Effect of low-pass filter on structural index of magnetic anomalies
The structural index depends on the source types and the rate of the field decay with distance from the source. The structural index plays an important role in two interpretation techniques, i.e. the Euler deconvolution and Extended Euler deconvolution. This quantity in Euler deconvolution is an assumed quantity. In this approach, one can calculate the target depth and location using the prescribed structural index. A wrong structural index affects the target depths and locations. This is while the structural index in the Extended Euler deconvolution will be calculated. The Extended Euler deconvolution is a generalization of the 2D Euler deconvolution and Werner deconvolution that helps to stabilize the Euler deconvolution by providing three equations rather than one at each point. The noise in a data set corrupts the signal that the Extended Euler deconvolution searches for. Thus, the accuracies of locations, depths, and the structural index will decrease with the noise level. For noisy data, it is common to use a low-pass filter to suppress the noise effects before applying interpretation techniques. We considered the effect of applying a low-pass filter to magnetic data and calculated the structural index. The low-pass filter that we used was the Butterworth filter which has no ripple and is mathematically simple. In this study, we showed that for typical Euler deconvolution applications, the effect of the low-pass filtering will decrease the determined structural index from the theoretical value. To this end, we began with the magnetic potential of a vertical dipole with an SI of 2. The magnetic field had a structural index of 3 as it was the first order derivative of the potential. Then, we obtained the 2D Fourier transform of the vertical dipole potential. After that, the transformed potential was multiplied by the transfer function of the Butterworth filter in the wave number domain. The filtered potential of the dipole in the spatial domain was obtained by the inverse Fourier transform. We also did the above operations for the magnetic potential of the horizontal line of dipoles with a structural index of 1. In that case, a one-dimensional Fourier transform of the profile was applied. It was seen that the filtered field decayed slower than the unfiltered field. We studied the structural index in two horizontal locations, i.e. one directly over the target and another away from the target. Over the target, the structural index values were always equal to or less than 2 for the vertical dipole and 1 for the horizontal line of dipoles, depending on the cut-off wavenumber. Solutions at horizontal distances much greater than the depth to the target had structural indexes greater than 2 with an upper limit of 3 for a dipole and 1 with an upper limit of 2 for a horizontal line of dipoles.Â Upward continuation is also a low pass filter which does not change the structural index of a magnetic anomaly. We showed in this study that filtering the magnetic data by the Butterworth filter would decrease the structural index. Parameters of the Butterworth filter such as the order and cut-off wavelength directly affected the estimated structural index solutions. Once the wavelength values increased, it began to filter the field and the structural index. For higher orders of the filter, the structural index decreased more rapidly to the point at which the structural index was less than 1 for the vertical dipole for wavelengths more than 6.28 m. The results proved that one must take into account filtering for the application of theEuler deconvolution to locate magnetic dipole anomalies.Application of the low-pass filter to Chah Sorb magnetic data showed that the structural index decreased.
Iranian Journal of Geophysics, Volume:9 Issue:4, 2016
45 - 53
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