary distances that are not possible using space-domain operators. The final method treats downward continuation as an inverse problem, which allows the control of both FFT-induced noise and other noise that is intrinsic to the dataset. This method is computationally slow compared to the first two methods because of the inversion of large matrices that is required. The methods are demonstrated on synthetic models and on aeromagnetic data from the Bushveld igneous complex, South Africa.

Improved Downward Continuation of Potential Field Data

A number of techniques for downward continuation of potential field data, some already established in the literature and some novel, are tested and compared on synthetic and measured potential field profiles. A combination of Wiener filtering and Translation-Invariant denoising gives best results on synthetic data with added white noise. A Multiscale Edge Transform followed by a mild low-pass filter, and the ISVD method, prove to be the two most stable and robust approaches on measured data.

Potential field continuation: a comparative analysis of three different types of software

DARING.F is a new Fortran77 computer program which has been developed to perform the continuation of potential field data between arbitrary surfaces. The implemented equivalent source algorithm inverts a system of linear equations by using sparse matrix. A comparative analysis between the performance of this software and that of two computer programs (named UPWARD.F and UPNEW.F) previously written by the same authors is carried out. As a result of this analysis, some useful and important suggestions on how to obtain the highest level of accuracy of transformed data in various situations (i.e. large matrices of data, close surfaces) are given.

A computer program to perform the upward continuation of potential field data between arbitrary surfaces

A FORTRAN 77 computer program has been developed for performing the upward continuation of potential field data between general surfaces. The mathematical background is based on an equivalent source algorithm and on the consequent Fredholm integral equation of the second kind. A graphical test to illustrate the performance of the program demonstrates the program's ability to reduce significant topographic interference with the signal.

Calculation of Fourier Transforms by the Backus-Gilbert Method

Summary The linear inverse theory of Backus & Gilbert has been applied to the problem of calculating the Fourier transform of digitized data with the objective of assessing the effects of missingportions of the data series and of contamination of the signal by ' noise '. When ' noise ' in the data is of concern this method achieves a maximum decrease in the variance of the Fourier transform estimate for a minimum sacrifice in resolution, thereby optimizing the trade-off between resolution and accuracy. The effects of data gaps are easily treated and it is shown that it may sometimes be desirable to interpolate these gaps even though a large variance must be ascribed to the fabricated data. We also apply the Backus-Gilbert technique to the calculation of the reverse Fourier transform, and an application to the downward continuation of potential field data is given.

DESIGN OF SPATIAL FILTERS AND THEIR APPLICATION TO HIGH‐RESOLUTION AEROMAGNETIC DATA

Methods for the design of spatial filters are discussed in this paper. For a given response of a one‐dimensional filter, the weighting coefficients are calculated by solving a set of simultaneous equations with a simple matrix inversion procedure. In the case of a two‐dimensional filter, the method for obtaining the coefficients of a double Fourier series representing a set of given values is used to design the spatial operator. The problems connected with the length of the operator and the choice of a suitable decay in the high‐frequency response are discussed in detail. In order to show the usefulness of these methods, the paper presents several examples of operators designed for computing the vertical gradient, the second vertical derivative, and downward continuation of potential field data. A two‐dimensional vertical gradient filter is applied to the total field data obtained during a high‐resolution aeromagnetic survey over an area in the Precambrian Shield of Northeastern Ontario. The calculated gradient maps are compared with maps showing measured gradient values. The quality of the calculated maps in defining trends, patterns, and detailed features of anomalies shows the feasibility of obtaining very accurate vertical gradient maps from observed total field data.

Development of the COMMAP System: ABSTRACT

COMMAP is an automatic mapping system. It uses an automatic map reader for digitizing the input data, an IBM 704 computer for processing the data and a Benson Lehner Electroplotter for plotting and contouring the output. This system processes, plots, and contours all mappable data. Computations which can be preformed by the system include the following: (1) determination of regionals and residuals by polynomial surface-fitting techniques, (2) determination of regionals and residuals by various ring-average methods, (3) upward and downward continuation of potential field data, (4) first and second vertical derivatives by several methods. This paper covers the system in general and gives examples of tabulated, plotted and contoured output of the results for a number of specific field problems. End_of_Article - Last_Page 371------------