Response of a multilayered earth with layers having exponentially varying resistivities

Geophysics ◽  
1996 ◽  
Vol 61 (1) ◽  
pp. 180-191 ◽  
Author(s):  
Hyoung‐Soo Kim ◽  
Kiehwa Lee
Keyword(s):  
Recurrence Relation ◽  
Kernel Function ◽  
Excellent Agreement ◽  
Apparent Resistivity ◽  
Fortran Subroutine

The resistivity kernel function for calculating the apparent resistivity of a multilayered earth with layers that have exponentially varying resistivities is derived using a recurrence relation. This relation is applicable to general cases in which layers have either constant or exponentially varying resistivities. A FORTRAN subroutine that computes the apparent resistivity of Schlumberger, Wenner, and pole‐to‐pole array soundings for layers of exponentially varying resistivities is presented. Apparent resistivities of some models computed by the new kernel function are compared with those of the same models approximated by a number of constant resistivity layers. Apparent resistivities computed by both methods show excellent agreement.

On: “A simple method of interpreting dipole resistivity soundings” by S. Niwas and M. Israil (GEOPHYSICS, 52, 1412–1417, October 1987)

Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1647-1647
Author(s):  
Edward Szaraniec
Keyword(s):  
Linear Combination ◽  
Kernel Function ◽  
Apparent Resistivity ◽  
Simple Method ◽  
Resistivity Data ◽  
The Subject

The subject paper consists in approximating the apparent resistivity data by using a linear combination of suitable functions chosen in such a way that (1) they give a good approximation up to the desired precision and (2) they allow the kernel function to be determined analytically. Surprisingly enough, no mention is made that such an approach, especially directed toward interpretation of resistivity soundings, was first proposed by Santini and Zambrano (1981). The subject was subsequently continued by Kumar and Chowdary (1982) and commented by Santini and Zambrano (1982), Straub (1984), and Szaraniec (1982, 1984).

VES DIPOLE‐DIPOLE FILTER COEFFICIENTS

Geophysics ◽  
1977 ◽  
Vol 42 (5) ◽  
pp. 1037-1044 ◽  
Author(s):  
Douglas C. Nyman ◽  
Mark Landisman
Keyword(s):  
Kernel Function ◽  
Apparent Resistivity ◽  
Sampling Interval ◽  
Proper Selection ◽  
Filter Function ◽  
Inverse Transform ◽  
Phase Perturbation ◽  
Sampling Intervals ◽  
Electrical Sounding ◽  
Selection Of

The conversion of sampled Schlumberger and dipole‐dipole vertical electrical sounding (VES) apparent resistivity values into raised kernel function values is an important step in the interpretation of these data. This conversion involves the convolution of the sampled values, uniformly spaced on a log distance scale, with a set of filter coefficients. For Schlumberger and dipole‐dipole configurations, these coefficients can be calculated directly from the Schlumberger filter function. Oscillations of the filter coefficients at large indices (distances) can be minimized by proper selection of the sampling interval, as suggested by Koefoed. The choice of an optimal sampling interval has a more pronounced effect on the accuracy of the inverse transform (raised kernel function into apparent resistivity) than on that of the forward transform. The accuracy of the inverse transform can be improved for nonoptimal sampling intervals by “phase perturbation” of the filter function. Both transforms are sensitive to aliasing, which can be severe for certain dipole‐dipole configurations.

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.

NUMERICAL ANALYSIS OF RELATIVE RESISTIVITY FOR A HORIZONTALLY LAYERED EARTH

Geophysics ◽  
1963 ◽  
Vol 28 (2) ◽  
pp. 222-231 ◽  
Author(s):  
Seibe Onodera
Keyword(s):  
Numerical Analysis ◽  
Orthogonal Polynomials ◽  
Kernel Function ◽  
Apparent Resistivity ◽  
Complete System ◽  
Layered Earth ◽  
Relative Resistivity

The method of calculating the relative resistivity, which is the ratio of the apparent resistivity to the resistivity of the upper layer, for a multiple‐layered earth is given by means of the expansion of the kernel function according to a complete system of normalized orthogonal polynomials. The method, which includes estimation of the accuracy to be expected, is illustrated by application to a three‐layer earth.

A Comparison of the Bethesda and New Oxford Methods of Factor VIII Antibody Assay

1982 ◽  
Vol 47 (01) ◽  
pp. 072-075 ◽  
Author(s):  
D E G Austen ◽  
K Lechner ◽  
C R Rizza ◽  
I L Rhymes
Keyword(s):  
Factor Viii ◽  
Excellent Agreement ◽  
International Committee ◽  
The Other ◽  
Antibody Assay ◽  
Collaborative Trial

SummaryA collaborative trial has been carried out under the auspices of the International Committee on Thrombosis and Haemostasis to compare the Bethesda and New Oxford methods of antibody assay. It was found that errors between laboratories were much greater than those within laboratories and each laboratory had a bias whereby it always rated samples high or low with respect to the other laboratories. However there was excellent agreement in the order in which laboratories ranked antibody samples and if a standard antibody sample could be provided there would be a significant improvement in numerical agreement between laboratories. On average, for this exercise, a result for a given sample in Bethesda units was 1.21 times the result in New Oxford units although it must be stressed that this ratio could vary from sample to sample.

Sebuah Generalisasi Baru Barisan Fibonacci-Lucas

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Musraini M Musraini M ◽  
Rustam Efendi ◽  
Rolan Pane ◽  
Endang Lily
Keyword(s):  
Recurrence Relation ◽  
Initial Conditions ◽  
Lucas Sequence ◽  
Binet’S Formula

Barisan Fibonacci dan Lucas telah digeneralisasi dalam banyak cara, beberapa dengan mempertahankan kondisi awal, dan lainnya dengan mempertahankan relasi rekurensi. Makalah ini menyajikan sebuah generalisasi baru barisan Fibonacci-Lucas yang didefinisikan oleh relasi rekurensi B_n=B_(n-1)+B_(n-2),n≥2 , B_0=2b,B_1=s dengan b dan s bilangan bulat  tak negatif. Selanjutnya, beberapa identitas dihasilkan dan diturunkan menggunakan formula Binet dan metode sederhana lainnya. Juga dibahas beberapa identitas dalam bentuk determinan.   The Fibonacci and Lucas sequence has been generalized in many ways, some by preserving the initial conditions, and others by preserving the recurrence relation. In this paper, a new generalization of Fibonacci-Lucas sequence is introduced and defined by the recurrence relation B_n=B_(n-1)+B_(n-2),n≥2, with ,  B_0=2b,B_1=s                          where b and s are non negative integers. Further, some identities are generated and derived by Binet’s formula and other simple methods. Also some determinant identities are discussed.

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