In the context of passive acoustic monitoring of large whales, we propose a new method for localizing blue whales (Balaenoptera musculus) from the acoustic recordings of only one sensor. We use a precise modelling of the sound propagation thanks to SPECFEM, a spectral element code for solving wave propagation equations. Based on field measurements in Northern Chile, we ran a simulation on a large supercomputer. We also exploited a recording device, Bombyx II, for one and a half months, with visual monitoring of the zone by a group of experts. We find that the method applied to the south east Pacific song of blue whales gives theoretical results of about 50% success in position recovery. Since we have redundancy in our data, we were able to locate the whale with a precision of 500 m over a box of 10 km by 5 km in the case when we have both visual detection and a strong acoustic signal. More tests should be performed before validating this method, but these first results are encouraging.