Analytical Continuation of Geophysical Fields into the Area of Anomaly Sources by the Continued Fraction Method (CFCM)

摘要

Many works of the leading geophysicists are devoted to the method of analytical continuation of geophysical field from the measuring profile to the lower half-space. But promising results in this area are practically absent. Linear presentation of the field in the form of polynomials, Taylor or Fourier series leads to essential ill position of the inverse problem. Field description, close to reality, is the construction of the fractional-rational type. In this case the presence of function poles in the lower half-space corresponds adequately to the zeros in denominator. Method proposed below is based on the Pade approximants and its particular but important case -continued fractions. The proposed method is called - Continued Fraction Continuation Method.