Automatic lineament extraction from potential-field images using the Radon transform and gradient calculation

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. J31-J40 ◽  
Author(s):  
Lili Zhang ◽  
Jiansheng Wu ◽  
Tianyao Hao ◽  
Jialin Wang
Keyword(s):  
Radon Transform ◽  
Real Data ◽  
Extraction Methods ◽  
Magnetic Data ◽  
Transform Domain ◽  
Gradient Calculation ◽  
Linear Sections ◽  
Lineament Extraction ◽  
Automatic Lineament Extraction ◽  
Searching Method

Linear anomalies are critical in the interpretation of gravity and magnetic data. Visual identification of lineaments is usually done by experienced interpreters, and identification results then have to undergo a digitization or import procedure. The traditional identification method has unavoidable subjectivity and inefficiency. To overcome these limitations, we fuse the Radon transform (RT) with gradient calculation to process gravity or magnetic data and to realize automatic detection and extraction of lineaments. As part of the detection procedure, we define the RT-based mean gradient (MG), effective mean gradient (EMG), and residual mean gradient (RMG) in order to highlight long linear segments or to enhance short linear ones in the transform domain. The gradient forms are applied self-adaptively and self-selectively to gravity or magnetic images according to specific conditions. Gradient directions are also taken into account in the transformation procedure to emphasize the characteristics of linear anomalies. To extract the position and length of the detected lineaments from the transform domain, a constraint inverse searching method (CISM) is given and used to locate the starting and end points of the lineaments. The method can deal with the condition that there is at least one linear section in a specific direction or that separate linear sections may belong to one lineament. Through tests with synthetic images and with real data from the Haijiao upheaval area in the East China Sea Basin, the detection and extraction methods are shown to be more effective and robust than the conventional RT applications. The results from the real data roughly coincide with major geologic faults that are visually identified. These results show that the methods constitute a useful tool to aid fault interpretation.

The Shuey-Radon transform

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. V197-V206 ◽  
Author(s):  
Ali Gholami ◽  
Milad Farshad
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Matching Pursuit ◽  
Real Data ◽  
Transform Domain ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Linear System Of Equations ◽  
Matching Pursuit Algorithm ◽  
Zero Offset

The traditional hyperbolic Radon transform (RT) decomposes seismic data into a sum of constant amplitude basis functions. This limits the performance of the transform when dealing with real data in which the reflection amplitudes include the amplitude variation with offset (AVO) variations. We adopted the Shuey-Radon transform as a combination of the RT and Shuey’s approximation of reflectivity to accurately model reflections including AVO effects. The new transform splits the seismic gather into three Radon panels: The first models the reflections at zero offset, and the other two panels add capability to model the AVO gradient and curvature. There are two main advantages of the Shuey-Radon transform over similar algorithms, which are based on a polynomial expansion of the AVO response. (1) It is able to model reflections more accurately. This leads to more focused coefficients in the transform domain and hence provides more accurate processing results. (2) Unlike polynomial-based approaches, the coefficients of the Shuey-Radon transform are directly connected to the classic AVO parameters (intercept, gradient, and curvature). Therefore, the resulting coefficients can further be used for interpretation purposes. The solution of the new transform is defined via an underdetermined linear system of equations. It is formulated as a sparsity-promoting optimization, and it is solved efficiently using an orthogonal matching pursuit algorithm. Applications to different numerical experiments indicate that the Shuey-Radon transform outperforms the polynomial and conventional RTs.

Separation and imaging of seismic diffractions using migrated dip-angle gathers

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. S131-S143 ◽  
Author(s):  
Alexander Klokov ◽  
Sergey Fomel
Keyword(s):  
Radon Transform ◽  
Real Data ◽  
Separation Procedure ◽  
Shape Difference ◽  
Depth Migration ◽  
Time Migration ◽  
Reflection Angle ◽  
Radon Space ◽  
Dip Angle ◽  
Analytical Expressions

Common-reflection angle migration can produce migrated gathers either in the scattering-angle domain or in the dip-angle domain. The latter reveals a clear distinction between reflection and diffraction events. We derived analytical expressions for events in the dip-angle domain and found that the shape difference can be used for reflection/diffraction separation. We defined reflection and diffraction models in the Radon space. The Radon transform allowed us to isolate diffractions from reflections and noise. The separation procedure can be performed after either time migration or depth migration. Synthetic and real data examples confirmed the validity of this technique.

Simultaneous source separation using a robust Radon transform

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. V1-V11 ◽  
Author(s):  
Amr Ibrahim ◽  
Mauricio D. Sacchi
Keyword(s):  
Radon Transform ◽  
Real Data ◽  
Radon Transforms ◽  
Accurate Data ◽  
Quadratic Formula ◽  
Penalty Term ◽  
Source Data ◽  
The Cost ◽  
Simultaneous Source ◽  
Incoherent Noise

We adopted the robust Radon transform to eliminate erratic incoherent noise that arises in common receiver gathers when simultaneous source data are acquired. The proposed robust Radon transform was posed as an inverse problem using an [Formula: see text] misfit that is not sensitive to erratic noise. The latter permitted us to design Radon algorithms that are capable of eliminating incoherent noise in common receiver gathers. We also compared nonrobust and robust Radon transforms that are implemented via a quadratic ([Formula: see text]) or a sparse ([Formula: see text]) penalty term in the cost function. The results demonstrated the importance of incorporating a robust misfit functional in the Radon transform to cope with simultaneous source interferences. Synthetic and real data examples proved that the robust Radon transform produces more accurate data estimates than least-squares and sparse Radon transforms.

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.

Bayesian wavefield separation by transform-domain sparsity promotion

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. A33-A38 ◽  
Author(s):  
Deli Wang ◽  
Rayan Saab ◽  
Özgür Yilmaz ◽  
Felix J. Herrmann
Keyword(s):  
Bayesian Approach ◽  
Real Data ◽  
Transform Domain ◽  
Coherent Noise ◽  
Noise Sources ◽  
Wavefield Separation ◽  
Ground Roll ◽  
Successful Removal ◽  
Multiple Elimination ◽  
Made In

Successful removal of coherent-noise sources greatly determines seismic imaging quality. Major advances have been made in this direction, e.g., surface-related multiple elimination (SRME) and interferometric ground-roll removal. Still, moderate phase, timing, amplitude errors, and clutter in predicted signal components can be detrimental. Adopting a Bayesian approach, along with assuming approximate curvelet-domain independence of the to-be-separated signal components, we construct an iterative algorithm that takes predictions produced by, for example, SRME as input and separates these components in a robust manner. In addition, the proposed algorithm controls the energy mismatch between separated and predicted components. Such a control, lacking in earlier curvelet-domain formulations, improves results for primary-multiple separation on synthetic and real data.

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.

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.

Estimation of density, magnetization, and depth to source: A nonlinear and noniterative 3-D potential‐field method

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 814-830 ◽  
Author(s):  
Maurizio Fedi
Keyword(s):  
A Priori ◽  
Real Data ◽  
Field Method ◽  
Magnetic Data ◽  
System Of Equations ◽  
Source Depth ◽  
A Priori Information ◽  
Magnetization Direction ◽  
Priori Information ◽  
Magnetic Case

The depth to the top, or bottom, and the density of a 3-D homogeneous source can be estimated from its gravity or magnetic anomalies by using a priori information on the maximum and minimum source depths. For the magnetic case, the magnetization direction is assumed to be constant and known. The source is assumed to be within a layer of known depth to the top h and thickness t. A depth model, satisfying both the data and the a priori information is found, together with its associated density/magnetization contrast. The methodology first derives, from the measured data, a set of apparent densities [Formula: see text] (or magnetizations), which do not depend on the layer parameters h and t, but only on source thickness. A nonlinear system of equations based on [Formula: see text], with source thicknesses as unknowns, is constructed. To simplify the solution, a more practical system of equations is formed. Each equation depends on only one value of thickness. Solving for the thicknesses, taking into account the above a priori information, the source depth to the top (or to the bottom) is determined uniquely. Finally, the depth solutions allow a unit‐density gravity model to be computed, which is compared to the observed gravity to determine the density contrast. A similar procedure can be used for magnetic data. Tests on synthetic anomalies and on real data demonstrate the good performance of this method.

Amplitude preservation of Radon-based multiple-removal filters

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. V123-V126 ◽  
Author(s):  
Ethan J. Nowak ◽  
Matthias G. Imhof
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Transform Domain ◽  
Multiple Reflections ◽  
Avo Analysis ◽  
Amplitude Versus Offset ◽  
Amplitude Preservation ◽  
Amplitude Versus

This study examines the effect of filtering in the Radon transform domain on reflection amplitudes. Radon filters are often used for removal of multiple reflections from normal moveout-corrected seismic data. The unweighted solution to the Radon transform reduces reflection amplitudes at both near and far offsets due to a truncation effect. However, the weighted solutions to the transform produce localized events in the transform domain, which minimizes this truncation effect. Synthetic examples suggest that filters designed in the Radon domain based on a weighted solution to the linear, parabolic, or hyperbolic transforms preserve the near- and far-offset reflection amplitudes while removing the multiples; whereas the unweighted solutions diminish reflection amplitudes which may distort subsequent amplitude-versus-offset (AVO) analysis.

Enhancement of the total horizontal gradient of magnetic anomalies using the tilt angle

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. J33-J41 ◽  
Author(s):  
Francisco J. F. Ferreira ◽  
Jeferson de Souza ◽  
Alessandra de B. e S. Bongiolo ◽  
Luís G. de Castro
Keyword(s):  
Tilt Angle ◽  
Real Data ◽  
Magnetic Anomalies ◽  
Detection Methods ◽  
Magnetic Data ◽  
Horizontal Gradient ◽  
Geometrical Properties ◽  
Different Depths ◽  
Deep Sources ◽  
Derivatives Of

Magnetic anomaly maps reflect the spatial distribution of magnetic sources, which may be located at different depths and have significantly different physical and geometrical properties, complicating the identification of the corresponding geologic structures. Filtering techniques are frequently used to balance anomalies from shallow and deep sources, and to enhance certain features of interest, such as the edges of the causative bodies. Most methods used for enhancing magnetic data are based on vertical or horizontal derivatives of the magnetic anomalies or combinations of them, and the edges or centers of the sources are identified by maxima, minima, or null values in the transformed data. Normalized derivatives methods are used to equalize signals from sources buried at different depths. We present an edge detector method for the enhancement of magnetic anomalies, which is based on the tilt angle of the total horizontal gradient. The notable features of this method are that it produces amplitude maxima over the source edges and that it equalizes signals from shallow and deep sources. The method is applied to synthetic and real data. The effectiveness of the method is evaluated by comparing it with other edge detection methods that have been previously reported in the literature and that make use of derivatives. The results show that our method is less sensitive to variations in the depth of the sources and that it indicates the position of the edges of causative bodies in a more accurate fashion, when compared with previous methods, even for anomalies due to multiple interfering sources. These results demonstrate that the proposed method is a useful tool for the qualitative interpretation of magnetic data.

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