scholarly journals Three-dimensional interpretation of magnetic and gravity anomalies using the finite-difference similarity transform

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. L79-L90 ◽  
Author(s):  
Daniela Gerovska ◽  
Marcos J. Araúzo-Bravo ◽  
Kathryn Whaler ◽  
Petar Stavrev ◽  
Alan Reid
Keyword(s):  
Finite Difference ◽  
Random Noise ◽  
Source Parameters ◽  
Magnetization Vector ◽  
Real Data ◽  
Index Formula ◽  
Magnetic Data ◽  
Horizontal Position ◽  
Structural Index ◽  
Similarity Transform

We present an automatic procedure for interpretation of magnetic or gravity gridded anomalies based on the finite-difference similarity transform (FDST). It is called MaGSoundFDST (magnetic and gravity sounding based on the finite-difference similarity transform) and uses a “focusing” principle in contrast to deriving multiple clusters of many solutions as in the widely used Euler deconvolution method. The source parameters are characterized by isolated solutions, and the interpreter obtains parallel images showing the horizontal position, depth, and structural index [Formula: see text] value. The underlying principle is that the FDST of a potential field anomaly becomes zero or linear at all observation points when the central point of similarity (CPS) of the transform coincides with a source field’s singular point and a correct [Formula: see text] value is used. The procedure involves calculating a 3D function that evaluates the linearity of the FDST for a series of [Formula: see text] values, using a moving window and sounding the subsurface along a verticalline under each window center. We then combine the 3D results for different [Formula: see text] values into a single map whose minima determine the horizontal position of the sources. The [Formula: see text] value and the CPS depth associated with each minimum determine the [Formula: see text] value and depth of the corresponding source. Only one estimate characterizes a simple source, which is a major advantage over other window-based procedures. MaGSoundFDST uses only the measured anomalous field and its upward continuation, thus avoiding the direct use of field derivatives. It is independent of the magnetization-vector direction in the magnetic data case. The procedure accounts for a linear background of local gravity or magnetic anomalies and has been applied effectively to several cases of synthetic and real data. MaGSoundFDST shares common features with the magnetic and gravity sounding based on the differential similarity transform (MaGSoundDST) but is more stable in estimating depth and structural index in the presence of random noise.

Magnetization vector imaging for borehole magnetic data based on magnitude magnetic anomaly

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. D429-D444 ◽  
Author(s):  
Shuang Liu ◽  
Xiangyun Hu ◽  
Tianyou Liu ◽  
Jie Feng ◽  
Wenli Gao ◽  
...  
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Magnetization Vector ◽  
Real Data ◽  
Magnetic Anomalies ◽  
Magnetic Data ◽  
Preconditioned Conjugate Gradient ◽  
Magnetization Direction ◽  
Magnetization Intensity

Remanent magnetization and self-demagnetization change the magnitude and direction of the magnetization vector, which complicates the interpretation of magnetic data. To deal with this problem, we evaluated a method for inverting the distributions of 2D magnetization vector or effective susceptibility using 3C borehole magnetic data. The basis for this method is the fact that 2D magnitude magnetic anomalies are not sensitive to the magnetization direction. We calculated magnitude anomalies from the measured borehole magnetic data in a spatial domain. The vector distributions of magnetization were inverted methodically in two steps. The distributions of magnetization magnitude were initially solved based on magnitude magnetic anomalies using the preconditioned conjugate gradient method. The preconditioner determined by the distances between the cells and the borehole observation points greatly improved the quality of the magnetization magnitude imaging. With the calculated magnetization magnitude, the distributions of magnetization direction were computed by fitting the component anomalies secondly using the conjugate gradient method. The two-step approach made full use of the amplitude and phase anomalies of the borehole magnetic data. We studied the influence of remanence and demagnetization based on the recovered magnetization intensity and direction distributions. Finally, we tested our method using synthetic and real data from scenarios that involved high susceptibility and complicated remanence, and all tests returned favorable results.

Imaging depth, structure, and susceptibility from magnetic data: The advanced source-parameter imaging method

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. L31-L38 ◽  
Author(s):  
Richard S. Smith ◽  
Ahmed Salem
Keyword(s):  
Source Parameters ◽  
Thin Sheet ◽  
Signal Amplitude ◽  
Horizontal Cylinder ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Imaging Method ◽  
Structural Index ◽  
Synthetic Test ◽  
Vertical Contact

An important problem in the interpretation of magnetic data is quantifying the source parameters that describe the anomalous structure. We present a new method that uses various combinations of the local wavenumbers for estimating the depth and shape (structural index) of the structure. Because the estimates are derived from third derivatives of the magnetic data, they are noisy. However, there are multiple ways of calculating the depth and index, and these solutions can be averaged to give a stable estimate. Even so, a synthetic test shows that the results are erratic away from the locations where the analytic-signal amplitude is large. Hence, when we generate images of the depth and structural index, we make the results most visible where the analytic-signal amplitude is large and less visible where the signal is small. The advantage of the method is that estimates can be obtained at all locations on a profile and used to generate continuous profiles or images of the source parameters. This can be used to help identify the locations where interference might be corrupting the results. The structural index image can be used to determine the most appropriate type of model for an area. Assuming this model, it is possible to calculate the depth that would be consistent with the model and the data. Knowing both the depth and model, the analytic-signal amplitude can be converted to apparent susceptibility. If a vertical-contact model is assumed, the susceptibility contrast across the contact can be imaged. For the thin-sheet and horizontal-cylinder models, we can image the susceptibility-thickness and susceptibility-area products, respectively.

Stepped inversion of magnetic data

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. L21-L30 ◽  
Author(s):  
Soraya Lozada Tuma ◽  
Carlos Alberto Mendonça
Keyword(s):  
Magnetic Anomaly ◽  
Shape Function ◽  
Source Parameters ◽  
Real Data ◽  
Magnetic Data ◽  
Total Field ◽  
Magnetization Direction ◽  
Magnetization Intensity ◽  
Magnetic Inversion ◽  
Total Gradient

We present a three-step magnetic inversion procedure in which invariant quantities with respect to source parameters are inverted sequentially to give (1) shape cross section, (2) magnetization intensity, and (3) magnetization direction for a 2D (elongated) magnetic source. The quantity first inverted (called here the shape function) is obtained from the ratio of the gradient intensity of the total-field anomaly to the intensity of the anomalous vector field. For homogenous sources, the shape function is invariant with source magnetization and allows reconstruction of the source geometry by attributing an arbitrary magnetization to trial solutions. Once determined, the source shape is fixed and magnetization intensity is estimated by fitting the total gradient of the total-field anomaly (equivalent to the amplitude of the analytic signal of magnetic anomaly). Finally, the source shape and magnetization intensity are fixed and the magnetization direction is determined by fitting the magnetic anomaly. As suggested by numerical modeling and real data application, stepped inversion allows checking whether causative sources are homogeneous. This is possible because the shape function from inhomogeneous sources can be fitted by homogeneous models, but a model obtained in this way fits neither the total gradient of the magnetic anomaly nor the magnetic anomaly itself. Such a criterion seems effective in recognizing strongly inhomogeneous sources. Stepped inversion is tested with numerical experiments, and is used to model a magnetic anomaly from intrusive basic rocks from the Paraná Basin, Brazil.

Automatic interpretation of magnetic dike parameters using the analytical signal technique

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 551-561 ◽  
Author(s):  
Mehrdad Bastani ◽  
Laust B. Pedersen
Keyword(s):  
Source Parameters ◽  
Synthetic Data ◽  
Analytical Signal ◽  
Magnetic Data ◽  
Impact Structure ◽  
Horizontal Position ◽  
Coherent Signals ◽  
Automatic Interpretation ◽  
Horizontal Curvature ◽  
The Magnetic Field

The analytical signal of the magnetic field is used to automatically determine the source parameters of dikelike structures. The method is particularly useful for interpreting large amounts of data collected during airborne surveys because it makes full use of the high density of data along the flight lines while simultaneously checking for two‐dimensionality and strike directions by searching for coherent signals in neighboring profiles. The maximum horizontal curvature of the amplitude of the analytical signal is used to locate the dikes along a given profile. Tests with synthetic data show that the dike’s horizontal position is resolved accurately. Magnetic data from the Siljan impact structure in Sweden show that the estimated strikes are reliable and that dip, depth, and width estimates are coherent, especially for well‐isolated dikelike structures.

Automatic inversion of magnetic anomalies from two height levels using finite-difference similarity transforms

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. L75-L86 ◽  
Author(s):  
Petar Stavrev ◽  
Daniela Gerovska ◽  
Marcos J. Araúzo-Bravo
Keyword(s):  
Finite Difference ◽  
Potential Field ◽  
Random Noise ◽  
Inverse Operator ◽  
Large Data ◽  
Magnetic Data ◽  
Data Sets ◽  
Actual Measurement ◽  
Straight Line ◽  
Geometric Type

We solve the inverse magnetic problem for the depth and shape of simple sources in the presence of a regional field and truly random noise. We do not use noise-generating derivatives nor are we forced to solve complex systems of equations. Our inverse operator applies a new geometric type of field transform, the finite-difference similarity transform (FDST), that is based on a postulated degree of homogeneity in the potential field. Magnetic data from two height levels are required for the calculation of the FDSTs. The FDSTs are generated for an assumed central point of similarity (CPS) and a trial value (index) for the coefficient of similarity, and they are sensitive to the distance between the source and the CPS and to the agreement between the index and the degree of homogeneity in the data. When the CPS converges to a singular point in the potential field, say, the center or the topedge of the source, and when the trial index converges on the degree of homogeneity present in the data, the FDST drops in amplitude and its plot approaches a straight line, thereby signaling an interpretation for the source position and type. All inverse operations are fully automated and applicable to the interpretation of large data sets. The necessary data for the second level can be obtained by actual measurement or, alternatively, by deriving them from the data at the first level by an upward, analytical continuation. Upward continuation suppresses high-wavenumber random noise and thus contributes to a stable inversion. Model tests show that a suitable height for the second level is less than the expected depth of the source below the first level, while a suitable window length is about twice that depth. Examples show that the proposed inversion is effective on both model and field data. Note that this approach can be extended to the inversion of any component or derivative of the 2D or 3D magnetic or gravity fields from simple sources.

Interactive 2D magnetic inversion: A tool for aiding forward modeling and testing geologic hypotheses

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. L43-L50 ◽  
Author(s):  
Valeria C. Barbosa ◽  
João B. Silva
Keyword(s):  
Complex Geometry ◽  
Synthetic Data ◽  
Magnetization Vector ◽  
Real Data ◽  
Forward Modeling ◽  
Data Fitting ◽  
Magnetic Data ◽  
Magnetization Distribution ◽  
Magnetic Inversion ◽  
Geometric Elements

We present a method for inverting magnetic data with interfering anomalies produced by multiple complex 2D magnetic sources having arbitrary shapes and known magnetization vectors. Our method is stable and can recover a complex 2D magnetization distribution, leading to a reliable delineation of sectionally homogeneous sources with complex shapes. Our method, although similar to interactive forward modeling, is unique in that it automatically fits the observations and only requires that the interpreter know the outlines of the sources expressed by simple geometric elements such as points and line segments. Each geometric element operates as a skeletal outline of a particular homogeneous section of the magnetic source to be reconstructed. Also, the interpreter can define the geometric elements interactively without worrying about data fitting because data are fit automatically. The examples with synthetic data illustrate the good performance of the method in mapping the complex geometry of magnetic sources. The solution sensitivity to uncertainties in the a priori information shows that to produce good results, the uncertainty on the magnetization intensity of each homogeneous extent of the source should be smaller than 40%. A wrong magnetization vector direction can be detected easily because it often leads to poor data fitting and to estimated sources with abrupt borders. The method is also applied to two sets of real data from the Northwest Ore Body at Iron Mountain Mine, Missouri, and the Hatton-Rockall Basin in the northeast Atlantic Ocean. The estimated magnetization distribution in all tests demonstrates a good correlation of estimated magnetic sources with corresponding known geologic features.

scholarly journals MaGSoundDST — 3D automatic inversion of magnetic and gravity data based on the differential similarity transform

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. L25-L38 ◽  
Author(s):  
Daniela Gerovska ◽  
Marcos J. Araúzo-Bravo ◽  
Petar Stavrev ◽  
Kathryn Whaler
Keyword(s):  
Gravity Data ◽  
Magnetization Vector ◽  
Singular Points ◽  
Magnetic Data ◽  
Moving Window ◽  
Euler Deconvolution ◽  
Grid Data ◽  
Similarity Transform ◽  
Window Method ◽  
Structural Indices

We present an automatic procedure — Magnetic And Gravity SOUNDing Differential Similarity Transform (MaGSoundDST) — for inversion of regular or irregular magnetic- and gravity-grid data measured on even or uneven surfaces. It solves for horizontal position, depth, and structural index of simple sources and is independent of a linear background. In addition, it estimates the shape of sources consisting of several singular points and lines. The method uses the property of the differential similarity transform (DST) of a magnetic or a gravity anomaly to become zero or linear at all observation points when the central point of similarity of the transform, which we refer to as the probing point, coincides with a source’s singular point. It uses a measured anomalous field and its calculated or measured (gradiometry) first-order derivatives. The method is independent of the magnetization-vector direction in the magnetic data case and does notrequire reduction-to-the-pole transformed data as input. With MaGSoundDST, we provide an important alternative interpretation technique to the Euler deconvolution procedures, combining a moving-window method, whereby the solutions are linked to singular points of causative bodies, with an approach in which the solutions are linked to the real sources. The procedure involves calculating a 3D function that evaluates the linearity of the DST for different integer or noninteger structural indices, using a moving window. We sound the subsurface along a vertical line under each window center. Then we combine the 3D results for different structural indices and present them in three easy-to-interpret maps, avoiding the need for clustering techniques. We deduce only one solution for location and type of simple sources, which is a major advantage over Euler deconvolution. Application to different cases of synthetic and real data shows the method’s applicability to various types of magnetic and gravity field investigations.

scholarly journals Determination of source parameters of simple-shaped geologic subsurface structures from self-potential anomalies using enhanced local wavenumber method

2019 ◽  
Vol 35 (1) ◽  
Author(s):  
Luan Pham Thanh
Keyword(s):  
Random Noise ◽  
Source Parameters ◽  
Synthetic Data ◽  
Horizontal Position ◽  
Subsurface Structures ◽  
Geometry Model ◽  
Simple Geometry ◽  
Local Wavenumber ◽  
Real Self ◽  
Self Potential

Simple geometry model structures can be useful in quantitative evaluation of self-potential data. In this paper, we solve local wavenumber equation to estimate the horizontal position,  the depth and the type of the causative source geometry by using a linear least-squares approximation. The advantages of the algorithm in determining the horizontal position and depth measure are its independency to shape factor of the sources and also its simple computations. The algorithm is built in Matlab environment. The validity of the algorithm is illustrated on variable noise-free and random noise included synthetic data from two-dimensional (2-D) models where the achieved parametric quantities coincide well with the actual ones. The algorithm is also utilized to real self-potential data from Ergani Copper district, Turkey. The results from the actual data application are in good agreement with the published literature for the study area. The source code of the algorithm is available from the authors on request.

scholarly journals 2D dipping dike magnetic data interpretation using a robust particle swarm optimization

2017 ◽  
Author(s):  
Khalid S. Essa ◽  
Mahmoud El-Hussein
Keyword(s):  
Particle Swarm Optimization ◽  
Mineral Exploration ◽  
Random Noise ◽  
Particle Swarm ◽  
Real Data ◽  
Data Interpretation ◽  
Magnetic Data ◽  
Model Parameters ◽  
Swarm Optimization ◽  
Ore Bodies

Abstract. A robust Particle Swarm Optimization (PSO) investigation for magnetic data by a 2D dipping dike has been presented. The interpretive model parameters are: the amplitude coefficient (K), the depth to the top of the dipping dike (z), exact origin of the dipping dike (x0), and the width of dipping dike (w). The inversion procedure is actualized to gauge the parameters of a 2D dipping dike structures where it has been confirmed first on synthetic models without and with different level of random noise. The results of the inversion demonstrate that the parameters derived from the inversion concur well with the true ones. The root mean square (RMS) is figured by the strategy which is considered as the misfit between the measured and computed anomalies. The technique has been warily and effectively applied to real data examples from China and UK with the presence of ore bodies. The present technique can be applicable for mineral exploration and ore bodies of dike-like structure embedded in the shallow and deeper subsurface.

Inversion of the power spectrum from magnetic anomalies

Geophysics ◽  
1994 ◽  
Vol 59 (3) ◽  
pp. 391-401 ◽  
Author(s):  
Juan Garca‐Abdeslem ◽  
Gordon E. Ness
Keyword(s):  
Magnetic Anomaly ◽  
Source Parameters ◽  
Real Data ◽  
Power Density Spectrum ◽  
Magnetic Data ◽  
Synthetic Spectrum ◽  
Model Parameters ◽  
Density Spectrum ◽  
Uniform Distributions ◽  
And Inversion

We develop methods for the modeling and inversion of the power‐density spectrum from magnetic anomaly data assuming that the crustal magnetic field is caused by an ensemble of vertical‐sided and uniformly magnetized prisms. The solution of the forward problem is achieved in the wavenumber domain, where a synthetic spectrum is given by the product of the mathematical expectations of single‐valued functions that describe depth, thickness, and horizontal dimensions of prisms in the ensemble. We use Gaussian and uniform distributions to describe the ensemble and provide a variety of functions from which different statistical models can be obtained. The solution of the inverse problem is achieved iteratively, starting from an initial set of model parameters. It is based on the ridge‐regression algorithm, and its usefulness is assessed in a number of examples with numeric, synthetic and real data spectra. The methods are first tested on the spectrum obtained from a simple artificial magnetic anomaly and on the artificial spectrum caused by an ensemble of source bodies and are found to be capable of recovering the source parameters. Next, the methods are applied to marine magnetic data from a survey offshore of the Yucatán Peninsula, Mexico. The results of this last application are consistent with the crustal structure observed at Chicxulub hole.

Sign in / Sign up

Export Citation Format

Share Document