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

Abstract

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 Q C , 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-Q C model (Q C = Q 0 f n ) at 1-Hz reference frequency, our results yield estimates for Q 0 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-Q C 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-Q C , 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 Supporting Information:• Supporting Information S1

A Frequency-Dependent Model for the Shape of the Fourier Amplitude Spectrum of Acceleration at High Frequencies

“…10 (e.g. Aki, 1980a;Singh and Herrmann, 1983;Toksöz et al, 1988;Havskov et al, 2016;Wang and Shearer, 2019). As pointed out in the Methodology section, we use the notation ζ instead of ζ 1 at f 0 = 1 Hz.…”

The Earth's Surface Controls the Depth‐Dependent Seismic Radiation of Megathrust Earthquakes

“…The spectral model fits the shape of far‐field P‐wave pulses that originate from circular crack ruptures with uniform stress drop and elliptical slip distribution (Brune, 1970; Eshelby, 1957; Madariaga, 1976). It is common to perform spectral fitting over the spectrum of the far‐field body‐wave pulse of the entire event, which is the moment‐rate pulse (Abercrombie & Rice, 2005; Allmann & Shearer, 2009; Trugman & Shearer, 2017; W. Wang & Shearer, 2019). Slip rate functions and overall moment‐rate functions differ because the latter is the spatial integration of the former.…”

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

“…The M w measurement, or equivalently the scalar moment M 0 , may benefit from the coda stability. Efforts have been made on determining earthquake magnitudes ( M L or M w ; e.g., Bakun, 1984; Baltay et al., 2010; Izutani & Kanamori, 2001; Mayeda & Walter, 1996; Mayeda et al., 2003; Suteau & Whitcomb, 1979; Wang & Shearer, 2019). These studies generally use relatively high‐frequency data (mostly >0.2 Hz and the minimum of 0.01 Hz) at regional distances and analyze the amplitude of coda envelopes or the duration of coda signals by methods such as statistical regression and spectrum modeling.…”