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We consider the problem of velocity inversion/calibration in passive survey, where the seismic source is also an unknown. In earthquake detection or microseismic localization, the major task is to reconstruct the passive seismic sources, but due to the source-velocity coupling, source reconstructions are inherently affected by inaccurate knowledge of the velocity, bringing the need of velocity calibration. We propose a source independent velocity calibration method that recovers the velocity without the source information, thus providing a better ground for source inversion. Unlike existing methods that assume sources to be a linear combination of separated point sources, the proposed method allows sources to lie on a line singularity (representing rock cracks), as long as the activation time is relatively brief. The proposed approach is based on the observation that the spatial distribution of the source is separable from the velocity model after a proper Helmholtz domain projection. 

This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the manifold as a whole as opposed to treating each local region independently? We answer these two questions affirmatively by proposing and analyzing an optimization framework that separates the sparse component from the manifold under noisy data. Theoretical error bounds are provided when the tangent spaces of the manifold satisfy certain incoherence conditions. We also provide a near optimal choice of the tuning parameters for the proposed optimization formulation with the help of a new curvature estimation method. The efficacy of our method is demonstrated on both synthetic and real datasets.