One-Dimensional Dynamical Modeling of Earthquakes: A Review

Abstract

3. This relation is commonly considered to hold up for a wide range of events (Hanks 1977). However, for Japanese earthquakes, Shimazaki (1986) AbstrActStudies of the power-law relations of seismicity and earthquake source parameters based on the one-dimensional (1-D) Burridge-Knopoff's (BK) dynamical lattice model, especially those studies conducted by Taiwan's scientists, are reviewed in this article. In general, velocity-and/or state-dependent friction is considered to control faulting. A uniform distribution of breaking strengths (i.e., the static friction strength) is taken into account in some studies, and inhomogeneous distributions in others. The scaling relations in these studies include: Omori's law, the magnitude-frequency or energy-frequency relation, the relation between source duration time and seismic moment, the relation between rupture length and seismic moment, the frequency-length relation, and the source power spectra. The main parameters of the one-dimensional (1-D) Burridge-Knopoff's (BK) dynamical lattice model include: the decreasing rate (r) of dynamic friction strength with sliding velocity; the type and degree of heterogeneous distribution of the breaking strengths, the stiffness ratio (i.e., the ratio between the stiffness of the coil spring connecting two mass elements and that of the leaf spring linking a mass element and the moving plate); the frictional drop ratio of the minimum dynamic friction strength to the breaking strength; and the maximum breaking strength. For some authors, the distribution of the breaking strengths was considered to be a fractal function. Hence, the fractal dimension of such a distribution is also a significant parameter. Comparison between observed scaling laws and simulation results shows that the 1-D BK dynamical lattice model acceptably approaches fault dynamics.

b-Values Observations in Taiwan: A Review

“…This model has since been applied to dynamically simulate earthquake occurrences and then simulation results were applied to interpret the GR's FM law of earthquakes (Otsuka 1972;Yamashita 1976;Rundle and Jackson 1977;Aki 1984, 1986;Carlson and Langer 1989;Carlson 1991;Carlson et al 1991;Wang 1991Wang , 1994aWang , 1995Wang , 1996Wang , 1997Knopoff et al 1992;Shaw et al 1992;Shaw 1994Shaw , 1995Schmittbuhl et al 1996). A detailed review about the model and its applications can be seen in Wang (2008). Burridge and Knopoff (1967) mentioned that the system exhibits the GR law, with b ≈ 1.…”

Fractal and Morlet-wavelet analyses of M ≥ 6 earthquakes in the South-North Seismic Belt, China

“…In 1944, the frequency-magnitude relation found by Gutenberg and Richter (1944) is the first scaling law to represent self-similarity of earthquake phenomena (Chen and Koyama 1995;Main 1996;Wang 1988Wang , 2008Wang et al 2015). Current studies also lead to that self-similarity or scale-invariance is a common property of natural phenomena.…”

“…For the M ≥ 6 earthquakes that occurred in the region during 1901-2008, Wang (2013 studied the memory effect in the earthquake magnitude sequences and inter-event time using the fluctuation analysis technique. The calculated results show that the exponents of scaling law offluctuation versus window length are less than 0.5 for the earthquake magnitude sequences and interevent time.…”

A study of earthquake recurrence based on a one-body spring-slider model in the presence of thermal-pressurized slip-weakening friction and viscosity

“…Modeling earthquake recurrence based on different models has been long made and is reviewed by Bizzarri (2012a, b) and Franović et al (2016). Among the models, the spring-slider model has been used to study fault dynamics and earthquake physics (see Wang, 2008). Burridge and Knopoff (1967) proposed the one-dimensional N-body model (abbreviated as the 1-D BK model henceforth).…”