3D magnetotelluric inversion using a limited-memory quasi-Newton optimization

The limited-memory quasi-Newton method with simple bounds is used to develop a novel, fully 3D magnetotelluric MT inversion technique. This nonlinear inversion is based oniterativeminimizationofaclassicalTikhonovregularized penalty function. However, instead of the usual model space of log resistivities, the approach iterates in a model space with simple bounds imposed on the conductivities of the 3D target. The method requires storage proportional to 2 ncp N,whereNisthenumberofconductivitiestoberecovered and ncp is the number of correction pairs practically, only a few. These requirements are much less than those imposed byotherNewtonmethods,whichusuallyrequirestorageproportional toN M orN N, where M is the number of data tobeinverted.Thederivativesofthepenaltyfunctionarecalculated using an adjoint method based on electromagnetic fieldreciprocity.Theinversioninvolvesallfourentriesofthe MT impedance matrix; the x3D integral equation forwardmodeling code is used as an engine for this inversion. Convergence, performance, and accuracy of the inversion are demonstrated on synthetic numerical examples.After investigating erratic resistivities in the upper part of the model obtainedforoneoftheexamples,weconcludethatthestandard Tikhonov regularization is not enough to provide consistently smooth underground structures.An additional regularizationhelpstoovercometheproblem.

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