Although the non-uniqueness of the solution is commonly mentioned in the context of studies that perform spectral decompositions to separate source and propagation effects, its impact on the interpretation of the results is often overlooked. The purpose of this study is to raise awareness on this important subject for modelers and users of the models and to evaluate the impact of strategies commonly applied to constrain the solution. In the first part, we study the connection between the source-station geometry of an actual data set and the properties of the design matrix that defines the spectral decomposition. We exemplify the analyses by considering a geometry extracted from the data set prepared for the benchmark Community Stress Drop Validation Study (Baltay et al., 2021). In the second part, we analyze two different strategies followed to constrain the solutions. The first strategy assumes a reference site condition where the average site amplification for a set of stations is constrained to values fixed a-priori. The second strategy consists in correcting the decomposed source spectra for unresolved global propagation effects. Using numerical analysis, we evaluate the impact on source scaling relationships of constraining the corner frequency of magnitude 2 events to 30 Hz when the true scaling deviates from this assumption. We show that the assumption can not only shift the overall seismic moment versus corner frequency scaling but can also affect the source parameters of larger events and modify their spectral shape.

On the 22nd of May 2021, although no alarming precursory unrest had been reported, Nyiragongo volcano erupted and lava flows threatened about 1 million of inhabitants living in the cities of Goma (Democratic Republic of Congo) and Giseny (Rwanda). After January 1977 and January 2002, it was the beginning of the third historically known flank eruption of Nyiragongo volcano and the first ever to be recorded by dense measurements both on the ground and from space. In the following days, seismic and geodetic data as well as fracture mapping revealed the gradual southward propagation of a shallow dike from the Nyiragongo edifice underlying below Goma airport on May 23-24, then Goma and Gisenyi city centers on May 25-26 and finally below the northern part of Lake Kivu on May 27. Southward migration of the associated seismic swarm slowed down between May 27 and June 02. Micro seismicity became more diffuse, progressively activating transverse tectonic structures previously identified in the whole Lake Kivu basin. Here we exploit ground based and remote sensing data as well as inversion and physics-based models to fully characterize the dike sized, the dynamics of dike propagation and its arrest against a structural lineament known as the Nyabihu Fault. This work highlights the shallow origin of the dike, the segmented dike propagation controlled by the interaction with pre-existing fracture networks and the incremental crater collapse associated with drainage which led to the disappearance of the world’s largest long-living lava lake on top of Nyiragongo.