A Simple Model to Relate the Elastic Ratio Gamma of a Critically Self-Organized Spring-Block Model with the Age of a Lithospheric Downgoing Plate in a Subduction Zone

Abstract

In 1980, Ruff and Kanamori (RK) published an article on seismicity and the subduction zones where they reported that the largest characteristic earthquake (Mw) of a subduction zone is correlated with two geophysical quantities: the rate of convergence between the oceanic and continental plates (V) and the age of the corresponding subducting oceanic lithosphere (T). This proposal was synthetized by using an empirical graph (RK-diagram) that includes the variables Mw, V and T. We have recently published an article that reports that there are some common characteristics between real seismicity, sandpaper experiments and a critically self-organized spring-block model. In that paper, among several results we qualitatively recovered a RK-diagram type constructed with equivalent synthetic quantities corresponding to Mw, V and T. In the present paper, we improve that synthetic RK-diagram by means of a simple model relating the elastic ratio γ of a critically self-organized spring-block model with the age of a lithospheric downgoing plate. In addition, we extend the RK-diagram by including some large subduction earthquakes occurred after 1980. Similar behavior to the former RK-diagram is observed and its SOC synthetic counterpart is obtained.

Estimating the Epicenter of an Impending Strong Earthquake by Combining the Seismicity Order Parameter Variability Analysis with Earthquake Networks and Nowcasting: Application in the Eastern Mediterranean

“…To achieve this determination, one uses an EQ catalog to calculate from the 'small' EQs, which are defined as those with magnitude M < M λ , but above a threshold M σ , i.e., of magnitude M ∈ [M σ , M λ ), the level of hazard for 'large' M ≥ M λ EQs. The lower threshold M σ is typically the completeness threshold of the EQ catalog used [33], while the EQ catalogs employed [33,116,116,117,123,124,136] are global seismic catalogs such as the Advanced National Seismic System Composite Catalog or the NEIC PDE catalog. For such global catalogs, a M σ = 4.0 magnitude threshold was considered [116,117] for applications in EQ-prone areas outside the United States, such as those in Greece, Japan, and India.…”

“…It is the scope of the present paper to show that by combining the above two NTA results with the modern method of nowcasting EQs [33], an estimate of the epicenter of the impending EQ with M ≥ 7.1 in the eastern Mediterranean region is achieved. EQ nowcasting employs natural time, which is unique in its characteristics [116], to estimate seismic risk by means of an EQ potential score (EPS) and found many useful applications, both regionally and globally [33,[116][117][118][119][120][121][122][123][124][125][126]. EQ nowcasting [33] has, so far, focused on describing the current state of fault systems.…”

Nowcasting Avalanches as Earthquakes and the Predictability of Strong Avalanches in the Olami-Feder-Christensen Model

“…Despite some limitations of the OFC model, where the criticality of the model is perhaps the most worrisome (it seems that the self-organized criticality behavior of the model is lost by introducing variations in the model rules [ 67 , 68 ] for example by replacing the OBC with periodic boundary conditions [ 69 ], by introducing frozen noise in the local degree of dissipation [ 70 ], i.e., by considering at each site a different instead of just , where is a random number coming from the uniform distribution in the interval which is kept constant throughout the simulation, or in its threshold value [ 71 ], and by including lattice defects [ 72 ]), the OFC model has been able to successfully reproduce qualitative important features observed in real seismicity such as the GR law [ 19 ], the stair graphs for the cumulative frequency [ 49 , 73 , 74 , 75 , 76 , 77 , 78 ] and also very recently, the Ruff–Kanamori diagram [ 79 , 80 ]. Also as far as EQ predictability [ 81 ] or Omori law [ 82 , 83 ] are concerned, the OFC model appears to be closer to reality than others [ 84 ].…”

On the Possibility of Reproducing Utsu’s Law for Earthquakes with a Spring-Block SOC Model

“…For a more detailed description of the equations and to deepen the choice of elast parameters, we recommend reading reference [9] where we present an extensive review on this topic. Based on the work of Perez Oregon et al [21][22][23], in which they simulated severa seismic regions considering the age of the subduction plate and the convergence velocit to reproduce the maximum magnitude earthquake for each region and also using the OF spring-block model, 29 simulations were performed, same as in [21], using lattices of 10 × 100 blocks and one million iterations. The synthetic age of the subduction zone was ob tained considering the interval from 0 to 160 Myr proposed by Ruff and Kanamori [29 and defining 𝑒 as the normalized age of the tectonic plates.…”

“…For our part, we have published several articles in which we found some similarities between the OFC model and real seismicity [3,[21][22][23][24][25][26][27][28]. We can outline the ability to emulate real-life seismic subduction zones by including the age of the lithospheric plate and the rate of convergence, both transformed into their synthetic counterparts in the spring-block model [21]; we were also able to reproduce the so-called Ruff-Kanamori diagram [21,23,29] that relates the age of the subduction plate with the convergence rate of the plates and the maximum characteristic earthquake for a given zone. In a different paper, we suggested that the Gutenberg-Richter parameters a and b are positively correlated [24].…”