Self-similarity Of Earthquakes Research Articles

Source parameters for small-moderate earthquakes in Marmara Region (Turkey)

The main aim of this study is to investigate the self-relation and self-similarity of earthquakes in and around the Marmara Sea (NW Turkey) by using these obtained source parameters. With this purpose, spectral source parameters for 77 small to moderate earthquake (3.5 ≤ ML ≤ 5.2) that occurred during 2004–2018 have been determined from P and S wave spectra according to Brune’s source model by using regional broadband seismograms. The average ratio of P/S wave corner frequency is found to be 1.3 that suggesting higher corner frequency for P wave. The static stress drops range from 0.1 and 136 MPa with a median value of 9.8 MPa (98 bars). The high stress drops for these events can indicate high frictional strength and low strain-rate of the faults. Similarly, the low values of the stress drop can indicate a general weakness of the faults in the study area. There is no clear dependence between the seismic moment and the static stress drop in the analyzed events but some events which have lower seismic moment value also have lower stress drop. Obtaining results indicated the corner frequency decreases with increasing of the seismic moment. Also, a slight depth dependence of the corner frequency has been observed for the analyzed events. Shallower events have larger corner frequency value than deeper events. Also, a clear depth dependence of the stress drop values has not been observed. However, the depth dependence of the seismic moment is seen more clearly. Our results indicated that the deeper events have larger seismic moment values in the study area. In spite of scattering in small events, a linear relationship between local magnitude (ML) and moment magnitude (MW) could be obtained as MW = 1.4261(± 0.31) + 0.6399(± 0.08)ML from P waves spectra and MW = 0.0136(± 0.21) + 0.9883(± 0.05)ML from S wave spectra and calculated MW values are consistent with waveform inversion (centroid moment tensor — CMT) results. These relationships may be useful for seismic hazard studies in the study area.

A Review on Scaling of Earthquake Source Spectra

In this review paper, the theoretical and observational studies of scaling of earthquake source displacement spectra (abbreviated as source spectra) are compiled and discussed. The earlier studies, including the kinetic models proposed by several authors [including Haskell (Bull Seismol Soc Am 56:125–140, 1966) and Aki (J Geophys Res 72:1217–1231, 1967), provided the so-called ω−1, ω-square, and ω-cube models. Aki (1967) favored the ω-square model and also assumed constant stress drop, Δσ, and self-similarity of earthquakes. Some observations agree to one of the two models, but others do not. Hence, numerous alternative forms of the three scaling models to interpret the observations have been made by seismologists. For the corner frequencies, fc, the seismic moment Mo scales with fc in the form of Mo ~ f c −3 . For fcP of the P-waves and fcS of the S-waves, fcP > fcS is more reasonable than fcP < fcS. Mo scales as T D 3 , where TD is the duration time of source rupture and inversely related to fc, for both small and large events. The second corner frequency or cut-off frequency, fmax, at higher ω, that exists in the source spectra could be yielded by source, path, and site effects. The mechanisms to cause the patch corner frequency are still open. Analytical and numerical studies of the scaling laws based on the dislocation (e.g., Aki 1967), cracks (e.g., Walter and Brune in J Geophys Res 98(B3):4449–4459, 1993), spring-slider (e.g., Shaw in Geophys Res Lett 20:643–646, 1993), and statistical physics models (e.g., Hanks in J Geophys Res 84:2235–2242, 1997), including self-organized criticality (e.g., Bak et al. in Phys Rev Lett 59:381–384, 1987), show different scaling laws under various physical conditions.

Scale dependence in earthquake phenomena and its relevance to earthquake prediction.

The recent discovery of a low-velocity, low-Q zone with a width of 50-200 m reaching to the top of the ductile part of the crust, by observations on seismic guided waves trapped in the fault zone of the Landers earthquake of 1992, and its identification with the shear zone inferred from the distribution of tension cracks observed on the surface support the existence of a characteristic scale length of the order of 100 m affecting various earthquake phenomena in southern California, as evidenced earlier by the kink in the magnitude-frequency relation at about M3, the constant corner frequency for earthquakes with M below about 3, and the sourcecontrolled fmax of 5-10 Hz for major earthquakes. The temporal correlation between coda Q-1 and the fractional rate of occurrence of earthquakes in the magnitude range 3-3.5, the geographical similarity of coda Q-1 and seismic velocity at a depth of 20 km, and the simultaneous change of coda Q-1 and conductivity at the lower crust support the hypotheses that coda Q-1 may represent the activity of creep fracture in the ductile part of the lithosphere occurring over cracks with a characteristic size of the order of 100 m. The existence of such a characteristic scale length cannot be consistent with the overall self-similarity of earthquakes unless we postulate a discrete hierarchy of such characteristic scale lengths. The discrete hierarchy of characteristic scale lengths is consistent with recently observed logarithmic periodicity in precursory seismicity.

A preliminary study of earthquake self-similarity phenomena

A preliminary study of earthquake self-similarity phenomena