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| Titel |
About well-posed definition of geophysical fields' |
| VerfasserIn |
Konstantin Ermokhine, Ludmila Zhdanova, Tamara Litvinova |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250073612
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| Zusammenfassung |
| We introduce a new approach to the downward continuation of geophysical fields based on
approximation of observed data by continued fractions. Key Words: downward continuation,
continued fraction, Viskovatov’s algorithm. Many papers in geophysics are devoted to the
downward continuation of geophysical fields from the earth surface to the lower halfspace.
Known obstacle for the method practical use is a field’s breaking-down phenomenon near the
pole closest to the earth surface. It is explained by the discrepancy of the studied fields’
mathematical description: linear presentation of the field in the polynomial form, Taylor or
Fourier series, leads to essential and unremovable instability of the inverse problem since the
field with specific features in the form of poles in the lower halfspace principally can’t be
adequately described by the linear construction. Field description by the rational fractions is
closer to reality. In this case the presence of function’s poles in the lower halfspace
corresponds adequately to the denominator zeros. Method proposed below is based on the
continued fractions. Let’s consider the function measured along the profile and
represented it in the form of the Tchebishev series (preliminary reducing the argument
to the interval [-1, 1]): There are many variants of power series’ presentation by
continued fractions. The areas of series and corresponding continued fraction’s
convergence may differ essentially. As investigations have shown, the most suitable
mathematical construction for geophysical fields’ continuation is so called general
C-fraction:
where ( , z designates the depth) For construction of C-fraction corresponding to power
series exists a rather effective and stable Viskovatov’s algorithm (Viskovatov B. “De la
methode generale pour reduire toutes sortes des quantitees en fraction continues”. Memoires
de l’ Academie Imperiale des Sciences de St. Petersburg, 1, 1805). A fundamentally new
algorithm for Downward Continuation (in an underground half-space) a field measured at the
surface, allows you to make the interpretation of geophysical data, to build a cross-section,
determine the depth, the approximate shape and size of the sources measured at the surface of
the geophysical fields. Appliance of the method are any geophysical surveys: magnetic,
gravimetric, electrical exploration, seismic, geochemical surveying, etc. Method
was tested on model examples, and practical data. The results are confirmed by
drilling. |
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