We investigate the possibility to estimate the depths of earthquakes of moderate magnitude (3.5>M<5.5) from teleseismic data, using the Comprehensive Nuclear‐Test‐Ban Treaty Organization monitoring system. To face new problems that arise from the weakness of the magnitudes we want to deal with, two methods were developed. First, a depth‐phase recognition method is applied, based on a new improved cepstral analysis. In addition, we develop a focal mechanism genetic algorithm inversion that focuses on depth resolution through an envelope‐fitting procedure and adapted reproduction and mutation functions. Six events of interest were analyzed to validate these new proposed methods. First, the teleseismic depth of the recent Corsica earthquake (France, 7 July 2011) was estimated at about 26 km, whereas regional inversions do not provide any constraints. This proposed depth has a direct impact for regional tectonic studies, as this implies that this earthquake occurred in the continental crust. In contrast, the shallow Sardinia event (Italy, 3 January 2011) took place in the oceanic crust. The depth of the Virginia event (United States, 23 August 2011) was also constrained using these methods, and we show that it is possible to constrain the focal depth even for weak magnitude events, such as the mb 3.6 Ardèche earthquake (France, 3 August 2011). In the case of the Po Plain earthquake (Italy, 27 January 2012), this provides another example of the great interest in teleseismic analysis, where the detection of the Moho reflected phase (pmP) shows without doubt an upper‐mantle event. Finally, the Murcia event (Spain, 11 May 2011) shows the limits of these methods for very shallow events (<4–5  km). We show that these new depth determinations improve our ability to understand the geologic processes, as they provide complementary information on the source and are not affected by lateral crustal heterogeneities.

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