SPECTRAL ANALYSIS OF GRAVITY AND MAGNETIC ANOMALIES DUE TO TWO‐DIMENSIONAL STRUCTURES

Geophysics ◽  
1975 ◽  
Vol 40 (6) ◽  
pp. 993-1013 ◽  
Author(s):  
B. K. Bhattacharyya ◽  
Lei‐Kuang Leu
Keyword(s):  
Linear Equations ◽  
Magnetic Anomalies ◽  
Dimensional Structure ◽  
Approximation Technique ◽  
System Of Equations ◽  
Two Dimensional ◽  
System Of Linear Equations ◽  
Unknown Parameters ◽  
Low Frequencies ◽  
Gravity And Magnetic

The expressions for the spectra of both gravity and magnetic anomalies due to a two‐dimensional structure consist of (except for a factor) sums of exponentials. The exponents of these exponentials are functions of frequency and the locations of the corners of the polygonal cross‐section of the structure. Two computationally feasible methods for determining the exponents from a given spectrum are described in this paper; they are essentially based on the generation of a system of linear equations. The unknown coefficients in this system of equations are functions of the corner locations. The first method requires expansion of the exponentials in the expressions for the spectra in the form of a series and works reliably when the amplitudes of low frequencies are analyzed. The unknown parameters are determined fairly accurately with this method by suitable combinations of the spectra of the observed anomaly and its moments. The second method utilizes an exponential approximation technique for producing the system of linear equations. If only the spectrum of the anomaly is used, the system of equations becomes ill‐conditioned in most cases resulting in grossly inaccurate solutions. However, particular combinations of the spectra of the anomaly and its first and second order moments are found to improve significantly the behavior of the system of equations and thus the quality of results. It has also been found that the mean values of corner locations can be calculated fairly accurately by taking the ratios of the spectra of the anomaly and its moments. Once the corner locations are found, computation of the density contrast in the case of a gravity anomaly and the magnetization contrast for a magnetic anomaly is straightforward.

scholarly journals To the Solution of Geometric Inverse Heat Conduction Problems

2021 ◽  
Vol 24 (1) ◽  
pp. 6-12
Author(s):  
Yurii M. Matsevytyi ◽  
◽  
Valerii V. Hanchyn ◽  
Keyword(s):  
Heat Conduction ◽  
Iterative Process ◽  
Regularization Parameter ◽  
Outer Boundary ◽  
Linear Equations ◽  
The Body ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
System Of Linear Equations ◽  
Inverse Heat Conduction Problems

On the basis of A. N. Tikhonov’s regularization theory, a method is developed for solving inverse heat conduction problems of identifying a smooth outer boundary of a two-dimensional region with a known boundary condition. For this, the smooth boundary to be identified is approximated by Schoenberg’s cubic splines, as a result of which its identification is reduced to determining the unknown approximation coefficients. With known boundary and initial conditions, the body temperature will depend only on these coefficients. With the temperature expressed using the Taylor formula for two series terms and substituted into the Tikhonov functional, the problem of determining the increments of the coefficients can be reduced to solving a system of linear equations with respect to these increments. Having chosen a certain regularization parameter and a certain function describing the shape of the outer boundary as an initial approximation, one can implement an iterative process. In this process, the vector of unknown coefficients for the current iteration will be equal to the sum of the vector of coefficients in the previous iteration and the vector of the increments of these coefficients, obtained as a result of solving a system of linear equations. Having obtained a vector of coefficients as a result of a converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to select the regularization parameter in such a way that this discrepancy is within the measurement error. The method itself and the ways of its implementation are the novelty of the material presented in this paper in comparison with other authors’ approaches to the solution of geometric inverse heat conduction problems. When checking the effectiveness of using the method proposed, a number of two-dimensional test problems for bodies with a known location of the outer boundary were solved. An analysis of the influence of random measurement errors on the error in identifying the outer boundary shape is carried out.

A geophysical interpretation of the geology of Conception Bay, Newfoundland

1983 ◽  
Vol 20 (9) ◽  
pp. 1421-1433 ◽  
Author(s):  
H. G. Miller
Keyword(s):  
Magnetic Susceptibility ◽  
Volcanic Rocks ◽  
Magnetic Anomalies ◽  
Vertical Movement ◽  
Geophysical Data ◽  
Two Dimensional ◽  
Geophysical Interpretation ◽  
Gravity And Magnetic ◽  
Conception Bay ◽  
Avalon Peninsula

Geophysical data from Conception Bay and the adjacent peninsulas of the Avalon Peninsula, Newfoundland are presented and quantitatively interpreted using two-dimensional models to interpret the geology beneath the bay. The portion of the bay underlain by mafic volcanic rocks is determined and the maximum extent of the Cambro-Ordovician rocks containing the Wabana hematite deposit is delineated. All gravity and magnetic anomalies in the area are explained in terms of density and magnetic susceptibility variations confined to the upper 12 km of the crust. The geophysical models indicate that mafic volcanics underlie a significant portion of the study area and are more extensive than indicated by the surface outcrop on land. The models also indicate significant vertical movement on the Topsail Fault and on the extension of a fault passing out into the bay near Holyrood. The Cambro-Ordovician sediments are confined to the southern portion of the block bounded by these faults. The geophysical data are unable to detect the presence of the mafic volcanics east of the Topsail Fault in the study area.

Theoretical analysis of aquifer response due to dewatering at Welland

1970 ◽  
Vol 7 (2) ◽  
pp. 205-216 ◽  
Author(s):  
E. O. Frind
Keyword(s):  
Differential Equation ◽  
Horizontal Plane ◽  
Linear Equations ◽  
Model Parameters ◽  
Two Dimensional ◽  
Construction Site ◽  
System Of Linear Equations ◽  
Flow Conditions ◽  
Observation Wells ◽  
And Storage

The investigation of the regional response of an aquifer due to depressurization at the Welland Canal construction site is discussed in this paper. The aquifer consists of the upper fractured zone of the bedrock, overlain by a poorly-permeable confining layer which permits recharge and discharge through leakage. The permeability in the aquifer varies throughout the area.As no exact solution exists, a mathematical model is developed. The model is two-dimensional in the horizontal plane and represents the non-homogeneous continuum of the aquifer by a finite number of nodes arranged in a grid. From the differential equation of flow, a system of linear equations is derived and solved by computer. Unsteady flow conditions are approximated by solving the system for discrete steps in time, from commencement of pumping up to equilibrium. Model parameters, consisting of the nodal values of transmissibility, leakance, and storage coefficient, are established by simulation of an actual period of pumping, for which the regional response is determined from readings at observation wells. After using one observed case, the model can be employed to solve any number of practical problems relating to the aquifer response within the area.

scholarly journals Análisis de algunas técnicas iterativas para sistemas de ecuaciones lineales y su estudio de la convergencia a través del número de condicionamiento

2020 ◽  
Vol 25 (4) ◽  
pp. 621-629
Author(s):  
Fernando Mesa ◽  
Diana Marcela Devia Narváez ◽  
German Correa Vélez
Keyword(s):  
Mathematical Model ◽  
Linear Equations ◽  
Jacobi Method ◽  
Direct Result ◽  
System Of Equations ◽  
System Of Linear Equations ◽  
Term Result ◽  
Short Term ◽  
Short Term Result ◽  
Starting Point

At present, numerical analysis provides us with powerful tools to determine the solution of various problems whose mathematical model can be represented by a system of linear equations, these tools correspond to a number of direct and iterative methods, among which are Carl's method. Gustav Jakob Jacobi and the Doolittle and Crout method, which we analyze and compare in this document. To do this we will initially explore the concepts of conditioning the problem to determine how stable is the system from which the model was obtained, until we reach the decomposition of LU arrays proposed in the Doolittle and Crout method. As a result of the analysis and comparison in this document, depending on what is sought when solving a system of equations, either very large or small enough for our computer, we can choose an approximation that will bring a short-term result with an error. Due to the starting point as proposed in the Jacobi method, or it is possible to reach a direct result by implementing fewer iterations as proposed in the Doolittle and Crout metho

The Optimal Filter Recurrence Calculating Method on a System of Equations Pseudo Solution in the Large Capacity of Computing Technology

2013 ◽  
Vol 850-851 ◽  
pp. 437-440
Author(s):  
Xiao Nan Xiao
Keyword(s):  
Linear Equations ◽  
Processing Method ◽  
Optimal Filter ◽  
System Of Equations ◽  
System Of Linear Equations ◽  
Computing Technology ◽  
Large Capacity ◽  
Filter Theory ◽  
Calculating Method ◽  
Pseudo Inverse

In the large capacity of computing technology, this article sets up the statistic recurrence calculating method of linear algebra pseudosolution by making use of the optimal filter theory. So we can get recurrence form of pseudosolution under the linear simultanuity and linear non-simultanuity instead of using the complex calculating pseudo-inverse matrix. This method is reliable and its effect is excellent. The results of the discussion show that the method of this article will provide an effective mathematic processing method in order to realize the optimal calculating of complex system of linear equations in the large capacity of calculating.

scholarly journals Method of Infinite System of Equations for Problems in Unbounded Domains

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Dang Quang A ◽  
Tran Dinh Hung
Keyword(s):  
Numerical Experiments ◽  
Infinite System ◽  
Linear Equations ◽  
Unbounded Domains ◽  
Uniform Grid ◽  
System Of Equations ◽  
System Of Linear Equations ◽  
One Dimensional ◽  
Infinite Domains ◽  
Artificial Boundaries

Many problems of mechanics and physics are posed in unbounded (or infinite) domains. For solving these problems one typically limits them to bounded domains and find ways to set appropriate conditions on artificial boundaries or use quasi-uniform grid that maps unbounded domains to bounded ones. Differently from the above methods we approach to problems in unbounded domains by infinite system of equations. In this paper we present starting results in this approach for some one-dimensional problems. The problems are reduced to infinite system of linear equations. A method for obtaining approximate solution with a given accuracy is proposed. Numerical experiments for several examples show the effectiveness of the offered method.

TIME-MINIMAL LINEAR SYSTOLIC ARRAYS FOR THE TOEPLITZ SYSTEM OF LINEAR EQUATIONS

1995 ◽  
Vol 05 (03) ◽  
pp. 461-474
Author(s):  
GABRIEL OKŠA
Keyword(s):  
Linear Equations ◽  
Systolic Arrays ◽  
System Of Equations ◽  
System Of Linear Equations ◽  
Strongly Regular ◽  
Toeplitz System

In this paper, two linear systolic arrays for the solution of general, strongly regular Toeplitz system of equations are presented. They arise from systolization of the efficient serial Schur-like algorithm. Both arrays are time-minimal and they complete the solution in 3n – 4 time cycles (without the initialization and the retrieval of results). The first array requires 2n – 2 processors, and the second one uses only n – 1 processors.

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