A Method to Determine Moment Magnitudes of Large Earthquakes Based on the Long‐Period Coda

We present a novel and robust method for estimating moment magnitudes (Mw) of large earthquakes with long‐period and long‐lasting coda energy. Fitting the energy with a simple decay model, we derive a straightforward relationship between the coda energy and the Mw. Tests with both real and synthetic data of 10 globally distributed large earthquakes (Mw > 8) verify the method and the results are stable and reliable even with a fast calculation of synthetics for a 1D model. Tests also show that the method is applicable for earthquakes with Mw above 7.5–8.0 with energy sufficiently greater than the ambient noise. The method removes or reduces the effects of geometric spreading, focal mechanism, source rupture process, and the actual Earth structure, making it advantageous for estimating the magnitudes of large earthquakes. The new long‐period coda moment magnitude (Mwo) estimations are similar to the conventional solutions but are slightly larger (by 0.04 on average). Plain Language Summary A method is proposed to measure the size of a large earthquake using the very low‐frequency energy that lasts for a very long time (more than 10 hr) after the earthquake. Using only one parameter from a simple formula describing the decay of the energy, we connect the coda energy and the size of an earthquake. The method is reliable and stable because the coda energy is less affected by the details of the source properties and Earth structure. It is applicable to earthquakes with magnitude greater than 7.5–8.0. Key Points A new method is proposed to measure moment magnitudes of large earthquakes with long‐period and long‐lasting coda energy Globally recorded data and synthetic waveforms demonstrate the reliability and robustness of the method The method is advantageous for estimating large‐earthquake magnitudes with minimum influence from Earth structure and source complexities