HR: 1330h
AN: GP13A-05    [Abstracts]
TI: On the Application of Euler Deconvolution to the Analytic Signal
AU: * Fedi, M
EM: fedi@unina.it
AF: University of Naples 'Federico II', Largo S. Marcellino, 10, Naples, 80131 Italy
AU: Florio, G
EM: gflorio@unina.it
AF: University of Naples 'Federico II', Largo S. Marcellino, 10, Naples, 80131 Italy
AU: Pasteka, R
EM: pasteka@uni.sk
AF: Comenius University, Mlynska dol., Bratislava, 84215 Slovakia (Slovak Republic)
AB: In the last years papers on Euler deconvolution (ED) used formulations that accounted for the unknown background field, allowing to consider the structural index (N) an unknown to be solved for, together with the source coordinates. Among them, Hsu (2002) and Fedi and Florio (2002) independently pointed out that the use of an adequate m-order derivative of the field, instead than the field itself, allowed solving for both N and source position. For the same reason, Keating and Pilkington (2004) proposed the ED of the analytic signal. A function being analyzed by ED must be homogeneous but also harmonic, because it must be possible to compute its vertical derivative, as well known from potential field theory. Huang et al. (1995), demonstrated that analytic signal is a homogeneous function, but, for instance, it is rather obvious that the magnetic field modulus (corresponding to the analytic signal of a gravity field) is not a harmonic function (e.g.: Grant & West, 1965). Thus, it appears that a straightforward application of ED to the analytic signal is not possible because a vertical derivation of this function is not correct by using standard potential fields analysis tools. In this note we want to theoretically and empirically check what kind of error are caused in the ED by such wrong assumption about analytic signal harmonicity. We will discuss results on profile and map synthetic data, and use a simple method to compute the vertical derivative of non-harmonic functions measured on a horizontal plane. Our main conclusions are: 1. To approximate a correct evaluation of the vertical derivative of a non-harmonic function it is useful to compute it with finite-difference, by using upward continuation. 2. We found that the errors on the vertical derivative computed as if the analytic signal was harmonic reflects mainly on the structural index estimate; these errors can mislead an interpretation even though the depth estimates are almost correct. 3. Consistent estimates of depth and S.I. are instead obtained by using a finite-difference vertical derivative of the analytic signal. 4. Analysis of a case history confirms the strong error in the estimation of structural index if the analytic signal is treated as an harmonic function.
DE: 1517 Magnetic anomaly modeling
SC: Geomagnetism and Paleomagnetism [GP]
MN: 2005 Joint Assembly