Improved Fourier terrain correction, Part II

Geophysics ◽  
1996 ◽  
Vol 61 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Robert L. Parker
Keyword(s):  
Power Series ◽  
Variable Thickness ◽  
Grid Point ◽  
Main Idea ◽  
Terrain Correction ◽  
Potential Fields ◽  
Fourier Methods ◽  
Convergence Problems ◽  
Thickness Layer ◽  
Level Plane

Fourier methods for potential fields have always been developed with the simplification that the calculation surface is a level plane. The Fourier approach can be extended to deal with an uneven observation surface. I consider the case of terrain correction for gravity surveys, in which the attraction of a variable‐thickness layer is calculated at points on its upper surface. The main idea is to use a power series in topographic height that is then converted into a series of convolutions. To avoid convergence problems, a cylindrical zone around the observer must be removed from the Fourier treatment and its contribution computed directly. The resultant algorithm is very fast: in an example based on a recent survey, the new method is shown to be more than 300 times faster than a calculation based on summing contributions from a column of material under each topographic grid point.

scholarly journals Forensic Engineering Evaluation of Excessive Differential Settlement on Compressible Clays

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
Rune Storesund ◽  
Alan Kropp
Keyword(s):  
Variable Thickness ◽  
Differential Settlement ◽  
Housing Project ◽  
Root Cause ◽  
Forensic Engineering ◽  
Thickness Layer

This forensic engineering (FE) study evaluated root cause errors associated with excessive differential settlements on a housing project constructed on top of a variable thickness layer of highly compressible clays. The structures were reported to have experienced differential settlements on the order of 2 to 10 in. across 40 ft. The FE study examined fundamental assumptions, granularity/resolution of the settlement and differential settlement analyses, and finalized grading plan vs. the conceptual grading plan used as a basis for the differential settlement predictions. The FE study found numerous discrepancies between the “idealized site” used as a basis of analysis and the “actual site” as constructed.

Effect of Scanning Direction on Microstructure and Mechanical Properties of Part Formed via Variable Thickness Layer Cladding Deposition

2019 ◽  
Vol 46 (8) ◽  
pp. 0802003
Author(s):  
周显新 Xianxin Zhou ◽  
辛博 Bo Xin ◽  
巩亚东 Yadong Gong ◽  
张伟健 Weijian Zhang ◽  
张海权 Haiquan Zhang
Keyword(s):  
Mechanical Properties ◽  
Variable Thickness ◽  
Scanning Direction ◽  
Microstructure And Mechanical Properties ◽  
Thickness Layer

Analytical solution for the buckling of rectangular plates under uni-axial compression with variable thickness and elasticity modulus in the y-direction

2009 ◽  
Vol 224 (1) ◽  
pp. 33-41 ◽  
Author(s):  
M Saeidifar ◽  
S N Sadeghi ◽  
M R Saviz
Keyword(s):  
Differential Equation ◽  
Analytical Solution ◽  
Power Series ◽  
Boundary Conditions ◽  
Variable Thickness ◽  
Elasticity Modulus ◽  
Plate Motion ◽  
Transverse Displacement ◽  
Buckling Loads ◽  
Simply Supported

The present study introduces a highly accurate numerical calculation of buckling loads for an elastic rectangular plate with variable thickness, elasticity modulus, and density in one direction. The plate has two opposite edges ( x = 0 and a) simply supported and other edges ( y = 0 and b) with various boundary conditions including simply supported, clamped, free, and beam (elastically supported). In-plane normal stresses on two opposite simply supported edges ( x = 0 and a) are not limited to any predefined mathematical equation. By assuming the transverse displacement to vary as sin( mπ x/ a), the governing partial differential equation of plate motion will reduce to an ordinary differential equation in terms of y with variable coefficients, for which an analytical solution is obtained in the form of power series (Frobenius method). Applying the boundary conditions on ( y = 0 and b) yields the problem of finding eigenvalues of a fourth-order characteristic determinant. By retaining sufficient terms in power series, accurate buckling loads for different boundary conditions will be calculated. Finally, the numerical examples have been presented and, in some cases, compared to the relevant numerical results.

DESIGN OF SMALL OPERATORS FOR THE CONTINUATION OF POTENTIAL FIELD DATA

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 488-506 ◽  
Author(s):  
Irshad R. Mufti
Keyword(s):  
Potential Field ◽  
Field Data ◽  
Grid Point ◽  
Frequency Characteristics ◽  
Potential Fields ◽  
Two Dimensional ◽  
Potential Field Data ◽  
Computational Work ◽  
Considerable Loss ◽  
Equivalent Operators

Two‐dimensional continuation of potential fields is commonly achieved by employing a continuation operator which consists of a number of coefficients operating upon uniformly gridded field data. To obtain accurate results, the size of the operator has to be quite large. This not only requires a lot of computational work, but also causes a considerable loss of information due to the reduced size of the field obtained after continuation. Small‐size “equivalent” operators were designed which are free from these drawbacks but yield accurate results. In order to demonstrate the efficiency of these operators, a potential field was continued upward by using 31×31 Tsuboi coefficients. This required 961 multiplications for computing the continued field at each grid point. When procedure was repeated using the equivalent operator, the number of multiplications required for each grid point was reduced to 15, the size of the resulting map was much larger, but the results in both cases were practically identical in accuracy. Frequency characteristics of the equivalent operators and the continuation of data very close to the boundary of the field map are discussed.

AXISYMMETRIC VIBRATIONS OF CIRCULAR AND ANNULAR PLATES WITH VARIABLE THICKNESS

2001 ◽  
Vol 01 (02) ◽  
pp. 195-206 ◽  
Author(s):  
M. EISENBERGER ◽  
M. JABAREEN
Keyword(s):  
Exact Solution ◽  
Power Series ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Plate Thickness ◽  
Frequency Equation ◽  
Axisymmetric Vibration ◽  
Vibration Frequencies ◽  
Annular Plates ◽  
Infinite Power

In this work the exact axisymmetric vibration frequencies of circular and annular variable thickness plates are found. The solution is obtained using the exact element method developed earlier. It allows for the exact solution of problems with general polynomial variation in thickness using infinite power series. The solution is exact up to the accuracy of the computer. The natural frequencies of vibration are found as the solutions of the frequency equation. Normalized values for the natural frequencies are given for linear, parabolic and cubic variations of the plate thickness, for circular and annular plates, with four types of boundary conditions on the inner and outer boundaries.

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