| Аннотация | Inverse source problems for elastic waves aim to reconstruct the characteristics of unknown sources from observed wave fields. These problems are of fundamental importance across multiple scientific and engineering disciplines. In geophysical exploration, they facilitate the optimization of seismic source designs for subsurface imaging and play a central role in earthquake source inversion to assess seismic hazards [ 1] . In engineering, inverse source techniques support structural health monitoring by enabling the localization of damage- induced wave sources in infrastructures such as bridges, buildings, and pipelines [ 2] . Further applications include non- destructivetestingfordetectingmaterialflaws[ 13] , and source localization inmedicalultrasoundimaging. These diverseapplicationshighlight the interdisciplinaryrelevance and practical importance of inverse source problems in advancing scientific understanding and enhancing infrastructure safety. Motivated by these critical applications, inverse scattering problems have been extensively studied within the broader framework of inverse scattering theory. Substantial theoretical progress has been made on the uniqueness and stability of source reconstruction; see, for instance, [ 3, 12, 22, 32] and the references therein. A comprehensive treatment of the general theory for wave equation- based inverse source problems can be found in the review article [ 3] . On the computational side, numerous numerical methods have been developed to reconstruct sources from radiated fields or far- field measurements. Over the past decades, approaches include recursive algorithms [ 5] , Fourier- based methods [ 10, 11, 26, 28, 30] , variational Bayesian techniques [ 15] , and a variety of sampling- type methods [ 7, 20, 27, 31] have been investigated for the inverse source problem together with the closely related inverse scattering problems. Although this method recovers the geometrical characteristics of targets, it is incapable of recovering the values of coefficients within targets. However, the convexification method recovers everything: locations, shapes, and values of coefficients inside targets, including the case of experimental data [ 17] . Compared with iterative reconstruction techniques, sampling- type methods offer significant computational advantages. Their formulations typically involve only low- cost integration operations, avoiding both iterative procedures and the need to solve forward problems. As a result, these methods are not only computationally efficient but also straightforward to implement. By carefully designing the indicator functions, it becomes possible to accurately recover both source locations and intensities—allowing qualitative sampling methods to yield quantitative reconstructions. |