Understanding the physics of the earthquake rupture mechanism is essential, given that earthquakes are among the most harmful natural disasters. Some earthquake source parameters such as radiated seismic energy and stress drop can be used to investigate the properties and dynamics of faulting. Estimates of these parameters have large uncertainties, leading to discrepancies among different studies, particularly investigations of the scaling relations of earthquakes.; In order to understand the physics of earthquakes and their behavior as a function of magnitude, it is necessary to have an idea of the uncertainties of the estimated parameters (e.g., when comparing two earthquakes). We have developed a method to estimate the uncertainties of the source parameters as measured from the seismic wave spectra. The large uncertainties expected require improving the methodologies used to obtain the source parameters. We present two methods that take advantage of the large amounts of seismic data available.; In the first method we attempt to separate the effects of anelastic attenuation from the earthquake source spectrum characteristics. Analyzing the latter we are able to obtain source parameters with significantly reduced scatter and which indicate that the earthquake rupture is self-similar in the magnitude range 1.8 to 3.4. In the second method we perform a weighted average of spectral ratios using 160 small earthquakes as empirical Green functions to obtain estimates of the source spectrum of the 2001 M5.1 Anza earthquake. The averaging scheme significantly reduces the uncertainties and allows us to estimate the radiated seismic energy for this earthquake with greater confidence than is otherwise possible.; Given that in the methods discussed above the seismic parameters were estimated from the spectrum of the seismic waves, we present a new multitaper algorithm that has significant bias reduction compared to standard multitaper techniques and at the same time reducing the roughness of the estimated spectrum. We show that the method has the ability to estimate both the spectrum and its slope, thus increasing the degrees of freedom if parameters are to be estimated.
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