An Improved Method to Determine Coda‐Q, Earthquake Magnitude, and Site Amplification: Theory and Application to Southern California

Seismic coda waves can be used to constrain attenuation, estimate earthquake magnitudes, and determine site amplification factors. We have developed a new multistation and multievent method to determine these three important seismic parameters simultaneously. We analyze 642 representative local (≤100 km) and shallow (≤20 km) earthquakes with catalog magnitudes between 1.8 and 5.4 in southern California at multiple frequency bands centered at 1.5, 3, 6, and 12 Hz. We find that the length of the moving average time window can affect the measurement of coda attenuation QC, but our tests indicate that the optimal window length is about 15 times the dominant data period. We use linear regression to fit each coda section and use only those portions that agree with the model decay rate with a correlation coefficient larger than 0.9. For a frequency‐dependent coda‐QC model (QC = Q0fn) at 1‐Hz reference frequency, our results yield estimates for Q0 and n of 107–288 and 0.42–1.14, respectively. Our coda magnitude estimates are linearly correlated with catalog magnitudes, and our observed lateral variations in coda‐QC and our site amplification factors are in general agreement with previous results, although there are notable differences at some locations. This approach provides a unified, accurate, and stable method to measure coda‐QC, earthquake magnitude, and site amplification using coda waves of locally recorded earthquakes. Key Points We develop a new coda‐Q method to determine coda magnitudes, site amplification factors, and coda attenuation simultaneously We introduce a sourceside coda attenuation together with the conventional stationside coda attenuation considering complex attenuation The multiple frequency source terms can be used to study the source spectral models and earthquake scaling relation