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The Potentials About a Point Electrode and Apparent Resistivity Curves for a Two-, Three-, and Four-Layer Earth

The Potentials About a Point Electrode and Apparent Resistivity Curves for a Two-, Three-, and Four-Layer Earth

Copyright Date: 1956
Edition: NED - New edition
Pages: 158
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  • Book Info
    The Potentials About a Point Electrode and Apparent Resistivity Curves for a Two-, Three-, and Four-Layer Earth
    Book Description:

    This publication will be useful to geophysicists, geologists, and others engaged in exploration for minerals by electrical methods, and may be used in theoretical studies of electrical prospecting. It makes available for the first time a comprehensive collection of 2268 master resistivity curves for a two-, three-, and four-layer earth. All previous collections of curves for Wenner electrode configuration are included, so the user will not need to refer elsewhere to complete his set of working curves. In addition, the basic potential data used in computing the curves is given in tables. Auxiliary tables are provided to reduce the graphic integration procedures to simple arithmetic. The integral in question occurs widely in solutions to Laplace’s equation.

    eISBN: 978-1-4529-3694-9
    Subjects: Physics

Table of Contents

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  1. Front Matter
    (pp. [i]-[ii])
  2. Acknowledgments
    (pp. [iii]-[iv])
    Harold M. Mooney and W. W. Wetzel
  3. Table of Contents
    (pp. [v]-2)
  4. Summary
    (pp. 3-3)
  5. I Use of the Tables and Curves
    (pp. 4-13)

    It is sometimes important to determine the geologic structure of the earth to depths of a few tens or hundreds of feet at a particular location. Many engineering fields require information on depth to bedrock, to sand, gravel, or clay layers, or to consolidated materials. Some examples of applications are mining operations, highway construction, damsite location, water supply problems, and geologic structure studies.

    The electrical resistivity method is one of two geophysical techniques that can sometimes provide this information without drilling. In practice the geophysical methods do not replace drilling, but may greatly reduce the amount needed. Drilling is often...

  6. II Mathematical Basis for the Tables and Curves
    (pp. 14-24)

    Physical statement: Electric current flows into the earth from a point source on the surface. The earth within the volume of interest consists of four horizontal layers. Compute the electric potential at a point on the surface. (See Figure 3.)

    Mathematical statement: A point source of current lies in the horizontal plane z =0. The material above this plane has infinite resistivity. Below the plane, discontinuities in electrical resistivity exist at depths z =D1,D2,D3, and infinity. The corresponding resistivities areR1,R2,R3, andR4. Compute a solution of Laplace’s equation at the point (r,θ,...

  7. III Tables
    (pp. 25-145)

    The values ofC1,C2,C3, etc. (see Section H of Part II) are tabulated for various values ofrandt. These coefficients permit numerical evaluation of the fundamental integral of equation 5. They can be applied to computing potentials and apparent resistivities foranynumber of horizontal layers, ofanythickness and resistivity, usinganyelectrode arrangement. The necessary preliminary to their use is the calculation ofA(t) from equation 2.

    The accuracy of the computed potentials depends upon the behavior ofA(t). We have assumed thatA(t) can be adequately approximated, over small intervals oft, by...

  8. Bibliography
    (pp. 146-146)