Derivative using complex variable conjugate approach for analytic signal of magnetic field anomaly due to 2D finite prism

Abstract

The complex variable conjugate approach has been derived analyticaly for derivative computation. Computational results are then used in calculating the amplitude of analytic signal. It is the square root of the square of the total magnetic field anomaly derivative. The total magnetic fields are generated by the upper and lower parts of a 2D finite prism, and subtraction of both parts yields the magnetic field anomaly. While the approach is obtained by truncating the Taylor series expansion of the total magnetic field function in argument of the complex conjugate in the h2 order-term. Truncating the series does not significantly affect the computational results. This is because when step-size h get smaller, and at h≤10−2, then the errors due to the series truncation became 0 (Kp→0). For derivative computation, the approach has precision on the order of 10−17 to 10−12 towards analytical settlement. On the order of h≤10−2, the approach is insensitive to the selection of step-size h for small numbers, so it can be done arbitrarily without any particular treatment or requires a complicated combination of numbers. The computational results of the analytic signal amplitude show that the positive and negative polarity on the magnetic profile is transformed into a positive profile only. This can facilitate the interpretation of actual magnetic data, especially in determining the causative source position of anomalies.