A note on electromagnetic field theory and 1D modeling of synthetic CSAMT data

Abstract: Controlled source audio magnetotellurics, or CSAMT, is one of the principal methods for electromagnetic measurements. A 1D model is a simple representation but a quite easy way to find the main features of the Earth's subsurface. The 1D inversion of CSAMT data that has been used in this report was presented by H.M. Maurer and X. Garcia (1995). The inversion was calculated with a Levenberg-Marquardt algorithm giving an iterative least-squares solution and the field calculations were based on those of Weidelt (1986). A cylindrical coordinate system was used to calculate the field response for a horizontal electric dipole. The main goal of this thesis has been to investigate these calculations and by using this, implement the field calculations of a horizontal magnetic dipole. The calculations are done with a numerical representation of the Hankel transformation. Using this approach, the program calculates the field response of a 1D layered earth model with a maximum of 10 layers. To find the sensitivities used in the Levenberg-Marquardt algorithm, a perturbation method has been used. Though the program was written with a semi-analytic method, this was not fully functional. To improve the sensitivities, this method has been reconstructed. To evaluate the program response, a program to calculate synthetic data has been written and synthetic data sets of four models has been used. Here, the calculations are made by the same numerical tables as the inversion program to avoid unnecessary errors. An exception is though made for the homogenous half space, where a simpler formulation has been used. Investigation of the program response show how well the field calculations corre- spond to the professional X3D program based on calculations by Avdeev et al. (2002). For higher (> 100 Hz) frequencies the deviation is alarmingly high which makes the result close to useless. This is though not seen in the lower frequencies where the result is much better. The deviation is also connected to the complexity of the model, i.e. the number of layers and resistivity contrast. This frequency problem is likely to be caused by failure in the numerical approximation for high frequencies. Due to the high frequency problem, a maximum of 100 Hz has been used when looking at the errors in the output models. When lowering the frequency range, there is some convergence for the simplest model, a homogenous half space. The more complex models do not converge for any frequency range and due to this, one conclusion is that the problem can be found in the inversion algorithm itself and not in the field calculations.