Estimating magnetic dike parameters using a non-linear constrained inversion technique: an example from the Särna area, west central Sweden

In this paper, we describe a non-linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low-pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non-linear least squares inversion of the high resolution magnetic field data along the flight lines. We use the Levenberg-Marquardt algorithm together with the trust-region-reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated gzz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of gzz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one. Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Sarna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.