Estimating the parameters of small earthquakes and their signals

This study is an attempt at a theoretical synthesis of the following earthquake parameters: the length and volume of the rupture zone, energy, magnitude, energy class, as well as the period and frequency of seismic signals. We have obtained the signal period (T) as a function of event energy (E) for a very broad class of events ranging from large earthquakes to microscopic ruptures (nanoearthquakes). It is shown for the first time here that earthquake energy is related to the period of the seismic signal in a power-law manner, with the exponent being equal to 6, which finds an explanation within the framework of dimension theory. We have examined a large amount of both onshore and hydroacoustic observations of seismic events of different energy levels. These observations include small seismic events in the frequency range 50–1000 Hz that we were observing in Kamchatka and in the Sakhalin-Kuril region. This has been the basis for deriving the experimental relationship T = f(E), in good agreement with theoretical estimates. We examined the degree of seismic signal attenuation versus frequency and distance to receiver for different media (including composite media); the attenuation incorporates, not only absorption in the medium (intrinsic attenuation), but also geometrical spreading. It is shown that signals at frequencies above 200 Hz are nearly completely attenuated in solids at distances below one kilometer from the source. We propose a formal quantitative criterion for classifying small seismic events into subclasses: small earthquakes (magnitude 1 ≤ M ≤ 3, frequency range 3Hz ≤ f ≤ 10 Hz); microearthquakes (magnitude −4 ≤ M ≤ 0, frequency range 20 Hz ≤ f ≤ 170 Hz), and microscopic ruptures or nanoearthquakes (M ≤ −5, frequency f ≥ 200 Hz). This classification was previously available on a descriptive level only.