Estimating the model resolution matrix for large seismic tomography problems based on Lanczos bidiagonalization with partial reorthogonalization

The PROPACK package developed by Larsen is able to efficiently and accurately estimate singular values and vectors for large matrices based on the Lanczos bidiagonalization with partial reorthogonalization. We incorporate the Pavtial Reorthogonalization Package (PROPACK) package into the double-difference seismic tomography code tomoDD and estimate the model resolution matrix for large seismic tomography problems. Compared to previous Least Squares QR (LSQR)-based methods for estimating the model resolution matrix the PROPACK-based method calculates the full resolution matrix and thus gives a complete description of how well the model is resolved. Several observations are drawn from the application to data from the 2001 eruption of Mt Etna: for this example, it is reasonable to use ray-sampling density information to characterize the model resolution qualitatively; the model resolution resulting from just velocity inversion bears a close linear relationship to that from simultaneous inversion but always overestimates resolution; and the inversion system using differential times has a greater ability to resolve the source region structure than the system using absolute times.