A METHOD FOR THE DIRECT INTERPRETATION OF ELECTRICAL SOUNDINGS MADE OVER A FAULT OR DIKE

Geophysics ◽  
1973 ◽  
Vol 38 (4) ◽  
pp. 762-770 ◽  
Author(s):  
Terry Lee ◽  
Ronald Green
Keyword(s):  
Bessel Functions ◽  
Direct Analysis ◽  
Hankel Transform ◽  
Approximation Technique ◽  
Polarization Data ◽  
Resistivity Data ◽  
Vertical Fault ◽  
Direct Interpretation ◽  
Electrical Soundings ◽  
Infinite Integral

The potential function for a point electrode in the vicinity of a vertical fault or dike may be expressed as an infinite integral involving Bessel functions. Beginning with such an expression, two methods are presented for the direct analysis of resistivity data measured both normal and parallel to dikes or faults. The first method is based on the asymptotic expansion of the Hankel transform of the field data and is suitable for surveys done parallel to the strike of the dike or fault. The second method is based on a successive approximation technique which starts from an initial approximate solution and iterates until a solution with prescribed accuracy is found. Both methods are suitable for programming on a digital computer and some illustrative numerical results are presented. These examples show the limitations of the methods. In addition, the application of resistivity data to the interpretation of induced‐polarization data is pointed out.

An infinite integral involving Bessel functions and parabolic cylinder functions

1937 ◽  
Vol 33 (2) ◽  
pp. 210-211 ◽  
Author(s):  
R. S. Varma
Keyword(s):  
Bessel Functions ◽  
Parabolic Cylinder ◽  
Parabolic Cylinder Functions ◽  
Infinite Integral

The object of this paper is to evaluate an infinite integral involving Bessel functions and parabolic cylinder functions. The following two lemmas are required:Lemma 1. provided that R(m) > 0.

An algorithm for the plane‐wave decomposition of point‐source seismograms

Geophysics ◽  
1990 ◽  
Vol 55 (10) ◽  
pp. 1380-1385 ◽  
Author(s):  
M. Dietrich
Keyword(s):  
Plane Wave ◽  
Point Source ◽  
Bessel Functions ◽  
Real Data ◽  
Hankel Transform ◽  
Considerable Reduction ◽  
Correct Formulation ◽  
Plane Wave Decomposition ◽  
Wave Decomposition ◽  
Discrete Integration

The correct formulation of the plane‐wave decomposition of point‐source seismograms involves a sequence of Fourier and Hankel transforms which can be evaluated in several ways. The procedure which is proposed here exploits the fact that the plane‐wave response is bandlimited along the horizontal slowness axis. This property permits to expand the Hankel transform into a Fourier‐Bessel series. In practice, this algorithm requires an interpolation in distance of the recorded dataset, but allows a considerable reduction of Bessel functions calculations. Numerical applications performed with synthetic and real data show that the Fourier‐Bessel summation technique yields results which are equivalent to a discrete integration of the Hankel transform.

An Infinite Integral of Four Bessel Functions

SIAM Review ◽  
1993 ◽  
Vol 35 (2) ◽  
pp. 299-299
Author(s):  
M. L. Glasser
Keyword(s):  
Bessel Functions ◽  
Infinite Integral

Correlation of vertical electrical sounding and borehole-log data for delineation of saltwater and freshwater aquifers

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. G11-G20 ◽  
Author(s):  
G. K. Hodlur ◽  
Ratnakar Dhakate ◽  
Rolland Andrade
Keyword(s):  
Cost Effective ◽  
Data Interpretation ◽  
Quantitative Relation ◽  
Well Log ◽  
Log Data ◽  
Resistivity Data ◽  
Electrical Sounding ◽  
Electrical Soundings ◽  
Longitudinal Unit Conductance ◽  
Freshwater Aquifers

In a case history from the Mahanadi basin (India), we demonstrate the use of resistivity data from electric-log soundings and from borehole logs to discriminate between saltwater and freshwater aquifers. We use interpreted data from eight surface-based vertical electrical soundings (VES) and electric well logs from three boreholes in this study. We establish a quantitative relation among longitudinal unit conductance S (obtained from VES), water resistivity [Formula: see text], and layer thickness h. We show that ambiguities in resistivity data interpretation limit its ability to distinguish between freshwater and saltwater aquifers. Electric well-log data interpretation is much more accurate but requires boreholes, which are not cost effective when exploring for groundwater. Integrating well-log-based estimates of [Formula: see text] into resistivity interpretation of surface-based soundings improves its ability to discriminate freshwater aquifers while maintaining cost-effective exploration.

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