scholarly journals A Constrained Nonlinear Programming Technique for Interpretation of Self-Potential Anomalies due to Two-Dimensional Inclined Sheets of Finite Depth Extent

2005 ◽  
Vol 16 (1) ◽  
pp. 21-33 ◽  
Author(s):  
J. ASFAHANI ◽  
M. TLAS
Keyword(s):  
Nonlinear Programming ◽  
Finite Depth ◽  
Two Dimensional ◽  
Programming Technique ◽  
Constrained Nonlinear Programming ◽  
Depth Extent ◽  
Self Potential

On: “A rapid graphical method for the interpretation of the self‐potential anomaly over a two‐dimensional inclined sheet of finite depth extent” by H. V. Ram Babu and D. Atchuta Rao (GEOPHYSICS, 53, 1126–1128, August 1988).

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1215-1216 ◽  
Author(s):  
L. Eskola ◽  
H. Hongisto
Keyword(s):  
Graphical Method ◽  
Theoretical Models ◽  
Finite Depth ◽  
The Self ◽  
Inversion Method ◽  
Two Dimensional ◽  
Depth Extent ◽  
Self Potential ◽  
Graphical Algorithm ◽  
Inclined Sheet

Ram Babu and Atchuta Rao (1988a, b) presented a graphical algorithm for the interpretation of a self‐potential anomaly over a sheet. Ram Babu and Atchuta Rao (1988b) also presented an inversion method based on iterative optimization for the self‐potential anomalies caused by spherical, cylindrical, and sheetlike bodies. The theoretical models on which the algorithms are based are very simple: for the sphere, an electrostatic dipole; for the cylinder, a line dipole; and for the sheet two line poles, the negative one along the upper edge of the sheet and the positive one along its lower edge.

Quantitative interpretation of self‐potential anomalies due to two‐dimensional sheet‐like bodies

Geophysics ◽  
1983 ◽  
Vol 48 (12) ◽  
pp. 1659-1664 ◽  
Author(s):  
D. Atchuta Rao ◽  
H. V. Ram Babu
Keyword(s):  
Finite Depth ◽  
Horizontal Gradient ◽  
Quantitative Interpretation ◽  
Two Dimensional ◽  
Analytical Relations ◽  
Depth Extent ◽  
Self Potential ◽  
Maximum Minimum ◽  
Inclined Sheet

A method for quantitative interpretation of self‐potential anomalies due to a two‐dimensional sheet of finite depth extent is proposed. In the case of an inclined sheet, positions and amplitudes of the maximum, minimum, and zero‐anomaly points are picked and then the origin is located on the horizontal gradient curve using the template of Rao et al (1965). The parameters of the sheet may be evaluated either geometrically or by using some analytical relations among the characteristic distances. When the sheet is vertical, the parameters may be evaluated using the positions of half and three‐quarter peak amplitudes.

A rapid graphical method for the interpretation of the self‐potential anomaly over a two‐dimensional inclined sheet of finite depth extent

Geophysics ◽  
1988 ◽  
Vol 53 (8) ◽  
pp. 1126-1128 ◽  
Author(s):  
H. V. Ram Babu ◽  
D. Atchuta Rao
Keyword(s):  
Graphical Method ◽  
Amplitude Ratio ◽  
Finite Depth ◽  
Ore Deposits ◽  
Characteristic Features ◽  
Zero Potential ◽  
Depth Extent ◽  
Self Potential ◽  
Sp Anomaly ◽  
Inclined Sheet

The inclined sheet is an important model for interpreting self‐potential (SP) anomalies over elongated ore deposits. Many techniques (Roy and Chowdhurry, 1959; Meiser, 1962; Paul, 1965; Atchuta Rao et al., 1982; Atchuta Rao and Ram Babu, 1983; Murty and Haricharan, 1985) have been proposed for interpreting SP anomalies over this model. We propose a simple graphical procedure for locating the upper and lower edges of an inclined sheet of infinite strike extent from its SP anomaly V(x) using a few characteristics points including [Formula: see text] [Formula: see text], and [Formula: see text] The amplitude ratio [Formula: see text], is shown to vary with θ, the dip of the sheet, making it possible to estimate θ. The two edges of the sheet are equidistant from the abscissa of [Formula: see text] the zero potential point. The sheet, when extrapolated onto the line of observation, meets the x‐axis at a point where [Formula: see text] From these characteristic features of V(x), the sheet can be located easily using the simple geometrical construction presented below.

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

Comparison principles for free-surface flows with gravity

1991 ◽  
Vol 230 ◽  
pp. 231-243 ◽  
Author(s):  
Walter Craig ◽  
Peter Sternberg
Keyword(s):  
Solitary Waves ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Immiscible Fluids ◽  
Steady Flows ◽  
Two Dimensional ◽  
Surface Flows ◽  
Ship Hulls ◽  
Geometrical Information ◽  
Supercritical Flows

This article considers certain two-dimensional, irrotational, steady flows in fluid regions of finite depth and infinite horizontal extent. Geometrical information about these flows and their singularities is obtained, using a variant of a classical comparison principle. The results are applied to three types of problems: (i) supercritical solitary waves carrying planing surfaces or surfboards, (ii) supercritical flows past ship hulls and (iii) supercritical interfacial solitary waves in systems consisting of two immiscible fluids.

Sign in / Sign up

Export Citation Format

Share Document