A rapid method for three‐dimensional modeling of magnetic anomalies

Geophysics ◽  
1991 ◽  
Vol 56 (11) ◽  
pp. 1729-1737 ◽  
Author(s):  
D. Bhaskara Rao ◽  
N. Ramesh Babu
Keyword(s):  
Computing Time ◽  
Optimization Technique ◽  
Three Dimensional ◽  
Magnetic Anomalies ◽  
Total Field ◽  
Arbitrary Polarization ◽  
Three Dimensional Modeling ◽  
Prismatic Bodies ◽  
Forward Calculation ◽  
Approximate Equations

A computer program has been developed for three‐dimensional analysis of total field magnetic anomalies due to arbitrary polarization suitable for present‐day personal computers. A vertical sided prism with arbitrary polarization is used as a basic model. A nonlinear optimization technique based on Marquardt’s algorithm is used to estimate all parameters of the model. A combination of prisms is used to analyze more complex magnetic fields. Analytical methods are used to estimate the derivatives required in the simultaneous solutions of the normal equations. Methods have been developed to minimize the computing time in forward calculation as well as in inversion. Approximate equations have been derived for rapid calculation of magnetic anomalies and partial derivatives of anomalies of prismatic bodies, which are valid beyond short distances from the sources. The algorithm has been developed in such a way that the use of the exact and approximate equations may be efficiently monitored as a trade‐off between accuracy and speed. The method is applied to analyze a synthetic anomaly contour map and the total field aeromagnetic anomalies in the offshore region of Mahanadi basin, Orissa, India.

AUTOMATIC THREE‐DIMENSIONAL MODELING FOR THE INTERPRETATION OF GRAVITY OR MAGNETIC ANOMALIES

Geophysics ◽  
1975 ◽  
Vol 40 (6) ◽  
pp. 1014-1034 ◽  
Author(s):  
A. Gerard ◽  
N. Debeglia
Keyword(s):  
Distribution Function ◽  
Fourier Transform ◽  
Iterative Method ◽  
Three Dimensional ◽  
Magnetic Anomalies ◽  
Average Depth ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
The Fourier Transform ◽  
Homogeneous Media

Transformation of gravity or magnetic anomaly maps into isodepth maps of a surface separating two homogeneous media may be accomplished by (1) systematically estimating an average depth and density or magnetization contrast for the surface and (2) using an iterative method to adjust local depths compared to the average depth of the surface. Average depth, density or magnetization contrast, and iterative adjustment of local depths are determined using the Fourier transform of the field to be interpreted and that of the field generated by an equivalent surface. This leads us to propose a method of estimating the average depth of the sources and a distribution function for the depths and then a complete and very economical algorithm for the calculation of the corresponding equivalent surface.

scholarly journals A Nonlinear Optimization Technique of Tunnel Construction Based on DE and LSSVM

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Xing Jun ◽  
Jiang Annan ◽  
Wen Zhiwu ◽  
Qiu Jingping
Keyword(s):  
Numerical Simulation ◽  
Support Vector Machine ◽  
Nonlinear Optimization ◽  
Computing Time ◽  
Optimization Technique ◽  
Three Dimensional ◽  
Least Square ◽  
Support Vector ◽  
Tunnel Construction ◽  
Feedback Analysis

Tunnel construction is a dynamic controlling system with observability and controllability; the feedback analysis requires identifying geophysics parameters and adjusting supporting parameters, and both of them are optimisation problems. The paper proposed a nonlinear optimization technique based on difference evolution arithmetic (DEA), least square support vector machine (LSSVM), and three dimensional numerical simulation. This method employs support vector machine with optimal architecture trained by the difference evolution arithmetic, instead of the time-consuming finite element analysis. Firstly, the three dimensional numerical simulation is used to create training and testing samples for LSSVM model construction. Then the nonlinear relationship between rock or anchoring parameters and displacement is constructed by support vector machine. Finally, the geophysics and supporting parameters are obtained by DE optimization arithmetic. The technique overcomes the conventional optimization method shortages of expending too much computing time and easily being limited in local optimal solution. This technique was verified by applying it to the feedback analysis of Dalian Metro in China, and the influence of the parameters of LSSVM and DE on the simulation ability of the algorithm was investigated.

MAGNETIC ANOMALIES DUE TO PRISM‐SHAPED BODIES WITH ARBITRARY POLARIZATION

Geophysics ◽  
1964 ◽  
Vol 29 (4) ◽  
pp. 517-531 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Polarization Vector ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
The Body ◽  
Simple Extension ◽  
Second Derivative ◽  
Positive Anomaly ◽  
Total Field ◽  
Arbitrary Polarization ◽  
Dip Angle

A study is made of magnetic anomalies due to prism‐shaped bodies with arbitrary polarization. Expressions of the total field and its first and second derivatives are derived on the assumption of uniform magnetization through out the body. Formulas for all possible cases in connection with a rectangular prism with vertical sides can be obtained either directly from this paper or by simple extension of the formulas given here. Using the exact expressions given in this paper, the total field and its derivatives are evaluated conveniently and rapidly with the aid of a digital computer. The effect of the dip angle anti declination of the polarization vector on the size and shape of the magnetic anomaly is then studied for the case when the earth’s normal total field vector has a dip angle of 60° and declination of 0°. With an increase in the dip angle of the polarization vector, the negative anomaly occurring on the north of the causative body diminishes in magnitude, whereas the positive and second derivative anomalies increase to maximum values and then decrease. With an increase in declination, this latter trend is repeated with the positive anomaly but the negative and second‐derivative anomalies decrease systematically. Both the positive and second‐derivative anomalies become more and more symmetrical with respect to the prismatic body with increase in either the inclination or declination of the polarization vector.

Analysis of magnetic field components anomalies due to homogeneous polyhedrons

2021 ◽  
Vol 39 (1) ◽  
Author(s):  
Eduardo Menezes de Souza Amarante ◽  
Edson Emanoel Starteri Sampaio
Keyword(s):  
Inverse Modeling ◽  
Three Dimensional ◽  
Magnetic Anomalies ◽  
Irregular Shapes ◽  
Local Coordinates ◽  
Prismatic Bodies ◽  
Para Determinar ◽  
Definition Of ◽  
Analytical Expressions ◽  
Polyhedral Bodies

ABSTRACT. A procedure for determining semi-analytical expressions for the magnetic fields caused by homogeneous polyhedral bodies based on Green's theorem has been developed. It constitutes a modification of previous developments for the gravity field of three-dimensional bodies and employs the discretization of the faces of the polyhedron by triangles and the definition of local coordinates for each triangle. A maximum misfit of less than 1.0\% between the values computed with these analytical expressions and those obtained with closed expressions for prismatic bodies, applied to a homogeneous cube, demonstrates the effectiveness of the procedure. Examples of magnetic maps due to octahedral bodies with different forms and orientations show that it is possible to obtain a qualitative distinction among their anomalies. Therefore, the present analysis constitutes a basis for future inverse modeling of convex polyhedrons and will be useful in geophysical exploration.Keywords: magnetic anomalies, polyhedral bodies, irregular shapes. Análise das componentes do campo magnético produzido por um poliedro homogêneoRESUMO. Foi desenvolvido um procedimento para determinar expressões analíticas para os campos magnéticos causados por corpos poliédricos homogêneos com base no teorema de Green. Constitui uma modificação dos desenvolvimentos anteriores para o campo gravitacional de corpos tridimensionais e emprega a discretização das faces do poliedro por triângulos e a definição das coordenadas locais para cada triângulo. Um erro máximo inferior a 1,0% entre os valores calculados com essas expressões analíticas e os obtidos com expressões fechadas para corpos prismáticos, aplicados a um cubo homogêneo, demonstra a eficácia do procedimento. Exemplos de mapas magnéticos devido a corpos octaédricos com diferentes formas e orientações mostram que é possível obter uma distinção qualitativa entre suas anomalias. Portanto, a presente análise constitui uma base para futura modelagem inversa de poliedros convexos e será útil na exploração geofísica.Palavras-chaves: anomalias magnéticas, corpos poliédricos, formas irregulares.

Dependence of the Deformation of 128×128 InSb Focal-plane Arrays on the Silicon Readout Integrated Circuit Thickness

2015 ◽  
Vol 9 (1) ◽  
pp. 170-174 ◽  
Author(s):  
Xiaoling Zhang ◽  
Qingduan Meng ◽  
Liwen Zhang
Keyword(s):  
Thermal Shock ◽  
Indium Antimonide ◽  
Integrated Circuit ◽  
Focal Plane ◽  
Three Dimensional ◽  
Fracture Probability ◽  
Focal Plane Arrays ◽  
Thermal Shock Test ◽  
Readout Integrated Circuit ◽  
Three Dimensional Modeling

The square checkerboard buckling deformation appearing in indium antimonide infrared focal-plane arrays (InSb IRFPAs) subjected to the thermal shock tests, results in the fracturing of the InSb chip, which restricts its final yield. In light of the proposed three-dimensional modeling, we proposed the method of thinning a silicon readout integrated circuit (ROIC) to level the uneven top surface of InSb IRFPAs. Simulation results show that when the silicon ROIC is thinned from 300 μm to 20 μm, the maximal displacement in the InSb IRFPAs linearly decreases from 7.115 μm to 0.670 μm in the upward direction, and also decreases linearly from 14.013 μm to 1.612 μm in the downward direction. Once the thickness of the silicon ROIC is less than 50 μm, the square checkerboard buckling deformation distribution presenting in the thicker InSb IRFPAs disappears, and the top surface of the InSb IRFPAs becomes flat. All these findings imply that the thickness of the silicon ROIC determines the degree of deformation in the InSb IRFPAs under a thermal shock test, that the method of thinning a silicon ROIC is suitable for decreasing the fracture probability of the InSb chip, and that this approach improves the reliability of InSb IRFPAs.

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