  In this paper we propose computationally efficient and robust methods for
estimating the moment tensor and location of micro-seismic event(s) for large
search volumes. Our contribution is two-fold. First, we propose a novel
joint-complexity measure, namely the sum of nuclear norms which while imposing
sparsity on the number of fractures (locations) over a large spatial volume,
also captures the rank-1 nature of the induced wavefield pattern. This
wavefield pattern is modeled as the outer-product of the source signature with
the amplitude pattern across the receivers from a seismic source. A rank-1
factorization of the estimated wavefield pattern at each location can therefore
be used to estimate the seismic moment tensor using the knowledge of the array
geometry. In contrast to existing work this approach allows us to drop any
other assumption on the source signature. Second, we exploit the recently
proposed first-order incremental projection algorithms for a fast and efficient
implementation of the resulting optimization problem and develop a hybrid
stochastic & deterministic algorithm which results in significant computational
savings.
