Ⓔ Inversion for Focal Mechanisms Using Waveform Envelopes and Inaccurate Velocity Models: Examples from Brazil by Juraci Carvalho, Lucas Vieira Barros, and Jiří Zahradník Abstract One of the major challenges for the moment tensor determination is as- sociated with the relatively low-magnitude events (M w ∼ 4) recorded by few regional stations at relatively large distances (300–600 km) and analyzed with standard veloc- ity models of the region. Difficulties arise from the fact that synthetics in standard models (e.g., those routinely used in the location) cannot properly match real wave- forms and favor the appearance of unmodeled time shifts and amplitude discrepancies (e.g., if VMs are constructed to minimize location residuals, they are not sensitive to uppermost shallow layers, which are insufficiently sampled by rays if shallow sources are missing). The situation is even worse when real waveforms can be matched but the retrieved focal mechanism is incorrect. This article investigates an alternative meth- odology that is more robust with respect to inappropriate velocity models: the inver- sion of waveform envelopes. The method is built on an empirical basis. It studies the effects of velocity models on synthetic waveforms and finds that the information about focal mechanism is encoded in the variation of the envelope shapes and amplitudes among the seismogram components. Besides synthetic tests, the method has been tested on real data comprising two earthquakes in Brazil: the 2010 M w 4.3 Mara Rosa (MR) and the 2017 M w 4.3 Maranhão earthquakes. When compared with solutions from previous studies, based on many polarities and ad hoc path-specific velocity models, we obtained in both cases the same mechanism with a single 1D model and a single-station polarity constraint. The envelope inversion is a promising technique that might be useful in similar sparse networks, such as the one in Brazil, where stan- dard waveform inversion, in general, is not fully efficient. Electronic Supplement: Figures of waveform comparisons and tables of ampli- tude ratio due to velocity model (ARMOD) values and velocity models. Introduction The initial determinations of focal mechanisms in Brazil were done by Mendiguren and Richter (1978), Assumpção and Suárez (1988), Assumpção (1998a,b, 1992), and Ferreira et al. (1998). New studies on focal mechanisms were done by Barros et al. (2009, 2015), Chimpliganond et al. (2010), Lima Neto et al. (2013), Agurto-Detzel et al. (2014), Oliveira et al. (2015), and Dias et al. (2016). Whereas the initial focal mechanism solution was constrained with the use of the first- motion polarities (P phases) and/or the amplitude ratios of the body-wave phases, the more recent works also use wave- form inversion. For example, Zahradník et al. (2015) revis- ited the previous solution of Barros et al. (2015) for the 2010 M w 4.3 Mara Rosa (MR) earthquake, which occurred in the state of Goiás, Brazil, performing waveform inversion pre- constrained by first-motion polarities according to Fojtíková and Zahradník (2014). Carvalho et al. (2016) retrieved focal mechanisms of 11 aftershocks (M w 0.8–1.4) of the MR earthquake by inverting full waveforms using temporary lo- cal stations and a local velocity model, the same as used in this work (VM2). The waveform inversion was feasible up to ∼10 MSW, in which MSW is the minimum shear wave- length. For example, for V S ∼ 3:0 km=s, and the maximum inversion frequency ∼2 Hz, the MSW is ∼1:5 km; hence, 10 MSW is about 15 km. Dias et al. (2016) demonstrated the possibility of significantly extending the feasible epicentral distance range (65 MSW) using ad hoc velocity models, spe- cifically derived for each source–station path by inverting Love- and Rayleigh-wave dispersion curves of the same event for which the moment tensor is calculated. Polarities were used in their consistency check of the inversion results. In all these attempts, the authors struggle with the inac- curacy of the existing velocity models of the region. Although 138 Bulletin of the Seismological Society of America, Vol. 109, No. 1, pp. 138–151, February 2019, doi: 10.1785/0120180119 Downloaded from https://pubs.geoscienceworld.org/ssa/bssa/article-pdf/109/1/138/4627747/bssa-2018119.1.pdf by UNIVERSIDADE DE BRASILIA, Juraci Carvalho on 05 February 2019