Abstract

We describe a technique to estimate the seismic moment of acoustic emissions and other extremely small seismic events. Unlike previous calibration techniques, it does not require modeling of the wave propagation, sensor response, or signal conditioning. Rather, this technique calibrates the recording system as a whole and uses a ball impact as a reference source or empirical Green’s function. To correctly apply this technique, we develop mathematical expressions that link the seismic moment M0 of internal seismic sources (i.e., earthquakes and acoustic emissions) to the impulse, or change in momentum Δp, of externally applied seismic sources (i.e., meteor impacts or, in this case, ball impact). We find that, at low frequencies, moment and impulse are linked by a constant, which we call the force‐moment‐rate scale factor forumla. This constant is equal to twice the speed of sound in the material from which the seismic sources were generated. Next, we demonstrate the calibration technique on two different experimental rock mechanics facilities. The first example is a saw‐cut cylindrical granite sample that is loaded in a triaxial apparatus at 40 MPa confining pressure. The second example is a 2 m long fault cut in a granite sample and deformed in a large biaxial apparatus at lower stress levels. Using the empirical calibration technique, we are able to determine absolute source parameters including the seismic moment, corner frequency, stress drop, and radiated energy of these magnitude −2.5 to −7 seismic events.

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