The Research of the Frequency Domain Dipole Layer Method for the Processing and Transformation of Potential Field on Curved Surface

2009 ◽  
Vol 52 (5) ◽  
pp. 1139-1155
Author(s):  
Wan-Yin WANG ◽  
Jin-Lan LIU ◽  
Zhi-Yun QIU ◽  
Chang-Chun YU ◽  
Yi-Jian HUANG
Keyword(s):  
Frequency Domain ◽  
Potential Field ◽  
Curved Surface ◽  
Layer Method ◽  
Dipole Layer

On: “Correction of topographic distortions in potential‐field data: A fast and accurate approach” by Jianghai Xia, Donald R. Sprowl, and Dana Adkins‐Heljeson (April 1993 GEOPHYSICS, p. 515–523).

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1874-1874
Author(s):  
David A. Chapin
Keyword(s):  
Point Source ◽  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
New Method ◽  
Potential Fields ◽  
Potential Field Data ◽  
Source Method ◽  
Equivalent Point ◽  
Breakthrough Technology

Xia et al. do an excellent job developing a new method for using the equivalent point source method in the frequency domain. The transformation from a varying datum to flat datum has always been a major problem in potential fields data. This is because the existing methods to perform this transformation have tended to be cumbersome, time‐consuming, and expensive. I congratulate the authors for this breakthrough technology.

A simple derivation of Cordell’s stripping filter

Geophysics ◽  
1994 ◽  
Vol 59 (3) ◽  
pp. 488-490 ◽  
Author(s):  
Adebayo Aina
Keyword(s):  
Frequency Domain ◽  
Potential Field ◽  
Simple Derivation ◽  
Regional Background ◽  
Deep Source ◽  
Local Anomalies

The presence of a strong regional (deep source) anomaly often makes the identification of local (shallow source) anomalies difficult. It may become necessary to either separate the regional and the residual, or carry out an operation on the observed map that enhances the local anomalies at the expense of the regional background. The problem of separation of deep and shallow‐source potential field anomalies is one of the oldest problems in geophysics. Various authors (Griffin, 1949; Nettleton, 1954; Abdelrahman et. al., 1985, for example) have presented details and schemes for separating residual and background anomalies. More recently, Cordell (1985) through Green’s equivalent stratum theorem obtained a filter in the frequency domain that may be used for separating shallow and deep‐source potential field anomalies.

RECURSION FILTERS FOR DIGITAL PROCESSING OF POTENTIAL FIELD DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 712-726 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Vertical Gradient ◽  
Two Dimensional ◽  
Single Variable ◽  
Potential Field Data ◽  
Recursive Filter ◽  
Rational Expression

Zero‐phase two‐dimensional recursive filters, with a specified frequency domain response, have been designed for processing potential field data. In the case of second vertical derivative filters, it is possible to use the rational approximation of symmetrical functions of a single variable for the design of a short recursive filter. The filter so designed has an excellent response in the frequency domain. For vertical gradient and continuation filters, a method is developed for obtaining, by the least‐squares method, a rational expression for a two‐dimensional symmetrical function. In order to ensure the stability of the recursive filter, the denominator of the rational expression is approximated by a product of two factors, each being a function of a single variable. Finally, to keep the error of the filter response as small as possible, an iterative procedure is used for adjusting the zeros of the denominator and then determining the coefficients of the numerator of the rational expression.

Failures of the perfectly-matched layer method in frequency-domain seismic wave modelling in elastic anisotropic media

2019 ◽  
Author(s):  
Bing Zhou ◽  
Stewart Greenhalgh ◽  
Xu Liu ◽  
Youcef Bouzidi ◽  
Mohamed Kamel Riahi ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Seismic Wave ◽  
Anisotropic Media ◽  
Perfectly Matched Layer ◽  
Wave Modelling ◽  
Layer Method

Comparison of Two Methods in Solving Rayleigh Dispersion Curves

2011 ◽  
Vol 66-68 ◽  
pp. 1848-1853
Author(s):  
Bo Qin ◽  
Yan Mei Cao ◽  
He Xia
Keyword(s):  
Thin Layer ◽  
Frequency Domain ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Curves ◽  
Layered Soil ◽  
Layer Method ◽  
Soil Model ◽  
Thin Layer Method

The Rayleigh dispersion curves of multilayered soil are calculated by means of thin-layer method and rapid scalar method, respectively, in which two-layered and three-layered soil model are adopted. In addition, the disperse properties of multilayered soil are analyzed, and it is found that thin layer method is superior to rapid scalar method in low frequency domain, while in the high frequency domain it has little difference between each other.

scholarly journals Lidar-based surface following control for unmanned aerial vehicles

2021 ◽  
Author(s):  
Devin Simms
Keyword(s):  
Potential Field ◽  
Tracking Error ◽  
Vertical Surface ◽  
Curved Surface ◽  
Control Technique ◽  
Flat Surfaces ◽  
Field Control ◽  
Superior Surface ◽  
Axis Parallel ◽  
Wall Following

A simulation study is performed on a quadcopter which uses a LIDAR sensor to allow a quadcopter to navigate along and maintain a set distance from an unknown vertical surface. The dynamic equations of a quadcopter are linearized about the hovering equilibrium. For the purpose of design, all surfaces are assumed to be flat and any variations in shape are considered to be disturbances. The design process begins with the development of a potential field control design to allow the quadcopter to autonomously follow a flat surface, while maintaining a desired distance from the surface. To allow the quadcopter to follow a curved surface, the potential field technique is modified to maintain the xb axis parallel to the surface. Finally a wall following technique that directly uses the minimum range measurement to maintain the distance from the surface is developed. To simulate the control designs, a non-linear quadcopter model is used along with a model of a 2D scanning LIDAR sensor. The potential field control technique tracks flat surfaces with no steadystate error, though when curved surface following is added, a tracking error problem occurs due to measurement noise. The wall following design proves to be the superior surface following technique with greater robustness to steady-state error and results in relatively small tracking errors when navigating sinusoidal surfaces and corners.

Formulation of the boundary element method in the wavenumber–frequency domain based on the thin layer method

2015 ◽  
Vol 161 ◽  
pp. 1-16 ◽  
Author(s):  
João Manuel de Oliveira Barbosa ◽  
Eduardo Kausel ◽  
Álvaro Azevedo ◽  
Rui Calçada
Keyword(s):  
Boundary Element Method ◽  
Thin Layer ◽  
Frequency Domain ◽  
Boundary Element ◽  
Layer Method ◽  
Thin Layer Method ◽  
Element Method

scholarly journals DIRAC EQUATION ON A CURVED (2+1)-DIMENSIONAL HYPERSURFACE

2012 ◽  
Vol 27 (03) ◽  
pp. 1250016 ◽  
Author(s):  
MEHMET ALI OLPAK
Keyword(s):  
Dirac Equation ◽  
Thin Layer ◽  
Curved Surface ◽  
Graphene Sheets ◽  
Electron Systems ◽  
Dimensional Electron ◽  
Layer Method ◽  
Thin Layer Method ◽  
Special Case ◽  
Relativistic Equations

Interest on (2+1)-dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behavior of electrons is effectively described by relativistic equations. Having this fact in mind, the following problem is studied in this work: when a spin-1/2 particle is constrained to move on a curved surface, is it possible to describe this particle without giving reference to the dimensions external to the surface? As a special case of this, a relativistic spin-1/2 particle which is constrained to move on a (2+1)-dimensional hypersurface of the (3+1)-dimensional Minkowskian spacetime is considered, and an effective Dirac equation for this particle is derived using the so-called thin layer method. Some of the results are compared with those obtained in a previous work by Burgess and Jensen.

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