Nonlinear inversion for arbitrarily-oriented anisotropic models II: Inversion techniques

We present output models from inversion of a synthetic surface wave dataset. We implement new 3-D finite-frequency kernels, based on the Born approximation, to invert for upper mantle structure beneath western North America. The kernels are formulated based on a hexagonal symmetry with an arbitrary orientation. Numerical tests were performed to achieve a robust inversion scheme. Four synthetic input models were created, to include: isotropic, constant strength anisotropic, variable strength anisotropic, and both anisotropic and isotropic together. The reference model was a simplified version of PREM (dubbed PREM LIGHT) in which the crust and 220 km discontinuity have been removed. Output models from inversions of calculated synthetic data are compared against these input models to test for accurate reproduction of input model features, and the resolution of those features. The object of this phase of the study was to determine appropriate nonlinear inversion schemes that adequately recover the input models. The synthetic dataset consists of collected seismic waveforms of 126 earthquake mechanisms, of magnitude 6-7 from Dec 2006 to Feb 2009, from the IRIS database. Events were selected to correlate with USArray deployments, and to have as complete an azimuthal coverage as possible. The events occurred within a circular region of radius 150^o centered about 44^o lat, -110^o lon (an arbitrary location within USArray coverage). Synthetic data were calculated utilizing a spectral element code (SEM) coupled to a normal mode solution. The mesh consists of a 3-D heterogeneous outer shell, representing the upper mantle above 450 km depth, coupled to a spherically symmetric inner sphere. From the synthetic dataset, multi-taper fundamental mode surface wave phase delay measurements are taken. The orthogonal 2.5π -prolate spheroidal wave function eigentapers (Slepian tapers) reduce noise biasing, and can provide error estimates in phase delay measurements. This study is a preliminary phase of a larger goal to integrate surface wave data and SKS splitting data. The kernels used here are formulated in a consistent framework as recent 3-D finite-frequency kernels used to invert SKS splitting data. This consistency will allow for inversion of both surface wave data and SKS splitting data together to improve tomographic image resolution of anisotropic structure of the upper mantle.