Evaluation of Model Resolution with Various Forward Theory and Parameterization: A Synthetic Study

計畫名稱:Evaluation of Model Resolution with Various Forward Theory and Parameterization: A Synthetic Study

所屬單位:地質系

研究團隊:地球物理研究室

計畫主持人:洪淑蕙

研究人員:張毓軒

資源需求:gfortran complier with OpenMP library, Intel-fortran compiler with MPI library

使用期間:2009/05~

研究主題:
Evaluation of Model Resolution with Various Forward Theory and Parameterization: A Synthetic Study

研究內容概述:
Whether different forward theories (data rules) and parameterizations employed in tomographic imaging lead to the improvement of the resulting Earth structures has been a focus of attention in the seismological community. Recent advance in tomographic theory has gone beyond ray theory and incorporated the 3-D sensitivity kernels of frequency-dependent travel-time data into probing the mantle velocity heterogeneity. On the other hand, the idea of multiscale parameterization has been introduced to deal with naturally uneven data distribution and spatially-varying model resolution in the inversion. The multi-resolution model automatically built through the wavelet decomposition and synthesis results in the non-stationary spatial resolution and data-adaptive resolvable scales. Because the Gram matrix of sensitivity kernels that relates observed data to seismic velocity variations is usually too large to be practically inverted by singular value decomposition (SVD), the iterative LSQR algorithm is instead used in the inversion which inhibits the calculation of model resolution and covariance to assess the model performance. With the increasing computing power, the SVD of the large Gram matrix becomes viable by the parallel PROPACK solver. In this study, we test the resolvability of a synthetic 3-D random model using ground-truth travel-time residuals and various data rules and parameterizations. The source-receiver configuration mimics the borehole tomography. The tradeoff relations between model covariances (errors) and model spreads for the models with the same data rule and parameterization are used to determine the optimal models. The optimal finite-frequency models always yield larger model norms and lower model misfits regardless of the parameterization and regularization adopted in the inversion. The optimal multi-scale models also yield larger model norms and longer-wavelength structures and have smaller model covariances obtained with damping regularization. The inversion based on finite-frequency theory, multi-scale parameterization, and damping regularization leads to the best-fitting model.

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