PEMODELAN SIGNAL ANALITIK ANOMALI MEDAN MAGNET DIPOL BERBASIS HAMPIRAN VARIABEL KOMPLEKS
Complex-step approximation is derived by truncating a Taylor series in form of complex argument. In this research, complex-step approximation was tested in terms of accuracy and stability to analytic (manual) solving and compared to ordinary finite-difference method, and then used to calculated...
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| Format: | Theses and Dissertations NonPeerReviewed |
| Published: |
[Yogyakarta] : Universitas Gadjah Mada
2011
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| Online Access: | https://repository.ugm.ac.id/90152/ http://etd.ugm.ac.id/index.php?mod=penelitian_detail&sub=PenelitianDetail&act=view&typ=html&buku_id=52592 |
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| Summary: | Complex-step approximation is derived by truncating a Taylor series in
form of complex argument. In this research, complex-step approximation was
tested in terms of accuracy and stability to analytic (manual) solving and
compared to ordinary finite-difference method, and then used to calculated
gradient and Hessian in analytic signal equation.
Based on the test results, complex-step approximation was extremely easy
to implement and run, highly accurate and had high numerical stability for
conducting derivative computation compared to finite-difference method. Besides
that, it was ruling out the need to search for optimal step size repeatedly to yield
minimum error in approximation. For finite-difference, relative error Er
approached to 1 when h decreased to 10
-100
. Furthermore, it was applied to
calculated gradients and Hessians from dipole magnetic field anomalies to
obtained 3D analytic signal amplitude. The modeling results showed that the
analytic signal amplitude depended on the direction of the main field vector, the
direction of the magnetic dipole vector and the distance of between the anomaly
causative source and the observation point on the earth surface or on (x,y,r)
coordinates. |
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