Rapid construction of equivalent sources using wavelets

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. L51-L59 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Sparse Matrix ◽  
Coefficient Matrix ◽  
Magnetic Data ◽  
Dense Matrix ◽  
Wavelet Domain ◽  
Space Domain ◽  
Equivalent Source ◽  
Equivalent Sources

We have developed a fast algorithm for generating an equivalent source by using fast wavelet transforms based on orthonormal, compactly supported wavelets. We apply a 2D wavelet transform to each row and column of the coefficient matrix and subsequently threshold the transformed matrix to generate a sparse representation in the wavelet domain. The algorithm then uses this sparse matrix to construct the the equivalent source directly in the wavelet domain. Performing an inverse wavelet transform then yields the equivalent source in the space domain. Using upward continuation of total-field magnetic data between uneven surfaces as examples, we have compared this approach with the direct solution using the dense matrix in the space domain. We have shown that the wavelet approach can reduce the CPU time by as many as two orders of magnitude.

scholarly journals Interpolation of magnetic anomalies over an oceanic ridge region using an equivalent source technique and crust age model constraint

2021 ◽  
Author(s):  
Duan Li ◽  
Jinsong Du ◽  
Chao Chen ◽  
Qing Liang ◽  
Shida Sun
Keyword(s):  
Plate Tectonics ◽  
Magnetic Anomalies ◽  
Background Field ◽  
Source Model ◽  
Magnetic Data ◽  
Magnetization Distribution ◽  
Equivalent Source ◽  
Oceanic Ridge ◽  
Age Model ◽  
Equivalent Sources

Abstract. Marine magnetic surveys over oceanic ridge regions are of great interest for investigations of structure and evolution of oceanic crust, and have played a key role in developing the theory of plate tectonics (Dyment, 1993; Maus et al, 2007; Vine and Matthews, 1963). In this study, we propose an interpolation approach based on the dual-layer equivalent source model for the generation of a magnetic anomaly map based on sparse survey line data over oceanic ridge areas. In this approach, information from an ocean crust age model is utilized as constraint for the inversion procedure. The constraints can affect the magnetization distribution of equivalent sources following crust age. The results of synthetic tests show that the obtained magnetic anomalies have higher accuracy than those obtained by other interpolation methods. Meanwhile, considering the unclear on the true magnetization directions of sources and the background field in the synthetic model, well interpolation result can still be obtained. We applied the approach to magnetic data obtained from five survey lines east of the Southeast Indian Ridge. This prediction result is useful to improve the lithospheric magnetic field models WDMAMv2 and EMAG2v3, in the terms of spatial resolution and the consistency with observed data.

Reduction to the pole and transformations of scattered magnetic data using Newtonian equivalent sources

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. L67-L73 ◽  
Author(s):  
Fernando Guspí ◽  
Iván Novara
Keyword(s):  
Real Data ◽  
Computer Time ◽  
Magnetic Data ◽  
Newtonian Potential ◽  
Two Stage ◽  
Magnetization Direction ◽  
Magnetic Dipoles ◽  
Equivalent Source ◽  
Reduction To The Pole ◽  
Equivalent Sources

We have developed an equivalent-source method for performing reduction to the pole and related transforms from magnetic data measured on unevenly spaced stations at different elevations. The equivalent source is composed of points located vertically beneath the measurement stations, and their magnetic properties are chosen in such a way that the reduced-to-the-pole magnetic field generated by them is represented by an inverse-distance Newtonian potential. This function, which attenuates slowly with distance, provides better coverage for discrete data points. The magnetization intensity is determined iteratively until the observed field is fitted within a certain tolerance related to the level of noise; thus, advantages in computer time are gained over the resolution of large systems of equations. In the case of induced magnetization, the iteration converges well for verticalor horizontal inclinations, and results are stable if noise is taken into account properly. However, for a range of intermediate inclinations near 35°, a factor tending to zero makes it necessary to perform the reduction through a two-stage procedure, using an auxiliary magnetization direction, without significantly affecting the speed and stability of the method. The performance of the procedure was tested on a synthetic example based on a field generated on randomly scattered stations by a random set of magnetic dipoles, contaminated with noise, which is reduced to the pole for three different magnetization directions. Results provide a good approximation to the theoretical reduced-to-the-pole field using a one- or a two-stage reduction, showing minor noise artifacts when the direction is nearly horizontal. In a geophysical example with real data, the reduction to the pole was used to correct the estimated magnetization direction that originates an isolated anomaly over Sierra de San Luis, Argentina.

scholarly journals X-ray image denoising based on wavelet transform and median filter

2020 ◽  
Vol 5 (2) ◽  
pp. 435-442
Author(s):  
Hanlei Dong ◽  
Liguo Zhao ◽  
Yunxing Shu ◽  
Neal N. Xiong
Keyword(s):  
Wavelet Transform ◽  
Wavelet Coefficient ◽  
Median Filter ◽  
Coefficient Matrix ◽  
Wavelet Domain ◽  
Denoising Method ◽  
X Ray ◽  
Standard Pulse ◽  
Soft Threshold ◽  
The Difference

AbstractThis paper mainly proposed and researched based on wavelet transform, and then used the X-map denoising technique of value filter. In other words, the value image was filtered in the spatial domain, and the value filtering was used as the standard pulse (salt) noise, also used as in the wavelet domain. After the filtered image was decomposed by biorthogonal double wavelet transform, a wavelet coefficient matrix was generated, and a soft threshold quantisation process was performed on the wavelet coefficients to produce a new wavelet coefficient matrix. In the end, they used a new wavelet coefficient matrix for image reconstruction. The processing resulted that the denoising method proposed in this paper showed that the X image can be denoised, which not only reduced the X-picture-like noise but also preserved the X-picture-like details as much as possible. It also helped to enhance diagnostic accuracy and reduced the difference in reading.

Using an equivalent source with positivity for low-latitude reduction to the pole without striation

Geophysics ◽  
2014 ◽  
Vol 79 (6) ◽  
pp. J81-J90 ◽  
Author(s):  
Yaoguo Li ◽  
Misac Nabighian ◽  
Douglas W. Oldenburg
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Equatorial Region ◽  
Magnetic Data ◽  
Data Sets ◽  
Low Latitude ◽  
Equivalent Source ◽  
Large Scale Data ◽  
Reduction To The Pole ◽  
Equivalent Sources

We present a reformulation of reduction to the pole (RTP) of magnetic data at low latitudes and the equator using equivalent sources. The proposed method addresses both the theoretical difficulty of low-latitude instability and the practical issue of computational cost. We prove that a positive equivalent source exists when the magnetic data are produced by normal induced magnetization, and we show that the positivity is sufficient to overcome the low-latitude instability in the space domain. We further apply a regularization term directly to the recovered RTP field to improve the solution. The use of equivalent source also naturally enables the processing of data acquired on uneven surface. The result is a practical algorithm that is effective at the equatorial region and can process large-scale data sets with uneven observation heights.

scholarly journals Feasibility of simplified integral equation modeling of low-frequency marine CSEM with a resistive target

Geophysics ◽  
2009 ◽  
Vol 74 (5) ◽  
pp. F107-F117 ◽  
Author(s):  
Shaaban A. Bakr ◽  
Trond Mannseth
Keyword(s):  
Integral Equation ◽  
Sparse Matrix ◽  
Approximate Solutions ◽  
Coefficient Matrix ◽  
Background Field ◽  
Petroleum Exploration ◽  
Equation Modeling ◽  
Dense Matrix ◽  
Matrix Methods ◽  
Marine Csem

We have assessed the accuracy of a simplified integral equation (SIE) modeling approach for marine controlled-source electromagnetics (CSEM) with low applied frequencies and a resistive target. The most computationally intensive part of rigorous integral equation (IE) modeling is the computation of the anomalous electric field within the target itself. This leads to a matrix problem with a dense coefficient matrix. It is well known that, in general, the presence of many grid cells creates a computational disadvantage for dense-matrix methods compared to sparse-matrix methods. The SIE approach replaces the dense-matrix part of rigorous IE modeling by sparse-matrix calculations based on an approximation of Maxwell’s equations. The approximation is justified theoretically if a certain dimensionless parameter [Formula: see text] is small. As opposed to approximations of the Born type, the validity of the SIE approach does not rely on the anomalous field to be small in comparison with the background field in the target region. We have calculated [Formula: see text] for a range of parameter values typical for marine CSEM, and compared the SIE approach numerically to the rigorous IE method and to the quasi-linear (QL) and quasi-analytic (QA) approximate solutions. It is found that the SIE approach is very accurate for small [Formula: see text], corresponding to frequencies in the lower range of those typical for marine CSEM for petroleum exploration. In addition, the SIE approach is found to be significantly more accurate than the QL and QA approximations for small [Formula: see text].

Wavelet-Based Pavement Distress Classification

2005 ◽  
Vol 1940 (1) ◽  
pp. 89-98 ◽  
Author(s):  
Jian Zhou ◽  
Peisen Huang ◽  
Fu-Pen Chiang
Keyword(s):  
Wavelet Transform ◽  
Radon Transform ◽  
High Frequency ◽  
High Amplitude ◽  
Experimental Results ◽  
Wavelet Domain ◽  
Wavelet Coefficients ◽  
Step Method ◽  
Space Domain ◽  
Pavement Distress

A two-step method–-wavelet transform followed by Radon transform–- is proposed for pavement distress classification. First, a pavement image is decomposed into different frequency subbands by wavelet transform. Distress is transformed into the high-amplitude wavelet coefficients, which are referred to as the details, in the high-frequency subbands. The wavelet modulus is calculated by combining the horizontal, vertical, and diagonal details. Since distress, especially crack, has dominant orientations in both the space domain and the wavelet domain, Radon transform is then applied to the wavelet modulus to transform cracks into peaks in the Radon domain. The patterns and parameters of the peaks are finally used for distress classification. Both simulated and experimental results demonstrate that the proposed two-step method is an effective method for pavement distress classification.

Gradient-boosted equivalent sources for gridding large gravity and magnetic datasets

2021 ◽  
Author(s):  
Santiago Rubén Soler ◽  
Leonardo Uieda
Keyword(s):  
Jacobian Matrix ◽  
Least Squares Method ◽  
Computational Cost ◽  
Magnetic Data ◽  
Gradient Boosting ◽  
Equivalent Source ◽  
Harmonic Field ◽  
Gravity And Magnetic ◽  
Data Points ◽  
Equivalent Sources

<p>The equivalent source technique is a well known method for interpolating gravity and magnetic data. It consists in defining a set of finite sources that generate the same observed field and using them to predict the values of the field at unobserved locations. The equivalent source technique has some advantages over general-purpose interpolators: the variation of the field due to the height of the observation points is taken into account and the predicted values belong to an harmonic field. These make equivalent sources a more suited interpolator for any data deriving from a harmonic field (like gravity disturbances and magnetic anomalies). Nevertheless, it has one drawback: the computational cost. The process of estimating the coefficients of the sources that best fit the observed values is very computationally demanding: a Jacobian matrix with number of observation points times number of sources elements must be built and then used to fit the source coefficients though a least-squares method. Increasing the number of data points can make the Jacobian matrix to grow so large that it cannot fit in computer memory.</p><p>We present a gradient-boosting equivalent source method for interpolating large datasets. In it, we define small subsets of equivalent sources that are fitted against neighbouring data points. The process is iteratively carried out, fitting one subset of sources on each iteration to the residual field from previous iterations. This new method is inspired by the gradient-boosting technique, mainly used in machine learning solutions.</p><p>We show that the gradient-boosted equivalent sources are capable of producing accurate predictions by testing against synthetic surveys. Moreover, we were able to grid a gravity dataset from Australia with more than 1.7 million points on a modest personal computer in less than half an hour.</p>

Medical Image Feature Matching Based on Wavelet Transform and SIFT Algorithm

2011 ◽  
Vol 65 ◽  
pp. 497-502
Author(s):  
Yan Wei Wang ◽  
Hui Li Yu
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Medical Image ◽  
Feature Matching ◽  
Image Feature ◽  
Scale Invariant ◽  
Sift Algorithm ◽  
Matching Algorithm ◽  
Invariant Feature ◽  
Scale Invariant Feature

A feature matching algorithm based on wavelet transform and SIFT is proposed in this paper, Firstly, Biorthogonal wavelet transforms algorithm is used for medical image to delaminating, and restoration the processed image. Then the SIFT (Scale Invariant Feature Transform) applied in this paper to abstracting key point. Experimental results show that our algorithm compares favorably in high-compressive ratio, the rapid matching speed and low storage of the image, especially for the tilt and rotation conditions.

Constrained 3D inversion of magnetic data with structural orientation and borehole lithology: A case study in the Macheng iron deposit, Hebei, China

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. B121-B133 ◽  
Author(s):  
Shida Sun ◽  
Chao Chen ◽  
Yiming Liu
Keyword(s):  
Remanent Magnetization ◽  
Magnetic Data ◽  
Iron Deposit ◽  
Reference Field ◽  
Total Field ◽  
Equivalent Source ◽  
Structural Orientation ◽  
Amplitude Data ◽  
Ore Bodies

We have developed a case study on the use of constrained inversion of magnetic data for recovering ore bodies quantitatively in the Macheng iron deposit, China. The inversion is constrained by the structural orientation and the borehole lithology in the presence of high magnetic susceptibility and strong remanent magnetization. Either the self-demagnetization effect caused by high susceptibility or strong remanent magnetization would lead to an unknown total magnetization direction. Here, we chose inversion of amplitude data that indicate low sensitivity to the direction of magnetization of the sources when constructing the underground model of effective susceptibility. To reduce the errors that arise when treating the total-field anomaly as the projection of an anomalous field vector in the direction of the geomagnetic reference field, we develop an equivalent source technique to calculate the amplitude data from the total-field anomaly. This equivalent source technique is based on the acquisition of the total-field anomaly, which uses the total-field intensity minus the magnitude of the reference field. We first design a synthetic model from a simplified real case to test the new approach, involving the amplitude data calculation and the constrained amplitude inversion. Then, we apply this approach to the real data. The results indicate that the structural orientation and borehole susceptibility bounds are compatible with each other and are able to improve the quality of the recovered model to obtain the distribution of ore bodies quantitatively and effectively.

Wavelet transform to quantify heart rate variability and to assess its instantaneous changes

1999 ◽  
Vol 86 (3) ◽  
pp. 1081-1091 ◽  
Author(s):  
Vincent Pichot ◽  
Jean-Michel Gaspoz ◽  
Serge Molliex ◽  
Anestis Antoniadis ◽  
Thierry Busso ◽  
...  
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Nervous System ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Autonomous Nervous System ◽  
Dynamic Changes ◽  
Nonstationary Signals ◽  
Higher Doses

Heart rate variability is a recognized parameter for assessing autonomous nervous system activity. Fourier transform, the most commonly used method to analyze variability, does not offer an easy assessment of its dynamics because of limitations inherent in its stationary hypothesis. Conversely, wavelet transform allows analysis of nonstationary signals. We compared the respective yields of Fourier and wavelet transforms in analyzing heart rate variability during dynamic changes in autonomous nervous system balance induced by atropine and propranolol. Fourier and wavelet transforms were applied to sequences of heart rate intervals in six subjects receiving increasing doses of atropine and propranolol. At the lowest doses of atropine administered, heart rate variability increased, followed by a progressive decrease with higher doses. With the first dose of propranolol, there was a significant increase in heart rate variability, which progressively disappeared after the last dose. Wavelet transform gave significantly better quantitative analysis of heart rate variability than did Fourier transform during autonomous nervous system adaptations induced by both agents and provided novel temporally localized information.

Sign in / Sign up

Export Citation Format

Share Document