To: “Direct Interpretation of Geoelectric Measurements by the Use of Linear Filter Theory,” by Sri Niwas, GEOPHYSICS, v. 40, p. 121–122.

Geophysics ◽  
1975 ◽  
Vol 40 (5) ◽  
pp. 886-886
Keyword(s):  
Linear Filter ◽  
Filter Theory ◽  
Direct Interpretation

In the article, “Direct Interpretation of Geoelectric Measurements by the Use of Linear Filter Theory”, by Sri Niwas, Geophysics, v. 40, p. 121–122, the following corrections should be made: (1) In Figure 1, the Y-axis is in fact the Z-axis, and the Z-axis is the Y-axis (as referred to in the text). (2) In Figure 1, the resistivity of the dike is [Formula: see text] and that of the subsequent medium is [Formula: see text]. (3) Equation (9) should be [Formula: see text]

DIRECT INTERPRETATION OF GEOELECTRIC MEASUREMENTS BY THE USE OF LINEAR FILTER THEORY

Geophysics ◽  
1975 ◽  
Vol 40 (1) ◽  
pp. 121-122 ◽  
Author(s):  
Sri Niwas
Keyword(s):  
Kernel Function ◽  
Apparent Resistivity ◽  
Linear Filter ◽  
Intermediate Step ◽  
Electrical Measurements ◽  
Filter Theory ◽  
Direct Interpretation ◽  
Order Of Magnitude ◽  
Electrical Soundings

In a recent paper Lee and Green (1973) worked out a method for direct interpretation of electrical soundings made over a fault or dike (see Figure 1). They computed the kernel function using the method developed by Meinardus (1970). However, Koefoed (1968), while dealing with direct interpretation of electrical measurements made over a horizontally layered earth, showed that the relative variations in the apparent resistivity were not of the same order of magnitude in the corresponding kernel curve; thus, any method based on the determination of this function as the intermediate step would lead to a loss of information and hence to incorrect interpretation. Koefoed (1970) introduced a function T(λ) called the resistivity transform (a function related to the kernel function) as an intermediate step. Ghosh (1971) used linear filter theory and gave a simple and quick procedure to obtain the T(λ) function from the apparent resistivity field curve. He cited the properties of the T function as, (1) it is solely determined by the layer distribution; (2) it is an unambiguous representation of the [Formula: see text] function; and (3) for small and large values of 1/λ it approaches the [Formula: see text] curves.

The use of comparison filters in linear filter theory

1983 ◽  
Vol 24 (11) ◽  
pp. 2550-2552 ◽  
Author(s):  
Harry E. Moses
Keyword(s):  
Linear Filter ◽  
Filter Theory

Quantitative analysis by reconstruction of HREM focal series

1994 ◽  
Vol 52 ◽  
pp. 740-741
Author(s):  
W. Coene ◽  
A. Thust ◽  
M. Op de Beeck ◽  
D. Van Dyck
Keyword(s):  
Phase Retrieval ◽  
Image Plane ◽  
Initial Guess ◽  
Recursive Least Squares ◽  
Objective Lens ◽  
Electron Wave ◽  
Electron Sources ◽  
Original Algorithm ◽  
Coherent Field ◽  
Direct Interpretation

Compared to conventional electron sources, the use of a highly coherent field-emission gun (FEG) in TEM improves the information resolution considerably. A direct interpretation of this extra information, however, is hampered since amplitude and phase of the electron wave are scrambled in a complicated way upon transfer from the specimen exit plane through the objective lens towards the image plane. In order to make the additional high-resolution information interpretable, a phase retrieval procedure is applied, which yields the aberration-corrected electron wave from a focal series of HRTEM images (Coene et al, 1992).Kirkland (1984) tackled non-linear image reconstruction using a recursive least-squares formalism in which the electron wave is modified stepwise towards the solution which optimally matches the contrast features in the experimental through-focus series. The original algorithm suffers from two major drawbacks : first, the result depends strongly on the quality of the initial guess of the first step, second, the processing time is impractically high.

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