1. A passive monitoring method to detect the presence of and characterize a micro-seismic event occurring in the subsurface, the method comprising: processing seismic data recorded by a plurality of seismic receivers arranged on the earth surface, said seismic data comprising acquisition noise and a wave field generated by the micro-seismic event, said wave field being drowned in the noise; and performing a waveform inversion directly on the seismic data recorded by the seismic receivers without prior detection of the wave field generated by the micro-seismic event, wherein the length of a recording is subdivided into contiguous elementary time windows Δt, for each elementary time window Δt, a position (x,y,z) associated with a synthetic seismogram S x,y,z,t is selected to have the smallest deviation from the recorded seismic data in said elementary time window, and wherein the length of the recording is divided into contiguous periods of time, a duration of a period of time, lying between the duration of an elementary time window and the total duration of the recording, is calculated, a median value is calculated out of minimum deviations, between the recorded data and the synthetic seismogram, for each period of time, and each minimum deviation of the period of time under consideration is divided by the calculated median value to obtain a contrast criterion C such that: C = Max ⁡ ( h ⁡ ( t ) ) Mean ⁡ ( h ⁡ ( t ) ) , in which: Max(h(t)) is the minimum deviation of the period of time under consideration, and Mean(h(t)) is the median value.