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We present a methodological framework for developing scientific mobility indicators based on bibliometric data. Using an author name disambiguation algorithm we identify nearly 16 million disambiguated authors from all publications covered in the Web of Science in the 2008-2015 period. Based on the information provided in each bibliographic record and across individuals’ publication record, we track international mobility of scientists and propose a classification of scientific mobility by which to analyze the phenomenon of scientific mobility. We distinguish between migrants and travelers based on the traces they leave. We find that 3.7% of researchers in our data set are mobile. Within these, travelers represent 72.7% of all mobile scholars. Still, migrants seem to consistently have higher scientific impact. We then apply the classification at the country level by further expanding these two classes based on the directionality of scientists movement (incoming and outgoing). Our findings point out as to the potentialities of our classification to further understand the effect of mobility in individuals, countries or fields, among others.