Correlation of seismic behavior with crustal deformation and rheology in the Taiwan orogen

   Every year, over 10,000 earthquakes with magnitudes greater than 4 are recorded worldwide, and more than 200 of them strike the Taiwan region. As might be expected, larger-magnitude earthquakes are less abundant and occur less frequently than smaller-magnitude ones. The earthquake frequency-magnitude distribution in a given region and time period is well characterized by the Gutenberg-Richter law, which depicts a statistical straight-line relationship between the earthquake magnitude (M) and the logarithm of the number of earthquakes with a magnitude exceeding M (logN) [Gutenberg and Richter, 1944]. The global average of the b-value, namely, the negative of the slope of the regression line between logN and M, is close to 1, and its variation is commonly used to indicate the relative occurrence frequencies of large and small events. A lower b-value suggests a larger proportion of large earthquakes, and vice versa.
   Based upon observations of both microcrack events during rock failure experiments and natural seismic events, it has long been recognized that the b-value exhibits an inverse dependence on the applied stress. Schorlemmer et al. [2005] established a universal correlation between the b-value and the associated faulting styles or focal mechanisms; they concluded that the b-value decreases successively from normal to strike-slip to thrust events and that this trend is largely governed by the increases in the tectonic loading stresses required for faulting and earthquake nucleation. However, this generic relationship has drawn substantial attention with regard to the plausible use of the b-value as an earthquake precursor, because the b-value may decline as the loading stress increases prior to exceeding the frictional strength of the fault zone, thereby causing an earthquake.
   Taiwan is situated at the convergent junction of two plates: the Eurasian Plate (EP) subducts eastward beneath the Philippine Sea Plate (PSP) in southern Taiwan, while the subduction polarity flips in northeastern Taiwan as the PSP subducts beneath the EP into the Earth’s interior. The oblique collision along the Luzon arc between the northwest-moving PSP and the Eurasian continental margin is generally believed to have initiated as early as 8 million years ago, thereby producing the intensively deformed, north-south-trending orogenic belts and varied lithotectonic regimes throughout Taiwan [Suppe, 1984]. Currently active mountain building processes result in a rapid rate of crustal deformation and a frequent recurrence of seismicity with a diversity of faulting styles, making Taiwan one of the most seismically hazardous regions in the world in addition to one of the best natural laboratories for earthquake research. To assess whether the tectonic stresses from plate convergence contribute to the seismic behavior of the young orogen and to evaluate whether the stress-dependent b-value observed worldwide holds true for the tectonically complex region of Taiwan, we investigate the lateral and depth variations in the earthquake b-values and explore their correlations with the predominant faulting mechanisms, crustal deformation and stress regimes in the Taiwan orogen.
   Accordingly, we employ approximately 350,000 earthquakes reported by the Central Weather Bureau (CWB) of Taiwan that occurred between 1991 and 2015 to map the spatial variations in the b-values across the different lithotectonic regimes of Taiwan. Our analysis demonstrates that the b-value dependence on the faulting style and stress holds for Taiwan, which encompasses a diversity and complexity of deformation domains [Chen et al., 2016]. Through a comparison with the strain rate (which is proportional to the stress) field deduced from GPS measurements, we corroborate that the earthquake frequency-magnitude distribution is largely governed by the underlying stress conditions. Lower b-values are detected in the two thrust zones of western and eastern Taiwan that are subjected to greater compressive stresses, while higher b-values are observed in the extensional mountain ranges sandwiched in between those thrust zones (Figure 1). In addition, the variation in the b-values with depth clearly reflects the characteristics of the crustal rheology within the Taiwan orogen, revealing a brittle upper crust characterized by a strength that increases with depth down to ~15-20 km followed by a transition to ductile deformation in the weaker middle crust (see Figure 4 in Chen et al. [2016]).
   Our findings imply that the b-value has the potential to act as a stress meter that can not only help illuminate the deformation patterns and mechanical properties of crustal rocks at great depths throughout active continental margins but also monitor the spatiotemporal changes in the fault strength and provide insight into warning signs of forthcoming earthquakes. However, it is worth mentioning that the earthquakes occurring within the same seismic provinces throughout Taiwan usually comprise mixed-type focal mechanisms. Therefore, the direct application of reduced b-values observed from all events in a short time window as a seismic precursor should be employed with caution, since those b-values can also be modified by changes in the style of faulting.
Figure 1. Lateral variation of the earthquake b-value and strain-rate field in Taiwan. (a) Lateral variations in the earthquake frequency-magnitude distribution (b-value) in Taiwan. The focal spheres represent the representative fault styles of earthquakes occurring in each area of 15x15 km2. (b) The differential strain-rate (stress) field calculated from the difference between the two principal strain rates deduced from GPS observations over the period of 2004-2009. Black inward and gray outward arrows refer to horizontal compression and extension, respectively, and indicate the directions of the two principal strain-rate axes with lengths that are proportional to the magnitudes of the principal strain rates.
2. Gutenberg, B., and Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34(4), 185-188.
3. Schorlemmer, D., Wiemer, S., and Wyss, M. (2005). Variations in earthquake-size distribution across different stress regimes. Nature, 437(7058), 539-542. DOI:10.1038/nature04094
4. Suppe, J. (1984). Kinematics of arc-continent collision flipping of subduction, and back-arc spreading near Taiwan. Memoir of the Geological Society of China, 6, 21-33.

Shu-Huei Hung
Professor, Department of Geosciences