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A fast method to compute the potential in the multisphere model

J C de Munck1, M J Peters

  • 1Low Temperature Department, University of Twente, Enschede, The Netherlands.

IEEE Transactions on Bio-Medical Engineering
|November 1, 1993
PubMed
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This study improves potential calculations in multilayered spheres by using an addition-subtraction method with asymptotic approximations. This enhances convergence for accurate conductivity analysis in geophysical applications.

Area of Science:

  • Geophysics
  • Electromagnetism
  • Applied Mathematics

Background:

  • Calculating potential distribution in multilayered spheres is crucial for geophysical exploration.
  • Standard spherical harmonics expansions exhibit slow convergence when source and field points are close.
  • Piecewise constant conductivity models are common in subsurface studies.

Purpose of the Study:

  • To develop an efficient method for calculating potential distribution in multilayered spheres.
  • To improve the convergence rate of series expansions for potential calculations.
  • To provide formulas in Cartesian coordinates for practical applications.

Main Methods:

  • Derivation of a series expansion for potential distribution from a dipole source.
  • Calculation of an asymptotic approximation of the potential.

Related Experiment Videos

  • Application of the addition-subtraction method to accelerate convergence.
  • Formulation of results in Cartesian coordinates.

    • Main Results:

    • An improved series expansion method for potential distribution is presented.
    • The addition-subtraction method significantly enhances convergence rates.
    • The asymptotic solution offers insights into potential dependence on conductivity.
    • Formulas are provided in Cartesian coordinates, simplifying computations.

    Conclusions:

    • The proposed method offers efficient and accurate potential calculations in multilayered spheres.
    • Improved convergence is achieved, particularly in challenging near-field scenarios.
    • The Cartesian coordinate formulation facilitates practical implementation and inverse algorithm development.