Efficient and Scalable Algorithms for the Inversion of Very Large AEM Datasets
Casper Kirkegaard, Esben Auken · 2012
Recently the standard size of airborne electromagnetic (AEM) datasets has been growing rapidly, while many surveys at the same time focus on modern applications that require very high resolution. Often, the particular target structures of interest cannot be identified directly from the data and approximate inversions or data transform techniques also prove insufficient. This type of application includes environmental studies of aquifers, salinity and geology and also cases of relevance to the mining industry e.g. uranium exploration. In these cases highly accurate full non-linear inversion provides the only reliable solution, which is a computational challenge. In designing an inversion scheme for these types of problems it is further advantageous to utilize as many assumptions as possible. The target structures of interest can often be regarded locally one dimensional, quasi layered and spatially coherent which can be integrated in the inversion. If inverting multiple soundings at a time for a set of spatially constrained 1D models, information is allowed to propagate spatially and a vastly improved model result can be obtained. Ideally, entire surveys should be inverted at a time in huge constrained problems, but poor scaling properties of the underlying algorithms typically makes this impossible. We discuss how we have implemented custom algorithms for scalable spatially constrained inversion of very large AEM datasets. Our algorithm for solving systems of linear equations is essential, since it scales linearly with the size of the dataset in terms of both memory consumption and solve time. This type of scalability basically allows for inverting arbitrarily large datasets at a time in huge spatially constrained problems. An example of the significant improvement that can be gained from full survey inversion is provided. We further show how model uncertainty estimates can be obtained in linear time for large problems and how we have parallelized our code for many-core computer architectures.