Derivative analysis of SP anomalies

Geophysics ◽  
1998 ◽  
Vol 63 (3) ◽  
pp. 890-897 ◽  
Author(s):  
El‐Sayed Mohamed Abdelrahman ◽  
Ahmed Abu Baker Ammar ◽  
Hamdy Ismail Hassanein ◽  
Mahfooz Abdelmottaleb Hafez
Keyword(s):  
Shape Factor ◽  
Random Noise ◽  
Theoretical Data ◽  
Window Length ◽  
Continuous Curve ◽  
Shape Factors ◽  
Derivative Analysis ◽  
Common Intersection ◽  
The Common ◽  
Self Potential

Numerical second horizontal derivative self‐potential (SP) anomalies obtained from SP data using filters of successive window lengths (graticule spacings) can be used to determine the shape and depth of a buried structure. For a fixed window length, the depth is determined using a simple formula for each shape factor. The computed depths are plotted against the shape factors on a graph. All points for a fixed window length are connected by a continuous curve (window curve). The solution for the shape and depth of the buried structure is read at the common intersection of the window curves. The method is applied to theoretical data with and without random noise and tested on a field example from Turkey.

New methods for shape and depth determinations from SP data

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1202-1210 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Hesham M. El‐Araby ◽  
Abdel‐Rady G. Hassaneen ◽  
Mahfooz A. Hafez
Keyword(s):  
Least Squares ◽  
Shape Factor ◽  
Least Squares Method ◽  
Random Noise ◽  
Theoretical Data ◽  
Derivative Analysis ◽  
Higher Derivatives ◽  
Optimum Order ◽  
Simple Linear Equation ◽  
Sp Anomaly

We have extended our earlier derivative analysis method to higher derivatives to estimate the depth and shape (shape factor) of a buried structure from self‐potential (SP) data. We show that numerical second, third, and fourth horizontal‐derivative anomalies obtained from SP data using filters of successive window lengths can be used to simultaneously determine the depth and the shape of a buried structure. The depths and shapes obtained from the higher derivatives anomaly values can be used to determine simultaneously the actual depth and shape of the buried structure and the optimum order of the regional SP anomaly along the profile. The method is semi‐automatic and it can be applied to residuals as well as to observed SP data. We have also developed a method (based on a least‐squares minimization approach) to determine, successively, the depth and the shape of a buried structure from the residual SP anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin, the problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of form f(z) = 0. Knowing the depth and applying the least‐squares method, the shape factor is determined using a simple linear equation. Finally, we apply these methods to theoretical data with and without random noise and on a known field example from Germany. In all cases, the depth and shape solutions obtained are in good agreement with the actual ones.

Magnetic interpretation using a least-squares, depth-shape curves method

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. L23-L30 ◽  
Author(s):  
El-Sayed M. Abdelrahman ◽  
Khalid S. Essa
Keyword(s):  
Least Squares ◽  
Magnetic Anomaly ◽  
Least Squares Method ◽  
Random Noise ◽  
Synthetic Data ◽  
Theoretical Data ◽  
Magnetic Anomalies ◽  
Shape Factors ◽  
Characteristic Points ◽  
Horizontal Cylinders

We have developed a least-squares approach to depth determination from residual magnetic anomalies caused by simple geologic structures. By normalizing the residual magnetic anomaly using three characteristic points and their corresponding distances on the anomaly profile, the problem of determining depth from residual magnetic anomalies has been transformed into finding a solution to a nonlinear equation of the form z = f(z). Formulas have been derived for spheres, horizontal cylinders, thin dikes, and contacts. The method is applied to synthetic data with and without random noise. We have also developed a method using depth-shape curves to simultaneously define the shape and depth of a buried structure from a residual magnetic anomaly profile. The method is based on determining the depth from the normalized residual anomaly for each shape factor using the least-squares method mentioned above. The computed depths are plotted against the shape factors on a graph. The solution for the shape and depth of the buried structure is read at the common intersection of the depth-shape curves. The depth-shape curves method was successfully tested on theoretical data with and without random noise and applied to a known field example from Ontario.

A new method for shape and depth determinations from gravity data

Geophysics ◽  
2001 ◽  
Vol 66 (6) ◽  
pp. 1774-1780 ◽  
Author(s):  
El‐Sayed M. Abdelrahman ◽  
Tarek M. El‐Araby ◽  
Hesham M. El‐Araby ◽  
Eid R. Abo‐Ezz
Keyword(s):  
Shape Factor ◽  
Gravity Data ◽  
Theoretical Data ◽  
The United States ◽  
Random Errors ◽  
Simple Method ◽  
Shape Factors ◽  
Family Of Curves ◽  
The Relationship ◽  
Good Agreement

We have developed a simple method to determine simultaneously the shape and depth of a buried structure from residualized gravity data using filters of successive window lengths. The method is similar to Euler deconvolution, but it solves for shape and depth independently. The method involves using a relationship between the shape factor and the depth to the source and a combination of windowed observations. The relationship represents a parametric family of curves (window curves). For a fixed window length, the depth is determined for each shape factor. The computed depths are plotted against the shape factors, representing a continuous, monotonically increasing curve. The solution for the shape and depth of the buried structure is read at the common intersection of the window curves. This method can be applied to residuals as well as to the Bouguer gravity data of a short or long profile length. The method is applied to theoretical data with and without random errors and is tested on a known field example from the United States. In all cases, the shape and depth solutions obtained are in good agreement with the actual ones.

Triangulating Topological Spaces

1997 ◽  
Vol 07 (04) ◽  
pp. 365-378 ◽  
Author(s):  
Herbert Edelsbrunner ◽  
Nimish R. Shah
Keyword(s):  
Homotopy Equivalent ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Voronoi Cells ◽  
Delaunay Complex ◽  
Common Intersection ◽  
Finite Set ◽  
The Common ◽  
Nerve Theorem

Given a subspace [Formula: see text] and a finite set S⊆ℝd, we introduce the Delaunay complex, [Formula: see text], restricted by [Formula: see text]. Its simplices are spanned by subsets T⊆S for which the common intersection of Voronoi cells meets [Formula: see text] in a non-empty set. By the nerve theorem, [Formula: see text] and [Formula: see text] are homotopy equivalent if all such sets are contractible. This paper proves a sufficient condition for [Formula: see text] and [Formula: see text] be homeomorphic.

The Relation Between Solidity and the Other Shape Factors for Complete Optimum Meridian Profile of Impeller With Guidevane

2007 ◽  
Author(s):  
Takuji Tsugawa
Keyword(s):  
Shape Factor ◽  
Large Diameter ◽  
Axial Direction ◽  
The Other ◽  
Shape Factors ◽  
Flow Angle ◽  
Diffusion Factor ◽  
Blade Number ◽  
Outlet Flow ◽  
Angle Blade

In the previous paper, the solidity is independent shape factor of the optimum meridian profile by diffusion factor. But, the solidity is often calculated by the other shape factors, for example, the inlet and outlet flow angle, blade length, blade number and the co-ordinates of impeller meridian profile. So, in this paper, the solidity is treated as dependent shape factor and is calculated by the impeller meridian co-ordinates and flow angle. In the previous paper, the impeller meridian inlet is axial direction. In this paper, the inlet mixed flow angle of impeller inlet is one of additional shape factor. As the result, the impeller with guidevane complete meridian profile is calculated for the large diameter of guidevane outlet and the detailed meridian profile of impeller inlet.

Experimental study of punching coefficients and shape factor for two-layered soils

1979 ◽  
Vol 16 (4) ◽  
pp. 802-805 ◽  
Author(s):  
A. J. Valsangkar ◽  
G. G. Meyerhof
Keyword(s):  
Experimental Study ◽  
Bearing Capacity ◽  
Shape Factor ◽  
Model Tests ◽  
Punching Shear ◽  
Deep Foundations ◽  
Layered Soils ◽  
Shape Factors ◽  
Capacity Theory ◽  
Strip Footings

The ultimate bearing capacity of deep foundations has been investigated for the case of a strong layer overlying a weak stratum. The studies are based on model tests using buried circular and strip footings for a range of layer thicknesses. Based on the previously developed bearing capacity theory, the punching shear coefficients and corresponding shape factors have been evaluated.

Shape Factors and Feasibility of Sheet Metal Hydroformed Components

2015 ◽  
Vol 651-653 ◽  
pp. 1134-1139
Author(s):  
Teresa Primo ◽  
Gabriele Papadia ◽  
Antonio del Prete
Keyword(s):  
Shape Factor ◽  
Point Of View ◽  
Element Analysis ◽  
Shape Factors ◽  
Limit Values ◽  
Limit Value ◽  
Experimental Campaign ◽  
Correct Calculation ◽  
Proper Comparison ◽  
Definition Of

The authors have investigated, in other paper, the problem related to the definition of a “set of shape factors” in order to declare the feasibility of a product through sheet hydroforming. In particular the defined shape factors are three different a-dimensional coefficients by which it is possible to declare the feasibility of a product through the calculation, in different sections, of the three previous shape factors. The robustness of this methodology is related to the correct calculation of the “limit value” of each shape factor. In fact the feasibility is reached if, in any section, the calculated shape factors are higher than their respective limit values. In this paper the authors have performed an extensive numerical and experimental campaign, taking into account a different geometry respect to that of the first paper, in order to: re-calculate the limit value for each shape factor and, then, verify the correctness of the limit values exposed in the previous first paper. The numerical campaign has been used, after the evaluation of the accuracy of the numerical model, in order to study the feasibility of the product without engaging the hydroforming machine. Finite Element Analysis (FEA) has been extensively used in order to investigate and define each shape factor with a proper comparison to the macro feasibility of the chosen component geometry. The limit values that have been calculated by the authors in this paper are slightly different from those calculated in the first paper. From this point of view it is possible that, although the shape factors are a-dimensional coefficients, they are affected by different choices of the users as, for example, the dimensions of the initial blank. Anyway, the small differences in the shape factors limit values do not adversely affect the use of the shape factors in order to predict the feasibility of the product.

Effect of Porosity on Mechanical Properties of Rubber

1995 ◽  
Vol 68 (2) ◽  
pp. 219-229 ◽  
Author(s):  
A. I. Kasner ◽  
E. A. Meinecke
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Shape Factor ◽  
Compression Modulus ◽  
Stress Strain ◽  
Shape Factors ◽  
Porosity Level ◽  
Apparent Modulus ◽  
Analytical Expressions ◽  
Cylindrical Samples

Abstract Cylindrical samples, with different shape factors and levels of porosity, were prepared from a model EPDM compound and tested in compression. The modulus was reduced considerably with the introduction of porosity, especially when the shape factor was high. The stress-strain curves showed nonlinearity which depends on the shape factor and porosity level, and is related to bubble closure. The apparent modulus of bonded blocks was found to consist of two components: homogeneous compression modulus and a hydrostatic contribution. The first was obtained by compression of blocks between lubricated compression plates. It can be predicted from analytical expressions adapted from composite theories for high density foams in tension. The second arises from the pressure buildup inside the bonded blocks and depends on the shape factor and the porosity level. These moduli, after correcting for compressibility, were used to develop approximate relations describing the stress-strain curves of porous bonded blocks. The stress-strain curves of samples with different shape factors and levels of porosity could be predicted from experimental data or FEA estimates.

scholarly journals Removal of Random Noise in Seismic Data by Time-varying Window-length Time-frequency Peak Filtering

2016 ◽  
Vol 64 (5) ◽  
pp. 1703-1714 ◽  
Author(s):  
Pengjun Yu ◽  
Yue Li ◽  
Hongbo Lin ◽  
Ning Wu
Keyword(s):  
Seismic Data ◽  
Random Noise ◽  
Time Varying ◽  
Window Length ◽  
Time Frequency ◽  
Frequency Peak
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