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4D inversion of L1 and L2 norm minimizations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Jung Tsourlos, P. Supper, Robert |
| Copyright Year | 2012 |
| Abstract | A new 4-dimensional (4D) inversion algorithm is developed so that any of data misfits and model roughness in the space and time domains can be selectively minimized either in terms of L1 norm or in L2 norm. This study is motivated by the experiences that a 4D inversion adopting full L2 norm minimization may sometimes result in a model too smoothly varying with time. It is further encouraged by the realization that a particular criterion of either L1 or L2 norm cannot universally be the optimal approach for accurately reconstructing the subsurface condition. Along with this development of the algorithm, we try to overcome the difficulties of jointly choosing two optimal regularization parameters in the space and time domains. To achieve this, we devise automatic determination methods not only of the Lagrangian multipliers for the space-domain smoothness constraint but also of the regularization parameter for penalizing the model roughness along the time axis. Both kinds of the regularization parameters are actively updated as data misfits and model roughness vary at each iteration step. We conducted inversion experiments using synthetic and field monitoring data to test the proposed algorithms and further to compare the performance of L1 norm and L2 norm minimizations. Both of the synthetic and field data experiments proved that the automatic determination method developed in this study is very effective for calculating the ground changes that are closer to the ground truth than the approaches of using pre-determined parameter values. Synthetic data examples showed that L1 norm minimization of the time-domain roughness could cure the problem of unnecessary smooth model changes when the subsurface changes are locally confined, but at the same time, the L2 norm approach would be more reasonable when the changes are expected widespread. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://opac.geologie.ac.at/wwwopacx/wwwopac.ashx?command=getcontent&server=images&value=BR0093_106_A.pdf |
| Alternate Webpage(s) | https://www.geologie.ac.at/fileadmin/user_upload/dokumente/pdf/projekte/tempel/SeitenausBerichteGeolBA93_S106-113.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
