ABSTRACT
This chapter explores the application of compressive sensing (CS) to the ubiquitous problem of spatiotemporal seismic source localization and the inversion of the seismic moment tensor. These are prevailing problems in applied geophysics and an important component of seismic monitoring in fields ranging from uniaxial and triaxial compression experiments at laboratory scale, hydraulic injections, mining, and earthquake and volcano monitoring. The chapter focuses on the problem of seismic moment tensor representation in terms of a sparse superposition of Green functions. Seismic sources have finite dimensions, but equivalent point-source approximations are frequently used to simplify their analysis. The analysis of the spectral norm of cross products provides an initial estimate of the expected uncertainties in the estimation of source locations using block orthogonal matching pursuit (BOMP). The incorporation of CS into the source monitoring problem is straightforward and requires only the introduction of the encoding matrix. Many of the challenging aspects of CS source monitoring are found in its practical implementation.
