Distributed Acoustic Sensing (DAS) is establishing as a promising technique in Seismology. This novel system turns a fibre optic cable into a continuous single component array with very dense spatial sampling. Simplicity of installation and availability of telecommunication cables (dark fibres) make the technique very advantageous for investigating harsh environments like seafloors, sensing up to hundreds of kilometres of fibre with fine spatial resolution. Given the high potential, the technology has been successfully tested in recent years for several earthquake monitoring tasks, such as location, subsurface characterization, focal mechanism determination, tomography, or source back projection. The transferability of standard seismological tools to DAS data is straightforward when working with time picking, while analysis of the amplitude content of the signal demands further research. This is the case of earthquake source characterization, where standard approaches require conversion of strain rate data into more classical kinematic quantities (i.e. acceleration or velocity). In this work we develop a new formulation that allows to estimate source parameters without the need for conversion. We start from the description of the far-field strain radiation emitted from a circular seismic rupture, showing that the time integral of the strain is related to the Source Time Function. Using this quantity, we develop the spectral modelling allowing for frequency domain inversion of DAS data for estimation of moment magnitude and corner frequency. The formulation accounts for the unique azimuthal sensitivity of the cable in the radiation pattern average, and explicitly shows DAS enhanced sensitivity to slow scattered waves propagating beneath the fibre.We validated the proposed approach on two case-studies, for events in local magnitude range 0.4 - 4.3, comparing the results with estimates from standard seismic instruments. Earthquakes recorded on a 150km long cable offshore the coast of central Chile during a 1-month DAS survey exhibit scale invariant stress drops, with an average of Δσ=(0.8±0.6)MPa. Also, moment magnitude estimates agree with results from standard seismic instruments. The analysis of small magnitude events (ML
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