A frequency-domain method to inverse moving source problem with unknown radiating moment
This addresses the problem of imaging moving sources with unknown moments for applications in fields like seismology or acoustics, representing an incremental advancement in factorization methods.
The paper tackles the inverse moving source problem by recovering the spatial support and excitation instants of a time-dependent source using far-field data from two opposite directions, establishing uniqueness for the convex hull and demonstrating effectiveness through numerical simulations in 2D and 3D.
This paper introduces a multi-frequency factorization method for imaging a time-dependent source, specifically to recover its spatial support and the associated excitation instants. Using far-field data from two opposite directions, we establish a computational criterion that characterizes both the unknown pulse moments and the narrowest strip (perpendicular to the direction) enclosing the source support. Central to our inversion scheme is the construction of indicator functions, defined pointwise over the spatial and temporal sampling variables. The proposed inversion scheme permits the recovery of the $Î$-convex support domain from far-field data at sparse observation directions. Uniqueness in determining the convex hull of the support and the excitation instants-using all observation directions-is also established as a direct consequence of the factorization method. The effectiveness and feasibility of the approach are examined through comprehensive numerical simulations in two and three dimensions.