11:00 AM - 1:00 PM
[SEM16-P01] Development of magnetic inversion code using minimum support regularization and some simulations using the code.
Keywords:inversion, magnetic survey
Various kinds of magnetic inversions estimating subsurface magnetization structure from surface total magnetic field have been proposed. A typical inversion uses objective function with regularization term of the L1 or L2 norm of the model (Li & Oldenburg, 1996). The recent studies propose using regularization terms of both L1 and L2 norms (Utsugi, 2019; 2021) and other characteristic norms such as residual norm (Fournier & Oldenburg, 2019) have also been developed. This study focuses the regularization term of minimum support (Portniaguine & Zhdanov, 1999;2002) and developed the inversion code using python 3. The developed code implements the data space inversion algorithm (Kordy et al., 2016) to save memory store. The minimum support regularization term is expected to suppress making fictious images which are insensitive to surface magnetic data. Using the developed code, we performed simulation to test how much degree the minimum support regularization term suppresses fictious images and how it affects the model resolution. While Portniaguine & Zhdanov (1999; 2002) use cooling or Tikonov method to determine the hyper parameter, we will also compare the results with those obtained by Occam inversion (Constable, et al., 1986).
The model space in the simulation is 1000 m x 1000 m x 1000 m and is discretized by a cube on 50 m each side. Two models were considered: one was composed of a single 200 m cube at a depth of 50 m beneath the center of model space with a magnetization of 2 A/m, and the other was composed of two of the same cubes aligned horizontally 150 m apart. The synthetic data were total magnetic field sampled at a height of 50 m above surface and 50 m horizontally equal spaced. The 5 % Gaussian noises were added to the synthetic data.
The simulation results of the first model show a more suppressed subsurface imaginary image and a clearer boundary between the magnetized object and the background compared to the model estimated by L2-norm minimization. Here, the L2-norm minimization is not a cooling method, but a solution obtained by the Lagrange undecided multiplier formulation of the functional consisting of the sum of the residual squares of the data and the L2-norm.
The simulation results of the second model showed that only the inversion with Minimum Support could recognize two magnetized objects 150 m apart. In the case of the inversion without Minimum Support, the two anomalies interfered with each other and created an apparent anomaly in the depth. When the spacing of the cubes was changed, the two objects could not be recognized even with Minimum Support when the spacing was 100 m. However, when the magnetization strength of the cubes was set to 5 A/m, the objects could be recognized with Minimum Support. Furthermore, when the depth of the cubes was set to 0 m, two objects could be recognized with Minimum Support, whereas two objects could not be recognized at 50 m intervals even when the magnetization was set to 5 A/m. This indicates that the resolution of magnetization depends on the depth and intensity of magnetization in that order.
The model space in the simulation is 1000 m x 1000 m x 1000 m and is discretized by a cube on 50 m each side. Two models were considered: one was composed of a single 200 m cube at a depth of 50 m beneath the center of model space with a magnetization of 2 A/m, and the other was composed of two of the same cubes aligned horizontally 150 m apart. The synthetic data were total magnetic field sampled at a height of 50 m above surface and 50 m horizontally equal spaced. The 5 % Gaussian noises were added to the synthetic data.
The simulation results of the first model show a more suppressed subsurface imaginary image and a clearer boundary between the magnetized object and the background compared to the model estimated by L2-norm minimization. Here, the L2-norm minimization is not a cooling method, but a solution obtained by the Lagrange undecided multiplier formulation of the functional consisting of the sum of the residual squares of the data and the L2-norm.
The simulation results of the second model showed that only the inversion with Minimum Support could recognize two magnetized objects 150 m apart. In the case of the inversion without Minimum Support, the two anomalies interfered with each other and created an apparent anomaly in the depth. When the spacing of the cubes was changed, the two objects could not be recognized even with Minimum Support when the spacing was 100 m. However, when the magnetization strength of the cubes was set to 5 A/m, the objects could be recognized with Minimum Support. Furthermore, when the depth of the cubes was set to 0 m, two objects could be recognized with Minimum Support, whereas two objects could not be recognized at 50 m intervals even when the magnetization was set to 5 A/m. This indicates that the resolution of magnetization depends on the depth and intensity of magnetization in that order.