Optimizing a layered and laterally constrained 2D inversion of resistivity data using Broyden's update and 1D derivatives |
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| Authors: | Anders V Christiansen Esben Auken |
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| Institution: | The Hydrogeophysics Group, Department of Earth Sciences, University of Aarhus, Finlandsgade 6-8, 8200 Aarhus N, Denmark |
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| Abstract: | Dense profile-oriented resistivity data allows for 2D and 3D inversions. However, huge amounts of data make it practically impossible to do full 2D or 3D inversions on a routine basis. Therefore, a number of approximations have been suggested over the years to speed up computations. We suggest using a combination of Broyden's update on the Jacobian matrix with derivatives calculated using a 1D formulation on a parameterized 2D model of locally 1D layered models. The approximations bring down the effective number of 2D forward responses to a minimum, which again gives us the ability to invert very large sections. Broyden's update is not as useful with a parameterized problem as is the case with a smooth minimum structure problem that has been the usual application. 1D derivatives, however, seem to be very effective when initiating a full 2D solution with Broyden's update. We compare the different methods using two different kinds of data on two synthetic models and on two field examples. The most effective and reliable optimization combines 1D derivatives with a full 2D solution and Broyden's update. When using Broyden's update the Jacobian matrix needs to be reset every once in a while. We do this whenever the difference in data residual from the previous iteration is less than 5%. This combined inversion method reduces the computation time approximately a factor of 3 without losing model resolution. |
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| Keywords: | Inversion 2D DC resistivity Optimizations Broyden's update 1D derivatives |
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