Interpreting potential field anomaly of an isolated source of regular geometry revisited

Geophysics ◽  
2017 ◽  
Vol 82 (5) ◽  
pp. IM41-IM48 ◽  
Author(s):  
Indrajit G. Roy
Keyword(s):  
Potential Field ◽  
Regularization Parameter ◽  
A Priori ◽  
Synthetic Data ◽  
Practical Method ◽  
Regularization Technique ◽  
First Order ◽  
Gravity And Magnetic ◽  
Optimal Value ◽  
Gravity And Magnetic Anomaly

I have developed an improved practical method for interpreting a symmetrical-shaped potential field anomaly due to an isolated source body of regular geometric configuration. The method uses the first-order horizontal derivative of the logarithmically transformed absolute value of the anomaly in estimating the source-body parameters, such as the location, depth of burial, and shape factor. To tackle noise in data, a regularization technique is designed, which ensures a robust estimate of the first-order derivative of logarithmically transformed data. The regularization technique uses an optimal value of regularization parameter that, although noise dependent, requires no a priori knowledge of the noise level in the data. A graphical method is designed to determine an optimal value of the regularization parameter from the position of the local minimum of a specially defined functional with respect to the regularization parameters. Numerical tests have been conducted on the noise-contaminated synthetic data to validate the proposed method. The successful application of the method on published field data for the gravity and magnetic anomaly suggests the applicability of the method.

Functional approach to the search for quasi-optimal value of regularization parameter in downward continuation of potential field

Geophysics ◽  
2021 ◽  
pp. 1-34
Author(s):  
Roland Karcol ◽  
Roman Pašteka
Keyword(s):  
Regularization Parameter ◽  
Gravity Data ◽  
Synthetic Data ◽  
Downward Continuation ◽  
Magnetic Data ◽  
Problem Solution ◽  
Ordnance Survey ◽  
Boundary Estimation ◽  
Optimal Value ◽  
Regional Gravity

The Tikhonov regularized approach to the downward continuation of potential fields is a partial but strong answer to the instability and ambiguity of the inverse problem solution in studies of applied gravimetry and magnetometry. The task is described with two functionals, which incorporate the properties of the desired solution, and it is solved as a minimization problem in the Fourier domain. The result is a filter in which the high-pass component is damped by a stabilizing condition, which is controlled by a regularization parameter (RP) — this parameter setting is the crucial step in the regularization approach. The ability of using the values of the functionals themselves as the tool for RP setting in the comparison with commonly used tools such as various types of LP norms is demonstrated, as well as their possible role in the source’s upper boundary estimation. The presented method is tested in a complex synthetic data test and is then applied to real detailed magnetic data from an unexploded ordnance survey and regional gravity data as well to verify its usability.

A new source location and attribute recognition method based on correlation analysis of gravity and magnetic anomaly

2020 ◽  
Author(s):  
Baoliang Lu ◽  
Tao Ma ◽  
Shengqing Xiong ◽  
Wanyin Wang
Keyword(s):  
Potential Field ◽  
Source Area ◽  
High Density ◽  
Low Density ◽  
Field Source ◽  
Geological Body ◽  
Gravity And Magnetic ◽  
Attribute Recognition ◽  
Parameter Values ◽  
Gravity And Magnetic Anomaly

<p>The traditional gravity and magnetic correspondence analysis tends to have high correlation outside the field source area. In order to overcome the disadvantage, we propose a new method for identify the source position and attribute, which is based on similarity and vertical derivative of potential field. In this method, we put forward a new gravity and magnetic correlation parameter (GMCP), which can effectively reduce the range of potential field source and indicate the field intensity information. The distribution of the non-zero areas of GMCP reflects the size of the source. GMCP discriminant parameter values of positive and negative reflect the source attribute. When GMCP is greater than zero, it is a positive correlation indicating that there are high-density and high-magnetization or low-density and low-magnetization homologous bodies in this region; When GMCP is less than zero, it is negative correlation indicating that there are high-density and low-magnetic or low-density and high-magnetic density homologous bodies in this region. GMCP goes to zero, which means no gravity-magnetic homologous geological body. Complex models test results with different noise level and actual data processing of South China Sea Basin show the correctness and validity of identification of the proposed methods.</p>

On: “Geophysical Analysis in Central Indiana using Potential Field Continuation,” by A. J. Rudman, Judson Mead, Joseph F. Whaley, and Robert F. Blakely (GEOPHYSICS, October 1971, p. 878–890)

Geophysics ◽  
1972 ◽  
Vol 37 (6) ◽  
pp. 1047-1047
Author(s):  
Douglas J. Guion
Keyword(s):  
Gravity Anomaly ◽  
Magnetic Anomaly ◽  
Potential Field ◽  
Downward Continuation ◽  
Gravity Effect ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Anomaly ◽  
Field Continuation ◽  
Hamilton County

I read with interest the article concerning modeling the Hamilton County, Indiana, gravity and magnetic anomaly. The authors’ method for outlining the igneous body by downward continuation aroused my curiosity to the point that I decided to study the results in detail. My investigation revealed that the calculated gravity effect of the model did not satisfy the observed gravity anomaly. In fact, the amount of mismatch is quite serious.

Linearized least‐squares method for interpretation of potential‐field data from sources of simple geometry

Geophysics ◽  
2004 ◽  
Vol 69 (3) ◽  
pp. 783-788 ◽  
Author(s):  
Ahmed Salem ◽  
Dhananjay Ravat ◽  
Martin F. Mushayandebvu ◽  
Keisuke Ushijima
Keyword(s):  
Potential Field ◽  
Least Squares Method ◽  
Random Noise ◽  
The United States ◽  
Horizontal Gradient ◽  
Potential Field Data ◽  
Anomalous Field ◽  
Simple Geometry ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Anomaly

We present a new method for interpreting isolated potential‐field (gravity and magnetic) anomaly data. A linear equation, involving a symmetric anomalous field and its horizontal gradient, is derived to provide both the depth and nature of the buried sources. In many currently available methods, either higher order derivatives or postprocessing is necessary to extract both pieces of information; therefore, data must be of very high quality. In contrast, for gravity work with our method, only a first‐order horizontal derivative is needed and the traditional data quality is sufficient. Our proposed method is similar to the Euler technique; it uses a shape factor instead of a structural index to characterize the buried sources. The method is tested using theoretical anomaly data with and without random noise. In all cases, the method adequately estimates the location and the approximate shape of the source. The practical utility of the method is demonstrated using gravity and magnetic field examples from the United States and Zimbabwe.

scholarly journals Regularization of backward time-fractional parabolic equations by Sobolev-type equations

2020 ◽  
Vol 28 (5) ◽  
pp. 659-676
Author(s):  
Dinh Nho Hào ◽  
Nguyen Van Duc ◽  
Nguyen Van Thang ◽  
Nguyen Trung Thành
Keyword(s):  
Error Estimates ◽  
Parabolic Equations ◽  
Regularization Parameter ◽  
A Priori ◽  
Sobolev Type ◽  
A Posteriori ◽  
Parameter Choice ◽  
Numerical Tests ◽  
Ill Posed ◽  
Parameter Choice Rules

AbstractThe problem of determining the initial condition from noisy final observations in time-fractional parabolic equations is considered. This problem is well known to be ill-posed, and it is regularized by backward Sobolev-type equations. Error estimates of Hölder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable noniterative numerical scheme. The theoretical error estimates are confirmed by numerical tests for one- and two-dimensional equations.

scholarly journals Regularity of Weakly Well-Posed Characteristic Boundary Value Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-39 ◽  
Author(s):  
Alessandro Morando ◽  
Paolo Secchi
Keyword(s):  
Energy Estimate ◽  
Boundary Value ◽  
A Priori ◽  
Regularity Of Solutions ◽  
First Order ◽  
Characteristic Boundary ◽  
Partial Differential System ◽  
Constant Multiplicity ◽  
Well Posed ◽  
Smooth Data

We study the boundary value problem for a linear first-order partial differential system with characteristic boundary of constant multiplicity. We assume the problem to be “weakly” well posed, in the sense that a uniqueL2-solution exists, for sufficiently smooth data, and obeys an a priori energy estimate with a finite loss of tangential/conormal regularity. This is the case of problems that do not satisfy the uniform Kreiss-Lopatinskiĭ condition in the hyperbolic region of the frequency domain. Provided that the data are sufficiently smooth, we obtain the regularity of solutions, in the natural framework of weighted conormal Sobolev spaces.

scholarly journals A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Jinghuai Gao ◽  
Dehua Wang ◽  
Jigen Peng
Keyword(s):  
Helmholtz Equation ◽  
Regularization Method ◽  
Regularization Parameter ◽  
A Priori ◽  
Inverse Source Problem ◽  
A Posteriori ◽  
Modified Helmholtz Equation ◽  
Numerical Tests ◽  
Theoretical Frame ◽  
Set Up

An inverse source problem in the modified Helmholtz equation is considered. We give a Tikhonov-type regularization method and set up a theoretical frame to analyze the convergence of such method. A priori and a posteriori choice rules to find the regularization parameter are given. Numerical tests are presented to illustrate the effectiveness and stability of our proposed method.

Overview of regional geophysical studies in Manitoba and northwestern Ontario

1982 ◽  
Vol 19 (11) ◽  
pp. 2049-2059 ◽  
Author(s):  
D. H. Hall ◽  
W. C. Brisbin
Keyword(s):  
Greenstone Belt ◽  
Seismic Velocities ◽  
Crustal Layer ◽  
Northwestern Ontario ◽  
Reflection And Refraction ◽  
Gravity And Magnetic ◽  
Winnipeg River ◽  
Lower Crustal ◽  
Gravity And Magnetic Anomaly

This paper presents an overview of six geophysical projects (seismic reflection and refraction, gravity and magnetic anomaly interpretation, specific gravity and magnetic property measurements) carried out in an area in Manitoba and northwestern Ontario bounded by 93 and 96°W longitude, and 49 and 51°N latitude.The purpose of the surveys was to define crustal structure in the Kenora–Wabigoon greenstone belt, the Winnipeg River batholithic belt, the Ear Falls – Manigotagan gneiss belt, and the Uchi greenstone belt. The following conclusions emerge.In all of the belts, a major discontinuity divides the crust into the commonly found upper and lower crustal sections. At the top of the lower crust, a seismically distinct layer (the mid-crustal layer) occurs. Seismic velocities in this layer suggest either intermediate to basic igneous rocks or metamorphic rocks of the amphibolite facies.Crustal geophysical characteristics vary sufficiently among the four belts to justify the classification of all four as distinct subprovinces of the Superior Province.Cet article présente une vue générale sur six projets de géophysique (réflexion et réfraction sismique, interprétation d'anomalies de gravité et magnétiques, déterminations de densité et de propriétés magnétiques) réalisés dans une région du Manitoba et du nord-ouest de l'Ontario encadrée par les longitudes 93 et 96°O et les latitudes 49 et 51°N.

scholarly journals Atmospheric Duct Estimation Using Radar Sea Clutter Returns by the Adjoint Method with Regularization Technique

2014 ◽  
Vol 31 (6) ◽  
pp. 1250-1262 ◽  
Author(s):  
Xiaofeng Zhao ◽  
Sixun Huang
Keyword(s):  
Genetic Algorithm ◽  
Parabolic Equation ◽  
Adjoint Method ◽  
Regularization Parameter ◽  
Background Field ◽  
Sea Clutter ◽  
Regularization Technique ◽  
Atmospheric Duct ◽  
Adjoint Approach ◽  
Space Range

Abstract This paper focuses on retrieving the atmospheric duct structure from radar sea clutter returns by the adjoint approach with the regularization technique. The adjoint is derived from the split-step Fourier parabolic equation method, and the regularization term is constructed by the background refractivity field. To ensure successful implementations of the regularization, the L-curve criterion is used to find the optimal regularization parameter. The feasibility of the proposed method is validated by the numerical simulations of different noise-level clutter returns, as well as a real clutter profile measured by the S-Band Space Range Radar located in Wallops Island. In the process of inversions, the refractivity profile is first obtained by genetic algorithm, and then it is used as the background field for the adjoint method. The retrieved results indicate that, with an appropriate regularization parameter, the structure of the background refractivity profile can be improved by the proposed method.

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