FORWARD AND INVERSE MODELLING OF A GRAVITY FIELD RESULTING FROM A DENSITY INTERFACE USING PARK-OLDENBURG METHOD

Year 2002, Volume: 4 Issue: 1, 37 - 51, 01.01.2002

Coşkun Sarı Ali Levent Akyol

Abstract

In order to reach the inverse solution for the perturbing body giving rise to the gravitational anomaly
through the rearrangement of the formula used for the rapid calculation of such anomaly caused by a two
dimensional uneven layer of material. The scheme calculates the Fourier transform of the gravitational anomaly
as the sum of Fourier transforms of powers of the perturbing topography. This method is computationally much
more efficient than calculating the gravitational field by breaking up the model into a set of prisms whose
contributions are calculated separately and summed. Essentially this method comprises of computations
involving Fourier transformations, which are relatively fast and straightforward with the FFT algorithm. Its
speed makes the method to be presented as a practical one. The effects of the two parameters, the density
contrast (ρ) and the level at which the inversion is made (zo) are observed, cause the nonuniqueness of the
inversion. Without additional information constraining these parameters, the ambiguity in the gravity
interpretation can not be reduced. Convergence of the inversion is ensured by a suitable low pass filter in
frequency domain. However, if the assumed density was too small or reference level too large, no topography
could be found which would give rise to an observed anomaly. The ability of this inversion scheme to handle
large numbers of model points without greatly decreasing the numerical stability or greatly increasing the
computation time makes it particularly attractiv

Keywords

Gravity, Inversion, Iterative scheme, Density interface, Fourier transform

PARKER–OLDENBURG YÖNTEMİ İLE GRAVİTE VERİLERİNİN DÜZ VE TERS MODELLEMESİ (YOĞUNLUK ARAYÜZEYİNİN SAPTANMASI)

Abstract

through the rearrangement of the formula used for the rapid calculation of such anomaly caused by a two dimensional uneven layer of material. The scheme calculates the Fourier transform of the gravitational anomaly as the sum of Fourier transforms of powers of the perturbing topography. This method is computationally much more efficient than calculating the gravitational field by breaking up the model into a set of prisms whose contributions are calculated separately and summed. Essentially this method comprises of computations involving Fourier transformations, which are relatively fast and straightforward with the FFT algorithm. Its speed makes the method to be presented as a practical one. The effects of the two parameters, the density contrast (ρ) and the level at which the inversion is made (zo) are observed, cause the nonuniqueness of the inversion. Without additional information constraining these parameters, the ambiguity in the gravity interpretation can not be reduced. Convergence of the inversion is ensured by a suitable low pass filter in frequency domain. However, if the assumed density was too small or reference level too large, no topography could be found which would give rise to an observed anomaly. The ability of this inversion scheme to handle large numbers of model points without greatly decreasing the numerical stability or greatly increasing the computation time makes it particularly attractive

Keywords

Gravite, Ters çözüm, Yineleme, Yoğunluk arayüzeyi, Fourier dönüşümü

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