PEMODELAN SIGNAL ANALITIK ANOMALI MEDAN MAGNET DIPOL BERBASIS HAMPIRAN VARIABEL KOMPLEKS - MANAN, ABDUL ([Yogyakarta] : Universitas Gadjah Mada, 2011)
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.