Objective estimation of source parameters and local Q values by simultaneous inversion method

Details Objective estimation of source parameters and local Q values by simultaneous inversion method Objective estimation of source parameters and local Q values by simultaneous inversion method

Nov 1982

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982pepi...30..197m&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 30, Issue 2-3, p. 197-208.

Physics

9

Scientific paper

Accurate estimation of the physical parameters of earthquake sources requires an objective basis for determining the spectral parameters SO, the low-frequency level, fc, the corner frequency, and γ, the high-frequency decay rate. Knowledge of the appropriate Q value is also necessary. In most cases, however, the estimation of these parameters is rather subjective, being accomplished usually by visual fitting of some schematic spectral shape to the observations, and the average of Q over possible regional variations is sometimes used without sufficient evidence as representative of the local value.
An objective method of simultaneous inversion is presented in this study for the estimation of source parameters and local Q values. According to theoretical predictions as well as to many observational results, an observed spectrum may be reasonably regarded as a sample from an ensemble of the form O(f)=SO[(f/fc)a+1]-bexp(- πftQ-1), where a and b are positive constants and γ = ab. For earthquakes occurring in a confined region and observed at a nearby station, the constants a and b are common and a single value may be used as the local value of Q. The observed spectra of K earthquakes at L frequency points give K × L data, while the number of unknowns to be estimated is 2 K + 3, that is, the SO and c values for the K earthquakes, and the values of a, b, and Q. For K × L > 2K +3, least-squares estimators are obtained so as to minimise s2=ɛɛ[ln(Okl)-ln(Skl)+πfltkQ-1]2. A numerical test using an artificial data set indicates that a stable solution is obtained, and the errors in the parameters SO and fc are less than 20%, for a data standard deviation of 0.2.
This method has been applied to actual data sets for small earthquakes occurring near Miyako on the Pacific coast of the Northeastern part of Japan which were observed at a nearby station. The solution converges sufficiently at the third or fourth iteration step, the data standard deviation being 0.2. The source parameters and the Q value thus estimated are in good accordance with those obtained by another, independent method. The present method gives reliable data for an accurate scaling model, because the source parameters are obtained by a standard technique for a variety of earthquake sizes.

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