Multidimensional scaling visualization of earthquake phenomena

Abstract

Earthquakes are associated with negative events, such as large number of casualties, destruction of buildings and infrastructures, or emergence of tsunamis. In this paper, we apply the Multidimensional Scaling (MDS) analysis to earthquake data. MDS is a set of techniques that produce spatial or geometric representations of complex objects, such that, objects perceived to be similar/distinct in some sense are placed nearby/distant on the MDS maps. The interpretation of the charts is based on the resulting clusters since MDS produces a different locus for each similarity measure.In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analyzed. The events, characterized by their magnitude and spatiotemporal distributions, are divided into groups, either according to the FlinnEngdahl seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Spacetime and Space-frequency correlation indices are proposed to quantify the similarities among events. MDS has the advantage of avoiding sensitivity to the nonuniform spatial distribution of seismic data, resulting from poorly instrumented areas, and is well suited for accessing dynamics of complex systems. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools, for understanding the global behavior of earthquakes.

In memory of Professor José António Tenreiro Machado (1957–2021)

“…MDS analysis was also performed to evaluate fractional-order systems [ 32 ] and stock markets [ 33 ]. Another area of interest to MDS visualization was earthquake phenomena [ 34 ]. MDS maps proved to be intuitive and useful visual representations of complex relationships of seismic events.…”

Multidimensional scaling analysis of virus diseases

“…We can observe that the Canberra index leads to poor clustering. Nonetheless, we should note that MDS is merely a mathematical clustering and visualization tool and that a physical perspective of the reported results must be found in the light of the comparison index [90]. Therefore, a further explanation about physical mechanisms associated with the results must be envisaged by standard complementary procedures.…”

Integer and fractional-order entropy analysis of earthquake data series

“…We adopt the moment magnitude, M W , as the scale of reference and convert different scales (e.g., local magnitude, M L , surface-wave magnitude, M S , body-wave magnitude, M B , and duration magnitude M D ) to M W . This is accomplished by taking samples of events with magnitudes expressed in various scales and computing the relations between scales using an orthogonal regression algorithm [10,30]. For example, Fig.…”